Thursday, August 23, 2018

Moral Ought Facts are Non-Natural


In my third Maverick Christian Vlog episode I refer to a scholarly paper which is called A Folk Semantics Argument for Moral Non-Naturalism. 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.

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.

Next I’ll explain some philosophy lingo before explaining the math used in the paper.

Philosophical Terminology

Moral semantics 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.”

A stipulative definition 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 fully justified 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.

A hypothetical imperative takes the form of something like, “If you want to do X, you should do Y” 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 ought used in hypothetical imperatives is called a hypothetical ought.

A category mistake (or category error) 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.

Set Theory

Some Basics

Sets are collections of stuff where order and duplicates are irrelevant. For example, the followings sets are all identical.

{1, 2, 3, 4}
{1, 2, 2, 3, 4}
{4, 3, 2, 1}

There’s the empty set, sometimes symbolized as {} which is a set that has no members.

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:
A = {1, 5, 9}
B = {1, 5, 7, 8}
C = {2, 3}

(element of)
1 ∈ AFor any set S, x ∈ S means that x is an element of S.

(not an element of)
1 ∉ CFor any set S, x ∉ S means that x is not an element of S.

A ∩ B = {1, 5}Given sets S and T, S ∩ T contains all the elements x such that x ∈ S and x ∈ T.

A ∪ B = {1, 5, 7, 8, 9}Given sets S and T, S ∪ T contains all the elements x such that x ∈ S or x ∈ T.

{1, 5} ⊆ BGiven sets S and T, S is a subset of T if and only if each member of S is also a member of T.

(not a subset)
{2, 9} ⊄ BGiven sets S and T, S is not a subset of T if and only if it is not the case that S ⊆ T.

The set “All x such that x > 3” can be symbolized like this:

{ x | x > 3 }

The set “All x ∈ A such that x > 3” can be symbolized as:

{ x ∈ A | x > 3 }

That set described above would be {5, 9}.


Unlike sets were order and duplicates don’t matter, they do matter in tuples. The following are all different from each other:
(1, 2, 3, 4)
(1, 2, 2, 3, 4)
(4, 3, 2, 1)
Those who have taken algebra might remember the tuple known as the ordered pair:
(2, 3)
(11, -3)
Relations are sets of tuples, with a binary relation being a set of ordered pairs. For example, suppose we have this set:
{Diana, Steve, Barbara}
The relation “taller-than” could consist of this set of ordered pairs, where e.g. Diana is taller than Steve.
{(Diana, Steve), (Steve, Barbara), (Diana, Barbara)}
If we symbolize our taller relation as T then we could say that (Diana, Steve) ∈ T.

Relations between different sets are also possible. Suppose we have these two sets:
L = {Reed, Scott, Clark}
F = {Sue, Jean, Lois}
And the “is-husband-of” relation is a relation from set L to set F; e.g. Reed is the husband of Sue:
H = {(Reed, Sue), (Scott, Jean), (Cark, Lois)}
An inverse of a binary relation R goes like this:
R-1 = {(y, x) | (x, y) ∈ R}
For example, the inverse of the “is-husband-of” relation would be the “is-wife-of” and be this:
H-1 = {(Sue, Reed), (Jean, Scott), (Lois, Clark)}
A relation from set A to set B is a function if each member of A is paired off with exactly one member of B. The “input” part of a function is the domain (set A) and the “output” part is called the range (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.

Suppose relations S and T are the following:
S = {(1, 2), (10, 11)}
T = {(2, 3), (11, 12)}
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:
{(x, z) | (x, y) ∈ S and (y, z) ∈ T}
In our example, T ∘ S would be the following:
{(1, 3), (10, 12)}
Suppose relation V is the following:
V = {(1, 2), (1, 3), (1, 9), (2, 3), (2, 4)}
Because the relation is binary, V(x, ⋅) is { y | (x, y) ∈ V }

V(1, ⋅) = {2, 3, 9}
V(2, ⋅) = {3, 4}

Formal Logic

Deductive Arguments

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 deductively valid or valid. An example of a deductively valid argument:
  1. If it is raining, then my car is wet.
  2. It is raining.
  3. Therefore, my car is wet.
The above example uses a famous rule of logic called modus ponens which has this structure:
  1. If P, then Q
  2. P
  3. Therefore, Q.
Another famous rule of logic is called modus tollens where “not-Q” means “Q is false.”
  1. If P, then Q
  2. Not-Q
  3. Therefore, not-P.
An argument is deductively invalid or invalid if it is not deductively valid. An example of an invalid argument:
  1. If it is raining, then my car is wet.
  2. My car is wet.
  3. Therefore, it is raining.
In logic lingo, a deductively valid argument with all its premises being true is called a sound argument. And since a valid argument having true premises guarantees the truth of its conclusion, a sound deductive argument has a true conclusion.

