tag:blogger.com,1999:blog-46310237975638415542024-02-21T03:44:19.948-06:00Maverick ChristianPhilosophical musings etc.Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comBlogger149125tag:blogger.com,1999:blog-4631023797563841554.post-23473627800764186972023-05-10T12:16:00.012-05:002024-02-16T21:43:20.623-06:00The Moral Argument (A Quick Version)<style type="text/css"> <!--
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<a href="https://maverickchristian.blogspot.com">Home</a> > <a href=" https://maverickchristian.blogspot.com/p/site-map.html#_philosophy">Philosophy</a> > <a href="https://maverickchristian.blogspot.com/p/site-map.html#_atheism_theism">Atheism/Theism</a>
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<h3 class="subHeader">Intro</h3>
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The moral argument is a family of arguments that use morality as a reason to believe in God. The version of the moral argument I’ll be discussing:
<ol>
<li>If God does not exist, then objective moral wrongness does not exist.</li>
<li>Objective moral wrongness does exist.</li>
<li>Therefore, God exists.</li>
</ol>
But for this, it’s important to define our terms.
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<h3 class="subHeader">Moral Semantics</h3>
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To roughly define what I mean by “morality” I’ll explain the sort of “ought” used in moral obligations. Some oughts are purely descriptive, e.g., when “If you want to do well in school, you ought to study” just means something like “As a matter of practical necessity, you need to study to do well in school.” Some oughts prescribe in a way that is not purely descriptive; e.g. someone saying “You shouldn’t torture infants” might be using this sort of ought, and this is the type of “ought” I’m using in my definition of morality (e.g., an action is morally wrong for someone only if they ought not to do it). Very roughly, by “moral wrongness exists” I mean that there are true facts of what people ought not do using the aforementioned not-purely-descriptive sort of “ought,” e.g., it is a fact that it is morally wrong for a man to torture infants just for fun.
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An important feature of this moral semantics is that <a href="https://maverickchristian.blogspot.com/2018/08/moral-ought-facts-are-non-natural.html">it implies that moral wrongness is non-natural</a>; i.e., it is not part of the natural, physical world. (Facts of physics, chemistry, etc. are purely descriptive, whereas the property of moral wrongness is not purely descriptive.) Another implication of this moral semantics is that, barring the supernatural, non-natural moral properties like moral wrongness would be causally inert (since anything outside the natural world causally influencing the natural world would be supernatural) and empirically undetectable (such causally inert moral properties could not interact with photons etc.).
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To illustrate, imagine a moral nihilist (who does not believe in moral wrongness) and a moral realist (who does believe in moral wrongness) observe some jerk kick a dog just for fun. The dog whimpers in pain and runs away. Both agree on all physiological and psychological facts, e.g., that the dog felt pain and suffered minor injury. The moral nihilist says, “I don’t think moral wrongness is attached to that action.” The moral realist says, “I think moral wrongness <em>is</em> attached to that action.” There is no <em>empirical</em> way to determine who is right here; both views agree on all the same empirical facts. In this sense, moral wrongness is empirically undetectable. Notice also that moral wrongness being non-natural is largely why it is invisible and empirically undetectable in this scenario.
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In the context of the moral argument, by moral wrongness being <em>objective</em> I mean that it exists independently of human belief and perception of it.
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<h3 class="subHeader">Arguing for Moral Objectivism</h3>
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Perhaps the quickest way to argue for moral objectivism is to simply point to an example of an objective moral truth, i.e., one that holds independently of human opinion. Consider the largely uncontroversial fact that it is morally wrong for a man to torture infants just for fun. That this is objectively morally wrong can be shown with this thought experiment: would it remain morally wrong if a baby torturer thought otherwise and killed everyone who didn’t agree with him? It seems that it would be, and thus we have an example of an objective moral truth. The step-by-step reasoning goes like this:
<ol type="a">
<li>In the thought experiment, something remains morally wrong even when all human opinion thinks otherwise (since the torturer killed off everyone who doesn’t agree with him);</li>
<li>in which case the moral truth “It’s morally wrong for a man to torture infants just for fun” would be holding despite human opinion;</li>
<li>in which case it seems we have an example of an objective moral truth (i.e., holding true independently of human opinion) thereby giving us objective morality.</li>
</ol>
If (a), (b), and (c) are all true as they seem to be, then we have an example of an objective moral truth. (For those who disagree, do you disagree with (a), (b), or (c)? If so, which one(s)?)
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<h3 class="subHeader">Arguing for the First Premise</h3>
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It is a theorem of mathematics and propositional logic that <a href="https://maverickchristian.blogspot.com/2013/08/if-then-probably-c-entails-probably-if.html">“Given A, probably C” entails “Probably, if A then C.”</a> Applied here, “Given God’s nonexistence, objective moral wrongness probably doesn’t exist” entails “Probably, if God does not exist then objective moral wrongness does not exist.” My general approach then is to assume arguendo that atheism is true and see if that leads to objective moral wrongness probably not existing. That approach can be broken down into two components:
<ol start="4">
<li>If atheism is true, we do not have good reason to believe in objective moral wrongness.</li>
<li>If atheism is true, we have good <em>prima facia</em> grounds to disbelieve in objective moral wrongness.</li>
</ol>
For (4), I’ll argue that barring the supernatural, we don’t have any good reason to believe that objective moral wrongness exists. Recall that moral wrongness is empirically undetectable, but if so, how do we know about it? In practice we rely on moral intuition (intuition in the philosophical sense of the term, which is about what is immediately present to one’s consciousness and what the consciousness immediately apprehends). How does moral intuition deliver knowledge of moral truths? The theist could say that God designed our cognitive faculties (as via superintended evolution) in such away that when they are functioning properly we intuit certain moral truths, just as we intuit elementary truths of logic and arithmetic.
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But for atheism, moral intuition delivering moral knowledge is problematic. Recall that objective moral wrongness is non-natural, and since anything outside the natural world causally affecting the natural world would be supernatural, then barring the supernatural such moral properties like moral wrongness are causally inert and would have no causal influence over whether our brains would produce moral intuitions, and so we'd have the same moral intuitions regardless of whether moral wrongness existed. This would seem to undercut such intuition from properly justifying our belief in morality.
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To illustrate, suppose a cyborg has a metal-detecting implant that is designed to give her the intuition that a widget in her hand contains metal if and only if the widget contains metal. But suppose her metal-detecting implant malfunctions and it delivers the cybernetic metal intuition regardless of whether the widget contains metal. Then even if the widget in her hand contained metal, and she believed it contained metal solely on the basis of her cybernetic metal intuition, her true belief wouldn’t be knowledge. The same applies to brains producing moral intuition if such intuition would exist regardless of whether morality existed. Like the malfunctioning metal-detector implant, even if the belief in moral wrongness were true, this belief wouldn’t be knowledge. Moreover, if the cyborg knew that her implant would deliver the cybernetic metal intuition regardless of whether the widget contained metal, this would serve as a <em>defeater</em> for her belief (where a <em>defeater</em> is something that undermines the justification of a belief). The same applies to knowing that one’s brain would deliver the intuition of moral wrongness existing regardless of whether moral wrongness existed.
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Of course, this all assumes that moral wrongness is causally inert and that no relevant supernatural intervention takes place. The atheist could get around this problem by positing us humans having supernatural clairvoyance of these invisible and non-natural properties, but these seems awfully far-fetched. It is more likely on atheism that we do not have moral knowledge.
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Further analogies could be made. For example, suppose we define a “spirit” as an incorporeal conscious being; e.g., (to borrow a bit from Carl Sagan) an invisible, incorporeal dragon that has no causal influence over the physical world. Consider the following Invisible Dragon Scenario, where nearly everyone in the world believes in an invisible dragon that approves and disapproves of certain behaviors we do. The invisible dragon is of course empirically undetectable, and the only reason people believe in it is via an intuition of its existence due to a quirk of evolutionary development. If it were pointed out that people’s brains would give them the intuition for their invisible dragon beliefs regardless of whether the invisible dragon existed, this would provide a defeater for people’s invisible dragon beliefs. The same, I think, would go for moral wrongness on atheism, and I see no relevant difference between moral beliefs in what we could call the Atheism Scenario (people believe in moral wrongness on the basis of intuition, but moral wrongness is causally inert and has zero causal impact on whether our brains would give us moral intuitions) and the Invisible Dragon Scenario.
Some potential rebuttals:
<ul>
<li><strong>Moral supervenience is metaphysically necessary.</strong> One could say that moral wrongness associates with certain behaviors by metaphysical necessity (i.e., that it couldn’t have been otherwise), and this results in moral knowledge. This rebuttal is easily accommodated by modifying the thought experiment so that the invisible dragon is metaphysically necessary. It still seems the dragon intuition wouldn’t deliver knowledge.</li>
<li><strong>Reliabilism.</strong> Another objection is that our moral intuitions and therefore beliefs are produced by a reliable process, and thus moral intuitions deliver knowledge. This is dubious on atheism, since it’s just as easy to conceive of evolution producing a species with very different moral codes (note the vast differences <em>within</em> our species regarding moral beliefs among different cultures throughout history). Even so, this can be accommodated. Imagine that the physical laws have a high probability of producing accurate intuitions about the invisible dragon, though the dragon still has zero causal impact over what intuitions would emerge. Again, it seems like the dragon intuitions would fail to deliver knowledge.</li>
</ul>
The argument from moral knowledge in a nutshell:
<ol start="6">
<li>The dragon believers in the Invisible Dragon Scenario do not have knowledge for invisible dragon beliefs.</li>
<li>If the dragon believers in the Invisible Dragon Scenario do not have knowledge for invisible dragon beliefs, then moral realists in the Atheism Scenario do not have moral knowledge.</li>
<li>If moral realists in the Atheism Scenario do not have moral knowledge, then on atheism we do not have good reason to believe in objective moral wrongness.</li>
<li>Therefore, on atheism we do not have good reason to believe in objective moral wrongness.
</ol>
The justification for (8) is that the Atheism Scenario is more or less the situation we are in right now if atheism is true and moral wrongness exists (again, us having supernatural powers of clairvoyance is far-fetched). The justification for (7) is that no relevant difference exists between the Atheism Scenario and the Invisible Dragon scenario such that the dragon believers have knowledge for their dragon beliefs but the moral realists do not have moral knowledge in the Atheism Scenario. Two proposed relevant differences (metaphysical necessity and reliabilism) were already discussed, those two differences being incorporated into the Invisible Dragon Scenario.
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Premise (6) seems fairly obvious. Even so, one could bite the bullet and say that the dragon believers <em>would</em> have knowledge of the dragon (particularly in light of the reliabilist rebuttal), but for such a person I invite them to imagine them living in a world where belief in the invisible, incorporeal dragon is as common as belief in gods. Suppose you inform these dragon believers that they would have their dragon intuitions even if this invisible dragon did not exist. Wouldn’t this fact provide a defeater for their invisible dragon beliefs? It seems so, and that doesn’t seem like this should occur if the dragon believers really did have knowledge that the invisible dragon exists. Moreover, that sort of defeater also seems to apply to objective moral wrongness if atheism is true, and if that is the case then on atheism we do not have good reason to believe in objective moral wrongness.
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Having justified point (4), i.e., that if atheism is true, we do not have good reason to believe in objective moral wrongness; I’ll turn my attention to point (5), that if atheism is true we have good <em>prima facia</em> grounds to disbelieve in objective moral wrongness. My justification for this relies on what is known in philosophy as the argument from queerness.
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To illustrate the general idea behind the argument from queerness, imagine someone saying that an invisible unicorn is floating above their head. This claim is possible but not plausible and one would be <em>prima facia</em> justified (i.e., justified in the absence of further evidence) in disbelieving in this claim, because the invisible unicorn is “queer,” i.e., it wildly diverges from the types of things we know exist in a way to make it unlikely in the absence of evidence for it.
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On atheism, objective moral wrongness likewise seems queer: it is invisible, non-natural, and we would need something like supernatural clairvoyance to know it exists. This is wildly different from the types of thing we know exist, and thus on atheism we would have <em>prima facia</em> justification for disbelieving in objective moral wrongness.
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<h3 class="subHeader">Conclusion</h3>
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The moral argument being discussed here is this:
<ol>
<li>If God does not exist, then objective moral wrongness does not exist.</li>
<li>Objective moral wrongness does exist.</li>
<li>Therefore, God exists.</li>
</ol>
The type of moral semantics being used here is such that the moral “ought” is that type of ought that does not have only descriptive qualities. This leads to moral wrongness being non-natural and empirically undetectable. The justification for premise (2) is a proof by example: it is objectively morally wrong for a man to torture infants just for fun, as revealed in a thought experiment in which a man who doesn’t think it’s morally wrong kills everyone who doesn’t agree with him (in that situation, it would still be morally wrong).
<br /><br />
The justification for premise (1) is that given God’s nonexistence, it is likely that objective moral wrongness does not exist. The approach for this justification was twofold:
<ol start="4">
<li><strong>If atheism is true, we do not have good reason to believe in objective moral wrongness.</strong> There is no relevant difference between the Invisible Dragon Scenario and the Atheism Scenario, and if that is so, then on atheism we do not have good reason to believe that objective moral wrongness exists. To oversimplify somewhat: if atheism is true then we’d have our moral intuitions of objective moral wrongness existing regardless of whether it existed, and this seems to prevent such intuition from being a good reason to believe in objective moral wrongness (recall the illustration of the cyborg and her faulty metal-detecting implant).</li>
<li><strong>If atheism is true, we have good <em>prima facia</em> grounds to disbelieve in objective moral wrongness.</strong> This was justified via the argument from queerness. If moral wrongness exists, it is non-natural and we’d need something like supernatural clairvoyance to know it exists.</li>
</ol>
Both premises of the moral argument seem justifiably true, and if the premises are true the conclusion is correct regardless of what else might be true.
Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-75769256874841295172022-06-24T18:31:00.004-05:002023-08-30T13:27:56.431-05:00Conjunction and Conditional Probability<style type="text/css"> <!--
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<a href="https://maverickchristian.blogspot.com">Home</a> > <a href=" https://maverickchristian.blogspot.com/p/site-map.html#_philosophy">Philosophy</a> > <a href="https://maverickchristian.blogspot.com/p/site-map.html#_atheism_theism">Atheism/Theism</a>
<br />
<br />
<h3 class="subHeader">Intro</h3>
<br />
<br />
In this article I will prove that the probability of “Given A, probably C” is greater than or equal to the probability of “A and C are both true.” This has implications for the moral argument for the existence of God, for reasons I’ll explain next.
<br />
<br />
<h3 class="subHeader">Background</h3>
<br />
<br />
Behold the following moral argument:
<ol>
<li>If God does not exist, then objective morality does not exist.</li>
<li>Objective morality does exist.</li>
<li>Therefore, God exists.</li>
</ol>
In a previous article I provied via some basic mathematics and elementary propositional logic that <a href="https://www.maverick-christian.org/2013/08/if-then-probably-c-entails-probably-if.html">“Given A, probably C” entails “Probably, if A then C”</a>, e.g., “Given God’s nonexistence, objective morality probably does not exist” entails “Probably, if God does not exist then objective morality does not exist.” A lot of atheists disagreeing with the moral argument who concede that “Given God’s nonexistence, objective morality probably does not exist” are thus rationally committed to believing the first premise of the moral argument.
<br /><br />
However, some atheists who believe objective morality does not exist say they don’t agree with the first premise despite rationally committed to doing so (or at least rationally committed to the first premise being <em>probably</em> true). In this article I argue that atheists who believe that objective morality does not exist are rationally committed to believing <em>Given God’s nonexistence, objective morality probably doesn’t exist</em> which in turn implies <em>If God does not exist, then objective morality does not exist</em> is probably true.
<br/><br />
More precisely, I will use the power of mathematics to show that anyone who believes <em>God does not exist and objective morality does not exist</em> is rationally committed to believing <em>Given God’s nonexistence, objective morality probably does not exist</em>.
<br />
<br />
<h3 class="subHeader">The Proof</h3>
<br />
<br />
For brevity’s sake, I’ll use a bit of symbolic logic, where ∧ represents “and” and ¬ represents “not” as part of my abbreviations:
<br />
<br />
<table class="coloredEquals" cellspacing="0">
<tr class="odd"><td>G =</td><td>God exists.</td></tr>
<tr class="even"><td>¬G =</td><td>God does not exist.</td></tr>
<tr class="odd"><td>M =</td><td>Objective morality exists.</td></tr>
<tr class="even"><td>¬M =</td><td>Objective morality does not exist.</td></tr>
<tr class="odd"><td>¬G ∧ ¬M =</td><td>God does not exist and objective morality does not exist.</td></tr>
<tr class="even"><td>P(¬G ∧ ¬M) =</td><td>The probability that ¬G and ¬M are both true, i.e., the probability that <em>God does not exist and objective morality does not exist</em> is true.</td></tr>
<tr class="odd"><td>P(¬M|¬G) =</td><td>The probability of ¬M given ¬G, i.e. the probability of objective morality not existing given God’s nonexistence.</td></tr>
</table>
<br />
<br />
One assumption I will make is the person who believes that ¬G ∧ ¬M is true also believes that <span class="nobreak">¬G ∧ ¬M</span> is at least <em>probably</em> true. Generally speaking, to be rationally consistent, if you are to believe that some proposition P is true, you should also believe that P is at least <em>probably</em> true.
<br /><br />
To generalize, I’ll use two propositions <em>A</em> and <em>C</em>. The goal is to prove this is true:
<blockquote>
P(C|A) ≥ P(A ∧ C )
</blockquote>
To start with, note the following equation familiar to many high school graduates and intelligent middle school students:
<blockquote>
P(A ∧ C) = P(C|A) × P(A)
</blockquote>
What is the highest <span class="nobreak">P(A ∧ C)</span> can be if we hold <span class="nobreak">P(C|A)</span> constant? Well, we would want <span class="nobreak">P(A)</span> to be as high as it can be, which is 1. Thus, in finding an upper limit for <span class="nobreak">P(A ∧ C)</span>, this inequality is true:
<blockquote>
P(A ∧ C) ≤ P(C|A) × 1 <br />
⇔ P(A ∧ C) ≤ P(C|A)
</blockquote>
After finding this upper limit for <span class="nobreak">P(A ∧ C)</span>, there’s just one more step:
<blockquote>
P(A ∧ C) ≤ P(C|A)<br />
⇔ P(C|A) ≥ P(A ∧ C)
</blockquote>
Since <em>A</em> and <em>C</em> were of course arbitrary placeholders, we can use all sorts of propositions, including ¬G and ¬M. So for example this is true:
<blockquote>
P(¬M|¬G) ≥ P(¬G ∧ ¬M)
</blockquote>
<br />
<br />
<h3 class="subHeader">Conclusion</h3>
<br />
<br />
Thus anyone who believes <em>God does not exist and objective morality does not exist</em> is rationally committed to believing <em>Given God’s nonexistence, it is unlikely that objective morality’s existence</em>, since <span class="nobreak">P(¬M|¬G)</span> is going to be greater than or equal to the probability of ¬G ∧ ¬M.
<br /><br />
Since <em>God does not exist and objective morality does not exist</em> being probably true entails <em>Given God’s nonexistence, it is unlikely that objective morality’s existence</em>, which in turn entails that <em>If God does not exist, then objective morality does not exist</em>, one who believes <em>God does not exist and objective morality does not exist</em> should also believe that the first premise of the moral argument (<em>If God does not exist, then objective morality does not exist</em>) is at least probably true.
Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-69634913878769550302021-09-14T12:00:00.001-05:002021-09-15T17:59:25.359-05:00Can an Infinite Sequence of Coinflips Come Up All Heads?<style type="text/css"> <!--
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<br />
<br />
<h3 class="subHeader">Intro</h3>
<br />
<br />
If there is an infinite sequence of coinflips (for simplicity, assume that heads or tails are the only possible outcomes for each coinflip, and that this is a fair coin), is it possible for the coinflip to come up heads? I think so, but how do we prove it?
<br />
<br />
<h3 class="subHeader">Background</h3>
<br />
<br />
This issue bears relevance to the Eternal Society Argument against an infinite past. Roughly (in the <a href="http://aporia.byu.edu/pdfs/tisthammer-an_eternal_society_paradox.pdf">paper the Eternal Society Paradox was published</a>), an Eternal Society is a society that has existed for a beginningless, infinite duration of time and has the abilities of ordinary human beings in each year of its existence; e.g. in each year people in the society can flip coins, write books, sing songs, and pass on information possessed in the current year to the next year. Because of the society’s extremely modest abilities, it seems like an Eternal Society would be possible if an infinite past were possible (note that by “possible” in this article I’ll be referring to <em>metaphysical</em> possibility, as opposed to e.g. physical possibility).
<br /><br />
Now imagine the Eternal Society has the following Annual Coin-Flipping Tradition: each year they flip a coin. If the coin comes up heads and they never did a particular chant before, then they do the chant; otherwise they do not do the chant for that year.
<br /><br />
The coinflips are probabilistically independent events, so any particular infinite permutation of coinflips is equally unlikely but also equally possible. Consider scenario S<span class="sub">1</span> in which the coin came up heads for the first time last year for the Eternal Society practicing the aforementioned Annual Coin-Flipping Tradition. The Eternal Society gets together to do the chant for the first time. This seems like it would be possible if an infinite past were possible (an eternal society with the ability of ordinary humans, by which I mean the society has the ability of ordinary humans in each year of its existence, could surely do something like this), but this scenario is provably not possible.
<br /><br />
Again, the coinflips are probabilistically independent events, so if scenario S<span class="sub">1</span> were possible, then another scenario, that we can call scenario S<span class="sub">2</span>, would be possible: the coin came up heads each year of the infinite past for the Eternal Society engaging in the Annual Coin-Flipping Tradition. If the coin came up heads each year, did the Eternal Society ever do the chant? They would have had to have done the chant some year, because they would have done the chant last year if they hadn’t done it yet (since the coin came up heads last year). And yet any year you point to, there is a prior year in which they would have done the chant if they had not done the chant before. So they had to have done the chant (since the coin came up heads last year), yet they could not have done the chant (there is no year they could have done it), and so this scenario creates a logical contradiction.
<br /><br />
Although scenario S<span class="sub">1</span> is not directly self-contradictory, scenario S<span class="sub">1</span> is impossible because it implies the <em>possibility</em> of a logical contradiction. The Eternal Society argument against an infinite past goes like this:
<ol start="1">
<li>If an infinite past were possible, an Eternal Society would be possible.</li>
<li>If an Eternal Society were possible, then scenario S<span class="sub">1</span> would be possible.</li>
<li>If S<span class="sub">1</span> would be possible, then S<span class="sub">2</span> would be possible.</li>
<li>S<span class="sub">2</span> is not possible.</li>
<li>Therefore, an infinite past is not possible.</li>
</ol>
The Eternal Society Paradox Argument Against an Infinite Past is a <em>deductively valid</em> argument—the conclusion (line 5) follows logically and inescapably from the premises (lines 1-4). A <em>sound</em> argument is a valid argument with all true premises, so the only way the argument can fail to be sound is with a false premise.
<br /><br />
One could deny premise (1) particularly since that seems to be the most vulnerable premise, but as <a href="http://aporia.byu.edu/pdfs/tisthammer-an_eternal_society_paradox.pdf">the Eternal Society Paradox paper</a> says, “Surely there is something metaphysically suspicious about an infinite past if an eternal society with the abilities of ordinary humans can actualize a logical contradiction.” The idea that an infinite past is possible but an Eternal Society is not possible strikes me as overly <em>ad hoc</em> due to the Eternal Society’s extremely modest abilities (the abilities of ordinary humans in each year of its existence).
<br />
<br />
<h3 class="subHeader">An Objection</h3>
<br />
<br />
One objection I’ve seen is that it’s just not possible for a coin to come up heads infinitely many times, such that S<span class="sub">1</span> is possible (since both heads and tails coming up infinitely many times is possible) but S<span class="sub">2</span> is not (it’s impossible for an infinite sequence of heads to happen). The reasoning behind this may stem from a confusion of the law of large numbers or thinking that if the probability of heads is 50% for each trial, an infinite sequence of such trials leads to a probability of 0, and a probability of 0 means that it’s impossible (this is not true; <em>any</em> infinite particular permutation of coinflips where both heads or tails has a “probability of 0” as the number of trials goes to infinity; so this “probability of 0” reasoning would imply that <em>no</em> outcome is possible for an infinite sequence of fair coinflips). Regardless, can we mathematically prove that an infinite sequence of heads is possible under the conditions of the Eternal Society Paradox? We can.
<br />
<br />
<h3 class="subHeader">The Proof</h3>
<br />
<br />
To define some terms (with the caveat that different sources may define these terms slightly differently): in probability a random experiment like flipping a fair coin is called a <em>trial</em>. In the case of an individual coinflip for the scenario used here, the outcomes are <em>binary</em> meaning that there are only two possible outcomes (heads or tails). <em>Mutually independent</em> trials are where the probability of given trial’s outcome is unaffected by the outcomes of other trials, including any combination of the outcomes of the other trials. A <em>sample space</em> is the set of all possible outcomes of a random experiment.
<br /><br />
In the case of an infinite sequence of coinflips, each trial has exactly two possible outcomes, each trial is mutually independent (in the sense that the probability of the outcome is unaffected by the outcomes of other trials), and the probability is the same in each trial. Some additional assumptions to make the reasoning a bit easier to follow if nothing else: each candidate outcome for a trial (heads or tails) has a nonzero probability, and any outcome with a nonzero probability is possible. Let H represent “heads” and T represent “tails.”
<br/ ><br />
Recall that for each coinflip, both H and T have nonzero probabilities and thus both are possible. So the fact that the probability of given trial’s outcome is unaffected by the outcomes of other trials entails that <em>which outcomes are possible</em> for each trial is also unaffected by the outcomes of other trials.
<br /><br />
So for each trial (and thus each sequence element in the infinite sequence of coinflips):
<br/>
<br />
<table class="list" cellspacing="0" border="0">
<tr><td class="li"> (a) </td><td>both outcomes (H or T) are possible; and</td></tr>
<tr><td class="li"> (b) </td><td>which outcome is possible is unaffected by the outcomes of other trials.</td></tr>
</table>
<br />
<br />
Given the aforementioned conditions, since every element in the sequence has the property of heads or tails both being possible values regardless of the values of the other sequence elements, this permits any infinite sequence of the binary values.
<br /><br />
To illustrate, suppose we have a fair coin and the coinflips are mutually independent in the sense I described earlier, and there are an infinite number of coinflips. Can the first coinflip be heads? Yes, since for each sequence element, H or T is a possible outcome, which would include the first coinflip (confer (a)). Given that the first coinflip is heads, can the second coinflip also be heads? Yes, since the possible outcomes of the second coinflip is unaffected by the outcomes of other coinflips (confer (b)); hence both H and T can be used here. If the first two coinflips are heads, can the third one be also? Yes, because the possible outcomes of the third coinflip is unaffected by the outcomes of other coinflips (confer (b)), hence both H and T can be used here, and so on <em>ad infinitum</em> for all of the remaining sequence elements. And since the outcomes of heads is arbitrary here (e.g., we could just as well have used T, H, T for the first three sequence elements, and then choose whatever binary sequence we wish for the remaining sequence elements) this can be generalized so that the sample space consists of all infinite binary sequences.
<br /><br />
But since the set of all possible outcomes consists of all infinite binary sequences, this would include a sequence of coinflips coming up H for each trial.
Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-90577823895429756552021-09-09T22:53:00.004-05:002021-09-10T12:28:33.947-05:00Eben Alexander’s Questionable NDE<style type="text/css"> <!--
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<br />
<h3 class="subHeader">Intro</h3>
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<br />
Eben Alexander was on Capturing Christianity’s channel recently (as of this writing) on NDEs, titled <a href="https://www.youtube.com/watch?v=FDp0ToUfT8E">Eben Alexander Discusses His Wild NDE with Gary Habermas</a>. I mentioned some things in the comment but couldn’t post links (the YouTube algorithm erases my comments when I do for some reason) so I’m writing this short article here.
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<h3 class="subHeader">Fraud?</h3>
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At around <a href=" https://www.youtube.com/watch?v=FDp0ToUfT8E&t=4688s">1:18:08</a> to 1:26:00 Alexander responds to a question of mine, “What is Eben Alexander’s response to reported evidence that his NDE experience was fraudulent (e.g., testimony from one of the doctors who treated him)?”
<br /><br />
The genesis of this, as a casual internet might turn up, is the August 2013 issue of <em>Esquire</em> which published an exposé in an article called “<a href="https://www.esquire.com/entertainment/interviews/a23248/the-prophet/">The Prophet</a>” which can be read for free online. Alexander’s says his FAQ responds to the lawsuits, which it does, noting that they were settled (lawsuits usually are, particularly when it's not a close call) but doesn't respond to the e.g., the doctor's testimony against him. The NDE article he refers to is apparently <a href="https://digital.library.unt.edu/ark:/67531/metadc1125118/">Eben Alexander's Near-Death Experience: How an Esquire article Distorted the Facts</a> by Robert Mays (a guest editorial). That article does not interview Laura Potter, the key physician witness of the Esquire article (apparently she was unresponsive to telephone calls by this person). The article does claim a quote by her nonetheless supposedly issued to the Associated Press which if veridical would seem to cast doubt on the Esquire article, but I've been unable to verify the veracity of the quote (a google search turns up nothing solid).
<br /><br />
One of the reasons for suspicion is that at the time Eben Alexander had a far higher than normal lawsuit load against him, something he left out in this interview when he talked about his lawsuits (settlements are the norm, not the exception, and are usually done when it's not a close call about who would win). <a href="https://www.esquire.com/entertainment/interviews/a23248/the-prophet/">The Esquire article reports</a>:
<blockquote>By the time all his pending cases are resolved, Alexander will have settled five malpractice cases in the last ten years. Only one other Virginia-licensed neurosurgeon has settled as many cases in that time period, and none have settled more.
