Monday, January 6, 2020

Paulogia vs Capturing Christianity's Puddle Analogy Video

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Introduction



Someone named Paul has a YouTube channel called Paulogia and he posted a video titled Puddle Parable and Fine-Tuning (Capturing Christianity Response) responding to a Capturing Christianity’s Puddle Analogy video.

Background



For those who don’t know, fine-tuning 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.

The details of the fine-tuning argument vary upon its application, but the type of argument Cameron gives in his video (at around 1:34 to 1:58) is structured thusly:
  1. The probability that our universe would be life-permitting given naturalism is very, very low.
  2. The probability that our universe would be life-permitting given theism is not very, very low.
  3. Therefore, the fact that our universe is life-permitting provides evidence for Theism over Naturalism.
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 14:20 to 15:26:
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.
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.

Probability Distribution



In 23:20 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 itself 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.

Necessity



In 24:06 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 itself 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.

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 metaphysically 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 metaphysically 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.

Getting the Math Wrong



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;

Pr(A) = The probability of A being true; e.g. Pr(A) = 0.5 means “The probability of A being true is 50%.”
Pr(A|B) = The probability of A being true given that B is true. For example:
Pr(I am wet|It is raining) = 0.8
This means “The probability that I am wet given that it is raining is 80%.”


To recap a bit from my article on Bayes’ theorem, here’s one version of the theorem:

Pr(H|E) = 
Pr(H) × Pr(E|H)
Pr(E)


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 posterior probability of H, and Pr(H) is the prior probability 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.
  • N = Naturalism is true.
  • L = The universe is life-permitting.
  • T = Theism is true.
The structure of Cameron’s fine-tuning argument is basically this:
  1. The P(L|N) is very, very low.
  2. The P(L|T) is not very, very low.
    • (Such that P(L|T) > P(L|N).)
  3. Therefore, L provides evidence for T over N.
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.

At around 27:27 to 27:55 Paulogia parodies Cameron’s argument with this.
  1. The probability that I will roll a 3 on a 6-sided dice under naturalism is is 16.6%.
  2. The probability that I will roll a 3, given an all-powerful god who wants me to roll a 3 is 100%.
  3. [Conclusion:] the fact that I rolled a 3 provides evidence for Theism over Naturalism.
Using these two symbols:
  • G = An all-powerful god who wanted outcome X to occur existed. (The outcome in this case being the die coming up 3.)
  • O = The outcome X occurred.
The structure is this:
  1. The P(O|N) is 16.6%.
  2. The P(O|G) is 100%.
  3. Therefore, O provides evidence for T over N.
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:
  1. The P(O|N) is 16.6%.
  2. The P(O|G) is 100%.
    • Note that P(O|G) > P(O|N).
  3. Therefore, O provides evidence for G over N.
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:

P(G|O)
P(N|O)
 > 
P(G)
P(N)


Now note the following equation, which is sometimes called the odds form of Bayes’ theorem:

P(G|O)
P(N|O)
 = 
P(G)
P(N)
 × 
P(O|G)
P(O|N)


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:

If P(O|G) > P(O|N), then  
P(G|O)
P(N|O)
 > 
P(G)
P(N)


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:

P(T|L)
P(N|L)
 = 
P(T)
P(N)
 × 
P(L|T)
P(L|N)


If P(L|T) > P(L|N), then  
P(T|L)
P(N|L)
 > 
P(T)
P(N)


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 much 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.

Paulogia’s second parody is at round 28:01 to 28:24. In its original form it is this:
  1. The probability that I will win Lotto 6/49 with one ticket under naturalism is 1 in 14 million.
  2. 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%.
  3. [Conclusion:] Me winning Lotto 6/49 provides evidence for Theism over Naturalism.
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:
  1. The P(O|N) is 1 in 14 million.
  2. The P(O|G) is 100%.
  3. Therefore, O provides evidence for T over N.
Unlike Cameron’s actual argument, the conclusion can be false even with the premises true. How? The probability of God wanted specific person S to within the lottery given that God exists seems extremely 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 that 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 28:24 to 28:39 in which premise 1 is him not 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.