Basic Symbols and Rules of Inference

Here’s a summary of how the connectives in propositional work where p and q represent propositions (claims that are either true or false):

Type of
When it’s true/false
Conjunctionp and qp ∧ qTrue if both are true; otherwise false
Disjunctionp or qp ∨ qFalse if both are false; otherwise true
ConditionalIf p, then qp → qFalse if p is true and q is false; otherwise true
NegationNot-p¬pTrue if p is false; false if p is true

As suggested in the above table, the symbols →, ¬, ∨, and ∧ are called connectives. 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 simple statement and one more or more simple statements with one or more connectives is called a compound statement. For example, “¬P” and “A ∧ B” are compound statements.

The type of conditional (pq) being used here is called a material conditional. A material conditional is equivalent to “It is not the case that the antecedent (p) is true and the consequent (q) is false,” such that the only 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 modus ponens and modus tollens to be valid rules of inference, since in a true material conditional if the antecedent is true, then the consequent is true as well.

Speaking of which, here are those rules of inference I’ve already mentioned in symbolic form:

modus ponens
In English In Symbolic Logic
If p then q

Therefore, q
p → q

∴ q
modus tollens
In English In Symbolic Logic
If p then q

Therefore, not-p
p → q

∴ ¬p

In the convention I’m using, the lower case letters p, q, r,...z are placeholders for both simple and compound statements. Thus, below is a valid instance of modus tollens.
  1. (A ∧ B) → C
  2. ¬C

  1. ¬(A ∧ B) 1, 2, modus tollens
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 modus tollens.
  1. ¬C
  2. (A ∧ B) → C

  1. ¬(A ∧ B) 1, 2, modus tollens
Some rules of inference can be used in more than one way. Examples include disjunctive syllogism and simplification.

Disjunctive Syllogism
In English In Symbolic Logic
p or q

Therefore, q
p ∨ q

∴ q
p or q

Therefore, p
p ∨ q

∴ p
In English In Symbolic Logic
p and q

Therefore, p
p ∧ q

∴ p
p and q

Therefore, q
p ∧ q

∴ q

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:
  1. A ∨ (B ∧ C)
  2. ¬A

  1. B ∧ C 1, 2, disjunctive syllogism
  2. C 3, simplification
Not too hard, right? After learning the above rules of inference, you might even have mentally “seen” that C 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:


∴ p ∧ q
hypothetical syllogism
p → q
q → r

∴ p → r


In propositional logic, two statements are logically equivalent 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:

equivalencename of equivalence
p ⇔ ¬¬pdouble negation
p → q ⇔ ¬q → ¬ptransposition (also called contraposition)
¬(p ∧ q) ⇔ ¬p ∨ ¬qDe Morgan’s laws
¬(p ∨ q) ⇔ ¬p ∧ ¬q

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:
  1. A
  2. (C ∧ D) → ¬A

  1. ¬¬A → ¬(C ∧ D) 2, transposition
  2. A → ¬(C ∧ D) 3, double negation
  3. ¬(C ∧ D) 1, 4 modus ponens
  4. ¬C ∨ ¬D 5, De Morgan’s laws

Conditional Proofs

The conditional is symbolized as p → q where p is called the antecedent and q is called the consequent. The conditional proof aims to prove that a conditional is true, with the antecedent of the conditional being the conditional proof assumption 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:

conditional proof
a) p conditional proof assumption
c) p → q a-b, conditional proof

For example, suppose we want to prove A → (B ∧ C) from premises 1 and 2 below:
  1. A → B
  2. A → C

  1. A conditional proof assumption
    1. B 1, 3, modus ponens
    2. C 2, 3, modus ponens
    3. B ∧ C 4, 5, conjunction
  1. A → (B ∧ C) 3-6, conditional proof
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 if it is true then it properly leads to the consequent. Nothing in the proof above, for example, relies an A actually being true.

Predicate Logic

To give an example of predicate logic, consider the following symbolization key:

B(x) = x is a Bachelor.
U(x) = x is Unmarried.

The letters B and M in these examples are predicates which say something about the element they are predicating. Sometimes parentheses aren’t used; e.g. Bx being used to mean “x is a bachelor.” The symbol; ∀ means “For All” or “For Any” such that the following basically means “All bachelors are unmarried:”

universal quantification
In English In Symbolic Logic
For any x: [if x is B, then x is U] ∀x[B(x) → U(x)]

The domain of discourse is the set of things we’re talking about when we make statements like ∀x[B(x) → U(x)], such that the “∀x” means “For any x 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. c can signify a guy named “Charles” and we can let B(c) to signify c is B (i.e. Charles is a bachelor).