</blockquote>
Alexander had a powerful motive to acquire cash (settlements aren't necessarily cheap, especially if you undergo them far more than usual as Alexander did). Alexander had his alleged NDE when there was a $3 million lawsuit pending. He made a lot of money with his NDE, selling webinars and even co-founding an organization called “Eternea” where (at the time) <a href="https://web.archive.org/web/20130329124936/http://eternea.org/membership_opportunities.aspx">if you paid $1,200 a year or more</a>, you could qualify for a membership status called “archangel.” There was also a “Governor’s Guild” in which <a href="http://web.archive.org/web/20120902091611/http://www.eternea.org/Learning_about_Board/Learning_about_Board.htm">membership dues began at $10,000 per year</a>. Lifetime membership was offered to anyone who made a major lump sum gift of $25,000. To insinuate that there was no financial gain here (<a href="https://www.youtube.com/watch?v=FDp0ToUfT8E&t=5136s">1:25:36</a> to 1:25:59) strikes me as somewhat misleading.
<br /><br />
At <a href="https://www.youtube.com/watch?v=FDp0ToUfT8E&t=5031s">1:23:51</a> to 1:51:55 he says the Esquire article author (Luke Dittrich) was “obviously blackballed” by the industry, but the evidence he cites for this (not having published an article in the press for several years) seems insufficient, since it's unclear that writing articles for newspapers and magazines is his intended primary source of income. However, Alexander's claim that some 200 scientists questioned Dittrich's book appears to be factual (one can find it reported in <a href="https://www.scientificamerican.com/article/mit-challenges-the-new-york-times-over-book-on-famous-brain-patient/">Scientific American</a>) to at least some degree; there was dispute about Dittrich's characterizations of an MIT neuroscientist.
<br /><br />
I'm not saying that I know Eben Alexander is a grifter, but I think some amount of skepticism is warranted.
Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-39399972910720156182020-12-24T17:18:00.010-06:002023-08-02T22:27:17.447-05:00An Objection to the Eternal Society Paradox<style type="text/css"> <!--
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<br />
<h3 class="subHeader">Intro</h3>
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<br />
The Eternal Society Paradox is one in which an eternal society with the abilities of ordinary human beings in each year of its existence uses its modest abilities to create a logical contradiction, thereby casting doubt on the metaphysical possibility of an infinite past. If the past is finite, this in turn can be used as part of an argument for the universe having a transcendent personal cause. Jimmy Akin wrote an article that among other things critiqued the Eternal Society Paradox argument against an infinite past. The original link is <a href="https://jimmyakin.com/2020/11/the-kalaam-cosmological-argument-and-the-first-and-last-fallacy.html">here</a> but in case something disastrous happens, the archived link is <a href="https://archive.is/UxUL5">here</a>.
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<h3 class="subHeader">Background</h3>
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Roughly (in the <a href="http://aporia.byu.edu/pdfs/tisthammer-an_eternal_society_paradox.pdf">paper the Eternal Society Paradox was published</a>), an Eternal Society is a society that has existed for a beginningless, infinite duration of time and has the abilities of ordinary human beings in each year of its existence; e.g. in each year people in the society can flip coins, write books, sing songs, and pass on information possessed in the current year to the next year. Because of the society’s extremely modest abilities, it seems like an Eternal Society would be possible if an infinite past were possible (note that by “possible” in this article I’ll be referring to <em>metaphysical</em> possibility, as opposed to e.g. physical possibility).
<br /><br />
Now imagine the Eternal Society has the following Annual Coin Flipping Tradition (ACFT):
<blockquote>
For each year <em>y</em> in the beginningless, infinite past: the society flips a coin, and they do the chant if and only if these two conditions are met: (a) the coin comes up heads; (b) they never did the chant in a year prior to <em>y</em>.</blockquote>
Less technically but somewhat more roughly: ACFT is where every year they flip a coin and they do a chant in that year if and only if (a) the coin comes up heads; and (b) they never did the chant in a prior year. Even more crudely put: each year they flip a coin. If the coin comes up heads and they never did a particular chant before, then they do the chant; otherwise they do not do the chant for that year.
<br /><br />
The coin flips are probabilistically independent events, so any particular infinite permutation of coin flips is equally unlikely but also equally possible. Consider scenario S<span class="sub">1</span> in which the coin came up heads for the first time last year for the Eternal Society practicing the aforementioned Annual Coin Flipping Tradition. The Eternal Society gets together to do the chant for the first time. This seems like it would be possible if an infinite past were possible (an eternal society with the ability of ordinary humans, by which I mean the society has the ability of ordinary humans in each year of its existence, could surely do something like this), but this scenario is provably not possible.
<br /><br />
Again, the coin flips are probabilistically independent events, so if scenario S<span class="sub">1</span> were possible, then another scenario, that we can call scenario S<span class="sub">2</span>, would be possible: the coin came up heads each year of the infinite past for the Eternal Society engaging in the Annual Coin Flipping Tradition. If the coin came up heads each year, did the Eternal Society ever do the chant? They would have had to have done the chant some year, because they would have done the chant last year if they hadn’t done it yet (since the coin came up heads last year). And yet any year you point to, there is a prior year in which they would have done the chant if they had not done the chant before. So they had to have done the chant (since the coin came up heads last year), yet they could not have done the chant (there is no year they could have done it), and so this scenario creates a logical contradiction.
<br /><br />
Although scenario S<span class="sub">1</span> is not directly self-contradictory, scenario S<span class="sub">1</span> is impossible because it implies the <em>possibility</em> of a logical contradiction. The Eternal Society argument against an infinite past goes like this:
<ol start="1" class="start">
<li>If an infinite past were possible, an Eternal Society would be possible.</li>
<li>If an Eternal Society were possible, then scenario S<span class="sub">1</span> would be possible.</li>
<li>If S<span class="sub">1</span> would be possible, then S<span class="sub">2</span> would be possible.</li>
<li>S<span class="sub">2</span> is not possible.</li>
</ol>
<hr />
<ol class="end" start="5">
<li>Therefore, an infinite past is not possible.</li>
</ol>
The Eternal Society Paradox Argument Against an Infinite Past is a <em>deductively valid</em> argument—the conclusion (line 5) follows logically and inescapably from the premises (lines 1-4). A <em>sound</em> argument is a valid argument with all true premises, so the only way the argument can fail to be sound is with a false premise.
<br /><br />
One could deny premise (1) particularly since that seems to be the most vulnerable premise, but as <a href="http://aporia.byu.edu/pdfs/tisthammer-an_eternal_society_paradox.pdf">the Eternal Society Paradox paper</a> says, “Surely there is something metaphysically suspicious about an infinite past if an eternal society with the abilities of ordinary humans can actualize a logical contradiction.” The idea that an infinite past is possible but an Eternal Society is not possible strikes me as overly <em>ad hoc</em> due to the Eternal Society’s extremely modest abilities (the abilities of ordinary humans in each year of its existence).
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<h3 class="subHeader">The Rebuttal</h3>
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<br />
When using the phrase “Eternal Society Paradox” the author seems to have in mind specifically scenario S<span class="sub">2</span>. From the article:
<blockquote>…the solution [to the paradox] is straightforward: The Eternal Society Paradox is presupposing a logical contradiction.</blockquote>
How is this a solution? The fact that the Eternal Society Paradox (in scenario S<span class="sub">2</span>) entails a logical contradiction is part of the point; it’s not a solution to simply to concede part of the claim.
<blockquote>It presupposes a first and a last element to a supposedly infinite series, so the Eternal Society Paradox commits the First-and-Last Fallacy.</blockquote>
Simply calling something a fallacy doesn’t make it so. The “first-and-last fallacy” is described as follows:
<blockquote>The First-and-Last Fallacy occurs if and only if a person envisions a supposedly infinite series as having both a first and a last element.</blockquote>
I didn’t envision it, and neither did scenario S<span class="sub">2</span>. Indeed, part of the reason there’s a contradiction is that the scenario (if anything) envisions that <em>there is no first element</em>.
<br /><br />
Another problem with the objection is that the Eternal Society Paradox Argument is logically valid, so if the argument is unsound, which premise is false? At first blush at least, this objection doesn’t actually attack any premise of the argument! My conclusion was initially that this objection is a <a href="https://www.maverick-christian.org/p/glossary-of-philosophy-terms-etc.html#_red_herring" class="dfn">red herring</a> (for more on red herrings, see my <a href="https://www.youtube.com/watch?v=00MIK636fF4">red herring video</a>). But see the update below:
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<br />
<br />
<h3 class="subHeader">Update</h3>
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<br />
After personal communication with the author in 2023-07-31-MO I discovered I hadn’t quite correctly understood his objection. While at the time it wasn’t clear to me which premise he was attacking, it seems he was attacking the premise that says scenario S<span class="sub">2</span> is impossible. Although proof of its logical impossibility can be <a href="https://maverickchristian.blogspot.com/2020/11/eternal-society-paradox-symbolic-logic.html#argument3">proven via symbolic logic</a>, we won’t need to go into something so complex here. Here was Akin’s understanding of the Annual Coin-Flipping Tradition that I’ll label ACFT*:
<blockquote>
The society flips a coin each year of the infinite past. If the coin comes up heads, then they do the chant if and only if it’s the first time the coin comes up heads.
</blockquote>
The objection goes as follows: scenario S<span class="sub">2</span> is the conjunction of ACFT* and the coin coming up heads each year. Since there is no first year the coin came up heads, they never do the chant. There is no self-contradiction with ACFT* and the coin coming up heads each year; the society just never does the chant in any year. Therefore, S<span class="sub">2</span> is not self-contradictory and premise (4) is false. To think that in S<span class="sub">2</span> they had to do the chant assumes that there was a first year the coin came up heads (as well as a “last time” the coin came up heads, since there is a present year); hence a “First and Last Fallacy.”
<br /><br />
The problem is that ACFT* is not synonymous with ACFT. To see this I’ll use a <em>reductio ad absurdum</em> argument, which assumes the opposite of what we want to prove (the <em>reductio</em> assumption) and show that it leads to an absurdity (such as a self-contradiction). Recall that ACFT says that the society does the chant when these two conditions are met: (a) the coin comes up heads; and (b) they have not done the chant in a prior year. Assume for <em>reductio</em> that when following ACFT the society never did the chant in any year and the coin comes up heads each year. Now consider last year: are both conditions (a) and (b) met?
<ul>
<li>Condition (a) is met, since the coin came up heads last year.</li>
<li>Condition (b) is also met <em>since they never did the chant in a prior year.</em> (Since they never did the chant in <em>any</em> year.)</li>
</ul>
So on AFCT they would have done the chant last year since both conditions are met, which contradicts the original assumption that they never did the chant in any year. Thus it is logically impossible for them to have never done the chant if the coin came up heads each year and they followed AFCT. It also follows that ACFT and ACFT* are not equivalent; when the coin comes up heads each year, the society never doing the chant is possible on ACFT* but logically impossible on ACFT (since last year, both conditions (a) and (b) would have been met and they would have done the chant last year).
<br /><br />
Somewhat more formally, the <em>reductio</em> argument goes as follows, where the premise (6) is true by definition of the ACFT:
<ol start="6" class="start">
<li>If ACFT is true, then for any year <em>y</em>, the society does the chant in year <em>y</em> when (a) the coin comes up heads in year <em>y</em>; and (b) they did not do the chant prior to <em>y</em>. (Follows from the definition of ACFT)</li>
</ol>
<hr />
<ol start="7" class="end">
<li>In scenario S<span class="sub">2</span>, ACFT is true, the coin came up heads each year, and they never did the chant in any year. (<em>Reductio</em> assumption; we’ll show that this leads to an absurdity.)</li>
<li>Last year, the coin came up heads (follows from 7) and thus condition (a) is met.</li>
<li>Last year, they never did the chant in a prior year (follows from 7) and thus condition (b) is met.</li>
<li>Last year, conditions (a) and (b) are met. (Follows from 8 and 9.)</li>
<li>If conditions (a) and (b) are met last year, then they did the chant last year. (Follows from 6.)</li>
<li>They did the chant last year. (Follows from 10 and 11.)</li>
<li>They did not do the chant last year. (Follows from 7.)</li>
<li>They did the chant last year and they did not do the chant last year. (Follows from 12 and 13.)</li>
<li>Therefore, (7) is false. (Follows from <em>reductio</em> and 14.)</li>
</ol>
We know that scenario S<span class="sub">2</span> includes ACFT and that the coin came up heads each year, so the part of (7) that must be false is the idea that they never did the chant in any year.
<br />
<br />
<br />
<h3 class="subHeader">Conclusion</h3>
<br />
<br />
This illustrates an important lesson in spotting straw men; sometimes statements that might initially <em>appear</em> to be synonymous are actually subtly different, and sometimes that subtle difference matters when evaluating objections. When evaluating an objection, consider how that objection fares against the position <em>as it was originally stated</em>. In the case of the Eternal Society never having done the chant in scenario S2, when we apply ACFT’s conditions (a) and (b) to last year we see that they would have done the chant last year, whereas on ACFT* they would not have done the chant. I can understand why one might think that ACFT and ACFT* are synonymous, but that wasn’t quite true; they were strongly similar but subtly different, and that subtle difference made all the difference in the world.Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-29172781917885922362020-11-13T15:50:00.030-06:002023-08-02T07:56:58.489-05:00The Eternal Society Paradox Argument: Symbolic Logic Approaches<style type="text/css"> <!--
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<a href="https://maverickchristian.blogspot.com">Home</a> > <a href=" https://maverickchristian.blogspot.com/p/site-map.html#_philosophy">Philosophy</a> > <a href="https://maverickchristian.blogspot.com/p/site-map.html#_atheism_theism">Atheism/Theism</a>
<br />
<br />
<h2 class="subHeader">Introduction</h2>
<br />
<br />
In August 2020 the <a href="https://www.youtube.com/c/MaverickChristian">Maverick Christian YouTube channel</a> featured <a href="https://www.youtube.com/watch?v=0Cd7CbObR9o">an interview on the Eternal Society paradox</a>, something I’ve also talked about in article explaining <a href="https://maverickchristian.blogspot.com/2020/07/why-past-cannot-be-infinite.html">why the past cannot be infinite</a>. Here I’m going to dive into a symbolic logic approach to arguing for the premises of the Eternal Society paradox argument. This article is for logic nerds and less layperson-friendly than most of my other blog articles. I will, however, have at least rough English translations of symbolic logic for each of the premises right underneath the symbolic logic language. For those enterprising individuals who aren’t familiar with symbolic logic but want to try to understand it, I’ll explain some of the symbols in the next section.
<br />
<br />
<h2 class="subHeader">Some Symbolic Logic</h2>
<br />
<br />
Some of the logic I will use (including the various names for the rules of logic) can be found in this <a href= "https://maverickchristian.blogspot.com/2012/05/introductory-logic-part-1.html">introductory logic</a> page. I won’t go into the various rules of logic here but I will explain what some symbols mean. First there are symbols of basic propositional logic:
<br />
<br />
<table cellpadding="0" cellspacing="0" border="3" align="center" class="standardLogic">
<tr><th class="nowrap">Type of<br /><span class="nowrap">connective</span></th><th class="nowrap">English</th><th class="nowrap">Symbolic<br />Logic</th><th>When it’s true/false</th></tr>
<tr><td>Conjunction</td><td><b>p</b> and <b>q</b></td><td>p ∧ q</td><td>True if both are true; otherwise false</td></tr>
<tr><td>Disjunction</td><td><b>p</b> or <b>q</b></td><td>p ∨ q</td><td>False if both are false; otherwise true</td></tr>
<tr><td>Conditional</td><td>If <b>p</b>, then <b>q</b></td><td>p → q</td><td>False if <em>p</em> is true and <em>q</em> is false; otherwise true</td></tr>
<tr><td class="nowrap">Biconditional</td><td><b>p</b>, if and only if <b>q</b></td><td>p ↔ q</td><td>True if both have the same truth-value (i.e. both are true or both are false); otherwise false</td></tr>
<tr><td>Negation</td><td>Not-<b>p</b></td><td>¬p</td><td>True if <em>p</em> is false; false if <em>p</em> is true</td></tr>
</table>
<br />
<br />
To give an example of predicate logic, consider the following symbolization key:
<br />
<br />
<table class="inline" cellpadding="1" cellspacing="0" border="0">
<tr class="separate" style="background-color: #ddddff"><td class="equals">B(x)</td><td class="equals"> </td><td class="equals">=</td><td class="equals"> </td><td style="text-align: left;"><em>x</em> is a <em>B</em>achelor.</td></tr>
<tr class="separate" style="background-color: #ddddff"><td class="equals">U(x)</td><td class="equals"> </td><td class="equals">=</td><td class="equals"> </td><td style="text-align: left;"><em>x</em> is <em>U</em>nmarried.</td></tr>
</table>
<br />
<br />
The letters <em>B</em> and <em>M</em> in these examples are <em>predicates</em> which say something about the element they are <em>predicating</em>. Sometimes parentheses aren’t used; e.g. Bx being used to mean “<em>x</em> is a bachelor.” The symbol; ∀ means “For All” or “For Any” such that the following basically means “All bachelors are unmarried:”
<br />
<br />
<table cellpadding="0" cellspacing="0" border="3" align="center" class="standardLogic">
<tr><th colspan="2"><b>universal quantification</b></th></tr>
<tr class="line"><td colspan="2"> </td></tr>
<tr>
<th>In English</th>
<th>In Symbolic Logic</th>
</tr>
<tr>
<td>For any <strong>x</strong>: [if <strong>x</strong> is <strong>B</strong>, then <strong>x</strong> is <strong>U</strong>]
</td>
<td>
∀x[B(x) → U(x)]
</td>
</tr>
</table>
<br />
<br />
There’s also the <em>existential quantifier</em> ∃ that denotes the existence of something.
<br />
<br />
<table cellpadding="0" cellspacing="0" border="3" align="center" class="standardLogic">
<tr><th colspan="2"><b>existential quantification</b></th></tr>
<tr class="line"><td colspan="2"> </td></tr>
<tr>
<th>In English</th>
<th>In Symbolic Logic</th>
</tr>
<tr>
<td>There exists an <strong>x</strong>: [<strong>x</strong> is <strong>B</strong> and <strong>x</strong> is not <strong>U</strong>]
</td>
<td>
∃x[B(x) ∧ ¬U(x)]
</td>
</tr>
</table>
<br />
<br />
Note that ∀x¬[Fx] = ¬∃[Fx].
<br />
<br />
In philosophy, a <em>possible world</em> is a complete description of the way reality is or could have been like. On possible world semantics, a proposition is <em>possibly</em> true if and only if it is true in at least one possible world, and a proposition is <em>necessarily</em> true if and only if it is true in all possible worlds.
<br />
<br />
<table cellpadding="0" cellspacing="0" border="3" align="center" class="standardLogic">
<tr><th class="nowrap">English</th><th class="nowrap">Symbolic<br />Logic</th><th>When it’s true/false</th></tr>
<tr><td class="nowrap"><b>p</b> is possible</td><td class="nowrap">◊p</td><td>True if <em>p</em> is true in at least on possible world; otherwise false</td></tr>
<tr><td class="nowrap"><b>p</b> is necessary</td><td class="nowrap">□p</td><td>True if <em>p</em> is true in all possible worlds; otherwise false</td></tr>
<tr><td class="nowrap"><b>p</b> is not possible</td><td class="nowrap">¬◊p</td><td>True if <em>p</em> is false in all on possible worlds; otherwise true</td></tr>
</table>
<br />
<br />
Note that ¬◊p is equivalent to □¬p. Indeed, the ◊ and □ operators can even be defined in terms of each other; e.g. one could define ◊ as “true in at least one possible world” and then define □ as this:
<blockquote>
□p = ¬◊¬p
</blockquote>
<br />
<br />
<h2 class="subHeader">Eternal Society Paradox</h2>
<br />
<br />
Roughly, an Eternal Society is a society that has existed for a beginningless, infinite duration of time and has the abilities of ordinary human beings in each year of its existence; e.g. in each year people in the society can flip coins, write books, sing songs, and pass on information possessed in the current year to the next year. Because of the society’s extremely modest abilities, it seems like an Eternal Society would be possible if an infinite past were possible (note that by “possible” in this article I’ll be referring to <em>metaphysical</em> possibility, as opposed to e.g. physical possibility).
<br /><br />
Now imagine the Eternal Society has the following Annual Coin Flipping Tradition: each year they flip a coin. If the coin comes up heads and they never did a particular chant in a prior year, then they do the chant; otherwise they do not do the chant for that year. The coin flips are probabilistically independent events, so any particular infinite permutation of coin flips is equally unlikely but also equally possible. Consider scenario S<span class="sub">1</span> in which the coin came up heads for the first time last year for the Eternal Society practicing the aforementioned Annual Coin Flipping Tradition. The Eternal Society gets together to do the chant for the first time. This seems like it would be possible if an infinite past were possible (an eternal society with the ability of ordinary humans, by which I mean the society has the ability of ordinary humans in each year of its existence, could surely do something like this), but this scenario is provably not possible.
<br /><br />
Again, the coin flips are probabilistically independent events, so if scenario S<span class="sub">1</span> were possible, then another scenario, that we can call scenario S<span class="sub">2</span>, would be possible: the coin came up heads each year of the infinite past for the Eternal Society engaging in the Annual Coin Flipping Tradition. If the coin came up heads each year, did the Eternal Society ever do the chant? They would have had to have done the chant some year, because they would have done the chant last year if they hadn’t done it yet (since the coin came up heads last year). And yet any year you point to, there is a prior year in which they would have done the chant if they had not done the chant before. So they had to have done the chant (since the coin came up heads last year), yet they could not have done the chant (there is no year they could have done it), and so this scenario creates a logical contradiction.
<br /><br />
Although scenario S<span class="sub">1</span> is not directly self-contradictory, scenario S<span class="sub">1</span> is impossible because it implies the <em>possibility</em> of a logical contradiction. The Eternal Society argument against an infinite past goes like this:
<ol start="1">
<li>If an infinite past were possible, an Eternal Society would be possible.</li>
<li>If an Eternal Society were possible, then scenario S<span class="sub">1</span> would be possible.</li>
<li>If S<span class="sub">1</span> would be possible, then S<span class="sub">2</span> would be possible.</li>
<li>S<span class="sub">2</span> is not possible.</li>
<li>Therefore, an infinite past is not possible.</li>
</ol>
As mentioned in the paper, premises (1)-(3) can be understood as material conditionals, even though there is a sense in which I think the subjunctive mood is appropriate. Some people have disputed these premises, and to argue for them I’ll use symbolic logic.
<br />
<br />
<h2 class="subHeader">Defining the Predicates and Propositional Variables</h2>
<br />
<br />
With the domain of discourse being the years of the past, the predicates are defined as follows.
<ul>
<li>Py = There exists a year <em>y’</em> prior to year <em>y</em> in which the Eternal Society did the chant in year <em>y’</em>.</li>
<li>Cy = the chant is done in year <em>y</em>.</li>
<li>By = there exists a year before year <em>y</em>.</li>
<li>P<span class="sub">B</span>y = Where <em>y’</em> represents the year before <em>y</em>, Py’ is true (they did the chant in a year prior to <em>y’</em>).</li>
<li>C<span class="sub">B</span>y = The chant is done in the year before <em>y</em>.</li>
<li>Fy = the coin (indeterministic, probabilistically independent) is flipped in year <em>y</em>.</li>
<li>Hy = the coin comes up heads in year <em>y</em>.</li>
</ul>
The propositional variables are defined as follows:
<ul>
<li>I = the past is infinite and beginningless such that <em>I</em> entails ∀y[By].</li>
<li>L = the flipped coin came up heads for the first time last year.</li>
<li>V = ∀y[Hy].</li>
<ul>
<li>In English: the flipped coin came up heads every year.</li>
</ul>
<li>D = (I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)])</li>
<ul>
<li>In English: the past is infinite and for every year <em>y</em>: if a flipped coin came up heads in year <em>y</em> and the society did not do the chant in a prior year, then the society does the chant in year <em>y</em>, otherwise they do not do the chant in year <em>y</em>.</li>
</ul>
</li>
<li>A = ∀y[Fy] ∧ D = ∀y[Fy] ∧ (I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)])</li>
<ul>
<li>In English: the Eternal Society engages in the Annual Coin-Flipping Tradition.</li>
</ul>
<li>E = the Eternal Society (roughly, a society that has existed throughout the infinite, beginningless past and in each year, they can do what we humans can do in contemporary society, e.g. in any year they can flip coins and do chants) obtains.</li>
<li>S<span class="sub">1</span> = A ∧ L = ∀y[Fy] ∧ D ∧ L</li>
<ul>
<li>In English: Scenario S<span class="sub">1</span> obtains.</li>
<li>Note that it follows from this definition that S<span class="sub">1</span> entails A.
</ul>
<li>S<span class="sub">2</span> = A ∧ V = ∀y[Fy] ∧ (I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) ∧ ∀y[Hy]</li>
<ul>
<li>In English: scenario S<span class="sub">2</span> obtains (<em>A</em> is true and the coin comes up heads each year of the infinite past).</li>
</ul>
</ul>
<br />
<br />
<h2 class="subHeader">Argument 1: If ◊S<span class="sub">1</span> then ◊S<span class="sub">2</span></h2>
<br />
<br />
Where a <em>possible world</em> is the way the world is or could have been like, the modal operator □ is such that □P means that P is necessarily true (true in all possible worlds), and ◊P means that P is possibly true (true in at least one possible world).
<br /><br />
Here is an argument that if Scenario S<span class="sub">1</span> is possible then Scenario S<span class="sub">2</span> is possible. The justification for premise (7) below is that in the Annual Coin-Flipping Tradition the coin-flips are probabilistically independent and so any particular permutation of coin clips is possible for the Annual Coin-Flipping Tradition, including a permutation where the coin came up heads each year it was flipped.
