WLC Being a Duffer

Over in Craig-Land recently there was a discussion as to why WLC uses the modus tollens rather than the modus ponens in his moral argument.  That is to say, why does he use the double negative (specifically "if not god did not exist then objective moral values and duties would not exist") rather than something more comprehensible (such as "if objective moral values and duties exist then god exist").  I've touched on this before when I suggested that WLC does this to confuse and distract.  I also suggested in The modified WLC moral proof that the argument, structured as it is, can argue for the existence of god using anything you like - even totally meaningless things such as Kim Kardashian:

1. If god did not exist, the Kim Kardashian would not exist.

2. Kim Kardashian does exist.

3. Therefore god exists.

Amusingly, it would appear that WLC agrees.

At Reasonably Fallacious, WLC occasionally responds to fans in a Q&A column and in one response "Formulating the Moral Argument", he wrote this:

As you can see, p → q comes out false only when the antecedent clause is true and the consequent clause is false. (I know that seems weird, but that’s the way “→” is understood logically.)

So what does this imply for the first premise of the moral argument?

1. If God does not exist, objective moral values and duties do not exist.

Well, since God does exist, the antecedent clause is false. Therefore, no matter what the consequent clause is, (1) comes out true! (Look at our truth table above.) So it is also true that

1′. If God does not exist, objective moral values and duties do exist.

A falsehood implies anything! So for the theist, (1) and (1′) are said to be trivially true or vacuously true.

Can you see?

Falsehoods imply anything.  So the false claim that god exists would, by extension, imply the existence of "objective moral values and duties" as well as implying the non-existence of "objective moral values and duties".  The false claim that god exists would imply the existence of Kim Kardashian as well as implying the non-existence of Kim Kardashian.

Thank you, Dr Craig.  Torpedoing your own moral argument … well done.

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That is not, by any stretch of the imagination the only problem with that short text.  WLC claims that "p → q comes out false only when the antecedent clause is true and the consequent clause is false", by which he means that if p is true and q is false, then there is a problem with the claim that p → q.

Note that p → q is logical symbology for "if p, then q" (and in some instances "p implies q" or "p necessitates q").  What WLC is saying is that this is a "false" premise, if we have an instance in which we have p being true, and q not being true.  The claim that p → q doesn't say anything about instances in which there is no p, or where p is false.  Let's put this into words.

If Tiddles is a standard cat, then Tiddles has four legs.

If we were to look at Tiddles, confirm that Tiddles is a standard cat and yet find that Tiddles has five legs, then we would have cause to mistrust our premise.

If on the other hand, we were to find that Tiddles is not a standard cat, then we have no basis on which to argue anything.  This premise is quite limited.  It is not true to say that:

If Tiddles is not a standard cat, then Tiddles has five legs.

We could look at Tiddles, observe that she is a standard horse and then conclude that, despite not being a standard cat, she does in fact have four legs.  Or we could observe that Tiddles is standard giant pink seastar and has what we could call five legs.  Not being a cat doesn't give us much information about Tiddles.

But what WLC is telling us is that if p (in this case "Tiddles is not a standard cat") is false, then no matter what q is, then p → q will be true!  No, no, no no no.

That's not how it works.

The premise that "If Tiddles is a standard cat, then Tiddles has four legs" is true irrespective of what Tiddles is.  We just get to the first half of the premise (the conditional), check whether it applies and, if it doesn't, we move one thinking "this premise isn't relevant to the situation in which we find ourselves".

If it certainly not true to claim that, if Tiddles is not a standard cat that suddenly it would be true that, if things were otherwise and Tiddles were a standard cat, that Tiddles would be a pony.  It's nonsense and WLC should be ashamed to have written this.

It's rather worrisome that someone who relies so heavily on logic in his arguments, and who is responsible (to some extent) for teaching logic, should be such a duffer when it comes to explaining something as basic as how premises work.