A rule of predicate logic called Universal Instantiation allows us to instantiate a universal quantification (a ∀x[...] statement) for a specific individual, like so:
  1. ∀x[B(x) → U(x)]
  2. B(c)

  1. B(c) → U(c) 1, universal instantiation
  2. U(c) 2, 3, modus ponens
There’s a somewhat complicated rule called universal generalization (also called universal introduction) 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 x, 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.
  1. ∀x[A(x) → B(x)]
  2. ∀x[B(x) → C(x)]

  1. A(t) → B(t) 1, universal instantiation
  2. B(t) → C(t) 2, universal instantiation
  3. A(t) → C(t) 3, 4, hypothetical syllogism
  4. ∀x[A(x) → C(x)] 5, universal generalization
And that should be all the technical stuff you need to know to read A Folk Semantics Argument for Moral Non-Naturalism. 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.

Sunday, July 1, 2018

Can Objective Morality be Subjectively Perceived?

The Objection

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 subjectively perceived? Doesn’t the fact that supposedly objective morality is subjectively perceived mean we don’t really have any justification for accepting moral objectivism?

The answer to both questions is, “No.”


First, note that in practice, everything 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 are 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.

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 There can’t be any married bachelors is objectively true.

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.


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 moral epistemology (how moral truths are known) with moral ontology (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.

Friday, June 15, 2018

A Quick Argument for Objective Morality

Here’s a quick deductive argument for moral objectivism, where by moral truths being “objective” I mean that they hold independently of human opinion.

The Argument

  1. It is morally wrong for a man to torture an infant just for fun.
  2. 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.
  3. If (1) and (2) are true, then objective morality exists.
  4. Therefore, objective morality exists.
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:
  1. 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);
  2. 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;
  3. 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.
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)?)

You could deny premise (1). Do you believe there’s nothing morally wrong with torturing infants just for fun?

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?

Why I Like It

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.

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.

Wednesday, May 9, 2018

Fine-Tuning: Barnes vs Malpass (p. 3)

Fine-Tuning: Barnes vs Malpass
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An Alleged Inconsistency

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.

If A depends upon B for its existence then A is said to be ontologically dependent on B. Many theists believe the physical universe is ontologically dependent on God.

There are two major theories of time (though hybrid scenarios have been proposed). On one view of time, called the B-theory of time (also called tenseless theory of time or the static view of time), all moments in time are equally real. This contrasts with the A-theory of time (also called the tensed theory of time or dynamic 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.

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 timeless theist.

If there is a contradiction for a timeless God creating the universe, one idea is to try to justify this idea using conceptual analysis (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 mental states are causally irrelevant on naturalism 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.

In my blog article where I argued that mental states are causally irrelevant on naturalism 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.

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 t 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.

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.”[3] 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 t that did not exist in a previous time”).

Consider what would happen if a timeless God interacted with the physical spacetime of the universe on a B-theory of time, ceteris paribus. 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 in 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 causes things to happen might be considered a sort of “change” (in the sense that those 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.

Another view of God and eternity is that God is timeless sans the universe, and that the A-theory of time is correct. God creates the universe (and physical spacetime itself) at time t0 and enters into time at t0, but God did not exist before t0 since there was no “before” time t0. 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; sans the universe God had this intention timelessly and there was no prior time in which he did not have it), God did so at t0. God is ontologically prior to the universe but not temporally prior to the universe at t0, since there was nothing temporally prior to t0. For what it’s worth, this is the view of God creating the universe that I and a number of other theists adhere to.

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:
  1. Giving an analysis of “timeless” what sort of “change” he is talking about;
  2. why a Creator who is timeless sans creation would require it; and
  3. how exactly this generates an inconsistency in the scenario I described.
Unless and until he does that (or provides some other sufficient explanation), I think we have reason to be skeptical that a bona fide contradiction exists here.

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[3] Christian philosopher of time William Lane Craig defines God being “timeless” in much the same way.

Craig, William Lane; Time and Eternity: Exploring God’s Relationship To Time (Illinois: Wheaton, 2001)

Fine-Tuning: Barnes vs Malpass (p. 2)

Fine-Tuning: Barnes vs Malpass
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The Eye

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 (1:04:54 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?

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 A and B:
A: I think Stonehenge was designed.

B: We should be skeptical of that design inference to the point of not accepting it.

A: Why?

B: 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.
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” (1:06:33 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.

Barnes points out that, if cosmic fine-tuning is the result of design (1:07:52 to 1:09:22) the eye not 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.

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 1:15:53 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.

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.