<!-- Possibility of S1 implying the possibility of S2 -->
<ol class="start" start="6">
<li>□(S<span class="sub">1</span> → A)</li>
<ul>
<li>Scenario S<span class="sub">1</span> entails that the Annual Coin-Flipping Tradition obtains.</li>
</ul>
<li>□(A → ◊(A ∧ V))</li>
<ul>
<li>Necessarily: if the Annual Coin-Flipping Tradition obtains then heads coming up each year is a possible outcome.</li>
</ul>
<li>□(S<span class="sub">2</span> ↔ (A ∧ V))</li>
<ul>
<li>Necessarily: the Annual Coin-Flipping Tradition with the coin coming up heads each year obtains if and only if scenario S<span class="sub">2</span> obtains. (Recall that scenario S<span class="sub">2</span> is defined to be this way.</li>
</ul>
</ol>
<hr />
<ol class="middle" start="9">
<li>◊S<span class="sub">1</span> <span class="logic">conditional proof assumption</span>
</ol>
<ol class="middle">
<div class="middle">
<ol class="middle" start="10">
<li>¬◊S<span class="sub">2</span> <span class="logic">indirect proof assumption</span></li>
</ol>
<ol class="middle">
<div class="middle">
<ol class="middle" start="11">
<li>□¬S<span class="sub">2</span> <span class="logic">10, equivalence</span></li>
</ol>
<ol class="middle">
<table cellpadding="0" cellspacing="0" border="0" style="float: left;">
<tr><td>□</td></tr>
</table>
<table cellpadding="0" cellspacing="0" border="0">
<tr><td>
<div class="middle">
<ol class="middle" start="12">
<li>¬S<span class="sub">2</span> <span class="logic">10, T-reiteration</span></li>
<li>S<span class="sub">2</span> ↔ (A ∧ V) <span class="logic">8, T-reiteration</span></li>
<li>¬(A ∧ V) <span class="logic">12, 13, biconditional elimination</span></li>
</ol>
</div>
</td></tr>
</table>
</ol>
<ol class="middle" start="15">
<li>□¬(A ∧ V) <span class="logic">12-14, necessity intro</span></li>
</ol>
<ol class="middle">
<table cellpadding="0" cellspacing="0" border="0" style="float: left;">
<tr><td>□</td></tr>
</table>
<table cellpadding="0" cellspacing="0" border="0">
<tr><td>
<div class="middle">
<ol class="middle" start="16">
<li>□¬(A ∧ V) <span class="logic">15, S4-reiteration</span></li>
<li>¬◊(A ∧ V) <span class="logic">16, equivalence</span></li>
<li>A ↔ ◊(A ∧ V) <span class="logic">7, T-reiteration</span></li>
<li>¬A <span class="logic">16, 17, biconditional elimination</span></li>
<li>S<span class="sub">1</span> → A <span class="logic">6, T-reiteration</span></li>
<li>¬S<span class="sub">1</span> <span class="logic">19, 20, <em>modus tollens</em></span></li>
</ol>
</div>
</td></tr>
</table>
</ol>
<ol class="middle" start="22">
<li>□¬S<span class="sub">1</span> <span class="logic">16-21 necessity intro</span></li>
<li>¬◊S<span class="sub">1</span> <span class="logic">22, equivalence</span></li>
<li>◊S<span class="sub">1</span> ∧ ¬◊S<span class="sub">1</span> <span class="logic">9, 23, conjunction introduction</span></li>
</ol>
</div>
</ol>
<ol class="middle" start="25">
<li>◊S<span class="sub">2</span><span class="logic">10-24, indirect proof</span></li>
</ol>
</div>
</ol>
<ol class="end" start="26">
<li>◊S<span class="sub">1</span> → ◊S<span class="sub">2</span><span class="logic">9-25, conditional proof</span></li>
</ol>
<br />
<br />
<h2 class="subHeader">Argument 2: If ◊I then ◊E, and if ◊E then ◊S<span class="sub">1</span></h2>
<br />
<br />
Next is an argument for the idea that if an infinite past is possible, then an Eternal Society is possible and S<span class="sub">1</span> is possible. Premises (2) and (3) can be derived rigorously from lines (27)-(35) below:
<ol class="start" start="27">
<li>□(E → I)</li>
<ul>
<li>Necessarily: an Eternal Society existing implies the past is infinite.</li>
</ul>
<li>□(I → (I ∧ ∀y[Py ∨ ¬Py]))</li>
<ul>
<li>Necessarily: if the past is infinite, then (the past is infinite and for any year <em>y</em>, either the chant was done prior to year <em>y</em> or it is not the case that the chant was done prior to year <em>y</em>).</li>
</ul>
<li>□(I → (I ∧ ∀y[Fy → (Hy ∨ ¬Hy]))</li>
<ul>
<li>Necessarily: if the past is infinite, then (the past is infinite and for any year <em>y</em>, if the coin was flipped in <em>y</em> then either the coin landed heads in <em>y</em> or it is not the case that it landed heads in <em>y</em>.</li>
</ul>
<li>{◊I ∧ <span class="nobreak">□(I → (I ∧ ∀y[Py ∨ ¬Py]))</span> ∧ <span class="nobreak">□(I → (I ∧ ∀[Fy → (Hy ∨ ¬Hy]))</span>} → ◊E</li>
<ul>
<li>If [the infinite past is possible and necessarily: (if the past is infinite, then for any year <em>y</em> either the chant was done in a prior year or it is not the case the chant was done in a prior year) and necessarily (If the past is infinite, then for any year <em>y</em> if the coin was flipped then either it came up heads or it didn’t in year <em>y</em>)] then the Eternal Society is possible.</li>
</ul>
<li>◊E → ◊(E ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)])</li>
<ul>
<li>If the Eternal Society is possible, then it is possible for that Eternal Society do the following in each year <em>y</em>: if there is a flipped coin that comes up heads and the chant was done in a prior year they do the chant, otherwise they don’t.</li>
</ul>
<li>□{D ↔ (I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)])}</li>
<ul>
<li>Roughly, the letter <em>D</em> is defined as a placeholder letter to represent the following: the past is infinite and if for any year <em>y</em> there exists the flipped coin that comes up heads and the chant was not done in a prior year, then the chant is done in year <em>y</em>, otherwise the chant is not done in <em>y</em>.</li>
</ul>
<li>□(D ∧ E → ◊(D ∧ ∀y[Fy]))</li>
<ul>
<li>Necessarily: if the Eternal Society exists and <em>D</em> is true for that society (e.g. they do the chant depending on <em>inter alia</em> whether the coin came up heads), then it is possible for the Eternal Society to also actually flip a coin each year with <em>D</em> being true (thereby engaging in the Annual Coin-Flipping Tradition).</li>
</ul>
<li>◊(D ∧ ∀y[Fy]) → ◊(D ∧ ∀y[Fy] ∧ L)</li>
<ul>
<li>If the Annual Coin-Flipping Tradition is possible (the probabilistically independent coin is flipped each year etc.), then it is possible for the coin to have come up heads for the first time last year.</li>
</ul>
<li>□((D ∧ ∀y[Fy] ∧ L) ↔ S<span class="sub">1</span>)</li>
<ul>
<li>Roughly: S1 is defined to be the scenario in which the Annual Coin-Flipping Tradition is done and the coin comes up heads for the first time last year.</li>
</ul>
</ol>
<hr />
<ol class="middle" start="36">
<li>◊I <span class="logic">conditional proof assumption</span>
</ol>
<ol class="middle">
<div class="middle">
<ol class="middle" start="37">
<li>◊I ∧ □(I → (I ∧ ∀y[Fy → (Hy ∨ ¬Hy])) <span class="logic">28, 36, conjunction introduction</span></li>
<li>◊I ∧ □(I → (I ∧ ∀y[Fy → (Hy ∨ ¬Hy])) ∧ □(I → (I ∧ ∀y[Fy → (Hy ∨ ¬Hy]) <span class="logic">37, 29, conjunction introduction</span></li>
<li>◊E <span class="logic">30, 38, <em>modus ponens</em></span></li>
</ol>
</div>
</ol>
<ol class="middle" start="40">
<li>◊I → ◊E <span class="logic">36-39, conditional proof</span></li>
<li>□¬(D ∧ E) <span class="logic">conditional proof assumption</span></li>
</ol>
<ol class="middle">
<div class="middle">
<table cellpadding="0" cellspacing="0" border="0" style="float: left;">
<tr><td> □</td></tr>
</table>
<table cellpadding="0" cellspacing="0" border="0">
<tr><td>
<div class="middle">
<ol class="middle" start="42">
<li>¬(D ∧ E) <span class="logic">41, T-reiteration</span>
<li>E → I <span class="logic">27, T-reiteration</span></li>
<li>D ↔ (I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) <span class="logic">32, T-reiteration</span></li>
<li>E ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)] <span class="logic">indirect proof assumption</span></li>
<div class="middle">
<ol class="middle" start="46">
<li>E <span class="logic">45, conjunction elimination</span></li>
<li>I <span class="logic">43, 46, <em>modus tollens</em></span></li>
<li>(∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)] <span class="logic">45, conjunction elimination</span></li>
<li>I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)] <span class="logic">47, 48, conjunction introduction</span></li>
<li>D <span class="logic">44, 49, biconditional elimination</span></li>
<li>D ∧ E <span class="logic">46, 49, conjunction introduction</span></li>
<li>(D ∧ E) ∧ ¬(D ∧ E) <span class="logic">42, 51, conjunction introduction</span></li>
</ol>
</div>
</ol>
<ol class="middle" start="53">
<li>¬(E ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) <span class="logic">45-52, indirect proof</span></li>
</ol>
</div>
</td></tr>
</table>
<ol class="middle" start="54">
<li>□¬(E ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) <span class="logic">42-53, necessity intro</span></li>
</ol>
</div>
</ol>
<ol class="middle" start="55">
<li>□¬(D ∧ E) → □¬(E ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) <span class="logic">41-54, conditional proof</span></li>
<li>¬◊(D ∧ E) → ¬◊(E ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) <span class="logic">55, equivalence</span></li>
<li>◊(E ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) → ◊(D ∧ E) <span class="logic">56, transposition</span></li>
<li>◊E → ◊(D ∧ E) <span class="logic">28, 52, hypothetical syllogism</span> </li>
<li>□¬(D ∧ ∀y[Fy]) <span class="logic">conditional proof assumption</span></li>
</ol>
<ol class="middle">
<div class="middle">
<table cellpadding="0" cellspacing="0" border="0" style="float: left;">
<tr><td> □</td></tr>
</table>
<table cellpadding="0" cellspacing="0" border="0">
<tr><td>
<div class="middle">
<ol class="middle" start="60">
<li>□¬(D ∧ ∀y[Fy]) <span class="logic">59, S4-reiteration</span></li>
<li>¬◊(D ∧ ∀y[Fy]) <span class="logic">60, equivalence</span></li>
<li>(D ∧ E) → ◊(D ∧ ∀y[Fy]) <span class="logic">33, T-reiteration</span></li>
<li>¬(D ∧ E) <span class="logic">61, 62, <em>modus tollens</em></span></li>
</ol>
</div>
</td></tr>
</table>
<ol class="middle" start="64">
<li>□¬(D ∧ E) <span class="logic">65-68, necessity intro</span></li>
</ol>
</div>
</ol>
<ol class="middle" start="65">
<li>□¬(D ∧ ∀y[Fy]) → □¬(D ∧ E) <span class="logic">59-64, conditional proof</span></li>
<li>¬◊(D ∧ ∀y[Fy]) → ¬◊(D ∧ E) <span class="logic">65, equivalence</span></li>
<li>◊(D ∧ E) → ◊(D ∧ ∀y[Fy]) <span class="logic">66, transposition</span></li>
<li>◊E → ◊(D ∧ ∀y[Fy]) <span class="logic">58, 67, hypothetical syllogism</span> </li>
<li>◊E → ◊(D ∧ ∀y[Fy] ∧ L) <span class="logic">34, 68, hypothetical syllogism</span> </li>
<li>□¬S<span class="sub">1</span> <span class="logic">conditional proof assumption</span></li>
</ol>
<ol class="middle">
<div class="middle">
<table cellpadding="0" cellspacing="0" border="0" style="float: left;">
<tr><td> □</td></tr>
</table>
<table cellpadding="0" cellspacing="0" border="0">
<tr><td>
<div class="middle">
<ol class="middle" start="71">
<li>¬S<span class="sub">1</span> <span class="logic">70, T-reiteration</span></li>
<li>(D ∧ ∀y[Fy] ∧ L) ↔ S<span class="sub">1</span> <span class="logic">35, T-reiteration</span></li>
<li>¬(D ∧ ∀y[Fy] ∧ L) <span class="logic">71, 72 biconditional elimination</span></li>
</ol>
</div>
</td></tr>
</table>
<ol class="middle" start="69">
<li>□¬(D ∧ ∀y[Fy] ∧ L) <span class="logic">71-73, necessity intro</span></li>
</ol>
</div>
</ol>
<ol class="end" start="75">
<li>□¬S<span class="sub">1</span> → □¬(D ∧ ∀y[Fy] ∧ L) <span class="logic">70-74, conditional proof</span></li>
<li>¬◊S<span class="sub">1</span> → ¬◊(D ∧ ∀y[Fy] ∧ L) <span class="logic">75, equivalence</span></li>
<li>◊(D ∧ ∀y[Fy] ∧ L) → ◊S<span class="sub">1</span> <span class="logic">76, transposition</span></li>
<li>◊E → ◊S<span class="sub">1</span> <span class="logic">69, 77 hypothetical syllogism</span></li>
</ol>
Line (40) matches up with premise (1) (“If an infinite past is possible, then an eternal society is possible”) and line (78) matches up with premise (2) (“If an Eternal Society were possible, then scenario S<span class="sub">1</span> would be possible”).
<br />
<br />
<a id="argument3"></a>
<br />
<h2 class="subHeader">Argument 3: ¬◊S<span class="sub">2</span></h2>
<br />
<br />
Odd as it may seem, I’ve even seen some question premise (4), even though theoretically it should be an uncontroversial premise. In addition to the definition of scenario S<span class="sub">2</span> applied in premise (81) I make use of several necessary truths that apply to this situation, such as the beginningless, infinite past entailing that each year has a year before it (line (79)); that where <em>y’</em> is the year right before some arbitrary year <em>y</em>, if the chant was done in <em>y’</em> then the chant was done in a year prior to <em>y</em> (line (84)); and that if there exists a year <em>y</em> where the chant was done in a year prior to <em>y</em>, then there exists a year in which the chant was done (line 85).
<ol class="start" start="79">
<li>□(I → ∀y[By])</li>
<ul>
<li>The past being beginningless and infinite entails that for every <em>y</em> there exists a year before <em>y</em>.</li>
</ul>
<li>□(I → (∃y[Cy] ∨ ∃y[¬Cy]))</li>
<ul>
<li>The past being beginningless and infinite entails that either there exists a year in which the chant is done or there exists a year in which it is not the case that the chant was done.</li>
</ul>
<li>□(S<span class="sub">2</span> → (∀y[Fy] ∧ I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) ∧ ∀y[Hy]))</li>
<ul>
<li>Roughly, scenario S<span class="sub">2</span> is defined such that: the Annual Coin-Flipping Tradition in which the coin comes up heads each year. (Note that scenario S<span class="sub">2</span> is in fact defined this way.)</li>
</ul>
<li>□(∀y[¬Py → Cy] → ∀y[By → (¬P<span class="sub">B</span>y → C<span class="sub">B</span>y)])</li>
<ul>
<li>Necessarily: if (for every year <em>y</em>, if the chant is not done in a year prior to <em>y</em> then the chant is done in <em>y</em>) then (if there exists year <em>y’</em> before <em>y</em>, if the chant is not done in a year prior to <em>y’</em> then the chant is done in <em>y’</em>)</li>
</ul>
<li>□(∀y[P<span class="sub">B</span>y → Py])</li>
<ul>
<li>Necessarily: for any year <em>y</em> if there exists a year <em>y’</em> right before <em>y</em> and the chant was done prior to year <em>y’</em> then the chant was done prior to year <em>y</em>.</li>
</ul>
<li>□(∀y[C<span class="sub">B</span>y → Py])</li>
<ul>
<li>Necessarily: for any year <em>y</em> if there exists a year <em>y’</em> right before <em>y</em> and the chant was done in <em>y’</em>, then the chant was done prior to year <em>y</em>.</li>
</ul>
<li>□(∃y[Py] → ∃y[Cy])</li>
<ul>
<li>Necessarily: if there exists a year <em>y</em> in which the chant was done in a year prior to <em>y</em>, then there exists a year in which the chant was done.</li>
</ul>
</ol>
<hr />
<table cellpadding="0" cellspacing="0" border="0" style="float: left;">
<tr><td> □</td></tr>
</table>
<table cellpadding="0" cellspacing="0" border="0">
<tr><td>
<div class="middle">
<ol class="middle" start="86">
<li>I → ∀y[By] <span class="logic">79, T-reiteration</span></li>
<li>I → (∃y[Cy] ∨ ∃y[¬Cy]) <span class="logic">80, T-reiteration</span></li>
<li>S<span class="sub">2</span> ↔ (∀y[Fy] ∧ I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) ∧ ∀y[Hy] <span class="logic">81, T-reiteration</span></li>
<li>∀y[¬Py → Cy] → ∀y[By → (¬P<span class="sub">B</span>y → C<span class="sub">B</span>y)] <span class="logic">82, T-reiteration</span></li>
<li>∀y[P<span class="sub">B</span>y → Py] <span class="logic">83, T-reiteration</span></li>
<li>∀y[C<span class="sub">B</span>y → Py] <span class="logic">84, T-reiteration</span></li>
<li>∃y[Py] → ∃y[Cy] <span class="logic">85, T-reiteration</span></li>
<li>S<span class="sub">2</span> <span class="logic">indirect proof assumption</span></li>
<div class="middle">
<ol class="middle" start="94">
<li>(∀y[Fy] ∧ I ∧ (∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) ∧ ∀y[Hy] <span class="logic">88, 93, <em>modus ponens</em></span></li>
<li>∀y[Fy] <span class="logic">94, conjunction elimination</span></li>
<li>I <span class="logic">94, conjunction elimination</span></li>
<li>∀y[((Hy ∧ ¬Py) → Cy) ∧ (¬(Hy ∧ ¬Py) → ¬Cy)]) <span class="logic">94, conjunction elimination</span></li>
<li>∀y[Hy] <span class="logic">94, conjunction elimination</span></li>
<li>((Ha ∧ ¬Pa) → Ca) ∧ (¬(Ha ∧ ¬Pa) → ¬Ca) <span class="logic">97, universal instantiation</span></li>
<li>(Ha ∧ ¬Pa) → Ca <span class="logic">99, conjunction elimination</span></li>
<li>¬(Ha ∧ ¬Pa) → ¬Ca <span class="logic">99, conjunction elimination</span></li>
<li>∀y[(Hy ∧ ¬Py) → Cy] <span class="logic">100, universal generalization</span></li>
<li>∀y[¬(Hy ∧ ¬Py) → ¬Cy] <span class="logic">101, universal generalization</span></li>
<li>∀y[By] <span class="logic">86, 96, <em>modus ponens</em></span></li>
<li>¬Pb <span class="logic">conditional proof assumption</span></li>
</ol>
<ol class="middle">
<div class="middle">
<ol class="middle" start="106">
<li>Hb <span class="logic">98, universal instantiation</span></li>
<li>Hb ∧ ¬Pb <span class="logic">105, 106 conjunction introduction</span></li>
<li>(Hb ∧ ¬Pb) → Cb <span class="logic">102, universal instantiation</span></li>
<li>Cb <span class="logic">107, 108, <em>modus ponens</em></span></li>
</ol>
</div>
</ol>
<ol class="middle" start="110">
<li>¬Pb → Cb <span class="logic">105-109, conditional proof</span></li>
<li>∀y[¬Py → Cy] <span class="logic">110, universal generalization</span></li>
<li>Pc <span class="logic">conditional proof assumption</span></li>
</ol>
<ol class="middle">
<div class="middle">
<ol class="middle" start="113">
<li>¬¬Pc <span class="logic">112, double negation</span></li>
<li>¬Hc ∨ ¬¬Pc <span class="logic">113, disjunction addition</span></li>
<li>¬(Hc ∧ ¬Pc) <span class="logic">114, De Morgan’s law</span></li>
<li>¬(Hc ∧ ¬Pc) → ¬Cc <span class="logic">103, universal instantiation</span></li>
<li>¬Cc <span class="logic">115, 116, <em>modus ponens</em></span></li>
</ol>
</div>
</ol>
<ol class="middle" start="118">
<li>Pc → ¬Cc <span class="logic">112-117, conditional proof</span></li>
<li>∀y[Py → ¬Cy] <span class="logic">111, universal generalization</span></li>
<li>∀y[By → (¬P<span class="sub">B</span>y → C<span class="sub">B</span>y)] <span class="logic">89, 111, <em>modus ponens</em></span></li>
<li>Bd <span class="logic">104, universal instantiation</span></li>
<li>Bd → (¬P<span class="sub">B</span>d → C<span class="sub">B</span>d) <span class="logic">120, universal instantiation</span></li>
<li>¬P<span class="sub">B</span>d → C<span class="sub">B</span>d <span class="logic">121, 122, <em>modus ponens</em></span></li>
<li>C<span class="sub">B</span>d → Pd <span class="logic">91, universal instantiation</span></li>
<li>P<span class="sub">B</span>d → Pd <span class="logic">90, universal instantiation</span></li>
<li>¬Pd <span class="logic">indirect proof assumption</span></li>
</ol>
<ol class="middle">
<div class="middle">
<ol class="middle" start="127">
<li>¬P<span class="sub">B</span>d <span class="logic">125, 125, <em>modus tollens</em></span></li>
<li>¬C<span class="sub">B</span>d <span class="logic">124, 126, <em>modus tollens</em></span></li>
<li>¬¬P<span class="sub">B</span>d <span class="logic">123, 128, <em>modus tollens</em></span></li>
<li>¬P<span class="sub">B</span>d ∧ ¬¬P<span class="sub">B</span>d <span class="logic">127, 129, conjunction introduction</span></li>
</ol>
</div>
</ol>
<ol class="middle" start="131">
<li>Pd <span class="logic">126-130, indirect proof</span></li>
<li>Pd → ¬Cd <span class="logic">119, universal instantiation</span></li>
<li>¬Cd <span class="logic">131, 132, <em>modus ponens</em></span></li>
<li>∀y¬[Cy] <span class="logic">133, universal generalization</span></li>
<li>¬∃y[Cy] <span class="logic">134, quantifier negation</span></li>
<li>∃y[Cy] ∨ ∃y[¬Cy] <span class="logic">87, 96, <em>modus ponens</em></span></li>
<li>∃y[¬Cy] <span class="logic">135, 136, disjunctive syllogism</span></li>
</ol>
<ol class="middle">
<div class="middle">
<ol class="middle" start="138">
<li>¬Ce <span class="logic">137, existential instantiation</span></li>
<li>¬Pe → Ce <span class="logic">111, universal instantiation</span></li>
<li>¬¬Pe <span class="logic">138, 139, <em>modus ponens</em></span></li>
<li>Pe <span class="logic">140, double negation</span></li>
<li>∃y[Py] <span class="logic">141, existential introduction</span></li>
</ol>
</div>
</ol>
<ol class="middle" start="143">
<li>∃y[Py] <span class="logic">137-142, existential instantiation</span></li>
<li>¬∃y[Py] <span class="logic">92, 135, <em>modus tollens</em></span></li>
<li>∃y[Py] ∧ ¬∃y[Py] <span class="logic">143, 144, conjunction introduction</span></li>
</ol>
</div>
</ol>
<ol class="middle" start="146">
<li>¬S<span class="sub">2</span> <span class="logic">93-145, indirect proof</span></li>
</ol>
</div>
</td></tr>
</table>
<ol class="end" start="147">
<li>□¬S<span class="sub">2</span> <span class="logic">86-146, necessity intro</span></li>
<li>¬◊S<span class="sub">2</span> <span class="logic">147, equivalence</span></li>
</ol>
And there you have it; proof for ¬◊S<span class="sub">2</span>.
Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-33579592788240967312020-08-09T11:55:00.003-05:002021-06-03T08:05:55.320-05:00Mathematical Argument for God Debunked?<style type="text/css"> <!--
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<!-- Home > Philosophy > Atheism/Theism -->
<a href="https://maverickchristian.blogspot.com">Home</a> > <a href=" https://maverickchristian.blogspot.com/p/site-map.html#_philosophy">Philosophy</a> > <a href="https://maverickchristian.blogspot.com/p/site-map.html#_atheism_theism">Atheism/Theism</a>
<br />
<br />
<h2 class="subHeader">Introduction</h2>
<br />
<br />
Stephen Woodford has a YouTube channel called Rationality Rules and he posted a video titled <a href="https://www.youtube.com/watch?v=qgqwHOwbnts">Craig's Mathematical Argument for the Existence of God DEBUNKED</a> in which Woodford is himself responding to a Reasonable Faith video explaining that argument. In this article I’ll explain the argument (something like this is one of the reasons I retained my belief in God in moments of doubt) and respond to some of what Woodford said.
<br />
<br />
<h2 class="subHeader">The mathematical argument for God’s existence</h2>
<br />
<br />
To get a better idea behind the mathematical argument for God’s existence I’m going to kind of use a computer analogy. Consider these two conceivable universes:
<ol>
<li>A universe akin to a hard drive that has its ones and zeros randomly set; a chaotic jumbled mess, disorderly unpredictable behavior at every moment.</li>
<li>A universe akin to a complex computer program with sophisticated mathematical algorithms directing behavior; a universe with consistent mathematical patterns ubiquitously imprinted into nature via physical laws such that it makes physics almost ludicrously successful in precisely predicting behavior (examples: relativity and quantum mechanics). The physical laws are akin to a program’s mathematical algorithms in that behavior is directed in an orderly and predictable fashion.</li>
</ol>
To get a clearer idea of what I mean by universe (2), consider this equation for the relation between mass, velocity, and kinetic energy.
<br />
<br />
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Where <em>m</em><span class="sub">0</span> is the rest mass (roughly, the mass it has at zero velocity), <em>c</em> is the speed of light, and <em>v</em> is the velocity of the mass. Or for our purposes (well below the speed of light) it gets pretty close to this:
<br />
<br />
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<br />
So for example the approximate kinetic energy values for the following mass and velocity would be the following:
<br />
<br />
<table class="bonita">
<tr><th>K.E. (joules)</th><th>mass (kg)</th><th>velocity (m/s)</th></tr>
<tr class="odd"><td class="bold">9</td><td>2</td><td>3</td></tr>
<tr class="even"><td class="bold">18</td><td>4</td><td>3</td></tr>
<tr class="odd"><td class="bold">27</td><td>6</td><td>3</td></tr>
<tr class="even"><td class="bold">36</td><td>8</td><td>3</td></tr>
</table>
<br />
<br />
This provides a sort of mathematical elegance and robust consistency for the universe’s behavior. But we can conceive the kinetic energy relation being more like a randomized hard drive, where the kinetic energy values for various pairs of mass and velocity are assigned haphazardly with no meaningful pattern rather than fitting some neatly ordered equation:
<br />
<br />
<table class="bonita">
<tr><th>K.E. (joules)</th><th>mass (kg)</th><th>velocity (m/s)</th></tr>
<tr class="odd"><td class="bold">79</td><td>2</td><td>3</td></tr>
<tr class="even"><td class="bold">20</td><td>4</td><td>3</td></tr>
<tr class="odd"><td class="bold">13</td><td>6</td><td>3</td></tr>
<tr class="even"><td class="bold">24</td><td>8</td><td>3</td></tr>
</table>
<br />
<br />
With the universe also yielding different kinetic energy values for the same mass/velocity pairs for different locations. We can conceive the relation being even more like a randomized hard drive in that the relation changes unpredictably from moment to moment. This is all still <em>describable</em> with math just like a randomized hard drive is with its randomly set ones and zeros, but this doesn’t have the same <em>type</em> of robustly consistent mathematical elegance as in the case where this mathematical algorithm is ubiquitously imprinted into the universe:
<br />
<br />
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As you may have guessed, our universe operates like universe (2). Physics has been extraordinarily effective in predicting accurate and precise behavior thanks to the mathematical algorithms ubiquitously imprinted into nature. (The Reasonable Faith video describes this quite well at around <a href=" https://www.youtube.com/watch?v=QJBOiZXkKu8&t=0m39s">0:39</a> to 2:00, which among other things notes how scientists used math to pinpoint the location of a previously undiscovered planet, and Peter Higgs using math to predict an elementary particle which scientists found after exerting billions of dollars and millions of work-hours.) Conceivably, this scientific use of math didn’t have to be nearly as stunningly effective as we observe. So why is it?
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For theists the answer is simple: the universe has this remarkable mathematical order because it was designed. For the atheist, the only viable option for this type of mathematical applicability is that it’s just a happy coincidence. But a happy coincidence of this magnitude strikes some people as...too coincidental to be very plausible.
<br /><br />
The aforementioned Reasonable Faith video presents this mathematical argument for the existence of God (around <a href=" https://www.youtube.com/watch?v=QJBOiZXkKu8&t=4m21s">4:21</a> to 4:38</a>):
<ol>
<li>If God does not exist, the applicability of mathematics is just a happy coincidence.</li>
<li>But the applicability of mathematics is not just a happy coincidence.</li>
<li>Therefore, God exists.</li>
</ol>
<h2 class="subHeader">Woodford’s Response</h2>
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<br />
As I suggested earlier, Stephen Woodford of Rationality Rules responded to the Reasonable Faith video. For sake of time I’m not going to discuss everything Woodford says, instead focusing mostly on the argument from the universe’s mathematical order, but I would like to respond to couple somewhat off topic things.
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<br />
Regarding providing an alternative explanation for the effectiveness of mathematics Woodford’s video (around <a href="https://www.youtube.com/watch?v=QJBOiZXkKu8&t=8m23s">8:23</a> to 11:04</a>) shows clips of scholars some of which include the following:
<blockquote>
Sabine Hossenfelder: I don’t think it’s all that unreasonable that mathematics is effective in the natural sciences, because what is mathematics about? It is a way to describe patterns, to describe regularities, and that’s exactly what we do in the natural sciences.
<br /><br />
Steven Weinberg: I don’t think mathematics can ever be regarded as an explanation in itself of anything, and this has not always been—well, understand, perhaps it’s even still controversial—physical theories aren’t the way they are because of principles of mathematics. Principles of mathematics are the language in which we state our physical principles, and they are the way—the intellectual tools we use for calculating the consequences of those principles, but nothing is the way it is because of some mathematical principles.
<br /><br />
George Lakoff: It’s [mathematics] not in the world The world is as it is. Let’s take a very simple case. Take a spiral nebula. The logarithmic spiral is not in the nebula, it’s in your understanding of the nebula. The marvelous thing about mathematics is that we can create mathematics with our brains that fiat phenomena in the world remarkably. It is not a miracle that that’s the case because we have the capacity to see and understand the world, to categorize it in terms of what our brains do, and then we can create a mathematics out of that in a systematic way using what our brains allow us.
</blockquote>
None of that really answers the question at hand. For example, yes we describe regularities in the natural sciences, but conceivably these precise mathematical regularities didn’t have to exist, and their existence is exactly what is to be explained in the first place. This is no more an explanation for the consistent mathematical patterns in the universe than saying that the reason opium causes sleepiness is because of its dormitive powers, where “dormitive powers” just means it has the power to cause sleepiness. In philosophy this type of pseudo-explanation is called a “dormitive principle” where one reiterates the thing to be explained in different words, which potentially gives the illusion of an explanation where none existed. The rest of the clips, while they may say true or plausible stuff, also don’t answer why the universe has the remarkable mathematical structure it has, because again, the universe conceivably didn’t have to be this way (think back to the kinetic energy example, where the values for kinetic energy for given a mass/velocity pair could conceivably have varied from location to location or from one moment to the next).
<br /><br />
Woodford said he has an explanation, but what is it? At around <a href="https://www.youtube.com/watch?v=QJBOiZXkKu8&t=11m50s">11:50</a> to 12:02 in response to why the universe has such a stunningly elegant mathematical structure:
<blockquote>
At the risk of sounding like a broken record, it’s because the laws of the universe are robustly consistent.
</blockquote>
We kind of have a dormitive principle here. The Reasonable Faith video referenced Eugene Wigner’s paper <em>The Unreasonable Effectiveness of Mathematics in the Natural Sciences</em> which had this:
<blockquote>
It is, as Schrodinger has remarked, a miracle that in spite of the baffling complexity of the world, certain regularities in the events could be discovered. One such regularity, discovered by Galileo, is that two rocks, dropped at the same time from the same height, reach the ground at the same time. The laws of nature are concerned with such regularities.
</blockquote>
Yes, the laws of the universe are robustly consistent, so much so that we actually have mathematical algorithms ubiquitously imprinted into the universe in which physics is almost ludicrously successful in making accurate and precise predictions, <em>but that is exactly what is to be explained</em>. Reiterating the thing to be explained in different words is a non-answer; it’s the equivalent of, “Because I said so.”
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<br />
<h2 class="subHeader">Conclusion</h2>
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<br />
Ultimately the only viable alternative to design for why the universe behaves more a hard drive imprinted with algorithms, rather than a randomized hard drive with ones and zeros assigned haphazardly, is that it’s just a happy coincidence. A proposed explanation that is actually just a dormitive principle is a non-answer, stalls progress, and rots the mind. To be fair Woodford does say this in his video he might be missing something (<a href="https://www.youtube.com/watch?v=QJBOiZXkKu8&t=11m50s">15:54</a> to 15:57). He is, but to be fair to Woodford again, I don’t think the argument from mathematics was argued as strongly or as clearly as it could have been in a number of cases, including the video Woodford responded to. I think the argument from the universe’s mathematical order becomes clearer when you contrast our universe with the way physical reality conceivably could have been like, that is, it could conceivably have been more like a randomized hard drive and a lot less like software running elegant mathematical algorithms directing everything in a more orderly fashion.
Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-23814004590794302142020-07-01T18:09:00.001-05:002020-12-24T16:41:47.226-06:00Why the Past Cannot be Infinite<style type="text/css"> <!--
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<!-- Home > Philosophy > Atheism/Theism -->
<a href="https://maverickchristian.blogspot.com">Home</a> > <a href=" https://maverickchristian.blogspot.com/p/site-map.html#_philosophy">Philosophy</a> > <a href="https://maverickchristian.blogspot.com/p/site-map.html#_atheism_theism">Atheism/Theism</a>
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<h3 class="subHeader">Relevance to Theism</h3>
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A finite past bears relevance to the <em>kalam</em> cosmological argument (KCA) which goes like this:
<ol>
<li>Anything that begins to exist has a cause.</li>
<li>The universe begins to exist.</li>
<li>Therefore, the universe has a cause.</li>
</ol>
Further arguments are given to show that the cause of the universe is (among other things) a transcendent personal cause. If we have adequate grounds for thinking the universe has a transcendent personal cause, this gives at least some evidence for the truth of theism. I’ve justified premise (1) in my <a href="https://maverickchristian.blogspot.com/2013/02/ex-nihilo-nihil-fit.html">anything that begins to exist has a cause</a> article. In this article I’ll argue for premise (2) by arguing for a finite past.
