One reason why it should be OBVIOUS that Craig’s Kalam Cosmological Argument (hereafter: KCA) involves the fallacy of equivocation, is that Aquinas commits a very similar fallacy of equivocation in his cosmological arguments for God.

Every (or almost every) introduction to philosophy of religion course includes at least a brief examination of Aquinas’s Five Ways or Five Arguments for God.  So,  almost every philosophy student who has taken an introduction to philosophy of religion course has been exposed to the sort of fallacy of equivocation that occurs in KCA.

Let’s look at Aquinas’s first argument for God.  Here are a couple of key premises:

1. In the world some things are in motion.

2. Whatever is moved is moved by another.

To be “moved by another” is ambiguous.   This might mean either (a) “moved by AT LEAST ONE other thing” or it could mean (b)  “moved by EXACTLY ONE other thing”.   The premise is plausible on interpretation (a), but is clearly false on interpretation (b):

2a. Whatever is moved is moved by AT LEAST ONE other thing.

2b. Whatever is moved is moved by EXACTLY ONE other thing.

Premise (2b) is clearly FALSE, because it is possible for two moving objects to cause a third object to move, as when two moving billiard balls simultaneously bump up against a third stationary billiard ball and cause the third billiard ball to start moving.  So, for premise (2) of Aquinas’s first argument for God to have a chance of being true, we must interpret the ambiguous claim in (2) as meaning (2a).

But as the argument proceeds, Aquinas shifts into talking about a SINGLE first mover:

If that by which it is moved be itself moved, then this also must needs be moved by another, and that by another again.  But this cannot go on to infinity, because then there would be no first mover, and consequently, no other mover, seeing that subsequent movers move only inasmuch as they are moved by the first mover; …Therefore, it is necessary to arrive at a first mover, moved by no other; an this everyone understands to be God.

(Religious Belief and Philosophical Thought: Readings in the Philosophy of Religion, by William Alston, p.29 – excerpt from Summa Theologica).

Aquinas speaks of “the first mover” implying that there must only be ONE thing that initiates movement.  But even if there was just ONE SINGLE chain of one object moving another object moving another object, no matter how far back we go, we cannot infer that the prior cause of movement was a SINGLE object or thing; it might well be TWO or THREE or a THOUSAND things, because premise (2b) only supports an inference to there being AT LEAST ONE prior object or thing that causes the movement.

Aquinas then concludes that “this” first mover is understood to be God.  But to speak of “this” first mover, clearly implies that there was EXACTLY ONE such mover, and to identify the ultimate cause of motion as God, who is by definition,  ONE BEING, is also to assume that there is EXACTLY ONE such mover.  So, we see in Aquinas’s first argument for God, a clear shift between an ambiguous initial premise (2), which might refer to either (a) “moved by AT LEAST ONE other thing”   or to (b) “moved by EXACTLY ONE other thing”, to a conclusion that assumes that there must be EXACTLY ONE thing that is “the first mover”.  But premise (2) is plausible only if we give it interpretation (a) “moved by AT LEAST ONE other thing”, in which case the conclusion that there is EXACTLY ONE first mover does NOT logically follow.

Aquinas thus commits the fallacy of equivocation in his first argument for the existence of God, which is generally considered to be a cosmological argument.  

A similar equivocation fallacy occurs in Aquinas’s third argument for God. The third way is also considered to be a cosmological argument.  Here are some key premises [this is not the complete argument]:

1. If at one time [in the past] nothing was in existence, it would have been impossible for anything to have begun to exist.

 2.  If it would have been impossible for anything to have begun to exist [after some particular point in time in the past], then even now nothing would be in existence.

3. But it is absurd [i.e. false] that nothing is in existence now.

4. Therefore…there must exist something the existence of which is necessary.

I realize that (4) does not follow from premises (1), (2) and (3), but that is because I have left out some other premises of this argument.  My point here is that the meaning of “there must exist something” in premise (4) is nailed down by the logic of the argument supporting (4).  There could NOT have been a past time when nothing existed, so we can conclude that in every point in time in the past SOMETHING has existed, and this clearly means that AT LEAST ONE thing exists in any given point in time in the past (allowing that different things could exist at different points in time in the past).

So, when interpreted properly, (4) means this:

4a.  There must exist AT LEAST ONE thing the existence of which is necessary. 

But the conclusion that Aquinas draws requires that we assume the truth of a different premise:

4b.  There must exist EXACTLY ONE thing the existence of which is necessary.

Notice how the language of Aquinas shifts to talk about a SINGLE being or thing:

Therefore we cannot but admit the existence of some being having of itself its own necessity, and not receiving it from another, but rather causing in others their necessity.  This all men speak of as God.

(Religious Belief and Philosophical Thought, p.30)

The phrase “some being” is ambiguous between “EXACTLY ONE being” and “AT LEAST ONE being”, but in the very next sentence, Aquinas shifts to speaking about “This” which assumes that there is EXACTLY ONE being which has the sort of “necessity” in question.  And, of course, “God” by definition refers to a SINGLE being.  But the key premise that Aquinas is basing his conclusion on only talks about there being AT LEAST ONE being that has this sort of necessity.  So, once again, Aquinas commits the fallacy of equivocation.  The argument for premise (4) is logically valid only if we interpret (4) to mean (4a).  But Aquinas’s conclusion follows validly from premise (4) only if we interpret it to mean (4b).

In conclusion, IF I am correct that William Craig has committed a similar fallacy of equivocation in his cosmological argument (KCA), THEN the fallacy that Craig commits has about an 800 year history, and occurred in the most studied and examined versions of the cosmological argument, found in Aquinas’s Five Ways of arguing for the existence of God.