The Multiverse Hypothesis

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 The Grand Design.[2] For a multiverse to satisfactorily account for a life-permitting universe despite fine-tuning there are four desiderata:
  1. Varying constants and quantities. Obviously, the multiverse should have varying parameters across universes.
  2. Avoid the Boltzmann brain problem. 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.
  3. Not require fine-tuning. If whatever mechanism generates a World Ensemble itself requires fine-tuning, this would merely push the problem back a step instead of solving it.
  4. Independent evidence for it. 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.
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 1:21:06 to 1:21:16.

On the Attack

While Luke Barnes does well for the most part, the one where he faces real difficulty is Malpass gives his objections in 1:25:06 to 1:29:48 in which Malpass attacks the idea of an atemporally timeless God creating the universe.

Malpass asserts that a mind is necessarily a linear sequence of phenomenological experiences (1:27:17 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 (1:27:53 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.

My objection isn’t that Malpass gave bad arguments for these claims, but that he gave no 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. 1:26:44 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 1:29:27 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.

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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[2] Hawking, Stephen; Mlodinow, Loendard. The Grand Design (New York: Random House, Inc., 2010), p. 165.

Fine-Tuning: Barnes vs Malpass

Fine-Tuning: Barnes vs Malpass
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Capturing Christianity hosted a fine-tuning debate between Luke Barnes and Alex Malpass in 2018-04-21.

For those who don’t already know, cosmic fine-tuning 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 fine-tuning argument (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).

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.

Debate Overview

Opening Statements

Luke Barnes gives his opening statement starting at around 2:58 explaining fine-tuning and describing some of the science involved, giving examples of fine-tuning such as the masses of electrons and quarks (3:15 to 4:55, where if the parameters fall outside the narrow boundary not only do you not get life you don’t even get chemistry) and the Higgs field (6:23 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 (23:09 to 23:24).

Alex Malpass’s opening statement starts at around 25:15 and he more or less concedes the physics Barnes presents, at least arguendo (24:48 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.[1]

To his credit as a philosopher, Malpass presents the overall structure of the fine-tuning argument better than Barnes does at around 30:36 to 32:00.
  1. P(L | N) << 1 (the probability that the universe is Life-permitting given Naturalism is much less than 1)
  2. ~P(L | T) << 1 (it is not the case that the probability that the universe is Life-permitting given Theism is much less than 1)
  3. If E is more probable on H1 than H2, then E supports H1 over H2.
  4. Therefore, L is evidence for T over N.
Something called the odds form of Bayes theorem will be helpful here, the general structure of which is this where e.g. P(T|L) represents the probability of T (theism) given L (the universe is life permitting).


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 T and N, respectively. The lower P(T) is, the worse the posterior odds will be. This brings us to what Malpass calls the “Goldilocks hypothesis problem.”

Goldilocks Hypothesis Problem

One thing that affects the prior probability of a hypothesis (i.e. its probability prior to examining some particular data) is its content, 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 specific type of animal existing. Malpass correctly notes that there’s a trade off between the content of T, it’s prior probability P(T), and P(L|T).

If T were “An omnipotent God desires L” then P(L|T) will be high but at the cost of P(T) being low. To see why, let R represent “It rained this morning” and let TR be “An omnipotent God made it rain this morning” in which case P(R|TR) is high, but P(TR) 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 T is (thus packing more content in it), the lower the prior probability of T. Conversely, making T broader (having less content), e.g. T meaning nothing more than “an omnipotent being exists” will make P(T) greater; but making T broader in this way will make P(L|T) lower.

The Goldilocks hypothesis problem is how precisely to define the hypothesis T in such a way to not make it ad hoc (e.g. “An omnipotent God desires L”) 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, T can’t have too much content, but it also can’t have too little content. If T 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) (32:32 to 33:58). So how to define T in a good way so that P(T) and P(L|T) are both not so small?

Barnes gives a decent response to this (40:38 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 T is more or less “standard” theism where God is not only supremely powerful but also good, then T isn’t ad hoc and P(L|T) is not unreasonably low.

The Stalking-Horse Naturalism Hypothesis

Malpass explains what he calls the stalking horse naturalism hypothesis at around 49:33 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” (56:24 to 1:00:48) to result in a life-permitting universe, call this form of naturalism ND, such that P(L|ND) is high.

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 x that results in the universe falling into the extremely narrow parameters as specified in a certain mathematical equation. Then it seems that factor x 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.

Barnes gives a somewhat similar objection (1:01:10 to 1:03:01). Barnes points out that we’d have to consider P(ND|N), i.e. the probability of naturalism having that particular disposition given N simpliciter. 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(ND|N) is pretty comparable to P(L|N).

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[1] Hawking, Stephen; Mlodinow, Loendard. The Grand Design (New York: Random House, Inc., 2010), pp. 143-144, 157-162.