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Would a finite past mean that not even God is sempiternal (i.e. having existed for a beginningless, infinite duration)? Yes it would. One idea is that God is timeless <em>sans</em> creation. Note that if spacetime itself began to exist and our spacetime universe had a cause, that cause would have to transcend space and time. Whether you want to call this spacetime-transcending cause supernatural or not, such a cause would have to be something beyond the physical laws as we know them today. The fact that there is some sort of (at least) <em>de facto</em> supernatural cause beyond space and time creating the universe would seem to make atheism less plausible.
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<h3 class="subHeader">An Infinite Traversal</h3>
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Some philosophy lingo: a <em>potential infinite</em> is a collection that grows towards infinity without limit but never actually gets there. For example, if you started counting “one, two, three…” at a rate of one number per second and continued indefinitely, the number you’re at would grow larger and larger without limit but you’d never actually arrive at “infinity.” An <em>actual infinite</em> is a collection that really is infinite, such as the set of all positive whole numbers.
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Traversing an actual infinite region at a finite rate seems impossible. Suppose for example there were a road that starts at a particular location and is infinitely long. Someone named Jill Walker starts at the beginning of the road and walks at a rate of one meter per second. Will she ever traverse an infinite region? She will not; the distance (and time!) she traverses is a potential infinite only. What if she were given infinite time? The problem is that traversing an actual infinite amount of time <em>can never happen</em>. Even if she is given <em>unlimited</em> time she will never traverse an actual infinite amount of time or an actual infinite distance; both will be a potential infinite only.
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A similar problem occurs with a beginningless past: for a beginningless, infinite past to exist an actual infinite amount of time would need to be traversed, which is impossible, and thus we never would have arrived at the present moment. Another way to look at it: imagine if we viewed a universe with an infinite past and rewound it, traversing it at the same rate as time normally goes but backwards. Could we traverse the entirety of the infinite past? The infinite past would be impossible to completely traverse even given unlimited time. Similarly, going the other direction would be impossible because it requires an infinite traversal and we never would have arrived at the present moment (or at <em>any</em> moment, since any moment in the infinite past has an infinite amount of time before it).
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<br />
<h3 class="subHeader">The Eternal Society Paradox</h3>
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<br />
There are also various paradoxes one can make with an infinite past, an example of which is the <em>Eternal Society Paradox</em>. Roughly (in the <a href="http://aporia.byu.edu/pdfs/tisthammer-an_eternal_society_paradox.pdf">paper the Eternal Society Paradox was published</a>), an Eternal Society is a society that has existed for a beginningless, infinite duration of time and has the abilities of ordinary human beings in each year of its existence; e.g. in each year people in the society can flip coins, write books, sing songs, and pass on information possessed in the current year to the next year. Because of the society’s extremely modest abilities, it seems like an Eternal Society would be possible if an infinite past were possible (note that by “possible” in this article I’ll be referring to <em>metaphysical</em> possibility, as opposed to e.g. physical possibility).
<br /><br />
Now imagine the Eternal Society has the following Annual Coin Flipping Tradition: each year they flip a coin and if it comes up heads, they all get together to do a particular chant but only if they have never done the chant before. If the coin does not come up heads they do not do the chant for that year.
<br /><br />
The coin flips are probabilistically independent events, so any particular infinite permutation of coin flips is equally unlikely but also equally possible. Consider scenario S<span class="sub">1</span> in which the coin came up heads for the first time last year. The Eternal Society gets together to do the chant for the first time. This seems like it would be possible if an infinite past were possible (an eternal society with the ability of ordinary humans, by which I mean the society has the ability of ordinary humans in each year of its existence, could surely do something like this), but this scenario is provably not possible.
<br /><br />
Again, the coin flips are probabilistically independent events, so if scenario S<span class="sub">1</span> were possible, then another scenario, that we can call scenario S<span class="sub">2</span>, would be possible: the coin came up heads each year of the infinite past. If the coin came up heads each year, did the Eternal Society ever do the chant? They would have had to have done the chant some year, because they would have done the chant last year if they hadn’t done it yet (since the coin came up heads last year). And yet any year you point to, there is a prior year in which they would have done the chant if they had not done the chant before. So they had to have done the chant (since the coin came up heads last year), yet they could not have done the chant (there is no year they could have done it), and so this scenario creates a logical contradiction.
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Although scenario S<span class="sub">1</span> is not directly self-contradictory, scenario S<span class="sub">1</span> is impossible because it implies the <em>possibility</em> of a logical contradiction. The Eternal Society argument against an infinite past goes like this:
<ol start="4">
<li>If an infinite past were possible, an Eternal Society would be possible.</li>
<li>If an Eternal Society were possible, then scenario S<span class="sub">1</span> would be possible.</li>
<li>If S<span class="sub">1</span> would be possible, then S<span class="sub">2</span> would be possible.</li>
<li>S<span class="sub">2</span> is not possible.</li>
<li>Therefore, an infinite past is not possible.</li>
</ol>
One could deny premise (4) particularly since that seems to be the most vulnerable premise, but as <a href="http://aporia.byu.edu/pdfs/tisthammer-an_eternal_society_paradox.pdf">the Eternal Society Paradox paper</a> says, “Surely there is something metaphysically suspicious about an infinite past if an eternal society with the abilities of ordinary humans can actualize a logical contradiction.” The idea that an infinite past is possible but an Eternal Society is not possible strikes me as overly <em>ad hoc</em> due to the Eternal Society’s extremely modest abilities (the abilities of ordinary humans in each year of its existence).
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<br />
<h3 class="subHeader">Conclusion</h3>
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<br />
While there is also scientific evidence favoring a finite past, philosophical arguments seem to provide a strong case for <em>temporal finitism</em> (the view that the past is finite). For a beginningless, infinite past to exist an actual infinite amount of time would need to be traversed, which is impossible, and thus we never would have arrived at the present moment. Moreover, the Eternal Society Paradox shows that an eternal society with the abilities of ordinary humans would have been able to create a logical contradiction, which strongly suggests that an infinite past is metaphysically impossible.
Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-80138434085084604432020-06-16T21:58:00.000-05:002020-06-17T16:15:29.628-05:00The Pseudohumility of Christianity?<style type="text/css"> <!--
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<a href="http://maverickchristian.blogspot.com">Home</a> > <a href="http://maverickchristian.blogspot.com/p/site-map.html#_christianity">Christianity</a> > <a href="http://maverickchristian.blogspot.com/p/site-map.html#_christianity_general">General</a> <br />
<br />
Stephen Woodford has a YouTube channel called Rationality Rules and he posted a video titled <a href="https://www.youtube.com/watch?v=q26kn5wnANQ">The Pseudohumility of Christianity</a> attacking the humility of Christianity.
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<h2 class="subHeader">Arguments Against Christian Humility</h2>
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Christianity encourages its adherents to practice humility, e.g. Matthew 23:12 and Philippians 2:3. So what’s the issue? At around <a href="https://www.youtube.com/watch?v=q26kn5wnANQ&t=4m53s" target="_blank">4:53</a> Woodford says, “The issue is that these verses are predicated upon sheer arrogance, and here is where my rant starts.”
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He says that Christians believe there is one perfect God and that we’re created in his image (true so far), “which is a not-so-subtle way of saying we are, or close to, perfect.” What? Why think that? Exactly what it means to be created “in the image of God” is unclear and is debated among theologians (we are like God in some ways, having mind, will, and emotions—perhaps it means this). Woodford provides no evidence or argument for his particular exegesis nor does he cite any theologian who adheres to it; he gives only his word for this uncharitable interpretation. What should be needless to say is that Christianity teaches we are far from perfect, so far in fact that it is while we were enemies of God that Christ died for us (Romans 5:10), which is quite far from perfect indeed.
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At around <a href="https://www.youtube.com/watch?v=q26kn5wnANQ&t=5m15s" target="_blank">5:15</a> to 5:34 Woodford recognizes an alternate interpretation for being made in the image of God: us being created above animals and Woodford says this “stinks of hubris.” But does it? My parents chose that I exist because they wanted a child to love and care for, and presumably they valued me over any animal. Does this belief “stink of hubris”? After all, it’s not as if I did anything to deserve it. In a way it could be said that God “chose” us insofar as he created humans and we have greater value than animals, and Woodford seems to think this justifies his claim that it “stinks of hubris,” but this doesn’t seem to follow.
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At around <a href="https://www.youtube.com/watch?v=q26kn5wnANQ&t=5m41s" target="_blank">5:41</a> Woodford says that “most Christians believe that the universe was created for us in mind.” So? It doesn’t follow that most Christians believe that the universe was created <em>only</em> for us in mind; after all there’s an awful lot more to the universe than just us! (To say nothing of the untold legions of angels that also exist in reality!) At around <a href="https://www.youtube.com/watch?v=q26kn5wnANQ&t=5m45s" target="_blank">5:45</a> he also adds that most Christians believe that “we are a vital part in a grand divine plan.” Well, we are <em>a</em> part and we are “vital” in the sense that God loves us very much, but so what? It’s not as if we’re the <em>only</em> part of God’s plan; we could well be one of innumerable vital parts. At around <a href="https://www.youtube.com/watch?v=q26kn5wnANQ&t=5m48s" target="_blank">5:48</a> to 5:54 he notes the Christian belief that we have personal consciousnesses that outlast our bodies. Again, so? It’s not as if we’re the only beings who will outlast our bodies, e.g. angels. At around <a href="https://www.youtube.com/watch?v=q26kn5wnANQ&t=5m55s" target="_blank">5:55</a> to 6:08 he says many Christians believe they have a personal relationship with God (so?) and that God answers prayers (so?).
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I could go on, but you get the gist. It’s true that in many ways God is nice to us. Woodford’s arguments fail largely because of a failure to ask <em>why</em> God answers prayers, gives humans an afterlife, makes us part of his divine plan, etc. Does God do so because we’re so awesome when we’re not? If so, then this is arrogance. But if instead it’s merely due to God being generous, then this doesn’t imply arrogance. So which is it? Well, consider again Romans 5:10: Christ died for us when we were still God’s enemies. The reason God is so nice to us is not because we’re so awesome and deserving. Indeed, part of the Christian faith is that we’re not deserving! It’s because God is so generous in his sacrificial love. We don’t deserve eternal life; rather it’s a gift from God, so teaches Christianity. Thus, a litany of nice things that Christians believe God does for us (which Woodford apparently believes are “extraordinarily arrogant tenants,” around <a href="https://www.youtube.com/watch?v=q26kn5wnANQ&t=6m45s" target="_blank">6:45</a> to 6:51) fails to constitute a good argument for arrogance; the conclusion just doesn’t follow.
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<h2 class="subHeader">Conclusion</h2>
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I’ve seen multiple nontheists charge Christianity with arrogance, a claim often that they often supply with little to no evidence. After all, the Bible nowhere teaches that the universe was created <em>just</em> for us. Christianity teaches humility and explains why we have good reason to be humble; we are sinners in need of a savior, and it is while we were enemies of God that God sent his Son out of sacrificial love. It wasn’t because we deserved it. At around <a href="https://www.youtube.com/watch?v=q26kn5wnANQ&t=7m01s" target="_blank">7:01</a> to 7:06 Woodford says that “There is nothing humble about asserting the universe revolves around you.” He’s right, but he’s also wrong in thinking Christianity teaches anything of the sort; it doesn’t, and Woodford fails to provide sufficient evidence justifying this assertion (after all, for all we know there could be intelligent life in many other parts of reality whom God loves as well). Christianity suggests that, metaphorically speaking, the universe revolves around God, not us. We’re just fortunate to be in orbit.
Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-39292292933905883712020-06-14T12:34:00.001-05:002021-02-21T19:09:12.798-06:00Argument from Evil as an Internal Critique<style type="text/css"> <!--
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<h2 class="subHeader">Introduction</h2>
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Even if certain atheists reject moral objectivism, can such atheists still use the argument from evil as an internal critique of theism?
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<h2 class="subHeader">A Problem for Atheists Who Reject Moral Objectivism</h2>
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As I wrote about in my article <a href="http://maverickchristian.blogspot.com/2013/02/rosenbergs-argument-from-evil-folly.html" target="_blank">Rosenberg’s Argument from Evil Folly</a>, there’s a big problem for the atheist in using the argument from evil if the atheist in question believes objective morality does not exist. People can have different ideas of what sorts of things are morally good. Suppose for example a theist has a standard of goodness such that it’s good that God permits the evil we see for certain reasons that are morally sufficient on this standard of goodness. Some atheists might say that if God adopted their standard of goodness, God would not permit the evil we see. But without an objective moral standard, there’s no objective fact of the matter about <em>which</em> standard of goodness God would adopt if he existed, and thus there’d be no objective fact of the matter whether God would permit evil if he existed, in which case the argument from evil would collapse under its own weight.
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<h2 class="subHeader">A Solution?</h2>
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Another idea is to use the argument from evil as an internal critique. For example, couldn’t the atheist at least criticize the theist for having an inconsistency in the theist’s conception of goodness with respect to a perfectly good God allowing evil? That depends on the theist, but it’s relatively trivial to construct a view of goodness that is consistent with a perfectly good God allowing evil in the world. Suppose for example a hypothetical theist says that it is morally good for us humans to try to fight against evil (refraining from doing morally wrong actions, advancing medical technology, learning to share our food with the hungry, etc.) with the limited abilities that we have, with the obstacles we face etc. and that this is better than God making the evils any less bad, such that if God adopted this standard of goodness God would allow the evil we see (on this view, it’s good that God permits evil in the way that he does, but it’s not necessarily good that we humans permit evil; in a sense God and humans would have different responsibilities). Maybe this view of the hypothetical theist is wrong, but it’s not self-contradictory, and so there would be no inconsistency in this hypothetical theist’s conception of goodness with respect to a perfectly good God allowing evil.
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There is another way an atheist who isn’t a moral objectivist could supply an internal critique. God is not only perfectly morally good, he is also all-loving. In the June 2020 debate on <a href="https://www.youtube.com/watch?v=hNF9bTESZwE" target="_blank">Capturing Christianity between Cosmic Skeptic and Inspiring Philosophy</a>, Cosmic Skeptic said this at around <a href="https://www.youtube.com/watch?v=hNF9bTESZwE&1h46m23s" target="_blank">1:46:23</a>:
<blockquote>
Let’s not talk about good and evil because if they’re not objective maybe it’s unhelpful. But if you think that God is all-loving as a separate point then the question just reformulates itself. It’s not just a question about what’s loving and what’s not. It’s like we know facts about the universe. We know that children get cancer and we have to be committed to the view that that is loving; that it is loving to allow a child to get cancer. It’s the same problem as saying you have to accept that it is good or at least not evil for a child to get cancer. It would just be framed differently. Whatever the person believes, as you say Cameron that’s probably the best way to answer it, with any argument I ever make on any debate that I do, on any video I make, it’s always an argument of consistency—pretty much, most of the time. And that’s what I’m looking for here; is just consistency.<a href="#_endnote_2020_06_14" name="_cite_2020_06_14">[1]</a>
</blockquote>
Does it follow that if a loving God permits cancer, that it is <em>loving</em> to allow a child to get cancer? No. For starters, let’s ask this question: why assume that a loving God would not permit suffering? Presumably it’s because that if you love someone you value their well-being. It’s reasonable that loving someone implies valuing that person’s well-being, but the problem is that a <em>morally good</em> God might value <em>other</em> things as well, things that “interfere” with valuing one’s well-being.
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To give an example of how valuing someone’s well-being can conflict with another value, suppose a loving and just judge is tasked with sentencing a man who has committed a heinous crime. The judge loves everyone including the man she is sentencing, so she values the man’s well-being, but on the other hand she also values punishing those who commit heinous crimes. So, the judge gives the man a long prison sentence to pay for his crime, even though she loves the man (by virtue of loving everyone) and values his well-being, and even though a lengthy prison sentence would decrease the man’s well-being.
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Obviously the child Cosmic Skeptic has in mind hasn’t done anything wrong to deserve cancer, so the loving and just judge doesn’t work as analogy, but it <em>does</em> work to illustrate this point: values can conflict, including valuing someone’s well-being. If God is not <em>just</em> all-loving but also morally good, God could conceivably have other values that supersede the immediate well-being of humans. Imagine a hypothetical theist who believes God is all-loving but also believes that God is morally good, and that God adopts a standard of goodness such that it is good that God permits the observed suffering we see even though he loves us all, and that (at least in part) because God is all-loving our suffering in the mortal realm is finite and a pleasant everlasting life is available to every human who freely chooses God. This hypothetical theist grants it is not <em>loving</em> to permit suffering, but believes it is <em>good</em> that God permits the finite suffering we observe; God has values that supersede the immediate well-being of certain individuals. Again, maybe this view of the hypothetical theist is wrong, but it’s not self-contradictory, and so there would be no inconsistency in this hypothetical theist’s conception of goodness with respect to a perfectly good and all-loving God allowing evil.
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<h2 class="subHeader">Conclusion</h2>
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The problem of evil fails as an internal critique not just against a morally good God but an all-loving and morally good God, at least <em>tout court</em>. It’s reasonable that an all-loving God would value our well-being. However, a theist could believe that while God values our well-being because he is perfectly loving, this is only <em>one</em> of the things that God values, and that other values could outweigh our immediate well-being such that an all-loving God who is also perfectly morally good would permit the evil we see.
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I said that the problem of evil fails as an internal critique against an all-loving and morally good God <em>tout court</em>, but the problem of evil <em>could</em> succeed as an internal critique if the theist really did adopt a standard of moral goodness in which it is <em>not</em> good that God permits the evil we see. So in a way whether the argument from evil works as an internal critique depends on the theist. My objection is that the internal critique is not <em>inherently</em> successful; the theist could easily adopt a standard of moral goodness that evades the problem. Alternatively, the theist could say that while she knows some moral values (“moral values” in this case being “stuff that’s morally good”), she doesn’t necessarily know all the values, much less all values in conjunction with the appropriate weights for each value, such that for all she knows God has morally sufficient reasons for allowing the evil we see even if those reasons are beyond her ken (there are even more complications for whether to permit evil beyond knowing all the values and their appropriate weights, but for purposes of this blog article I’m mostly focusing on this).
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<a name="_endnote_2020_06_14" href="#_cite_2020_06_14">[1]</a> I’ve lightly edited the quote to remove some filler words such as “um” and “right” for better flow.
Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-7457407071879883232020-06-05T12:37:00.004-05:002020-06-09T07:12:22.652-05:00Great Cost of the Kalam?<style type="text/css"> <!--
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<a href="https://maverickchristian.blogspot.com">Home</a> > <a href=" https://maverickchristian.blogspot.com/p/site-map.html#_philosophy">Philosophy</a> > <a href="https://maverickchristian.blogspot.com/p/site-map.html#_atheism_theism">Atheism/Theism</a>
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<h2 class="subHeader">Introduction</h2>
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Stephen Woodford has a YouTube channel called Rationality Rules and he posted a video titled <a href="https://www.youtube.com/watch?v=Qm_6eB5bcos">Great Cost of the Kalam</a> claiming that the <em>kalam</em> cosmological argument is incompatible with libertarian free will (I’ll explain what both are shortly). A popular version of the <em>kalam</em> cosmological argument, popularized by American philosopher William Lane Craig, goes like this:
<ol>
<li>Anything that begins to exist has a cause.</li>
<li>The universe began to exist.</li>
<li>Therefore, the universe has a cause.</li>
</ol>
There are other ways to word the first premise (e.g. “Whatever begins to exist has a cause of its beginning” and “Everything that begins to exist has a cause”). <em>Libertarian freedom</em> is the ability to choose without being determined by prior causes; e.g. when choosing between chocolate and vanilla ice cream. <em>Determinism</em> is roughly the view that all events are determined by prior conditions, such that given the initial conditions only one outcome is possible. For example, determinism would say that when Sally selected chocolate over vanilla ice cream, given the initial conditions there was only one selection she could make, even if the initial conditions were that both were available at the grocery store and she had sufficient currency for both.
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<h2 class="subHeader">What is a cause?</h2>
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At around <a href="https://www.youtube.com/watch?v=Qm_6eB5bcos&t=2m30s">2:30</a> to 2:38 Woodford says this.
<blockquote>
A cause is a person or thing that gives rise to a phenomenon, action, or condition. It is a synonym of determinism.
</blockquote>
No, it’s not. Something bringing about the existence of something else is not synonymous with <em>deterministically</em> causing its existence. To give a hypothetical example, suppose a ray gun has a 30% probability of creating chocolate ice cream, with the outcome being truly indeterministic (i.e. identical initial conditions can produce different outcomes). Now suppose I turn on the ray gun and chocolate ice cream appears courtesy of the ray gun. Since the ray gun did indeed bring about the existence of the ice cream (albeit indeterministically) the ray gun <em>caused</em> the ice cream to exist. But if it is correct to say that in this scenario the ray gun caused the ice cream to exist, then it is not the case that causality is synonymous with determinism.
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To be fair though, there is one sense in which determinism and causality are related, and that has to do with the cause of an <em>event</em> (as in outcome 1 coming about versus outcome 2) as opposed to a cause of <em>the existence of a thing</em>. The difference is subtle but important. To illustrate, consider the case of two physically identical uranium-238 atoms <em>A</em> and <em>B</em>, where atom <em>A</em> emits an alpha particle and atom <em>B</em> does not. It may indeed be true that identical physical conditions can produce different outcomes, and while this would rule out the uranium atom deterministically bringing about the alpha particle, it doesn’t rule out indeterministic causation (viz. the uranium atom bringing about the alpha particle, after all it’s the uranium atom that emits it!). So let’s consider the theory that the uranium atom indeterministically causes the existence of the alpha particle. This theory would entail that the existence of the alpha particle (the existence of the <em>thing</em>) has a causal explanation, but this theory would also imply that there is no causal explanation for why uranium atom <em>A</em> emitted an alpha particle and physically identical uranium atom <em>B</em> did not, i.e. there wouldn’t be a causal explanation <em>for the different outcomes</em> between the two physically identical atoms (though there would be a “random chance” explanation for the difference), even though the <em>existence</em> of the alpha particle would have a causal explanation (viz. the uranium atom).<a href="#_endnote_2020_06_05_1" name="_cite_2020_06_05_1">[1]</a> The “anything that begins to exist has a cause” claim says that every <em>thing</em> that begins to exist has a cause, but allows for the possibility of uncaused <em>events</em> (e.g. outcome 1 coming about versus outcome 2) in the sense described earlier.
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As <a href="https://www.reasonablefaith.org/media/reasonable-faith-podcast/kalam-questions-and-more/">William Lane Craig</a> (the American philosopher who popularized the <em>kalam</em> cosmological argument in the 20th century) said:
<blockquote>
But in any case the reader needs to recall that the premise of the argument is very carefully formulated. It is: everything <em>that begins to exist</em> has a cause. That is deliberately formulated so as to allow for quantum indeterminacy with regard to events. This is quite consistent with admitting that there are events that occur without a cause. And so events that are, say, movements of a libertarian free will or decay of an atomic isotope or emission of a photon, we can happily admit, at least for the sake of argument, that those are uncaused events, and it wouldn't affect the truth of the premise, which concerns whether or not things can actually begin to exist without any causes.
</blockquote>
To reiterate, <em>kalam</em>’s causal premise prohibits <em>things</em> (alpha particles, mountains, people, root beer, etc.) beginning to exist without a caused, but does not prohibit uncaused <em>events</em> in the sense described earlier.
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<h2 class="subHeader">Libertarian Freedom</h2>
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At around <a href="https://www.youtube.com/watch?v=Qm_6eB5bcos&t=5m11s">5:11</a> to 5:32 Woodford says:
<blockquote>
According to libertarianism, that is according to the vast majority of theists, the will of a free agent is at least partially non-determined. Thus, by freely stating that whatever begins to exist has a cause, you have demonstrated the contrary. You have proven its falsehood. You are contradicting your statement though the very means in which you express it.
</blockquote>
Woodford mistakenly believes that libertarian freedom implies that free acts are uncaused, but this doesn’t follow. While some variants of libertarianism require that our acts be uncaused to be free, this isn’t true for all versions of libertarianism. One libertarian view called <em>agency theory</em> posits <em>agent-causation</em> whereby an agent (person, self) causes events without being determined by prior causes. So, a free act is not uncaused; it is indeterministically caused by an agent. The existence of the agent and its ability to have free will in turn could have been caused by something else.
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<h2 class="subHeader">Conclusion</h2>
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Woodford’s objection to the <em>kalam</em> cosmological argument for the libertarian proponent is that causality is synonymous with determinism, and the libertarian must hold to their free actions being uncaused, which would thus require the libertarian to not believe the <em>kalam</em>’s causal premise. Three main problems are: (1) causality is not synonymous with determinism; (2) indeterministic causation is still an option (e.g. a uranium atom indeterministically bringing about the existence of an alpha particle); (3) not all versions of libertarianism require an act be uncaused to be free (e.g. agency theory). It would seem therefore that this objection fails.
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<a name="_endnote_2020_06_05_1" href="#_cite_2020_06_05_1">[1]</a> At the same time, there is a sense in which there is a cause of the event for why <em>A</em> emitted the particle and <em>B</em> did not: the cause is time and chance acting on inherent properties of matter indeterministically bringing about the two different events (the inherent properties of uranium-238 determine the probability, which is why it has a measurable half-life, as opposed to there being no consistent probability among atoms of the same kind). To some degree it boils down to semantics of what a “cause” is.
Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-90628216434745568192020-04-06T23:08:00.000-05:002020-04-25T16:42:45.498-05:00Is the Kalām Cosmological Argument Slyly Circular?<style type="text/css"> <!--
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<br />
<h2 class="subHeader">Introduction</h2>
<br />
<br />
Cosmic Skeptic wrote an article called <a href="https://cosmicskeptic.com/2020/04/04/the-sly-circularity-of-the-kalam-cosmological-argument/"> The Sly Circularity of the Kalãm Cosmological Argument</a>. Before getting into the objection let’s review what the <em>kalam</em> cosmological argument (KCA) is.
<br />
<br />
<h2 class="subHeader">The <em>kalam</em> cosmological argument (KCA) </h2>
<br />
<br />
A <em>material cause</em> is the stuff something is made out of, and an <em>efficient cause</em> is that which produces an effect. For example, when an artist creates a wooden sculpture, the wood is the material cause and the artist is the efficient cause. The relevant version of the KCA, popularized by William Lane Craig, is this:
<ol>
<li>Everything that begins to exist has a cause.</li>
<li>The universe began to exist</li>
<li>Therefore, the universe has a cause.
</ol>
Let’s unpack the two premises further. For Craig, the first premise “Everything that begins to exist has a cause” includes both material and efficient causation. You can see that in this <a href="https://www.reasonablefaith.org/writings/question-answer/must-everything-that-begins-to-exist-have-a-material-cause/">Reasonable Faith webpage</a>. So to say that the universe began to exist without a cause would mean beginning to exist with no efficient cause and no material cause, i.e. coming into being from nothing.
<br /><br />
For the second premise, it should be noted that William Lane Craig defines “the universe” in way so that it “<a href="https://www.reasonablefaith.org/writings/popular-writings/existence-nature-of-god/the-kalam-cosmological-argument/">comprises all contiguous spacetime reality</a>.” If for example there were some pre-existing physical reality that caused the big bang to occur, that physical reality would itself be part of “the universe” as Craig is defining the term.
<br /><br />
This KCA is logically valid, i.e. the conclusion follows from the premises inescapably by the rules of logic such that it’s impossible to have true premises and a false conclusion. Since a sound argument is just a valid argument with all true premises, the only way this argument can fail to be sound is with a false premise.
<br />
<br />
<h2 class="subHeader">Cosmic Skeptic’s Rebuttal</h2>
<br />
<br />
In his article he said this:
<blockquote>However, I will stress that in granting that ‘the universe began to exist’, we are really granting that ‘the universe began to exist out of nothing’. If the universe were created out of preexisting material, we would be left with the question of where this material itself came from, and the argument would prove nothing important.
</blockquote>
Charitably, by “the universe began to exist out of nothing” he actually means the universe began to exist without a material cause, i.e. beginning to exist without arising from pre-existing material (it could still have an efficient cause). Recall though that by “the universe” Craig means it in such a way that it includes <em>all contiguous space-time</em>, so there can’t be any pre-existing material that the universe arose from since by definition that “pre-existing material” would itself be part of the universe.
<br /><br />
Cosmic Skeptic then says this:
<blockquote>
If ‘beginning to exist’ means anything philosophically significant in this context, it must mean beginning to exist ex nihilo.
</blockquote>
That’s not quite true; we could just define “the universe” in way so that it “comprises all contiguous spacetime reality” as <a href="https://www.reasonablefaith.org/writings/popular-writings/existence-nature-of-god/the-kalam-cosmological-argument/">William Lane Craig has done</a> and the conclusion of the KCA would be theologically significant, since among other things the universe beginning to exist (in the normal sense of the phrase) implies the universe did not arise from pre-existing material given Craig’s definition of “the universe.”
<br /><br />
With Cosmic Skeptic defining “begins to exist” as “beginning to exist without using pre-existing material to form it,” he interprets the first premise to mean “Everything that begins to exist [without using pre-existing material to form it] has a cause,” <em>even though this is not what the first premise actually means</em>.
<br /><br />
Having redefined “begins to exist” as “beginning to exist without using pre-existing material to form it,” he notes how we’ve never seen anything “begin to exist” because all the things that have begun to exist (in the normal sense of the term) were made out of pre-existing material.
<blockquote> What, then, within the universe, has truly begun to exist (from nothing) at a particular point in the past?
<br /><br />
Nothing. The answer is nothing. Energy cannot be created or destroyed, and thus nothing in physical existence ever ‘began to exist’ in the sense we are interested in.
</blockquote>
It’s a widespread myth that energy cannot be created or destroyed. The expansion of space means that photons can lose energy from redshifting (the wavelength of the photons gets longer as space expands, and the photons lose energy as a result; the cosmic microwave background radiation used to be orange and it lost energy to become microwaves), and the expansion of space also means more dark energy. You can see this fun <a href="https://www.youtube.com/watch?v=cnGYMe6GBeQ">Science Asylum video</a> for more on that.
<br /><br />
But for sake of argument let’s pretend energy is always conserved, and that nothing in the universe begins to exist in the redefined ex nihilo manner. Cosmic skeptic says this leads to a circularity in the KCA because the only thing that began to exist is the universe, so “Everything that begins to exist [without using pre-existing material to form it] has a cause” becomes “The universe has a cause” and we get this argument.