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:
  1. The P(O|N) is 1 in 14 million.
  2. The P(O|G) is 100%.
  3. Therefore, O provides evidence for G over N.
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 strong evidence. Why is the evidential force so negligible? Take the lottery case. The prior probability of an all-powerful god who wants me to win Lotto 6/49 is extremely small (since the probability of the deity wanting that 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.

Contrast all that with cosmic fine-tuning, letting F represent The universe is fine-tuned for life. While God wanting a specific random person to win the lottery given that God exists seems extremely small, does the probability of God wanted a universe with life 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.

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:

P(F|T)  = 
1
10,000


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):

P(F|N)  = 
1
1060


P(T)  = 
1
100


P(N)  = 
99
100


Now plug in those above values into the odds form of Bayes’ theorem:

P(T|F)
P(N|F)
 = 
P(T)
P(N)
 × 
P(F|T)
P(F|N)


If you do the math, P(T|F)/P(N|F) comes out overwhelmingly 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:

P(T) = not that low


P(F|T) = not that low


P(F|N) = extremely-super-duper-ultra-mega low


Then the result is that fine-tuning is going to be very strong evidence for theism over naturalism.

Conclusion



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.

16 comments:

  1. Fine tuning argumentJanuary 7, 2020 at 12:19 AM

    Hello,

    Thank you for this post.

    There is also academic paper which shows from mathematical analysis and systematic comparison of different hypothesis, that data strongly prefer theistic explanation.

    It is not just another paper, but very comprehensive, and detailed analysis which has more than 135 references.

    Here's direct link to academic paper:

    https://repository.hkbu.edu.hk/cgi/viewcontent.cgi?article=1447&context=etd_oa

    ReplyDelete
  2. Contrast all that with cosmic fine-tuning, letting F represent The universe is fine-tuned for atheists to live. Does the probability of "Zeus wanted a universe with atheists" given that Zeus exists, seem extremely small? It does not.

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    Replies
    1. Fine tuning argumentJanuary 7, 2020 at 2:03 AM

      You need to replace Zeus with designer and everything is fine.

      "Designer wanted a universe with atheists" given that designer exists. It doesn't small, as argument shows some types of being that is reason for universe should be there.

      Delete
    2. Well first of all, Zeus is A bad example because he did not create the universe, he is from this universe. However, I see what you mean. The problem is that we don’t say that the probability that the Christian god would create humans is not very vey low. We can’t be that specific. First of all, everything the fine tuning argument is saying is that there most likely exists a designer. Nothing more or less. Also, we are claiming that this designer made life possible nothing more or less. But your claiming Zeus made atheists, well him making humans and specifically atheist is by itself much more implausible than a designer making life possible.

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  3. This comment has been removed by the author.

    ReplyDelete
  4. "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."

    Yes, this is a good point that I noted as well whilst listening to both videos. In fact Paulogia almost managed to make it when he was arguing that P(F|N) is possibly 1/infinity. But it obviously escaped his notice that a probability can be expressed as, but is not the same as, a fraction, and so if P(F|N) = 1/infinity, then, given an infinite number of trials, P(F|N) = 1.

    However, it does not surprise me that Paulogia missed this point. I have listened to a couple of his videos and I don't think he is a very competent atheist apologist. More heat than light.

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  5. In the equation following the sentence, "Now note the following equation, which is sometimes called the odds form of Bayes’ theorem", should the left-hand-side denominator be P(N|O) instead of P(G|O)?

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  6. I can't refute your argument, I don't have the maths. But something that has always puzzled me about the fine tuning argument is, why would a designer go to the trouble of making the fundamental constants just so for life and us, but then design/allow parts of our environment to kill us in great numbers? I'm thinking of disease and natural disaster such as earthquakes and floods. The black death for example is something that went against the purpose of fine tuning, and can't be said to be fine tuned for us, but against us.