<ol>
<li>The universe has a cause.</li>
<li>The universe began to exist.</li>
<li>The universe had a cause.</li>
</ol>
But this argument is circular, since the conclusion (3) just reiterates (1).
<br /><br />
Now sure, if you mutilate the first premise of the KCA from “Everything that begins to exist has a [material or efficient] cause” to “The universe has a cause” then you get a circular argument, but at that point you’re no longer talking about the same argument! The <em>original</em> KCA is still not circular even if Cosmic Skeptic’s mutilated version of the KCA is.
<br />
<br />
<h2 class="subHeader">Conclusion</h2>
<br />
<br />
Cosmic skeptic makes some points that, even if true, don’t really go anywhere in establishing the relevant point. (For more on this sort of maneuver, I made a video about <a href="https://www.youtube.com/watch?v=00MIK636fF4">red herrings</a>.) For example, he says that for the first premise to be “philosophically significant” it needs to mean “beginning to exist without using pre-existing material to form it.” But even if that’s true, and as a sort of rescue effort (to make the KCA philosophically significant?) one modifies the KCA so that the first premise becomes “Anything that begins to exist without using pre-existing material to form it has a cause” and this modified first premise renders the modified KCA slyly circular, this modified KCA is not the original argument. One isn’t establishing that the <em>original</em> argument is “slyly circular” but is instead establishing a different point, viz. that the modified KCA is slyly circular.
<br /><br />
If it is true that on the actual meaning of the KCA’s premises and conclusion, the KCA’s conclusion isn’t “philosophically significant,” one can object to the KCA’s utility for theism on <em>that</em> grounds. As it stands, the alleged circularity doesn’t arise until one mutilates the KCA into a straw man.
Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-63349671124897144302020-01-06T13:59:00.000-06:002020-01-25T20:36:44.567-06:00Paulogia vs Capturing Christianity's Puddle Analogy Video<style type="text/css"> <!--
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<h2 class="subHeader">Introduction</h2>
<br />
<br />
Someone named Paul has a YouTube channel called Paulogia
and he posted a video titled <a href="https://www.youtube.com/watch?v=eJQ54wKlD2Q" target="_blank">Puddle Parable and Fine-Tuning (Capturing Christianity Response)</a> responding to a <a href="https://www.youtube.com/watch?v=MXCo0a9KBIw" target="_blank">Capturing Christianity’s Puddle Analogy video</a>.
<br />
<br />
<h2 class="subHeader">Background</h2>
<br />
<br />
For those who don’t know, <em>fine-tuning</em> refers to the observation that certain parameters of our universe (certain physical constants and quantities) are “fine-tuned” in the sense that if any of these parameters were altered even slightly, the universe would be life-prohibiting rather than life-permitting, and physical life would not have evolved. So why is the universe life-permitting rather than life-prohibiting? The cosmic fine-tuning being the result of design seems to be a good and straightforward explanation. Cosmic fine-tuning is taken as evidence for the universe having been designed, and this constitutes the fine-tuning argument.
<br /><br />
The details of the fine-tuning argument vary upon its application, but the type of argument Cameron gives in his video (at around <a href="https://www.youtube.com/watch?v=MXCo0a9KBIw&t=1m34s" target="_blank">1:34</a> to 1:58) is structured thusly:
<ol>
<li>The probability that our universe would be life-permitting given naturalism is very, very low.</li>
<li>The probability that our universe would be life-permitting given theism is not very, very low.</li>
<li>Therefore, the fact that our universe is life-permitting provides evidence for Theism over Naturalism.</li>
</ol>
The puddle analogy is where the water in the puddle notices that the hole he is in happens to fit him perfectly, and thinks the hole must be designed for him. This analogy is then used as an objection against the fine-tuning argument. How exactly? Well, it depends on how it’s applied. Cameron’s video criticizes the analogy for being too ambiguous because he can think of at least five interpretations, but I wouldn’t say that’s the puddle story’s fault exactly. The puddle story has multiple applications and criticism should be laid at the feet of the particular application in question. Still, one application is that just as the water can fit whatever hole it’s in, life could have evolved in pretty much whatever the universe happened to be. This application of the puddle analogy essentially denies fine-tuning, but this objection isn’t terribly plausible. To quote the non-Christian educational source PBS Space Time at around <a href="https://www.youtube.com/watch?v=q-6oU3jXAho&t=14m20s" target="_blank">14:20</a> to 15:26:
<blockquote>
Many people had the following objection: they say that the universe isn’t really fine-tuned for life or for observers because there could be many types of observer very different to ourselves that could potentially exist if the fundamental constants were different. Well, actually, fine tuning arguments for the fundamental constants [being fine-tuned for life] for the most part take that into account. We can probably assume that for an intelligent observer to emerge in any universe, that universe must be capable of forming complex structures—whether or not it looks like life as we know it. So the universe needs to last a reasonable amount of time, have stable regions, and energy sources for those structures to form, and have some building blocks—whether or not they look like atoms as we know them. Much of the parameter space that the constants of nature could have taken eliminate one or more of these factors. So while there may be many small parts of that parameter space where observers can arise, most of it—and hence most universes—should be devoid of observers.</blockquote>
Cameron responds to the fine-tuning denial application of the puddle analogy (albeit not with PBS Space Time) as well as others. Cameron’s video and Paulogia’s response are both fairly lengthy, clocking in at about half an hour each. So I won’t be responding to everything, but I will respond to some of the more salient points that Paulogia made.
<br />
<br />
<h2 class="subHeader">Probability Distribution</h2>
<br />
<br />
In <a href="https://www.youtube.com/watch?v=eJQ54wKlD2Q&t=23m20s" target="_blank">23:20</a> to 23:57 Paulogia says we don’t know whether the probability distribution of a particular fine-tuned parameter is equal across the range, but this isn’t a very effective objection. The type of probability distribution that would presumably help naturalism here is if there’s a giant spike of probability over the extremely narrow life-permitting range, but this would require the probability distribution <em>itself</em> to be fine-tuned for that extremely narrow life-permitting range! The fine-tuning for life would merely be pushed back a step and the problem wouldn’t be solved at all.
<br />
<br />
<h2 class="subHeader">Necessity</h2>
<br />
<br />
In <a href="https://www.youtube.com/watch?v=eJQ54wKlD2Q&t=24m06s" target="_blank">24:06</a> to 24:44 he raises the possibility that the life-permitting value is the way it is by necessity. The problem is that this necessity of physics would <em>itself</em> be fine-tuned to be within that extremely narrow life-permitting range, and it’s just as easy to conceive a physical necessity that lands somewhere on the far more enormous area of life-prohibiting universes. As with the fine-tuned probability distribution, this seems like pushing the fine-tuning problem back a step and doesn’t really solve the problem.
<br /><br />
Alternatively, perhaps Paulogia believes the necessity is not only one of physics but of some deeper metaphysical principle. My fine-tuned meteor shower scenario of a previous blog post once again helps to illustrate the problem. To recap, suppose a meteor shower clearly spelled out on the moon, “There is a cosmic designer; I supernaturally fine-tuned certain parameters of this universe so that this message would appear.” Now suppose we do find such fine-tuned parameters (certain physical constants and quantities) that can be expressed as numerical values, like a series of multiple dials that are set extremely precisely for the meteor shower text to appear. Suppose also that the parameters are physically necessary (the values are part of the rules of the universe, and no force purely within the universe can alter them) but the physical necessities are nonetheless fine-tuned so that if the values were altered even slightly, no meteor shower text would appear. Clearly there’s still sense in which it is incredibly unlikely that the fine-tuned physical necessities happen to be the way they are in the absence of a cosmic designer, because this fine-tuning just doesn’t seem to be <em>metaphysically</em> necessary. True, one could in this scenario claim that it is metaphysically necessary that we’d see such a meteor shower text, but that would seem highly implausible under the circumstances, not to mention severely ad hoc. A cosmic designer would seem to be the best explanation of the fine-tuned meteor shower text. But if we’re to be rationally consistent, we must apply the same logic for the fine-tuning in our universe: the parameters don’t seem to be <em>metaphysically</em> necessary, and if one is putting forth the metaphysical necessity of a fine-tuned life-permitting universe with no argument to back it up, it looks like an ad hoc and inferior alternative explanation to design, just as it would in the fine-tuned meteor shower scenario.
<br />
<br />
<h2 class="subHeader">Getting the Math Wrong</h2>
<br />
<br />
Paulogia makes some errors in reasoning in which some probability theory will be helpful. So here’s a little probability symbolization to get us started;
<br />
<br />
<table cellpadding="3" border="1" cellspacing="0" class="inline">
<tr>
<td class="mid_li">Pr(A) = </td><td>The probability of A being true; e.g. Pr(A) = 0.5 means “The probability of A being true is 50%.”</td>
</tr>
<tr>
<td class="mid_li">Pr(A|B) = </td><td>The probability of A being true given that B is true. For example: <blockquote>Pr(I am wet|It is raining) = 0.8</blockquote>This means “The probability that I am wet given that it is raining is 80%.”</td>
</tr>
</table>
<br />
<br />
To recap a bit from my <a href="https://www.maverick-christian.org/2012/09/bayes-theorem-quick-introduction.html">article on Bayes’ theorem</a>, here’s one version of the theorem:
<br />
<br />
<!-- Simple Bayes' theorem -->
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<br />
<br />
On the normal conception of evidence, evidence E is evidence for hypothesis H if P(H|E) > P(H), i.e. evidence E making H more likely than without that evidence. Pr(H|E) is called the <em>posterior probability</em> of H, and Pr(H) is the <em>prior probability</em> of H (as in “prior to taking E into account”). Notice that, all other factors being constant, the higher P(E|H) is, the greater P(H|E) is and thus the greater evidential force evidence E is for hypothesis H.
<ul>
<li>N = <em>Naturalism is true.</em></li>
<li>L = <em>The universe is life-permitting.</em></li>
<li>T = <em>Theism is true.</em></li>
</ul>
The structure of Cameron’s fine-tuning argument is basically this:
<ol>
<li>The P(L|N) is very, very low.</li>
<li>The P(L|T) is not very, very low.</li>
<ul style="list-style-type: disc;">
<li>(Such that P(L|T) > P(L|N).)</li>
</ul>
<li>Therefore, L provides evidence for T over N.</li>
</ol>
Thanks to the magic of math, the structure of this argument is logically valid, i.e. it’s impossible to have true premises and a false conclusion (more on this later). Note how T is in both 2 and 3 here. That’ll be important to remember in a little bit.
<br /><br />
At around <a href="https://www.youtube.com/watch?v=eJQ54wKlD2Q&t=27m27s" target="_blank">27:27</a> to 27:55 Paulogia parodies Cameron’s argument with this.
<ol>
<li>The probability that I will roll a 3 on a 6-sided dice under naturalism is 16.6%.</li>
<li>The probability that I will roll a 3, given an all-powerful god who wants me to roll a 3 is 100%.</li>
<li>[Conclusion:] the fact that I rolled a 3 provides evidence for Theism over Naturalism.</li>
</ol>
Using these two symbols:
<ul>
<li>G = <em>An all-powerful god who wanted outcome X to occur existed.</em> (The outcome in this case being the die coming up 3.)</li>
<li>O = <em>The outcome X occurred.</em></li>
</ul>
The structure is this:
<ol>
<li>The P(O|N) is 16.6%.</li>
<li>The P(O|G) is 100%.</li>
<li>Therefore, O provides evidence for T over N.</li>
</ol>
After Paulogia describes his parody, he adds “That doesn’t seem right.” In a way he’s correct, because this parody fails to match the structure of Cameron’s argument; note how T is in both 2 and 3 in Cameron’s argument but T is present only in 3 in Paulogia’s parody. Paulogia’s parody is logically and mathematically invalid, unlike Cameron’s argument. We can fix the parody by using this structure:
<ol>
<li>The P(O|N) is 16.6%.</li>
<li>The P(O|G) is 100%.</li>
<ul style="list-style-type: disc;">
<li>Note that P(O|G) > P(O|N).</li>
</ul>
<li>Therefore, O provides evidence for G over N.</li>
</ol>
The structure now sufficiently mirrors Cameron’s fine-tuning argument, but as a result the conclusion follows from the premises; assuming of course that our conception of “evidence” is such that a fact making something more likely would constitute evidence for that fact. We can say that O is evidence for G over N if the ratio of P(G|O) to P(N|O) is greater than the ratio of P(G) to P(N). Or put another way, O is evidence for G over N if this is true:
<br />
<br />
<table cellpadding="0" cellspacing="0" border="0" class="math">
<tr style="text-align: center;">
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">P(G|O)</td></tr>
<tr><td class="bottom">P(N|O)</td></tr>
</table>
</td>
<td> > </td>
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">P(G)</td></tr>
<tr><td class="bottom">P(N)</td></tr>
</table>
</td>
</tr>
</table>
<br />
<br />
Now note the following equation, which is sometimes called the <em>odds form of Bayes’ theorem</em>:
<!-- Odds form of Bayes theorem -->
<br />
<br />
<table cellpadding="0" cellspacing="0" border="0" class="math">
<tr style="text-align: center;">
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">P(G|O)</td></tr>
<tr><td class="bottom">P(N|O)</td></tr>
</table>
</td>
<td> = </td>
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">P(G)</td></tr>
<tr><td class="bottom">P(N)</td></tr>
</table>
</td>
<td> × </td>
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">P(O|G)</td></tr>
<tr><td class="bottom">P(O|N)</td></tr>
</table>
</td>
</tr>
</table>
<br />
<br />
Notice that the odds form of Bayes’ theorem entails that if P(O|G) > P(O|N), then O is evidence for G over N. In other words:
<!-- The inequality -->
<br />
<br />
<table cellpadding="0" cellspacing="0" border="0" class="math">
<tr style="text-align: center;">
<td>If P(O|G) > P(O|N), then</td>
<td> </td>
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">P(G|O)</td></tr>
<tr><td class="bottom">P(N|O)</td></tr>
</table>
</td>
<td> > </td>
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">P(G)</td></tr>
<tr><td class="bottom">P(N)</td></tr>
</table>
</td>
</tr>
</table>
<br />
<br />
Since P(O|G) > P(O|N), O is evidence for G over N, even if Paulogia thinks otherwise. It may be extremely weak and negligible evidence, but it is technically evidence nonetheless. The conclusion, “O provides evidence for G over N” follows logically from the premises, and the argument is logically valid. The same math applies to Cameron’s actual argument:
<!-- Odds form of Bayes theorem -->
<br />
<br />
<table cellpadding="0" cellspacing="0" border="0" class="math">
<tr style="text-align: center;">
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">P(T|L)</td></tr>
<tr><td class="bottom">P(N|L)</td></tr>
</table>
</td>
<td> = </td>
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">P(T)</td></tr>
<tr><td class="bottom">P(N)</td></tr>
</table>
</td>
<td> × </td>
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">P(L|T)</td></tr>
<tr><td class="bottom">P(L|N)</td></tr>
</table>
</td>
</tr>
</table>
<br />
<br />
<table cellpadding="0" cellspacing="0" border="0" class="math">
<tr style="text-align: center;">
<td>If P(L|T) > P(L|N), then</td>
<td> </td>
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">P(T|L)</td></tr>
<tr><td class="bottom">P(N|L)</td></tr>
</table>
</td>
<td> > </td>
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">P(T)</td></tr>
<tr><td class="bottom">P(N)</td></tr>
</table>
</td>
</tr>
</table>
<br />
<br />
If P(L|T) > P(L|N) then L is evidence for T over N, and Cameron’s argument is logically valid. That said, the conclusion of Cameron’s argument is quite modest; it doesn’t specify how <em>much</em> evidential support L brings, and the atheist could theoretically concede that Cameron’s argument is sound (valid + true premises) while also believing that L’s evidential force for theism over naturalism is small. How much evidence L brings will depend on the values in the odds form of Bayes’ theorem (P(L|T), P(L|N), etc.). I’ll comment more on that later.
<br /><br />
Paulogia’s second parody is at around <a href="https://www.youtube.com/watch?v=eJQ54wKlD2Q&t=28m01s" target="_blank">28:01</a> to 28:24. In its original form it is this:
<ol>
<li>The probability that I will win Lotto 6/49 with one ticket under naturalism is 1 in 14 million.</li>
<li>The probability that I will win Lotto 6/49 with one ticket, given an all-powerful god who wants me to win Lotto 6/49 is 100%.</li>
<li>[Conclusion:] Me winning Lotto 6/49 provides evidence for Theism over Naturalism.</li>
</ol>
As before, Paulogia’s parody fails to mirror Cameron’s actual argument due to a mathematically invalid structure, with this time O being the outcome of winning the 6/49 lottery:
<ol>
<li>The P(O|N) is 1 in 14 million.</li>
<li>The P(O|G) is 100%.</li>
<li>Therefore, O provides evidence for T over N.</li>
</ol>
Unlike Cameron’s actual argument, the conclusion can be false even with the premises true. How? The probability of <em>God wanted specific person S to within the lottery</em> given that God exists seems <em>extremely</em> small (assuming God cares at all about who wins the lottery and has a specific random person he wants to win, the prior probability of God wanting <em>that</em> specific person to win the lottery is extremely small). As such, the probability that you will win the lottery given that God exists is actually extremely small, so even though P(O|G) is very high, P(O|T) is very small, and if P(O|T) is as small as (or smaller than) P(O|N), winning the 6/49 lottery won’t be evidence for T at all and 3 would be false even with 1 and 2 being true. This parody fails as a critique of Cameron’s argument however because the parody fails to match the structure of Cameron’s actual argument. Cameron’s argument is logically valid, whereas this parody argument is logically invalid. The same problem occurs with the parody immediately following the winning-the-lottery one at around <a href="https://www.youtube.com/watch?v=eJQ54wKlD2Q&t=28m24s" target="_blank">28:24</a> to 28:39 in which premise 1 is him <em>not</em> winning the lottery, premise 2 is an all-powerful god wanting him to not win the lottery, and the conclusion is that him not winning the lottery is “evidence for Theism over Naturalism”; the conclusion doesn’t follow from the premises, unlike Cameron’s argument. The parody’s math is wrong.
<br /><br />
Suppose though we repair the winning-the-lottery parody argument so that it more closely fits the basic structure of Cameron’s argument as follows:
<ol>
<li>The P(O|N) is 1 in 14 million.</li>
<li>The P(O|G) is 100%.</li>
<li>Therefore, O provides evidence for G over N.</li>
</ol>
As with the repaired parody of the die coming up 3, it is indeed evidence for the theistic hypothesis. Still, in both the rolling-a-3 and winning-the-lottery cases the putative evidence doesn’t seem like very <em>strong</em> evidence. Why is the evidential force so negligible? Take the lottery case. The prior probability of <em>an all-powerful god who wants me to win Lotto 6/49</em> is extremely small (since the probability of the deity wanting <em>that</em> specific person to win seems extremely low, and then there is the probability of the deity caring who wins the lottery!). So even though P(O|T) is low, and G is specified in a way that cranks up P(O|G) to be 1, it does so at the price of plummeting P(G) to a vanishingly small value. It’s possible for P(E|H) to be very high and yet P(H|E) still be very small when P(H) has an extremely low probability to begin with (recall Bayes’ theorem), e.g. when H is an all-powerful deity wanting a specific person to win the lottery, H has an extremely small prior probability and thus P(H|E) ends up being very small.
<br /><br />
Contrast all that with cosmic fine-tuning, letting <em>F</em> represent <em>The universe is fine-tuned for life</em>. While God wanting a specific random person to win the lottery given that God exists seems extremely small, does the probability of <em>God wanted a universe with life</em> given that God exists seem extremely small? It does not. So as long as the prior probability of theism simpliciter isn’t too low and P(F|T) isn’t too low, cosmic-fine-tuning can potentially be very strong evidence for theism.
<br /><br />
To illustrate, suppose that the God of our conception has only a mild interest in creating a universe with life and a mild interest of creating a physical universe just right for life such that this is true:
<br />
<br />
<!-- P(F|T) = 1/10^6. -->
<table cellpadding="0" cellspacing="0" border="0" class="math">
<tr style="text-align: center;">
<td>
P(F|T)
</td>
<td> = </td>
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">1</td></tr>
<tr><td class="bottom">10,000</td></tr>
</table>
</td>
</tr>
</table>
<br />
<br />
Suppose also that the following values obtain (note that the P(F|N) value below is taken from one possible value that Paulogia raised from something Cameron said in his original video, though of course Paulogia raised the necessity and probability distribution objections):
<br />
<br />
<!-- P(F|N) = 1/10^60. -->
<table cellpadding="0" cellspacing="0" border="0" class="math">
<tr style="text-align: center;">
<td>
P(F|N)
</td>
<td> = </td>
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">1</td></tr>
<tr><td class="bottom">10<sup>60</sup></td></tr>
</table>
</td>
</tr>
</table>
<br />
<br />
<!-- P(T) = 1/100. -->
<table cellpadding="0" cellspacing="0" border="0" class="math">
<tr style="text-align: center;">
<td>
P(T)
</td>
<td> = </td>
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">1</td></tr>
<tr><td class="bottom">100</td></tr>
</table>
</td>
</tr>
</table>
<br />
<br />
<!-- P(N) = 99/100. -->
<table cellpadding="0" cellspacing="0" border="0" class="math">
<tr style="text-align: center;">
<td>
P(N)
</td>
<td> = </td>
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">99</td></tr>
<tr><td class="bottom">100</td></tr>
</table>
</td>
</tr>
</table>
<br />
<br />
Now plug in those above values into the odds form of Bayes’ theorem:
<br />
<br />
<table cellpadding="0" cellspacing="0" border="0" class="math">
<tr style="text-align: center;">
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">P(T|F)</td></tr>
<tr><td class="bottom">P(N|F)</td></tr>
</table>
</td>
<td> = </td>
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">P(T)</td></tr>
<tr><td class="bottom">P(N)</td></tr>
</table>
</td>
<td> × </td>
<td>
<table cellpadding="0" cellspacing="0" border="0" class="fraction">
<tr><td class="top">P(F|T)</td></tr>
<tr><td class="bottom">P(F|N)</td></tr>
</table>
</td>
</tr>
</table>
<br />
<br />
If you do the math, P(T|F)/P(N|F) comes out <em>overwhelmingly</em> in favor of theism over naturalism even if we gave the aforementioned implausibly low values for P(F|T) and P(T). I’m not saying the above values are accurate or even close to accurate, but I used those numbers to illustrate the following point. If the following are true:
<br />
<br />
<table cellpadding="0" cellspacing="0" border="0" class="math">
<tr style="text-align: center;">
<td>P(T) = not that low</td>
</table>
<br />
<br />
<table cellpadding="0" cellspacing="0" border="0" class="math">
<tr style="text-align: center;">
<td>P(F|T) = not that low</td>
</table>
<br />
<br />
<table cellpadding="0" cellspacing="0" border="0" class="math">
<tr style="text-align: center;">
<td>P(F|N) = extremely-super-duper-ultra-mega low</td>
</table>
<br />
<br />
Then the result is that fine-tuning is going to be very strong evidence for theism over naturalism.
<br />
<br />
<h2 class="subHeader">Conclusion</h2>
<br />
<br />
What amazed me about Paulogia’s response, and the responses of some internet atheists, is how they deliver remarkably bad objections to the fine-tuning argument. A much better objection is the multiverse hypothesis in which there’s a massive ensemble of universes with varying parameters such that at least one of them is life-permitting, thereby affecting the value of P(F|N). To be fair, this response does have its problems (there are a number of obstacles in making this a better explanation than design) but it’s certainly a lot better than pushing the fine-tuning back a step, or just getting math wrong.Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-43769328492827494052019-11-05T23:45:00.000-06:002019-11-23T07:19:33.007-06:00Genetically Modified Skeptic vs Arguments for God<style type="text/css"> <!--
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<h2 class="subHeader">Introduction</h2>
<br />
<br />
Drew McCoy has a YouTube channel called Genetically Modified Skeptic
and he posted a video titled <a href="https://www.youtube.com/watch?v=cpC8WtufJbo" target="_blank">The Arguments for God's Existence Tier List</a> responding to various arguments for theism. I’ll go through them in chronological order of the video.
<br />
<br />
<h2 class="subHeader">Pascal’s Wager</h2>
<br />
<br />
(<a href="https://www.youtube.com/watch?v=cpC8WtufJbo&t=1m38s" target="_blank">1:38</a> to 3:03)
<br /><br />
As Genetically Modified Skeptic (GMS) presents it, Pascal’s Wager is this: if you act as if God exists and God does exist, you have infinite gain in heaven and finite loss, whereas if you act as if God doesn’t exist and God doesn’t exist you have finite gain but infinite loss in hell. Summarized in a handy table:
<br />
<br />
<table class="bonita">
<tr><th>Belief</td><th>Gain if correct</th><th>Loss if wrong</th></tr>
<tr class="odd"><td class="bold">God</td><td>Infinite</td><td>Finite</td></tr>
<tr class="odd"><td class="bold">No God</td><td>Finite</td><td>Infinite</td></tr>
</table>
<br />
<br />
Given the gain and loss data above, the rational individual would act as if God does exist. If God exists, acting as if he does exist gives you infinite gain and at worst finite loss. Whereas if you lived as if God didn’t exist, your gain was at best finite and your loss was at worst infinite. Therefore, the rational person would act as if God does exist.
<br /><br />
GMS claims this commits the black and white fallacy, acting as if there are only two possibilites when there are actually a lot more. After all, there are many different religions with one or more gods. Which religion to pick?
<br /><br />
I think GMS is sort of right in his objection, but the version of Pascal’s Wager he attacks isn’t really the strongest. The strongest version of Pascal’s Wager I’ve seen is that <em>if</em> you’re in a situation in which atheism and Christianity are the two viable options (e.g. perhaps you believe the case for the Resurrection of Jesus is strong enough to be likely if God exists) and the probabilities between the two options are roughly equal, then you should act as if God exists. Of course, this is a particularly narrow application of Pascal’s Wager, but it is arguably true that <em>if</em> the conditions were met then you should act as if God exist. A nontheist might not think the aforementioned conditions are met, but if so that would be a different matter than whether it would be rational to act as if God exists if the conditions <em>were</em> met.
<br />
<br />
<h2 class="subHeader">The Ontological Argument</h2>
<br />
<br />
(<a href="https://www.youtube.com/watch?v=cpC8WtufJbo&t=3m6s" target="_blank">3:06</a> to 4:55)
<br /><br />
As GMS states, there are multiple forms of the Ontological Argument and GMS (tries to) address Anselm’s version of it. In Chapter 2 of <em><a href="https://sourcebooks.fordham.edu/source/anselm.asp" target="_blank">Proslogion</a></em> Anselm introduces the argument like this:
<blockquote>
For it is one thing for something to exist in a person's thought and quite another for the person to think that thing exists. For when a painter thinks ahead to what he will paint, he has that picture in his thought, but he does not yet think it exists, because he has not done it yet. Once he has painted it he has it in his thought and thinks it exists because he has done it. Thus even the fool is compelled to grant that something greater than which cannot be thought exists in thought, because he understands what he hears, and whatever is understood exists in thought. And certainly that greater than which cannot be understood cannot exist only in thought, for if it exists only in thought it could also be thought of as existing in reality as well, which is greater. If, therefore, that than which greater cannot be thought exists in thought alone, then that than which greater cannot be thought turns out to be that than which something greater actually can be thought, but that is obviously impossible. Therefore something than which greater cannot be thought undoubtedly exists both in thought and in reality.
</blockquote>
That’s a bit of a mouthful, so let’s do a bit of analysis and simplify it a bit. One popular analysis is such that Anselm considers God as that which nothing greater can be conceived, or what is often called the “greatest conceivable being” (GCB).
<ol>
<li>God is the greatest conceivable being (by definition); God exists in the mind and is thus conceivable.</li>
<li>Something that exists in reality is greater than that which exists only in the mind.</li>
</ol>
<ol>
<ol start="3">
<li>Suppose God, the greatest conceivable being (from 1), exists only in the mind and not in reality (i.e. God does not actually exist; which is the negation of what this argument attempts to prove).</li>
<li>Then there <em>is</em> a conceivable being that is greater (than the being in 4), namely God existing in reality (since as 2 says, something existing in reality is greater).</li>
<li>So it is conceivable for something to have been greater than God (from 4).</li>
<li>Since God is that which nothing greater is conceivable (from 1), then it is conceivable for something to be greater than that which nothing greater is conceivable (from 5).
</ol>
</ol>
<ol start="7">
<li>Statement (6) is absurd and cannot be rationally accepted, thus the claim of (3) must be rejected and the greatest conceivable being must exist.</li>
</ol>
As it stands I think this version of the ontological argument is unsuccessful, but not for the reason GMS claims. GMS bizarrely claims that Anslem’s argument has God’s existence as a premise, but this is not a premise in Anselm’s argument. It is a premise of Anselm’s argument that God exists <em>in the mind</em> but that’s not the same thing as God existing <em>simpliciter</em>.
<br /><br />
A more popular objection against Anselm’s argument is attacking premise (2), the notion that existence is a great-making property. One could even argue that “existence” isn’t really a property at all (the fancy philosophy way of putting it is “existence is not a predicate”). A statement like “God is omniscient” basically claims that if God exists this entity has the property of “omniscience” (I add “if God exists” because if there is no God, then there isn’t any God to have any properties). However, even trying to phrase it like “God has the property of existence” is basically saying that if God exists, he has the property of existence, in which case “has the property of existence” isn’t adding very much to saying what God is like if he exists, and so it isn’t a real property in the sense that omniscience, redness, and having a mass of eighteen kilograms are properties. Here’s a key portion of the Anselm text I quoted earlier:
<blockquote> And certainly that greater than which cannot be understood cannot exist only in thought, for if it exists only in thought it could also be thought of as existing in reality as well, which is greater.</blockquote>
Yes we can <em>think</em> of God existing in reality, but that wouldn’t make him exist in reality. Similarly, we can grant that God would exist if God existed, but that doesn’t mean he exists. (I think God <em>does</em> exist, but I don’t think this particular argument is successful; just because a view is correct doesn’t mean that every argument for that view is a good one.)
<br /><br />
Lots more can be said about the “existence is not a predicate” objection to premise (2), and the objection isn’t universally agreed upon, but it at least attacks a real rather than an imaginary premise.
<br />
<br />
<h2 class="subHeader">The <em>Kalam</em> Cosmological Argument</h2>
<br />
<br />
(<a href="https://www.youtube.com/watch?v=cpC8WtufJbo&t=4m56s" target="_blank">4:56</a> to 6:55)
<br />
<br />
The <em>kalam</em> cosmological argument (KCA) basically goes like this:
<ol>
<li>Anything that begins to exist has cause.</li>
<li>The universe began to exist.</li>
<li>Therefore, the universe has a cause.</li>
</ol>
After that, philosophers have given further arguments to try to show that the cause has some characteristics conducive for theism, e.g. the cause of the universe being nonphysical and unimaginably powerful. You can read more about that and the argument in general at this <a href="https://www.reasonablefaith.org/writings/popular-writings/existence-nature-of-god/the-kalam-cosmological-argument/" target="_blank">William Lane Craig article</a> (Craig is the philosopher famous for reigniting the KCA’s popularity in the late twentieth century).
<br /><br />
GMS’s objection is quite bizarre; he points out that the conclusion of the KCA (the universe has a cause) doesn’t by itself get you to God. That’s true, but irrelevant. The KCA syllogism doesn’t aspire to do that. The nature of the universe’s cause is left to other arguments.
<br />
<br />
<h2 class="subHeader">The Moral Argument</h2>
<br />
<br />
(<a href="https://www.youtube.com/watch?v=cpC8WtufJbo&t=6m59s" target="_blank">6:59</a> to 9:01)
<br />
<br />
The moral argument for God’s existence that GMS critiques is this:
<ol>
<li>If God does not exist, then objective moral values do not exist.</li>
<li>Objective moral values do exist.</li>
<li>Therefore, God exists.</li>
</ol>
Christian philosopher William Lane Craig has popularized this variety (Craig gets around, philosophically speaking, in apologetics circles). At <a href="https://www.youtube.com/watch?v=cpC8WtufJbo&t=7m18s" target="_blank">7:18</a> to 7:27 GMS essentially attacks a straw man as follows:
<blockquote>
This argument’s first premise is unsubstantiated. It doesn’t demonstrate that the only way objective moral values can exist is if God exists.
</blockquote>
But that is not what the first premise claims. The first premise doesn’t claim that objective moral values <em>cannot</em> exist if God does not exist, it claims that objective moral values <em>do not</em> exist if God does not exist. This is important because all one has to do to justify the first premise as probably true is to argue that it is <em>unlikely</em> that objective moral values exist if God does not exist. I did just that in my <a href="https://www.youtube.com/watch?v=vwLesZ23stA" target="_blank">debate on the moral argument</a> with Jeffery Jay Lowder of internet infidels fame, and I didn’t need to argue at all that God is <em>necessary</em> for objective morality to exist (though the first premise is slightly different in the debate, the general reasoning would apply).
At <a href="https://www.youtube.com/watch?v=cpC8WtufJbo&t=7m47s" target="_blank">7:47</a> to 7:58 GMS attacks another straw man:
<blockquote>
Some other moral arguments such as C.S. Lewis’s argument in <em>Mere Christianity</em> state that moral law has not been shown to have a natural origin so it must have come from a supernatural moral lawgiver. First of all, this is an argument from ignorance; not knowing does not excuse asserting an unsubstantiated answer. Second, evolution by natural selection is actually a pretty good explanation for why social species would behave according to practices which promote fairness, peace, and well-being among groups.
</blockquote>
As Lewis makes clear in chapter 3 of <em>Mere Christianity</em> by “moral law” Lewis is not talking about descriptive patterns of behavior as GMS seems to think here, so even if evolution by natural selection did explain why our species came up with the practices it did, this is irrelevant. Lewis is talking about the “oughtness” type of morality; e.g. men ought to be unselfish. As I’ve written before, <a href="https://www.maverick-christian.org/2018/08/moral-ought-facts-are-non-natural.html">moral oughts are non-natural</a>.
<br/><br />
Lewis never says that the moral law must have come from a supernatural moral lawgiver simply because it has not shown to have a natural origin. After observing that we do have this inner sense of the moral law (among other things), in chapter 4 Lewis says:
<blockquote>
All I have got to is a Something which is directing the universe, and which appears in me as a law urging me to do right and making me feel responsible and uncomfortable when I do wrong. I think we have to assume it is more like a mind than it is like anything else we know—because after all the only other thing we know is matter and you can hardly imagine a bit of matter giving instructions.</blockquote>
Among known stuff, Lewis believes a mind is the best explanation. Maybe you disagree with Lewis’s inference to the best explanation, but it is not the same thing as an argument from ignorance; Lewis doesn’t say “It hasn’t been shown to be a natural cause, therefore a supernatural moral lawgiver is behind it.” For one, it isn’t just that it hasn’t been <em>shown</em> to be a natural cause; Lewis believes we have good reason to think it’s just not the nature of inanimate matter to give instructions, whereas the same doesn’t apply so well to a mind. Whether you like or dislike this reasoning, it’s not of the form “It has not been shown that <em>p</em> is true, therefore <em>p</em> is false.”
<br /><br />
In <a href="https://www.youtube.com/watch?v=cpC8WtufJbo&t=8m28s" target="_blank">8:28</a> to 8:55 GMS asserts that this argument has the special ability he calls “denigrate” in which the user asserts or implies that their opponent lacks morals. The problem with this alleged “special ability” is that it’s not an ability of the argument at all. Nowhere does the argument say or imply that nontheist can’t be moral. William Lane Craig, incidentally, has made it clear on repeated occasions that the moral argument doesn’t claim that atheists can’t live a good and decent life.
<br />
<br />
<h2 class="subHeader">Argument from Personal Experience</h2>
<br />
<br />
(<a href="https://www.youtube.com/watch?v=cpC8WtufJbo&t=9m8s" target="_blank">9:08</a> to 12:59)
<br />
<br />
GMS puts the argument like this:
<ol>
<li>My personal experiences are reliable sources of information.</li>
<li>I personally experienced [insert God claim here].</li>
<li>Therefore [the God claim] is true.</li>
</ol>
William Lane Craig has been known to often assert that God can be immediately known and experienced, but even he claims this really isn’t an argument, e.g. in the <a href="https://www.reasonablefaith.org/media/debates/the-existence-of-the-christian-god-the-craig-curley-debate/">Craig-Curley debate</a> he says this:
<blockquote>
God can be immediately known and experienced. This isn't really an argument for God's existence; rather it's the claim that you can know God exists wholly apart from arguments simply by immediately experiencing Him…. If you're sincerely seeking God, then God will make His existence evident to you. The Bible promises, "Draw near to God and He will draw near to you" (James 4. 8). We mustn't so concentrate on the proofs that we fail to hear the inner voice of God speaking to our own heart. For those who listen, God becomes an immediate reality in their lives.
</blockquote>
This is more of an invitation than an argument. As an argument, I agree that it sucks—at least if you’re trying to use it to convince other people. There are instances in which subjective personal experiences can trump even objective evidence for the person who has had the experiences.
<br /><br />
Think that can’t happen? Imagine you’re on trial for a crime you know you didn’t commit because of your own personal experience of you not committing the crime, but all the objective evidence available to the court stands against you. You have no objective evidence you can give to the court to prove you are being framed, but you are still rational to believe in your own innocence. Subjective personal experience can be a powerful source of rational justification. <em>If</em> people really do have personal experiences of God, this can potentially be a source of rational justification for belief in God.
<br /><br />
But as an argument to convince <em>other</em> people, I don’t see it being much more useful than reporting your own personal experience of being innocent before a jury who sees the objective evidence heavily stacked against you.
<br /><br />
GMS notes that personal experiences can sometimes be delusory, which is true, but insufficient to reject our personal experiences (e.g. I’ll still trust my experience that I was alive in the twentieth century). He notes people can have conflicting personal experiences, which is again true, but still insufficient. People can look at the same set of data and disagree where the evidence points, thus having different intuitive experiences of where the evidence points, but I doubt that would make GMS reject anthropogenic climate change. That said, arguments from personal experiences like this are still not that useful to convince other people.
<br />
<br />
<h2 class="subHeader">Teleological (Fine-Tuning) Argument</h2>
<br />
<br />
(<a href="https://www.youtube.com/watch?v=cpC8WtufJbo&t=13m3s" target="_blank">13:03</a> to 16:13)
<br /><br />
For those who don’t know, <em>fine-tuning</em> refers to the observation that certain parameters of our universe (certain physical constants and quantities) are “fine-tuned” in the sense that if any of these parameters were altered even slightly, the universe would be life-prohibiting rather than life-permitting, and physical life would not have evolved. So why is the universe life-permitting rather than life-prohibiting? The cosmic fine-tuning being the result of design seems to be a good and straightforward explanation. Cosmic fine-tuning is taken as evidence for the universe having been designed.
<br /><br />
GMS makes the claim that this argument makes a false dichotomy fallacy at around <a href="https://www.youtube.com/watch?v=cpC8WtufJbo&t=13m43s" target="_blank">13:43</a> to 13:58:
<blockquote>
First it makes use of a false dichotomy presenting pure chance and an intelligent creator as the only two possibilities when it hasn’t successfully ruled out other options. There could perhaps be some purely physical rule to the universe which demands that these constants be the way they are.</blockquote>
William Lane Craig however has often introduced the fine-tuning argument this way:
<ol>
<li>The fine-tuning is due either to physical necessity, chance, or design.</li>
<li>It is not due to physical necessity or chance.</li>
<li>Therefore, it is due to design.</li>
</ol>
Now perhaps GMS doesn’t believe that physical necessity has been <em>successfully</em> ruled out, but if the third possibility of physical necessity <em>had</em> been considered as a possibility and the <a href="https://www.reasonablefaith.org/writings/question-answer/fine-tuning-and-physical-necessity">argumentation against physical necessity for fine-tuning</a> is just unsuccessful, this isn’t a case of a false dichotomy, since three possibilities were indeed considered.
<br /><br />
Perhaps the physical constants are physically necessary in the sense that their values (represented numerically in physics) are the way they are in the universe and there’s nothing within the physical universe that can change it (it would require something supernatural to affect them). Note that physical necessity is distinct from <em>metaphysical</em> necessity which is the necessity of the way things could have been in a more absolute sense. If we define a <em>possible world</em> as a complete description of the way reality is or could have been like, some believe there are possible worlds with different physical laws, and that is at least partly why we need empirical study to see what the physical laws of our universe are actually like. In contrast, there are no possible worlds with a married bachelor.
<br /><br />
But even if physical constants are <em>physically</em> necessary, we would end up with fine-tuned physical necessities and would not solve the problem or even really provide an alternative to chance.
<br /><br />
To illustrate why, consider the following Meter Shower Scenario. Suppose a meteor shower clearly spelled out on the moon, “There is a cosmic designer; I supernaturally fine-tuned certain parameters of this universe so that this message would appear.” Now suppose we do find such fine-tuned parameters that can be expressed as numerical values, like a series of multiple dials that are set extremely precisely for the meteor shower text to appear. Suppose also that the parameters are physically necessary (the values are part of the rules of the universe, and no force purely within the universe can alter them) but the physical necessities are nonetheless fine-tuned so that if the values were altered even slightly, no meteor shower text would appear. Clearly there’s still sense in which it is incredibly unlikely that the fine-tuned physical necessities happen to be the way they are in the absence of a cosmic designer, because this fine-tuning just doesn’t seem to be <em>metaphysically</em> necessary. True, one could in this scenario claim that it is metaphysically necessary that we’d see such a meteor shower text, but that would seem highly implausible under the circumstances. A cosmic designer would seem to be the best explanation of the meteor shower text.
<br /><br />
Similarly, even if the physical constants for a life-permitting universe are physically necessary, they don’t seem to be the sort of thing that is metaphysically necessary. The notion that there couldn’t have been a life-prohibiting universe to the point of a life-prohibiting universe being <em>metaphysically impossible</em> does not seem plausible.
<br /><br />
GMS continues at around <a href="https://www.youtube.com/watch?v=cpC8WtufJbo&t=13m59s" target="_blank">13:59</a> to 14:12:
<blockquote>
Second, this is an argument from ignorance because the arguer doesn’t know how such an unlikely thing could have possibly happened, they posit unsubstantiated explanation: a God, instead of saying, “I don’t know.”
</blockquote>
First, the conclusion is “design” not “God” (though to be fair, the fact—if it is so—that the universe was designed would make atheism considerably less plausible). Second, we <em>can</em> see how such an unlikely thing could have happened, it’s just…unlikely (in the absence of a cosmic designer). Third, is this really an argument from ignorance? Arguments from ignorance take the form of something like “It has not been shown that <em>p</em> is false, therefore <em>p</em> is true.” Maybe somewhere somebody has argued this way in presenting the fine-tuning argument, but it’s just not an inherent part of the reasoning.
<br /><br />
One could more charitably see the fine-tuning argument as an inference to the best explanation. To illustrate why, consider the Meteor Shower Scenario in which someone claims the fine-tuning for the meteor shower is clear evidence of design. Suppose a skeptic responded with this:
<blockquote>
You’re saying you don’t know how such an unlikely thing could have happened, we must posit an unsubstantiated explanation: a designer, instead of saying “I don’t know.”
</blockquote>
This rebuttal is less than convincing, in part because (1) simply saying that A is evidence for B here doesn’t by itself imply an argument from ignorance like the skeptic described above; (2) the fine-tuning being explained <em>is</em> the evidence for the posited “unsubstantiated” explanation of design; and (3) this response seems like a really desperate maneuver to avoid an intelligent designer of the cosmos.
<br /><br />
Lots more could be said about the fine-tuning argument, but the objection GMS gave here is highly unsuccessful, as were many of the objections presented in the video with respect to other arguments for theism.
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<h2 class="subHeader">Conclusion</h2>
<br />
<br />
Woodford’s replies relied heavily on fallacious and confused reasoning (the straw man fallacy in particular). Judging from the YouTube comments on Woodford’s video, many viewers didn’t notice that Woodford was attacking straw men. Granted, it’s understandable why they might not have known about Craig including both efficient and material causes for the “has a cause” notion because Woodford (for whatever reason) omitted mentioning that important fact. But even so, even if Craig had only the efficient cause in mind, Woodford’s attack on the first justification where Woodford concluded “This isn’t a distraction; it’s a refutation” would still be a distraction and not a refutation of any claim Craig actually made in the video clips. Woodford also accused Craig of a black-and-white fallacy Craig never made, and a fallacy of division Craig never made. Why did so many viewers not notice this?
<br /><br />
Think of how clever politicians dodge a question; they give an answer that contains material closely related to the actual question but nonetheless doesn’t answer it. <a href="https://maverickchristian.blogspot.com/p/glossary-of-philosophy-terms-etc.html#_red_herring" class="definition" title="Click here to see the definition of the term.">Red herrings</a> and straw men have a greater chance of hoodwinking the audience when the material is closely related to the matter at hand while still being irrelevant. For example, given the context, the position “If something [like the universe] can come into being from nothing, then it becomes inexplicable why just anything or everything doesn’t come into being from nothing” is <em>similar</em> to the claim “If the universe (the whole) came into being uncaused, then some things within the universe (the parts) are uncaused.” The positions are so similar one could understand how they could be confused for being the same claim when they aren’t. I’m not saying Woodford was deliberately deceiving his audience. In fact I think he probably wasn’t and that he made sincere errors in his thinking. You can try to spot such errors yourself by asking the following questions when person B attacks the position of person A:
<ul>
<li>What is person A’s actual position?</li>
<li>What is person B’s objection, and does this objection actually attack A’s position?</li>
<li>Is there a gap between what is claimed and what is shown when B attacks A’s position?</li>
</ul>
If one asked these questions, they might have noticed that “creation and causation are not two sides of the same coin” doesn’t attack Craig’s actual claim of “Something cannot come into being from nothing” supporting premise 1’. Even if Woodford showed that “creation and causation are not two sides of the same coin” there’s a gap between this and refuting the idea of “Something cannot come into being from nothing” supporting premise 1’.
<br /><br />
Straw men and red herrings are tragically common on the internet, and we should be careful about not only spotting such errors but being careful to avoid making them ourselves.
<br />
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<h2 class="subHeader">Craig’s Second Justification: The Inexplicability Objection</h2>
<br />
<br />
At around <a href="https://www.youtube.com/watch?v=Dqc42ZB24ew&t=11m35s">11:35</a> of Craig’s video, Craig says:
<blockquote>
If something can come into being from nothing, then it becomes inexplicable why just anything or everything doesn’t come into being from nothing. Think about it; why don’t bicycles and Beethoven and root beer out of nothing? Why is it only universes that can come into being from nothing? What makes nothingness so discriminatory?
</blockquote>
Woodford responds by strawmanning Craig again, claiming Craig made a fallacy of division he never made. For those who don’t know, the fallacy of division is the fallacy of incorrectly inferring something is true of the parts because it is true for the whole. The example Woodford gives is this:
<ol>
<li>The United States is rich.</li>
<li>The United States has citizens.</li>
<li>Therefore, the United States’ citizens are rich.</li>
</ol>
In the case of Craig, Woodford believes it’s something like “If the universe (the whole) came into being uncaused, then some things within the universe (the parts) are uncaused.” But this is a straw man; Craig never made this claim. To see how this fallacy of division (FOD) claim is not the same claim as Craig’s inexplicability claim, note how “The universe came into being uncaused and nothing within the universe is uncaused” is logically inconsistent with the FOD claim but logically consistent with Craig’s inexplicability claim (there’s no self-contradiction in the universe beginning to exist uncaused but it being inexplicable that anything and everything within the universe doesn’t come into being from nothing). Woodford never attacks Craig’s actual claim here.
<br /><br />
So why does Craig’s inexplicability claim matter? One reason is that, if true, it would seem to imply that “Something cannot come into being from nothing” is not merely the <em>best</em> explanation for why anything or everything doesn’t come into being from nothing, it’s the <em>only</em> explanation!
<br /><br />
There might be another reason. At around <a href="https://www.youtube.com/watch?v=Dqc42ZB24ew&t=11m35s">11:54</a> to 12:16 of Craig’s video, Craig says:
<blockquote>
Why is it only universes that can come into being from nothing? What makes nothingness so discriminatory? There can’t be anything about nothingness that favors universes for nothingness doesn’t have any properties. Nor can anything constrain nothingness since there isn’t anything to be constrained.
</blockquote>
It seems that Craig might believe it would be <a href="https://www.maverick-christian.org/p/glossary-of-philosophy-terms-etc.html#_special_pleading" class="definition" title="Click here to see the definition of the term.">special pleading</a> to say that universes can come into being from nothing but not other stuff like root beer and bicycles. Note that the reason behind this doesn’t have anything to do with “The parts have the property simply because the whole does” but rather the nature of nothingness itself.
<br />
<br />
<h2 class="subHeader">Craig’s Third Justification: Empirical Evidence</h2>
<br />
<br />
Craig says at around <a href="https://www.youtube.com/watch?v=Dqc42ZB24ew&t=12m17">12:17</a> of his video that “Common experience and scientific evidence confirm the truth of premise 1’.” Although Woodford doesn’t quote Craig’s third justification Woodford does kind of allude to it. He says this at around <a href="https://www.youtube.com/watch?v=LVyGk3vldMI&t=7m3s">7:03</a> to 7:29:
<blockquote>
Sure, nobody sincerely believes that macroscopic things can pop into existence without a cause, and for good reason: our empirical observations and more importantly, our objective verifiable evidence clearly shows that when macroscopic things ‘begin to exist’ they do so via causation. However, and this was Scott’s excellent point, the exact same objective, verifiable evidence equally shows that all new macroscopic things are comprised of material that already existed. Hence Craig and his ilk are cherry-picking in the extreme. They are confidently asserting that macroscopic things are caused in the classical sense, and yet they’re rejecting that all new macroscopic things are merely the rearrangement of already existing material.
</blockquote>
Does it follow that Craig and his ilk are cherry-picking observations? No, because not all inductive predicates are created equal. To illustrate, consider this inductive argument:
<ol>
<li>All observed humans came from other humans (whether via the standard way, in vitro fertilization, or whatever).</li>
<li>Therefore, all humans came from other humans.</li>
</ol>
If Woodford rejects this conclusion, does it mean he’s cherry-picking observations? No, that would be just as <em><a href="http://maverickchristian.blogspot.com/p/glossary-of-philosophy-terms-etc.html#_non_sequitur">non sequitur</a></em> as believing Craig and his ilk were cherry-picking observations. Whether you’re a creationist or evolutionist, you’ll probably recognize that there’s something wrong with this inductive argument. The problem is that not all inductive predicates (the predicate here being “came from other humans”) are “projectible” i.e. reasonable to extrapolate for the given extrapolation region. We have excellent reason to believe the predicate of (1) is not projectible. Similarly, Craig believes we have excellent reason to believe a predicate like “comprised of material that already exists” for the sample class of “new observed macroscopic physical objects” is not projectible. What reasons are those? Well, the universe began to exist and something cannot come into being from nothing, which together imply that the universe (a presumably macroscopic physical thing) was a new thing that did not have a material cause.
<br /><br />
Woodford accuses “Craig and his ilk” of “confidently asserting that macroscopic things are caused in the classical sense” but this doesn’t seem to be true either. Unfortunately Woodford never defines what he means by “classical causation” but presumably he means the causation of classical mechanics, which is deterministic and has the cause temporally precede the effect. Craig doesn’t believe either criteria holds for all macroscopic objects, especially the universe. Craig believes the universe began to exist and he also believes the universe’s cause was simultaneous with the effect, and he believes God indeterministically caused the universe into being.
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<h2 class="subHeader">Craig’s First Justification, Part 2: Denying Premise 1’</h2>
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In one of Woodford’s clips William Lane Craig says:
<blockquote>
To claim that something coming into being from nothing is worse than magic. When a magician pulls the rabbit out of a hat, at least you’ve got the magician, not to mention the hat. But if you deny premise 1’ you’ve got to think the whole universe just appeared at some point in the past for no reason whatsoever. But nobody sincerely believes that things, say, a horse or an Eskimo village can just pop into being without a cause.
</blockquote>
At around <a href="https://www.youtube.com/watch?v=LVyGk3vldMI&t=5m47s">5:47</a> to 6:33 Woodford addresses the claim that denying premise 1’ means you’d have to believe the whole universe came into being sometime in the past for no reason at all (i.e. came into being uncaused), to which Woodford promptly replies, “Except no, we don’t.” Except logic says, “Yes, we do.” Seriously, one can rigorously prove this using symbolic logic. For those who are logic savvy (if you’re not, see parts 1 and 2 of my <a href="https://maverickchristian.blogspot.com/2012/05/introductory-logic-part-1.html" target="_blank">introductory logic series</a> which contains all the information needed to follow the proof I will show; otherwise I will come back to plain English in a little bit), here are the propositional variables:
<ul>
<li><strong>B</strong> = the universe began to exist.</li>
<li><strong>C</strong> = the universe has cause of its beginning.</li>
</ul>
We can rigorously prove that believing the denial of premise 1’ (i.e. ¬(B → C)) means you logically have to believe that the universe began to exist without a cause (i.e. B ∧ ¬C).
<ol class="start">
<li>¬(B → C)</li>
</ol>
<hr />
<ol class="middle" start="2">
<li>¬(B ∧ ¬C) <span class="logic">indirect proof assumption</span></li>
</ol>
<ol class="middle">
<div class="middle">
<ol start="3" class="middle">
<li>¬B ∨ ¬¬C <span class="logic">2, De Morgan’s Law</span></li>
<li>¬B ∨ C <span class="logic">3, double negation</span></li>
<li>B <span class="logic">conditional proof assumption</span></li>
<div class="middle">
<ol class="middle" start="6">
<li>¬¬B <span class="logic">5, double negation</span></li>
<li>C <span class="logic">4, 6 disjunctive syllogism</span></li>
</ol>
</div>
</ol>
<ol start="8" class="middle">
<li>B → C <span class="logic">5-7 conditional proof</span></li>
<li>¬(B → C) ∧ (B → C) <span class="logic">1, 8 conjunction</span></li>
</ol>
</div>
</ol>
<ol class="end" start="10">
<li>B ∧ ¬C <span class="logic">2-9 indirect proof</span></li>
</ol>
Formal logic aside, how does Woodford dispute Craig’s claim? Woodford attacks a <a href="https://maverickchristian.blogspot.com/p/glossary-of-philosophy-terms-etc.html#_straw_man" class="definition" title="Click here to see the definition of the term.">straw man</a> and accuses Craig of a black-and-white fallacy (also known as “false dichotomy”) he never made: the universe either has a cause or it popped into being from nothing, when a third option to this false dichotomy is that the universe did not begin to exist (it always existed) and had no cause. Craig never says “Either the universe popped into being uncaused or it had a cause” in any of Woodford’s clips, nor does premise 1’ (“If the universe began to exist, then the universe has cause of its beginning”) imply any such dichotomy. The actual dichotomy premise 1’ implies is that either (a) the universe did not begin to exist; or (b) it had a cause. (I could use symbolic logic to prove this, but if you think about it and remember that 1’ says “If the universe began to exist, then the universe has cause of its beginning” you might see why this would imply that either the universe had a cause or it had no beginning.) So saying the universe is both uncaused and never began to exist would not at all constitute denying that <em>if</em> the universe began to exist, then the universe has cause of its beginning. If one denied premise 1’ and justified that denial by saying the universe always existed and was never caused, that would be committing the <a href="http://maverickchristian.blogspot.com/p/glossary-of-philosophy-terms-etc.html#_red_herring" class="definition" title="Click here to see the definition of the term.">red herring fallacy</a>.
<br /><br />
If you had trouble with the symbolic logic showing that denying the first premise meant you’d have to believe the universe began to exist uncaused, here’s one way to think about it: denying “Everything that begins to exist has a cause” commits you to believing there is something that began to exist that had no cause; denying “Every universe that began to exist had a cause” commits you to believing there’s a universe that began to exist without a cause, and if you narrow that claim to just this universe as 1’ does, denying 1’ commits you to believing our universe began to exist without a cause. Craig was absolutely right and Woodford just didn’t understand the logic of the situation.
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Rationality Rules vs. Craig’s Causal Premise</td></tr>
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<h2 class="subHeader">Introduction</h2>
<br />
<br />
Stephen Woodford has a YouTube channel called Rationality Rules and he posted a video titled <a href="https://www.youtube.com/watch?v=LVyGk3vldMI">Creation and Causation (a Reply to Dr. Craig)</a> responding to justifications of William Lane Craig’s premise 1’ “If the universe began to exist, then the universe has cause of its beginning,” which Craig contrasts from the less modest claim premise 1 “Whatever begins to exist has a cause of its beginning” (which Craig has had different wordings for, e.g. “Everything that begins to exist has a cause”). In this article I’ll go through Woodford’s replies.
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<h2 class="subHeader">Craig’s First Justification, Part 1: Coming into Being from Nothing</h2>
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<br />
Before getting to the first justification I’ll explain some philosophical terms. A <em>material cause</em> is the stuff something is made out of, and an <em>efficient cause</em> is that which produces an effect. For example, when an artist creates a wooden sculpture, the wood is the material cause and the artist is the efficient cause.
<br /><br />
Craig’s first justification is that “Something cannot come into being from nothing.” At <a href="https://www.youtube.com/watch?v=LVyGk3vldMI&t=3m22s">3:22</a> to 3:24 Woodford says that “to say that something has come into being is to say that something has begun to exist, that it’s been created” and later says the first sentence (“If the universe began to exist, then it has a cause”) is about causation, and the second (“Something cannot come from nothing’”) is about creation. But it’s really about both. For Craig, a premise like “Everything that begins to exist has a cause” includes both material and efficient causation. You can see that in this <a href="https://www.reasonablefaith.org/writings/question-answer/must-everything-that-begins-to-exist-have-a-material-cause/">Reasonable Faith webpage</a> but you can also see it <a href="https://www.youtube.com/watch?v=Dqc42ZB24ew&t=1h8m11s">in the very Kalam Cosmological Argument video</a> Woodford clips from (<a href="https://www.youtube.com/watch?v=Dqc42ZB24ew&t=1h8m11s">1:08:11</a> to 1:08:29):
<blockquote>
Now in the first premise, the premise doesn’t stipulate what kind of cause there has to be for what begins to exist. It’s just saying that something can’t come into existence without some sort of a cause—a material cause, an efficient cause, whatever.
</blockquote>
So to say that the universe began to exist without a cause means beginning to exist with no efficient cause and no material cause, i.e. coming into being from nothing.
<br /><br />
Woodford doesn’t seem to understand this, and he goes on an inadvertent tangent about quantum mechanics (which he doesn’t correctly understand) and classical causation that doesn’t really go anywhere relevant in addressing Craig’s actual claim.
<br /><br />
In talking about quantum superposition Woodford says “we see atoms both excited and not excited at the same time (which calls into question the law of noncontradiction)” which is misleading at best. There’s quantum mechanics, which has loads of math that is very good at making successful empirical predictions, and there are various empirically indistinguishable <em>interpretations</em> of quantum mechanics which put forth ideas about the underlying reality behind the math. I’ll spare you the mathematical details of eigenvalues and such (I recommend David Z. Albert’s excellent <em><a href="https://www.amazon.com/Quantum-Mechanics-Experience-David-Albert/dp/0674741137">Quantum Mechanics and Experience</a></em> for a gentle introduction to that sort of thing) instead giving a rough general idea behind the math. In some cases we have a mathematical structure representing the state of an object (e.g. an electron) and another mathematical structure called an operator that acts on the state to tell us what measurement we’d see for a given property (e.g. if the electron would be “spin up” when measured along a particular axis) if we did a particular measurement.
<br /><br />
In some cases, quantum mechanics will tell us “If you do that measurement, you’ll definitely get this result.” But in some cases, the state is in a <em>superposition</em> such that it can’t give us a definite answer as to what our measurement will be when combined with the operator, and quantum mechanics instead gives us the probabilities of the measurement results. So what’s really going on here behind the superposition math? One idea is that the object (e.g. electron) in question doesn’t have a definite property value for the property being measured until it’s actually measured. An even crazier idea, which Woodford presents here, is that the object both has the property and doesn’t have the property at the same time. However, that sort of contradiction <em>is nowhere in the math of quantum mechanics</em>. Mathematics can represent contradictions, and there are absolutely <em>no contradictions</em> in the math of quantum mechanics. The idea that a self-contradiction is present behind the math is an <em>interpretation</em> of quantum mechanics, and it is not a very plausible one.