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  7. I think it may be because fine tuning argues that the universe has been created suitable for human life in general. Although the Black Plague, earthquakes, disease, seem like they contradict this logic, one has to only notice that these events are the exception, not the rule. Seeing as Much much much more people die of cardiovascular disease at an old age rather than war,plagues, or natural disasters put together. I would argue that God permits these events to happen for a reason, but I don’t think that would convince you, and for good reason. You probably don’t believe in God and for that argument to work you have to presuppose God. However, I do hope my half baked explanation of how these disasters are an exception not the rule helps you understand the fine tuning argument a bit more.

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  8. A few points.

    1) Should you not edit this to speak specifically about Earth and not the 'Universe'? By all accounts outside of our atmosphere life is vanishingly rare if there is any at all. Human life even rarer still.

    2) Wouldn't it be accurate to say that given this mathematical working (not that I agree with it) it would allow you to arrive at 'Deism' and not necessarily 'Theism'? You could say it all started from a prime mover but following that on with some degree of certainty of who that prime mover was and that we know his, her or its mind is impossible?

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    1. What's wrong with his maths? It would be interesting to see your formulation!

      "allow you to arrive at 'Deism' and not necessarily 'Theism'?".

      Yes, the fine tuning argument just makes an argument for a designer of the universe, not a particular form of god, although one could argue that it would be more likely that a god who loves his creation is more likely to create a universe than one who is not.

      The universe is largely hostile to life, but then again the earth can be hostile too. Part of human progress, and indeed a theist might suggest part of our purpose, is to realised by overcoming the challenges faced by nature. I do not think it unreasonable to suspect that a small, ancient, civilisation living on an island in the Pacific might make a similar observation that the only part of the universe conducive to human life is the island they're living on, and therefore the theist would have to set the argument in terms of their island. But we wouldn't use the island example nowadays, and we may not use your universe example so readily if we develop ways to colonise uninhabitable parts of the universe.

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  9. The same parameters that allow for life also necessitate death.

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  10. Why would "P(F|N) = extremely-super-duper-ultra-mega low"? I grant that if it is, the math and logic holds. But it seems like it's a pretty big presupposition.

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    1. Note that I prefaced that with "If the following are true" in reference to Cameron's version of the fine-tuning argument. But to answer your question, it seems clear it would be that low if there was only a single universe in which to get the constants right (e.g. the fine-tuning of gravity relative to the density of matter, if it were off by more than one part in 10^60 physical life would not have evolved). While Cameron's first premise is vulnerable to attack I wouldn't call it a "presupposition" since it's based on the science of fine-tuning. It isn't something that's just assumed.

      That said, one can attack this premise by putting forth 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). The multiverse does have its problems, but at least it's a better objection than what Paulogia put forth in his video.

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  11. "does the probability of God wanted a universe with life given that God exists seem extremely small? It does not."
    Yes it does? By life here we probably have to mean something like "such and such physical stuff we observe" in order for our observations to play the evidential role the theist needs them to. In that case the probability is 0, or more precisely the value of 1 divided by increasing n approaches 0. We have no reason to think God would have to create precisely *this* incredibly large death trap with precisely *these* constants and physical happenings we observe in order to accomplish whatever His ends are, unless you're going to claim "precisely everything that happens in precisely this universe was His plan all along" in a very ad hoc fashion, since He is compossible with any logically possible state of affairs. On theism, mind-brain identity theory is straightforwardly false (since God is/has an immaterial mind), therefore we could have all the mental goods the theist wants (loving relationships yadda yadda) no matter what the material world looks like, ie. no matter how "badly" tuned it is. A universe so badly tuned that it's physically impossible for observers to exist in it (but would still do so via divine fiat or some other non-natural, logically possible intervention) would actually be significant evidence for theism, at least over naturalism.

    "The problem is that this necessity of physics would itself be fine-tuned to be within that extremely narrow life-permitting range"
    There is no range if the universe is necessary! The set of possible physics would just include the actual universe. Just because you can draw some numbers on a piece of paper, it doesn't mean they correspond to actual possibilia.

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