<br /><br />
Superposition confusion aside, Woodford kind of contradicts himself in this video at around <a href="https://www.youtube.com/watch?v=LVyGk3vldMI&t=5m4s">5:04</a> to 5:29, because he says quantum mechanics “hasn’t been shown to violate the law of conservation of energy. Every atom is accounted for; everything, so far as we know, is created from already existing material” (the conservation of energy isn’t exactly true since photon energy can be lost as space expands, but let’s ignore that for the nonce) yet he says we have billions of things “coming into being” without a “classical cause and perhaps even without a cause at all.” No, not without a cause at all, because he just conceded that all those things coming into being came from pre-existing material which means all those things had material causes.
<br /><br />
At <a href="https://www.youtube.com/watch?v=LVyGk3vldMI&t=5m4s">5:29</a> to 5:40 Woodford concludes with:
<blockquote>
Thus creation and causation are not two sides of the same coin, and it’s a mistake to treat them as such. This isn’t a distraction. It’s a refutation.
</blockquote>
It’s a distraction because it doesn’t refute any position Craig actually put forth in the clip Woodford showed. Quantum mechanics doesn’t do anything to show that things can come into being with no efficient cause and no material cause. Nor did anything Woodford say about quantum mechanics (as flawed as it was) show that causation and creation (coming into being) aren’t closely related. Nor did Craig <em>claim</em> they were closely related, at least not explicitly.
<br /><br />
But surely Craig at least <em>implied</em> creation and causation were closely related when used he “Something cannot come into being from nothing” to justify premise 1’? Yes, but specifics matter; the specific relation here is one of <em>justification</em>, viz. “Something cannot come into being from nothing” justifying “If the universe began to exist, then it has a cause.” If the universe began to exist without a cause (efficient or material) then it came into being from nothing, and if something cannot come into being (creation) from nothing, then premise 1’ is true, and causation and creation are intimately related in <em>that</em> sense. Perhaps there is a sense in which creation and causation are not closely related, but they are closely related in the sense of justifying premise 1’ and nothing Woodford said about quantum mechanics etc. addressed this relation. Woodford offered a lot of distraction but no real refutation of Craig’s actual claim here.
<br /><br />
Woodford could perhaps be forgiven for not realizing that Craig left it open whether the cause in 1’ is efficient or material (despite what Craig clearly said in the video Woodford quoted from), but even if it were an efficient cause Woodford’s reply still wouldn’t work. Suppose that by “cause” Craig only meant “efficient cause.” Would “Something cannot come from nothing” fail to justify “If the universe began to exist, then it has a cause”? No. In this context the “universe” includes all of contiguous physical spacetime, so if the universe began to exist at time <em>t</em> it couldn’t have a material cause because a material cause would be pre-existing material at some time <em>t*</em> < <em>t</em>, in which case the universe (which includes all of contiguous physical spacetime) existed at time <em>t*</em>, contradicting the claim the universe began to exist at <em>t</em>. So if the universe began to exist it could not have a material cause, and if it began to exist without an efficient cause also, then it began to exist without a material cause and without an efficient cause, i.e. it came into being from nothing. So “Something cannot come from nothing” still relevantly justifies premise 1’.
<br />
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Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-6812664809874978902018-08-23T21:50:00.001-05:002019-05-24T21:18:15.881-05:00Moral Ought Facts are Non-Natural<style type="text/css"> <!--
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<h2 class="subHeader">Introduction</h2>
<br />
<br />
In my <a href="https://youtu.be/ISFyXiyt54s">third Maverick Christian Vlog episode</a> I refer to a scholarly paper which is called <a href="https://www.academia.edu/37192929/A_Folk_Semantics_Argument_for_Moral_Non-Naturalism_Draft_">A Folk Semantics Argument for Moral Non-Naturalism</a>. In this blog entry I’ll provide some of the technical background so that those of us who aren’t analytic philosophers can better understand it.
<br /><br />
Why is it important that morality is non-natural? One reason is that it reveals that there is more to reality beyond the natural, physical world. Another reason is that morality being non-natural makes it so that atheism doesn’t fit in very well with the existence of morality, especially objective morality for reasons I explain in my third vlog episode. In contrast, the existence of an objective and non-natural morality makes perfect sense in a theistic worldview.
<br /><br />
Next I’ll explain some philosophy lingo before explaining the math used in the paper.
<br />
<br />
<h2 class="subHeader">Philosophical Terminology</h2>
<br />
<br />
<em>Moral semantics</em> is about how to define moral terms. In philosophy, the word “folk” refers to colloquial stuff that laypersons use; e.g. “folk psychology” is (an albeit derogatory) term for beliefs about the human mind that ordinary people accept. In the paper, “folk semantics” with respect to morality refers to what most ordinary people mean when they use terms like “morally wrong.”
<br /><br />
A <em>stipulative definition</em> assigns a meaning to a particular word or phrase to be used in a given context (as a philosophy paper). For example, in a philosophy paper one might give a stipulative definition of “fully justified” by saying, “I will say that a belief is <em>fully justified</em> to denote the belief being justified to the point where one can rationally say one knows it to be true.” Stipulative definitions are often used for conveniently assigning a label to some concept and won’t necessarily match the lexical (“dictionary”) definition.
<br /><br />
A <em>hypothetical imperative</em> takes the form of something like, “If you want to do <em>X</em>, you should do <em>Y</em>” and describes what to do as a matter of practical necessity to accomplish some goal. For example, “If you want to do well in school, you ought to study” meaning something like, “As a matter necessity, you need to study to do well in school.” The sort of <em>ought</em> used in hypothetical imperatives is called a <em>hypothetical ought</em>.
<br /><br />
A <em>category mistake</em> (or <em>category error</em>) is attributing a characteristic to something that it can’t possibly have because it’s not of the right category; e.g. saying that the number six has mass or volume, when the category of abstract objects is such that they can’t have mass or volume.
<br />
<br />
<h2 class="subHeader">Set Theory</h2>
<br />
<br />
<h3 class="subHeader">Some Basics</h3>
<br />
<br />
Sets are collections of stuff where order and duplicates are irrelevant. For example, the followings sets are all identical.
<br /><br />
{1, 2, 3, 4}<br />
{1, 2, 2, 3, 4}<br />
{4, 3, 2, 1}
<br /><br />
There’s the empty set, sometimes symbolized as {} which is a set that has no members.
<br /><br />
To illustrate some set operations, suppose our “universe” consists entirely of natural numbers 1 through 9. Now let A, B, and C be the following:
<blockquote>
A = {1, 5, 9}<br />
B = {1, 5, 7, 8}<br />
C = {2, 3}
</blockquote>
<table cellpadding="3" border="1" cellspacing="0" class="inline">
<tr><th>Symbol</th><th>Example</th><th>Explanation</th></tr>
<tr><td style="white-space: nowrap;">∈ <br />(element of)</td><td style="white-space: nowrap;">1 ∈ A</td><td>For any set S, x ∈ S means that x is an element of S.</td></tr>
<tr><td>∉<br />(not an element of)</td><td style="white-space: nowrap;">1 ∉ C</td><td>For any set S, x ∉ S means that x is not an element of S.</td></tr>
<tr><td>∩<br />(intersection)</td><td style="white-space: nowrap;"> A ∩ B = {1, 5}</td><td>Given sets S and T, S ∩ T contains all the elements x such that x ∈ S and x ∈ T.</td></tr>
<tr><td>∪<br />(union)</td><td style="white-space: nowrap;">A ∪ B = {1, 5, 7, 8, 9}</td><td>Given sets S and T, S ∪ T contains all the elements x such that x ∈ S or x ∈ T.</td></tr>
<tr><td>⊆<br />(subset)</td><td style="white-space: nowrap;">{1, 5} ⊆ B</td><td>Given sets S and T, S is a subset of T if and only if each member of S is also a member of T.</td></tr>
<tr><td>⊄<br />(not a subset)</td><td style="white-space: nowrap;">{2, 9} ⊄ B</td><td>Given sets S and T, S is not a subset of T if and only if it is not the case that S ⊆ T.</td></tr>
</table>
<br />
<br />
The set “All x such that x > 3” can be symbolized like this:
<br /><br />
{ x | x > 3 }
<br /><br />
The set “All x ∈ A such that x > 3” can be symbolized as:
<br /><br />
{ x ∈ A | x > 3 }
<br /><br />
That set described above would be {5, 9}.
<br />
<br />
<h3 class="subHeader">Relations</h3>
<br />
<br />
Unlike sets were order and duplicates don’t matter, they do matter in <em>tuples</em>. The following are all different from each other:
<blockquote>
(1, 2, 3, 4)<br />
(1, 2, 2, 3, 4)<br />
(4, 3, 2, 1)
</blockquote>
Those who have taken algebra might remember the tuple known as the ordered pair:
<blockquote>
(2, 3)<br />
(11, -3)
</blockquote>
Relations are sets of tuples, with a binary relation being a set of ordered pairs. For example, suppose we have this set:
<blockquote>
{Diana, Steve, Barbara}
</blockquote>
The relation “taller-than” could consist of this set of ordered pairs, where e.g. Diana is taller than Steve.
<blockquote>
{(Diana, Steve), (Steve, Barbara), (Diana, Barbara)}
</blockquote>
If we symbolize our taller relation as T then we could say that (Diana, Steve) ∈ T.
<br /><br />
Relations between different sets are also possible. Suppose we have these two sets:
<blockquote>
L = {Reed, Scott, Clark}<br />
F = {Sue, Jean, Lois}
</blockquote>
And the “is-husband-of” relation is a relation from set L to set F; e.g. Reed is the husband of Sue:
<blockquote>
H = {(Reed, Sue), (Scott, Jean), (Cark, Lois)}
</blockquote>
An <em>inverse</em> of a binary relation R goes like this:
<blockquote>
R<span class="sup">-1</span> = {(y, x) | (x, y) ∈ R}
</blockquote>
For example, the inverse of the “is-husband-of” relation would be the “is-wife-of” and be this:
<blockquote>
H<span class="sup">-1</span> = {(Sue, Reed), (Jean, Scott), (Lois, Clark)}
</blockquote>
A relation from set A to set B is a <em>function</em> if each member of A is paired off with exactly one member of B. The “input” part of a function is the <em>domain</eM> (set A) and the “output” part is called the <em>range</em> (set B). For instance, the “is-husband-of” relation is a function because each member L is paired off with exactly one member of F, with L being the domain and F being the range, whereas an “is-husband-of” relation would not be a function if there were polygamous marriages.
<br /><br />
Suppose relations S and T are the following:
<blockquote>
S = {(1, 2), (10, 11)}<br />
T = {(2, 3), (11, 12)}
</blockquote>
A composition of two relations S and T can be symbolized as T ∘ S, and when the relations are binary, the set of ordered pairs in such a composition goes like this:
<blockquote>
{(x, z) | (x, y) ∈ S and (y, z) ∈ T}
</blockquote>
In our example, T ∘ S would be the following:
<blockquote>
{(1, 3), (10, 12)}
</blockquote>
Suppose relation V is the following:
<blockquote>
V = {(1, 2), (1, 3), (1, 9), (2, 3), (2, 4)}
</blockquote>
Because the relation is binary, V(x, ⋅) is { y | (x, y) ∈ V }
<br /><br />
Examples:
<blockquote>
V(1, ⋅) = {2, 3, 9}<br />
V(2, ⋅) = {3, 4}
</blockquote>
<br />
<br />
<h2 class="subHeader">Formal Logic</h2>
<br />
<br />
<h3 class="subHeader">Deductive Arguments</h3>
<br />
<br />
A deductive argument tries to show that it’s logically impossible (i.e. self-contradictory, like a married bachelor) for the argument to have true premises and a false conclusion, and thus that the conclusion follows from the premises by the rules of logic. If it’s logically impossible for an argument to have true premises and a false conclusion the argument is <em>deductively valid</em> or <em>valid</em>. An example of a deductively valid argument:
<ol>
<li>If it is raining, then my car is wet.</li>
<li>It is raining.</li>
<li>Therefore, my car is wet.</li>
</ol>
The above example uses a famous rule of logic called <em>modus ponens</em> which has this structure:
<ol>
<li>If <b>P</b>, then <b>Q</b>
<li><b>P</b></li>
<li>Therefore, <b>Q</b>.
</ol>
Another famous rule of logic is called <em>modus tollens</em> where “not-Q” means “Q is false.”
<ol>
<li>If <b>P</b>, then <b>Q</b>
<li>Not-<b>Q</b></li>
<li>Therefore, not-<b>P</b>.
</ol>
An argument is <em>deductively invalid</em> or <em>invalid</em> if it is not deductively valid. An example of an invalid argument:
<ol>
<li>If it is raining, then my car is wet.</li>
<li>My car is wet.</li>
<li>Therefore, it is raining.</li>
</ol>
In logic lingo, a deductively valid argument with all its premises being true is called a <em>sound</em> argument. And since a valid argument having true premises guarantees the truth of its conclusion, a sound deductive argument has a true conclusion.
<br />
<br />
<h3 class="subHeader">Basic Symbols and Rules of Inference</h3>
<br />
<br />
Here’s a summary of how the connectives in propositional work where <em>p</em> and <em>q</em> represent <em>propositions</em> (claims that are either true or false):
<br />
<br />
<table cellpadding="0" cellspacing="0" border="3" align="center" class="standardLogic">
<tr><th>Type of<br />connective</th><th>English</th><th><span style="white-space: nowrap;">Symbolic</span><br />Logic</th><th>When it’s true/false</th></tr>
<tr><td style="white-space: nowrap;">Conjunction</td><td><b>p</b> and <b>q</b></td><td>p ∧ q</td><td>True if both are true; otherwise false</td></tr>
<tr><td style="white-space: nowrap;">Disjunction</td><td><b>p</b> or <b>q</b></td><td>p ∨ q</td><td>False if both are false; otherwise true</td></tr>
<tr><td style="white-space: nowrap;">Conditional</td><td>If <b>p</b>, then <b>q</b></td><td>p → q</td><td>False if <em>p</em> is true and <em>q</em> is false; otherwise true</td></tr>
<tr><td style="white-space: nowrap;">Negation</td><td>Not-<b>p</b></td><td>¬p</td><td>True if <em>p</em> is false; false if <em>p</em> is true</td></tr>
</table>
<br />
<br />
As suggested in the above table, the symbols →, ¬, ∨, and ∧ are called <em>connectives</em>. It’s a somewhat misleading name since ¬ doesn’t connect propositions even though the other three connectives do. Still, it’s a popular label a lot of logic textbooks use. While the terminology varies among writers, I’ll call a single letter a <em>simple statement</em> and one more or more simple statements with one or more connectives is called a <em>compound statement</em>. For example, “¬P” and “A ∧ B” are compound statements.
<br /><br />
The type of conditional (<strong>p</strong> → <strong>q</strong>) being used here is called a <em>material conditional</em>. A material conditional is equivalent to “It is not the case that the antecedent (<B>p</B>) is true and the consequent (<B>q</B>) is false,” such that the <em>only</em> way for a material conditional to be false is for it to have a true antecedent with a false consequent. A material conditional might seem like a pretty weak claim (in the sense that it doesn’t claim very much), since the antecedent and consequent don’t even have to be related to each other for a material conditional to be true. Thus, “If there is a married bachelor, then Minnesota is awesome” constitutes a true material conditional since it is not the case that we have a true antecedent (there is a married bachelor) with a false consequent (Minnesota is awesome). But it turns out that a material conditional is enough for <em>modus ponens</em> and <em>modus tollens</em> to be valid rules of inference, since in a true material conditional if the antecedent <em>is</em> true, then the consequent is true as well.
<br /><br />
Speaking of which, here are those rules of inference I’ve already mentioned in symbolic form:
<br />
<br />
<table cellpadding="0" cellspacing="0" border="3" align="center" class="standardLogic">
<tr><th colspan="2"><b><I>modus ponens</I></b></th></tr>
<tr class="line"><td colspan="2"> </td></tr>
<tr>
<th>In English</th>
<th>In Symbolic Logic</th>
</tr>
<tr>
<td>If <b>p</b> then <b>q</b><br>
<b>p</b><br>
<hr />
Therefore, <b>q</b>
</td>
<td>
p → q<br>
p<br>
<hr />
∴ q
</td>
</tr>
</table>
<table cellpadding="0" cellspacing="0" border="3" align="center" class="standardLogic">
<tr><th colspan="2"><b><I>modus tollens</I></b></th></tr>
<tr class="line"><td colspan="2"> </td></tr>
<tr>
<th>In English</th>
<th>In Symbolic Logic</th>
</tr>
<tr>
<td>If <b>p</b> then <b>q</b><br>
Not-<b>q</b><br>
<hr />
Therefore, not-<b>p</b>
</td>
<td>
p → q<br>
¬q<br>
<hr />
∴ ¬p
</td>
</tr>
</table>
<br />
<br />
In the convention I’m using, the lower case letters <em>p, q, r,...z</em> are placeholders for both simple and compound statements. Thus, below is a valid instance of <em>modus tollens</em>.
<ol class="start">
<li>(A ∧ B) → C</li>
<li>¬C</li>
</ol>
<hr />
<ol start="3" style="margin-top: 0em;">
<li>¬(A ∧ B) <span class="logic">1, 2, <I>modus tollens</I></span></li>
</ol>
It’s worth noting that the order of the premises doesn’t matter when using rules of inference. So below is also a valid use of <I>modus tollens</I>.
<ol class="start">
<li>¬C</li>
<li>(A ∧ B) → C</li>
</ol>
<hr />
<ol start="3" style="margin-top: 0em;">
<li>¬(A ∧ B) <span class="logic">1, 2, <I>modus tollens</I></span>
</ol>
Some rules of inference can be used in more than one way. Examples include <em>disjunctive syllogism</em> and <em>simplification</em>.
<br />
<br />
<!-- Disjunctive syllogism -->
<table cellpadding="0" cellspacing="0" border="3" align="center" class="standardLogic">
<tr><th colspan="2"><b>Disjunctive Syllogism</b></th></tr>
<tr class="line"><td colspan="2"> </td></tr>
<tr>
<th>In English</th>
<th>In Symbolic Logic</th>
</tr>
<tr>
<td><b>p</b> or <b>q</b><br>
Not-<b>p</b><br>
<hr />
Therefore, <b>q</b></td>
<td>p ∨ q<br>
¬p<br />
<hr />
∴ q</td>
</tr>
<tr>
<td><b>p</b> or <b>q</b><br>
Not-<b>q</b><br>
<hr />
Therefore, <b>p</b></td>
<td>p ∨ q<br>
¬q<br>
<hr />
∴ p</td>
</tr>
</table>
<!-- simplification -->
<table cellpadding="0" cellspacing="0" border="3" align="center" class="standardLogic">
<tr><th colspan="2"><b>simplification</b></th></tr>
<tr class="line"><td colspan="2"> </td></tr>
<tr>
<th>In English</th>
<th>In Symbolic Logic</th>
</tr>
<tr>
<td><b>p</b> and <b>q</b><br>
<hr />
Therefore, <b>p</b></td>
<td>p ∧ q<br>
<hr />
∴ p</td>
</tr>
<tr>
<td><b>p</b> and <b>q</b><br>
<hr />
Therefore, <b>q</b></td>
<td>p ∧ q<br>
<hr />
∴ q</td>
</tr>
</table>
<br /><br />
Before moving forward, I’ll introduce a quick example of how to use some rules of inference. Suppose we wanted to get C from premises 1 and 2 below:
<ol style="margin-bottom: 0em;">
<li>A ∨ (B ∧ C)</li>
<li>¬A</li>
</ol>
<hr />
<ol start=3 style="margin-top: 0em;">
<li>B ∧ C <span class="logic">1, 2, disjunctive syllogism</span></li>
<li>C <span class="logic">3, simplification</span></li>
</ol>
Not too hard, right? After learning the above rules of inference, you might even have mentally “seen” that <em>C</em> followed from premises 1 and 2 above. Hopefully you are familiar enough with the symbols by now for me to remove the training wheels of english translation. Some more rules of inference:
<br /><br />
<!-- Conjunction -->
<table cellpadding="0" cellspacing="0" border="3" align="center" class="standardLogic">
<tr><th><b>conjunction</b></th></tr>
<tr class="line"><td> </td></tr>
<tr>
<td>
p<br />
q<br />
<hr />
∴ p ∧ q
</td>
</tr>
</table>
<!-- hypothetical syllogism -->
<table cellpadding="0" cellspacing="0" border="3" align="center" class="standardLogic">
<tr><th><b>hypothetical syllogism</b></th></tr>
<tr class="line"><td> </td></tr>
<tr>
<td>
p → q<br />
q → r<br />
<hr />
∴ p → r
</td>
</tr>
</table>
<br />
<br />
<h3 class="subHeader">Equivalences</h3>
<br />
<br />
In propositional logic, two statements are <em>logically equivalent</em> whenever the connectives make it so that they’re always the same truth-value (i.e. both true or both false). Some rules of propositional logic are themselves equivalences, such as these:
<br />
<br />
<table cellpadding="0" cellspacing="0" border="3" align="center" class="standardLogic">
<tr><th>equivalence</th><th>name of equivalence</th></tr>
<tr class="line"><td colspan="2"> </td></tr>
<tr><td>p ⇔ ¬¬p</td><td>double negation</td></tr>
<tr class="line"><td colspan="2"> </td></tr>
<tr><td>p → q ⇔ ¬q → ¬p</td><td>transposition (also called contraposition)</td></tr>
<tr class="line"><td colspan="2"> </td></tr>
<tr><td>¬(p ∧ q) ⇔ ¬p ∨ ¬q</td><td rowspan=2>De Morgan’s laws</td></tr>
<tr><td>¬(p ∨ q) ⇔ ¬p ∧ ¬q</td></tr>
</table>
<br />
<br />
Equivalence rules can be used to replace stuff “inline” whenever their equivalence appears. As an example of how to use some equivalences, suppose we want to prove ¬C ∨ ¬D from premises 1 and 2 below:
<ol style="margin-bottom: 0em;">
<li>A </li>
<li>(C ∧ D) → ¬A</li>
</ol>
<hr />
<ol start="3" style="margin-top: 0em;">
<li>¬¬A → ¬(C ∧ D) <span class="logic">2, transposition</span></li>
<li>A → ¬(C ∧ D) <span class="logic">3, double negation</span></li>
<li>¬(C ∧ D) <span class="logic"> 1, 4 <I>modus ponens</I></span></li>
<li>¬C ∨ ¬D <span class="logic">5, De Morgan’s laws</span></li>
</ol>
<!-- Conditional Proofs --->
<h3 class="subHeader">Conditional Proofs</h3>
<br />
<br />
The conditional is symbolized as p → q where <em>p</em> is called the <em>antecedent</em> and <em>q</em> is called the <em>consequent</em>. The <em>conditional proof</em> aims to prove that a conditional is true, with the antecedent of the conditional being the <em>conditional proof assumption</em> which is often used to help show that if the antecedent is true then the consequent is true also. The structure of a conditional proof takes the following form below:
<br />
<br />
<!-- Conditional Proof -->
<table cellpadding="0" cellspacing="0" border="3" align="center" class="standardLogic">
<tr><th><b>conditional proof</b></th></tr>
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<tr><td>
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<tr><td style="vertical-align: bottom;">b)</td><td>
<div class="middle">
...<br />
q
</div></td></tr>
<tr><td>c) </td><td>p → q <span class="logic">a-b, conditional proof</span></td></tr>
</table>
</td></tr>
</table>
<br />
<br />
For example, suppose we want to prove A → (B ∧ C) from premises 1 and 2 below:
<ol class="start">
<li>A → B</li>
<li>A → C</li>
</ol>
<hr />
<ol class="middle" start="3">
<li>A <span class="logic">conditional proof assumption</span></li>
</ol>
<ol class="middle">
<div class="middle">
<ol class="middle" start="4">
<li>B <span class="logic">1, 3, <I>modus ponens</I></span></li>
<li>C <span class="logic">2, 3, <I>modus ponens</I></span></li>
<li>B ∧ C <span class="logic">4, 5, conjunction</span></li>
</ol>
</div>
</ol>
<ol class="end" start="7">
<li>A → (B ∧ C) <span class="logic">3-6, conditional proof</span></li>
</ol>
Notice that the validity of a conditional proof does not rely on the conditional proof assumption actually being true; rather it relies on the fact that <em>if it is true</em> then it properly leads to the consequent. Nothing in the proof above, for example, relies an <em>A</em> actually being true.
<br />
<br />
<h3 class="subHeader">Predicate Logic</h3>
<br />
<br />
To give an example of predicate logic, consider the following symbolization key:
<br />
<br />
<table class="inline" cellpadding="1" cellspacing="0" border="0">
<tr class="separate" style="background-color: #ddddff"><td class="equals">B(x)</td><td class="equals"> </td><td class="equals">=</td><td class="equals"> </td><td style="text-align: left;"><em>x</em> is a <em>B</em>achelor.</td></tr>
<tr class="separate" style="background-color: #ddddff"><td class="equals">U(x)</td><td class="equals"> </td><td class="equals">=</td><td class="equals"> </td><td style="text-align: left;"><em>x</em> is <em>U</em>nmarried.</td></tr>
</table>
<br />
<br />
The letters <em>B</em> and <em>M</em> in these examples are <em>predicates</em> which say something about the element they are <em>predicating</em>. Sometimes parentheses aren’t used; e.g. Bx being used to mean “<em>x</em> is a bachelor.” The symbol; ∀ means “For All” or “For Any” such that the following basically means “All bachelors are unmarried:”
<br />
<br />
<table cellpadding="0" cellspacing="0" border="3" align="center" class="standardLogic">
<tr><th colspan="2"><b>universal quantification</b></th></tr>
<tr class="line"><td colspan="2"> </td></tr>
<tr>
<th>In English</th>
<th>In Symbolic Logic</th>
</tr>
<tr>
<td>For any <strong>x</strong>: [if <strong>x</strong> is <strong>B</strong>, then <strong>x</strong> is <strong>U</strong>]
</td>
<td>
∀x[B(x) → U(x)]
</td>
</tr>
</table>
<br />
<br />
The <em>domain of discourse</em> is the set of things we’re talking about when we make statements like ∀x[B(x) → U(x)], such that the “∀<em>x</em>” means “For any <em>x</em> in the domain of discourse (i.e. set of things we’re talking about here).” We can let an individual lowercase letter signify a specific element in our domain of discourse; e.g. <em>c</em> can signify a guy named “Charles” and we can let <em>B(c)</em> to signify <em>c</em> is <em>B</em> (i.e. Charles is a bachelor).
<br /><br />
A rule of predicate logic called <em>Universal Instantiation</em> allows us to instantiate a universal quantification (a ∀<em>x</em>[...] statement) for a specific individual, like so:
<ol class="start">
<li>∀x[B(x) → U(x)]</li>
<li>B(c)</li>
</ol>
<hr />
<ol class="end" start="8">
<li>B(c) → U(c) <span class="logic">1, universal instantiation</span></li>
<li>U(c) <span class="logic">2, 3, <em>modus ponens</em></span></li>
</ol>
There’s a somewhat complicated rule called <em>universal generalization</em> (also called <em>universal introduction</em>) to get a universal quantification statement. Roughly, the idea is that if a statement contains some variable that is a placeholder for anything in the domain of discourse, we can generalize this to get “For any <em>x</em>, such-and-such holds true.” The universal generalization rule is fairly complicated (you can only use it under certain specified conditions) but the gist of universal generalization should be enough to follow along this proof.
<ol class="start">
<li>∀x[A(x) → B(x)]</li>
<li>∀x[B(x) → C(x)]</li>
</ol>
<hr />
<ol class="end" start="3">
<li>A(t) → B(t) <span class="logic">1, universal instantiation</span></li>
<li>B(t) → C(t) <span class="logic">2, universal instantiation</span></li>
<li>A(t) → C(t) <span class="logic">3, 4, hypothetical syllogism</span></li>
<li>∀x[A(x) → C(x)] <span class="logic">5, universal generalization</span></li>
</ol>
And that should be all the technical stuff you need to know to read <a href="https://www.academia.edu/37192929/A_Folk_Semantics_Argument_for_Moral_Non-Naturalism_Draft_">A Folk Semantics Argument for Moral Non-Naturalism</a>. You still might not find it an easy read if you’re not used to analytic philosophy, but at least you have the background knowledge even if applying it is a bit tricky.Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-52610385395659612992018-07-01T19:19:00.002-05:002018-07-09T22:06:25.761-05:00Can Objective Morality be Subjectively Perceived?
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<h3 class="subHeader">The Objection</h3>
<br />
<br />
One objection I’ve seen to objective morality on the internet, in one form or another, goes something like this: we use subjectively experienced intuition to believe in objective morality. This, somehow, is supposed to argue against objective morality or at least our justification for it. If belief in objective morality relies on subjective intuition, how can morality be objective if it’s <em>subjectively</em> perceived? Doesn’t the fact that supposedly objective morality is subjectively perceived mean we don’t really have any justification for accepting moral objectivism?
<br /><br />
The answer to both questions is, “No.”
<br/>
<br />
<h3 class="subHeader">Responses</h3>
<br />
<br />
First, note that in practice, <em>everything</em> we know about is subjectively perceived; our own perceptions (intuitive and sensory) are all we have to go on. Yes, we can ask other people to see if they share our experiences, but the perception that there even <em>are</em> other people relies on, you guessed it, our own subjective experiences. At the end of the day, subjective experiences, i.e. the experiences of the self, are used to justify all of our beliefs. The fact that something is subjectively perceived thus doesn’t imply that it isn’t objectively real; e.g. my subjective experiences can report a tree existing with that tree being objectively real.
<br /><br />
Second, some perceived truth being believed on the basis of subjectively experienced intuition doesn’t imply that the truth isn’t objective, even when people have disagreeing intuitions. If for example someone’s logic intuition told them there could be a married bachelor despite the self-contradiction, whereas your rational intuition says such a self-contradictory thing cannot exist, you’re still justified in believing that <em>There can’t be any married bachelors</em> is objectively true.
<br /><br />
Or to use an example perhaps closer to real life, suppose a creationist and evolutionist look at the same data, but have differing intuitive perceptions about where that evidence points (the evolutionist thinks it’s evidence for evolution, the creationist disagrees). Does that mean there’s no objective fact of the matter about whether the data is evidence for evolution? Clearly not. Disagreeing, subjectively experienced intuitions do not imply that the intuitively perceived truths are not objective, nor do such disagreeing intuitions imply that we can’t be justified in believing them to be objectively true.
<br/>
<br />
<h3 class="subHeader">How?</h3>
<br />
<br />
So how do confused objections like, “Morality is subjectively perceived, so it’s not objective” arise? Perhaps one reason for the confusion is a conflation between <em>moral epistemology</em> (how moral truths are known) with <em>moral ontology</em> (the reality of morality; e.g. whether it’s objective or subjective). The moral epistemology may, in one sense, be subjective. But it doesn’t follow that the moral truths themselves are not objective.
Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-77156372875162184082018-06-15T21:37:00.008-05:002023-05-12T21:19:38.528-05:00A Quick Argument for Objective Morality
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Here’s a quick deductive argument for moral objectivism, where by moral truths being “objective” I mean that they hold independently of human opinion.
<br />
<br />
<h3 class="subHeader">The Argument</h3>
<ol>
<li>It is morally wrong for a man to torture an infant just for fun.</li>
<li>It would remain morally wrong to torture an infant just for fun even if a baby torturer thought otherwise and killed everyone who didn’t agree with him.</li>
<li>If (1) and (2) are true, then objective morality exists.</li>
<li>Therefore, objective morality exists.</li>
</ol>
The justification for premise (3) is that once we accept the truth of (1) and (2) it leads to moral objectivism via this step-by-step reasoning:
<ol type="a">
<li>In the thought experiment of premise (2), something remains morally wrong even when all human opinion thinks otherwise (since the torturer killed off everyone who doesn’t agree with him);</li>
<li>in which case the moral truth “It’s morally wrong for a man to torture infants just for fun” would be holding despite human opinion;</li>
<li>in which case it seems we have an example of an objective moral truth (i.e., holding true independently of human opinion) thereby giving us objective morality.</li>
</ol>
If (a), (b), and (c) are all true as they seem to be, then we have an example of an objective moral truth. (For those who disagree, do you disagree with (a), (b), or (c)? If so, which one(s)?)
<br /><br />
You could deny premise (1). Do you believe there’s nothing morally wrong with torturing infants just for fun?
<br /><br />
You could bite the bullet and deny premise (2), say it’s not morally wrong for a man to torture infants just for fun as long as he believes otherwise and kills everyone who doesn’t with him. Do you think that’s a reasonable belief?
<br />
<br />
<h3 class="subHeader">Why I Like It</h3>
<br />
<br />
I think this is a good deductive argument for moral objectivism because it quickly reveals how intellectually pricey it is to deny objective morality. It’s not reasonable to believe that there’s nothing morally wrong with torturing infants just for fun, so premise (1) is not plausibly false. Likewise, it’s not reasonable to believe that it’s not morally wrong for a man to torture infants just for fun as long as he believes otherwise and kills everyone who doesn’t agree with him; so premise (2) is not plausibly false.
<br /><br />
This forces the disbeliever of moral objectivism in a very intellectually uncomfortable position, especially in a debate, because even if the disbeliever is willing to bite a bullet and reject a premise, most people won’t find the disbeliever’s premise rejection tenable.Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-22669471591810729782018-05-09T22:22:00.002-05:002018-05-16T21:52:34.474-05:00Fine-Tuning: Barnes vs Malpass (p. 3)
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<h3 class="subHeader">An Alleged Inconsistency</h3>
<br />
<br />
It seems Malpass’s reasoning was that a timeless being cannot change, and a timeless being causing something requires that timeless being change. Malpass, unfortunately, offered no argument for why a timeless being causing something would require that timeless being to change. To unpack why Malpass’s claims aren’t necessarily correct, a bit of philosophical background will be helpful.
<br /><br />
If <em>A</em> depends upon <em>B</em> for its existence then <em>A</em> is said to be <em>ontologically dependent</em> on <em>B</em>. Many theists believe the physical universe is ontologically dependent on God.
<br /><br />
There are two major theories of time (though hybrid scenarios have been proposed). On one view of time, called the <em>B-theory</em> of time (also called <em>tenseless</em> theory of time or the <em>static</em> view of time), all moments in time are equally real. This contrasts with the <em>A-theory</em> of time (also called the <em>tensed</em> theory of time or <em>dynamic</em> view of time) in which only the present is real, and things go out of existence when they existed in the past but no longer do (similarly, things can also come into existence as time progresses). One way to think about it is that the B-theory is more permitting of time travel than the A-theory; on the A-theory you can’t time travel to the future because the future hasn’t been made yet, and you can’t go back into the past because the past doesn’t exist anymore; only the present moment is real. On the B-theory of time however, the past, present, and future are all equally real.
<br /><br />
One view of God being timeless is that the B-theory of time is true and God transcends space and time, seeing all of the past, present, and future at once. For a timeless entity, there is no change; only being and nonbeing. Since God is outside time, he himself experiences no change and (at least in a metaphorical sense) everything happens “all at once” to him (God’s thoughts, intentions, beliefs, experiences, powers, etc. do not have phases of existence ordered by the relations “earlier than” and “later than”). God can causally interact with the physical space-time of our universe, including creating the universe, but he is not subsumed by it. Call a theist who accepts this view a <em>timeless theist</em>.
<br /><br />
If there is a contradiction for a timeless God creating the universe, one idea is to try to justify this idea using <em>conceptual analysis</em> (basically, breaking up a concept into simpler, constituent parts). In philosophy, one can use conceptual analysis to discuss philosophical issues just as I did when I argued that <a href="http://maverickchristian.blogspot.com/2018/03/mental-states-causally-irrelevant-naturalism.html">mental states are causally irrelevant on naturalism</a> with the help of symbolic logic. Could Malpass via conceptual analysis of “timeless” and “change” etc. derive a self-contradiction with such a deity interacting with the physical space-time of our universe in this manner? Maybe, but there’s a catch.
<br /><br />
In my blog article where I argued that <a href="http://maverickchristian.blogspot.com/2018/03/mental-states-causally-irrelevant-naturalism.html">mental states are causally irrelevant on naturalism</a> I used conceptual analysis of what I meant by mental states being causally irrelevant on naturalism and used symbolic logic to prove the validity of an argument (such that it’s self-contradictory to have true premises and a false conclusion) for the conclusion that mental states are causally irrelevant if naturalism were true. And yet the answer to whether mental states are causally irrelevant on naturalism is actually something like, “In one sense mental states are causally irrelevant, but in another sense that’s not necessarily true.” The catch is that my analysis of “mental states are causally irrelevant on naturalism” won’t necessarily match how a naturalist might understand the phrase. Similarly, it might be that an objector’s analysis of “timeless” and “change” won’t quite match what a theist has in mind.
<br /><br />
To illustrate, an argument against a timeless God causing things that someone could make is to define “timeless” in a sense similar to that provided earlier (not having phases of existence ordered by relations “earlier than” and “later than”) while also adding that a timeless being cannot change, where “an entity changes” is defined to mean something like, “an entity creating something at a time <em>t</em> that did not exist in a previous time.” On these definitions of “timeless” and “change,” a timeless entity (one who cannot change) cannot create anything in physical spacetime because “change” is defined in such a way that a timeless being cannot create anything in physical spacetime that did not exist before.
<br /><br />
The problem with this objection is that these definitions of a “timeless being” and “an entity changes” don’t seem to be what a timeless theist believes when she says that a timeless God cannot change. A theist might instead define “timeless” as “not having phases of existence related to each other by earlier and later.”<a href="#_endnote_2018_05_09_3" name="_cite_2018_05_09_3">[3]</a> A theist might define an entity “changing” in much the same way: different phases of existence related to each other by earlier and later, with there also being some difference between the two phases. This is of course different from the idiosyncratic definition of the earlier example (“an entity changes” is defined to mean “an entity creating something at a time <em>t</em> that did not exist in a previous time”).
<br /><br />
Consider what would happen if a timeless God interacted with the physical spacetime of the universe on a B-theory of time, <em>ceteris paribus</em>. Unlike temporal beings who have different intentions, experiences etc. at different times, everything would be happening to God “all at once” in terms of beliefs, thoughts, and experiences vis-à-vis physical spacetime. From God’s perspective, multiple instances of causally interacting with the universe at different times would be analogous to having multiple fingers simultaneously submerged in different places in a flowing creek; and instead of having different experiences at different times, God would experience the universe as a whole just as an animator can see all the frames of a short cartoon all at once. Just as an animator can causally affect each frame of the animation without being fully <em>in</em> the animation, God would causally interact with physical spacetime without being wholly subsumed by it. On this scenario, God and his thoughts, intentions, beliefs, experiences, powers, etc. would to him exist “all at once” and not have phases of existence related to each other by earlier and later. God in this sense would still be timeless even if he causally interacts with physical spacetime at different, multiple points. The instances where God <em>causes</em> things to happen might be considered a sort of “change” (in the sense that <em>those</em> instances are related to each other by earlier and later) but God himself would not change (his beliefs, intentions, experiences etc. still happen “all at once” to him). Even if this conception of God and the universe is false, it doesn’t appear to be self-contradictory.
<br /><br />
Another view of God and eternity is that God is timeless <em>sans</em> the universe, and that the A-theory of time is correct. God creates the universe (and physical spacetime itself) at time <em>t</em><span class="sub">0</span> and enters into time at <em>t</em><span class="sub">0</span>, but God did not exist before <em>t</em><span class="sub">0</span> since there was no “before” time <em>t</em><span class="sub">0</span>. This can get pretty tricky to wrap one’s head around but one way to look at it is this: if God did not have the intention to create universe, God would have existed eternally in a timeless state with no change. But since God did have the intention to create the universe (I’m using terms like “did have” for lack of a better terminology; <em>sans</em> the universe God had this intention timelessly and there was no prior time in which he did not have it), God did so at <em>t</em><span class="sub">0</span>. God is <em>ontologically</em> prior to the universe but not <em>temporally</em> prior to the universe at <em>t</em><span class="sub">0</span>, since there was nothing <em>temporally</em> prior to <em>t</em><span class="sub">0</span>. For what it’s worth, this is the view of God creating the universe that I and a number of other theists adhere to.
<br /><br />
This view of God might also be false, but again it’s hard to see how it’s self-contradictory. If Malpass wishes to argue that it is, I would recommend to him an analytical approach:
<ol>
<li>Giving an analysis of “timeless” what sort of “change” he is talking about;
<li>why a Creator who is timeless <em>sans</em> creation would require it; and</li>
<li>how exactly this generates an inconsistency in the scenario I described.</li>
</ol>
Unless and until he does that (or provides some other sufficient explanation), I think we have reason to be skeptical that a <em>bona fide</em> contradiction exists here.
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<a name="_endnote_2018_05_09_3" href="#_cite_2018_05_09_3">[3]</a> Christian philosopher of time William Lane Craig defines God being “timeless” in much the same way.
<br /><br />
Craig, William Lane; <em>Time and Eternity: Exploring God’s Relationship To Time</em> (Illinois: Wheaton, 2001)
Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-69015580173662946382018-05-09T22:21:00.001-05:002018-05-16T22:34:51.771-05:00Fine-Tuning: Barnes vs Malpass (p. 2)
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<a href="http://maverickchristian.blogspot.com/2018/05/fine-tuning-barnes-vs-malpass.html">Fine-Tuning: Barnes vs Malpass</a></td></tr>
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<h3 class="subHeader">The Eye</h3>
<br />
<br />
Malpass notes that we don’t accept a design inference for the eye; people once thought the eye was designed but now we know it’s the product of evolution; so couldn’t the same thing apply for cosmic fine-tuning (<a href="https://youtu.be/MXzM_tBPm-0?t=1h4m54s">1:04:54</a> to 1:07:51)? The implicit question seems to be, since we were wrong about the design inference about the eye, shouldn’t we also doubt the design inference of the universe?
<br /><br />
Although Malpass doesn’t explicitly make this argument, one could object that since we were wrong about the eye being designed, shouldn’t we doubt the design inference for cosmic fine-tuning? I think this sort of reasoning proves too much. Consider the following conversation between persons <em>A</em> and <em>B</em>:
<blockquote>
<em>A</em>: I think Stonehenge was designed.
<br /><br />
<em>B</em>: We should be skeptical of that design inference to the point of not accepting it.
<br /><br />
<em>A</em>: Why?
<br /><br />
<em>B</em>: There are some things that we thought were designed but actually weren’t, like the eye. Because our design inferences are so fallible, we shouldn’t accept a design inference for Stonehenge. Perhaps, like the eye, we will discover some way for natural processes to create it.
</blockquote>
The reason we don’t find this sort of argument convincing is because not all design inferences are equal. The grounds for thinking the eye was designed is different from that of Stonehenge, the Rosetta Stone, and various other artifacts. Despite claiming that the design inferences of the eye and cosmic fine-tuning are “extremely similar” (<a href="https://youtu.be/MXzM_tBPm-0?t=1h6m33s">1:06:33</a> to 1:06:36) there are some pretty stark differences (indeed, the two inferences aren’t even in the same branch of science). Unlike the case of the eye, the case for design for cosmic fine-tuning is based on hard numbers and rigorously defined models of physics. The scientific case for design in cosmic fine-tuning seems much stronger than the case for the eye. It isn’t clear how the two inferences are similar enough in a way where we should doubt a design inference for fine-tuning.
<br /><br />
Barnes points out that, if cosmic fine-tuning is the result of design (<a href="https://youtu.be/MXzM_tBPm-0?t=1h7m52s">1:07:52</a> to 1:09:22) the eye <em>not</em> being designed isn’t necessarily true (though it would be less direct). As an analogy, suppose a watch came from a watch factory; the watch itself was not directly designed but the watch factory was. Another objection he makes is that the physics of the universe is basically where naturalism “ends,” asking “What would be the case….” while staring at the fundamental laws of the universe.
<br /><br />
It’s still possible a non-design hypothesis could explain fine-tuning sometime in the future, just as it’s possible that a non-design hypothesis could someday explain Stonehenge. There’s also an outside chance that we are mistaken about fine-tuning as Luke Barnes concedes, since we’ve already been mistaken about one instance of fine-tuning (albeit the example Barnes offers was made on weaker grounds, done intuitively instead of on models like various other fine-tuning instances; see <a href="https://youtu.be/MXzM_tBPm-0?t=1h7m52s">1:15:53</a> to 1:17:20), though the instances of cosmic fine-tuning made on fairly strong grounds are quite numerous it seems relatively unlikely they will all be overturned.
<br /><br />
At any case, pointing out fallibility of human design inferences clearly seems insufficient, as does offering promissory notes of a future explanation. Claiming that the design inference for cosmic fine-tuning is similar to the design inference for the eye in a way that should make us doubt the design inference for fine-tuning isn’t terribly convincing, and indeed almost seems like an act of desperation if one doesn’t go into sufficient detail.
<br />
<br />
<h3 class="subHeader">The Multiverse Hypothesis</h3>
<br />
<br />
By my lights, the best bet for the atheist to avoid a design inference is a multiverse explanation in which there are so many universes with varying constants and quantities it’s likely that at least one of them would be life-permitting. This is one of the most popular responses for atheists to avoid a design inference among those who accept cosmic fine-tuning. It is, for example, the response atheist physicists Stephen Hawking and Leonard Mlodinow use in their book <em>The Grand Design</em>.<a href="#_endnote_2018_05_09_2" name="_cite_2018_05_09_2">[2]</a> For a multiverse to satisfactorily account for a life-permitting universe despite fine-tuning there are four desiderata:
<ol>
<li><strong>Varying constants and quantities.</strong> Obviously, the multiverse should have varying parameters across universes.</li>
<li><strong>Avoid the Boltzmann brain problem.</strong> The probability of a life-permitting universe (more specifically, one with intelligent interactive life) is so incredibly small that it’s far more likely for a universe with randomly-generated parameters to contain a single brain that briefly emerges from random fluctuations and has conscious experiences, such that on average there’d be far more Boltzmann brains than regular observers. On a multiverse hypothesis with this Boltzmann brain problem (and many such hypotheses do have this problem) it’s overwhelmingly more likely we’d be observing a different reality.</li>
<li><strong>Not require fine-tuning.</strong> If whatever mechanism generates a World Ensemble itself requires fine-tuning, this would merely push the problem back a step instead of solving it.</li>
<li><strong>Independent evidence for it.</strong> To illustrate why this is needed, imagine a scenario in which we switch the fine-tuning from intelligent interactive physical life to a meteor shower text on the moon that read, “Yes, there is a cosmic designer; I fine-tuned certain parameters so that this message would appear.” Suppose we discover that yes indeed, if certain initial parameters of the early universe were altered even slightly, no meteor shower text would appear. A sufficient multiverse hypothesis (with varying parameters etc.) would explain the meteor shower text, but would be severely ad hoc if there were no independent evidence for it. Design would be the best explanation.</li>
</ol>
It’s difficult to find a multiverse hypothesis that meets all four desiderata. Barnes specifically focuses on the third criterion, perhaps implicitly thinking of the fourth criterion if only to some limited degree (thinking only of those multiverse hypotheses that fit in with known science) at around <a href="https://youtu.be/MXzM_tBPm-0?t=1h21m06s">1:21:06</a> to 1:21:16.
<br />
<br />
<h3 class="subHeader">On the Attack</h3>
<br />
<br />
While Luke Barnes does well for the most part, the one where he faces real difficulty is Malpass gives his objections in <a href="http://www.youtube.com/watch?v=vS0n3YRyyrk&t=1h25m06s">1:25:06</a> to 1:29:48 in which Malpass attacks the idea of an atemporally timeless God creating the universe.
<br /><br />
Malpass asserts that a mind is necessarily a linear sequence of phenomenological experiences (<a href="https://www.youtube.com/watch?v=MXzM_tBPm-0&t=1h27m17s">1:27:17</a> to 1:27:24), such that a mind outside of time (outside of time there would be no change; only being and non-being) cannot exist. Malpass also claims a timeless being (<a href="https://www.youtube.com/watch?v=MXzM_tBPm-0&t=1h27m53s">1:27:53</a> to 1:29:48) causing something (somehow) requires that being to enter into a temporal relation in a way that makes it not timeless, thereby generating an inconsistency. Barnes didn’t offer much of an objection against this, but I have one.
<br /><br />
My objection isn’t that Malpass gave bad arguments for these claims, but that he gave <em>no</em> arguments for these claims. Malpass gave no argument for his claim that a mind is necessarily a linear sequence of phenomenological experiences. At first I thought his inability to personally conceive of it might be one of his reasons for thinking this (see e.g. <a href="https://www.youtube.com/watch?v=MXzM_tBPm-0&t=1h26m44s">1:26:44</a> to 1:27:46), but from the comments on his YouTube channel this doesn’t appear to be the case, despite sort of acting as if this were a reason to doubt such a timeless being in the debate (see <a href="https://www.youtube.com/watch?v=MXzM_tBPm-0&t=1h29m27s">1:29:27</a> to 1:29:31). Malpass also offered no argument for his claim that a timeless entity causing events requires that entity entering into a temporal relation in a way that makes it not timeless. In my humble opinion, Barnes should have pointed out that Malpass’s claims weren’t justified here.
<br /><br />
Malpass was kind enough to briefly reply to me on one of my YouTube comments on these two matters. I’ll discuss those two claims in more detail next as well as explain why I am skeptical his claims holds water.
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<a name="_endnote_2018_05_09_2" href="#_cite_2018_05_09_2">[2]</a> Hawking, Stephen; Mlodinow, Loendard. <em>The Grand Design</em> (New York: Random House, Inc., 2010), p. 165.Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-58559882661486135132018-05-09T22:20:00.001-05:002021-12-18T22:16:21.485-06:00Fine-Tuning: Barnes vs Malpass<style type="text/css"> <!--
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Fine-Tuning: Barnes vs Malpass</td></tr>
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<h2 class="subHeader">Introduction</h2>
<br />
<br />
Capturing Christianity hosted a <a href="https://www.youtube.com/watch?v=MXzM_tBPm-0">fine-tuning debate between Luke Barnes and Alex Malpass</a> in 2018-04-21.
<br /><br />
For those who don’t already know, cosmic <em> fine-tuning</em> is the observation that given the physical laws of our universe, certain constants (such as the mass of the electron) and quantities (such as the entropy of the early universe) in our universe are “fine-tuned” in the sense that the life-permitting parameters of the universe are extremely narrow, such that if they were altered even slightly physical life would not have existed. The <em>fine-tuning argument</em> (FTA) argues that the fine-tuning of the universe, i.e. that the universe is life-permitting instead of life-prohibiting in these circumstances, is evidence for theism (sometimes using a relatively modest conclusion; e.g. claiming that design is the best explanation for the universe being life-permitting).
<br /><br />
In my opinion the debate was excellent, and the debate was mostly over philosophy rather than the scientific claims. Perhaps that was to be expected, since the theist arguing on behalf of FTA (Luke Barnes) is a cosmologist and the person arguing against it is a philosopher. I’ll do an overview of the debate, but since the debate is nearly two hours long I’ll obviously have to skip over some details.
<br />
<br />
<h2 class="subHeader">Debate Overview</h2>
<br />
<br />
<h3 class="subHeader">Opening Statements</h3>
<br />
<br />
Luke Barnes gives his opening statement starting at around <a href="https://youtu.be/MXzM_tBPm-0?t=2m58s">2:58</a> explaining fine-tuning and describing some of the science involved, giving examples of fine-tuning such as the masses of electrons and quarks (<a href="https://youtu.be/MXzM_tBPm-0?t=3m15s">3:15</a> to 4:55, where if the parameters fall outside the narrow boundary not only do you not get life you don’t even get <em>chemistry</em>) and the Higgs field (<a href="https://youtu.be/MXzM_tBPm-0?t=6m23s">6:23</a> to 7:12). Barnes says there are good reasons for God to make a morally significant universe (and thus a universe with life), whereas on naturalism the sort of universe we’d expect is a dead one (<a href="https://youtu.be/MXzM_tBPm-0?t=23m09s">23:09</a> to 23:24).
<br /><br />
Alex Malpass’s opening statement starts at around <a href="https://youtu.be/MXzM_tBPm-0?t=25m15s">25:15</a> and he more or less concedes the physics Barnes presents, at least arguendo (<a href="https://youtu.be/MXzM_tBPm-0?t=24m48s">24:48</a> to 26:13) while noting that some disagree with the fine-tuning claim. Best I can tell though, while the scientific opinion isn’t unanimous, the consensus does seem to be that cosmic fine-tuning is real. I find it unlikely that atheist physicists like Stephen Hawking and Leonard Mlodinow would have affirmed fine-tuning if it weren’t real.<a href="#_endnote_2018_05_09_1" name="_cite_2018_05_09_1">[1]</a>
<br /><br />
To his credit as a philosopher, Malpass presents the overall structure of the fine-tuning argument better than Barnes does at around <a href="https://youtu.be/MXzM_tBPm-0?t=30m36s">30:36</a> to 32:00.
<ol>
<li>P(L | N) << 1 (the probability that the universe is <em>L</em>ife-permitting given <em>N</em>aturalism is much less than 1)</li>
<li>~P(L | T) << 1 (it is <em>not</em> the case that the probability that the universe is <em>L</em>ife-permitting given <em>T</em>heism is much less than 1)</li>
<li>If E is more probable on H1 than H2, then E supports H1 over H2.</li>
<li>Therefore, L is evidence for T over N.</li>
</ol>
Something called the <em>odds form of Bayes theorem</em> will be helpful here, the general structure of which is this where e.g. P(T|L) represents the probability of <em>T</em> (theism) given <em>L</em> (the universe is life permitting).
<br /><br />
<table border="0" cellpadding="0" cellspacing="0" class="inline">
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<!-- posterior odds -->
<td style="padding: 2px; text-align: center; border-right: 1px solid black; border-left: 1px solid black; border-bottom: 1px solid black;">posterior<br />odds</td>
<td> </td>
<!-- prior odds -->
<td style="padding: 2px; text-align: center; border-right: 1px solid black; border-left: 1px solid black; border-bottom: 1px solid black;">prior<br />odds</td>
<td> </td>
<!-- likelihood ratio -->
<td style="padding: 2px; text-align: center; border-right: 1px solid black; border-left: 1px solid black; border-bottom: 1px solid black;">likelihood<br />ratio</td>
</tr>
<tr>
<td style="text-align: center;">
<span style="border-right: 1px solid black;"> </span><span style="border-left: 1px solid black;"> </span></td>
<td> </td>
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<span style="border-right: 1px solid black;"> </span><span style="border-left: 1px solid black;"> </span></td>
<td> </td>
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<span style="border-right: 1px solid black;"> </span><span style="border-left: 1px solid black;"> </span></td>
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<!-- Pr(H|E)/Pr(~H|E) -->
<table border="0" cellpadding="1" cellspacing="0" class="fraction">
<tr><td class="top">P(T|L)</td></tr>
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<td>
=
</td>
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<!-- Pr(H)/Pr(~H) -->
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<tr><td class="top">P(T)</td></tr>
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×
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<!-- Pr(E|H)/Pr(E|~H) -->
<table border="0" cellpadding="1" cellspacing="0" class="fraction">
<tr><td class="top">P(L|T)</td></tr>
<tr><td class="bottom">P(L|N)</td></tr>
</table>
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<br /><br />
The theist wants the posterior odds to be greater than the prior odds. Of particular note in this debate will be the values of P(T) and P(N), i.e. the prior probabilities of <em>T</em> and <em>N</em>, respectively. The lower P(T) is, the worse the posterior odds will be. This brings us to what Malpass calls the “Goldilocks hypothesis problem.”
<br />
<br />
<h3 class="subHeader">Goldilocks Hypothesis Problem</h3>
<br />
<br />
One thing that affects the prior probability of a hypothesis (i.e. its probability prior to examining some particular data) is its <em>content</em>, i.e. how much it “claims.” For example, the claim “An animal exists” has less content than “A flatworm with two heads exists,” and so “An animal exists” has greater prior probability; it’s broader and has less content than the claim of a <em>specific type</em> of animal existing. Malpass correctly notes that there’s a trade off between the content of <em>T</em>, it’s prior probability P(T), and P(L|T).
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If <em>T</em> were “An omnipotent God desires <em>L</em>” then P(L|T) will be high but at the cost of P(T) being low. To see why, let <em>R</em> represent “It rained this morning” and let T<span class="sub">R</span> be “An omnipotent God made it rain this morning” in which case P(R|T<span class="sub">R</span>) is high, but P(T<span class="sub">R</span>) will have to be low since we can’t reasonably infer that an omnipotent deity caused it to rain every time it rains. The narrower and more specific <em>T</em> is (thus packing more content in it), the lower the prior probability of <em>T</em>. Conversely, making <em>T</em> broader (having less content), e.g. <em>T</em> meaning nothing more than “an omnipotent being exists” will make P(T) greater; but making <em>T</em> broader in this way will make P(L|T) lower.
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The Goldilocks hypothesis problem is how precisely to define the hypothesis <em>T</em> in such a way to not make it ad hoc (e.g. “An omnipotent God desires <em>L</em>”) which would give it a lower prior probability, but also not make it so broad that P(L|T) isn’t terribly large. Put another way, <em>T</em> can’t have too much content, but it also can’t have too little content. If <em>T</em> is defined too broadly with too little content, Malpass seems to think that there’s a risk that P(L|T) is equal to P(L|N) (<a href="https://youtu.be/MXzM_tBPm-0?t=32m32s">32:32</a> to 33:58). So how to define <em>T</em> in a good way so that P(T) and P(L|T) are both not so small?
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Barnes gives a decent response to this (<a href="https://youtu.be/MXzM_tBPm-0?t=40m38s">40:38</a> to 43:56). God is a free and morally good being who would choose the best actions, and a morally significant universe with free agents would be good. So if <em>T</em> is more or less “standard” theism where God is not only supremely powerful but also good, then <em>T</em> isn’t ad hoc and P(L|T) is not unreasonably low.
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<h3 class="subHeader">The Stalking-Horse Naturalism Hypothesis</h3>
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Malpass explains what he calls the <em>stalking horse naturalism hypothesis</em> at around <a href="https://youtu.be/MXzM_tBPm-0?t=49m33s">49:33</a> to 57:14). If the theist can give God some sort of disposition to make P(L|T) relatively high, couldn’t the naturalist do the same thing? The naturaliast could give naturalism a “mysterious disposition” (<a href="https://youtu.be/MXzM_tBPm-0?t=56m24s">56:24</a> to 1:00:48) to result in a life-permitting universe, call this form of naturalism N<span class="sub">D</span>, such that P(L|N<span class="sub">D</span>) is high.
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The disposition for God to make P(L|T) not that low seems reasonable on theism (God being good), but physical reality having a disposition to result in a life-permitting universe seems rather ad hoc and potentially does little more than push the problem back a step. To illustrate, suppose naturalism’s disposition is some factor <em>x</em> that results in the universe falling into the extremely narrow parameters as specified in a certain mathematical equation. Then it seems that factor <em>x</em> would itself be fine-tuned so that it points to one set of narrow parameters rather than another set of parameters. In other words, naturalism’s disposition would itself have to be finely-tuned to be disposed to have one narrow set of parameters instead of some other set of parameters.
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Barnes gives a somewhat similar objection (<a href="https://youtu.be/MXzM_tBPm-0?t=1h1m10s">1:01:10</a> to 1:03:01). Barnes points out that we’d have to consider P(N<span class="sub">D</span>|N), i.e. the probability of naturalism having that particular disposition given N <em>simpliciter</em>. Naturalism could have had a disposition for a dead universe instead of a life-permitting universe, and when a set of parameters is chosen at random, there are far more dead universes than living universes. The impression I’m given is that Barnes is thinking that P(N<span class="sub">D</span>|N) is pretty comparable to P(L|N).
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<a name="_endnote_2018_05_09_1" href="#_cite_2018_05_09_1">[1]</a> Hawking, Stephen; Mlodinow, Loendard. <em>The Grand Design</em> (New York: Random House, Inc., 2010), pp. 143-144, 157-162.
Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.comtag:blogger.com,1999:blog-4631023797563841554.post-74999548352995975052018-03-25T07:20:00.003-05:002018-11-18T10:12:05.904-06:00Mental States are Causally Irrelevant on Naturalism (p. 5)[This page is no longer valid]Maverick Christianhttp://www.blogger.com/profile/04286456663634536819noreply@blogger.com