A Good Reason for WLC's Modus Tollens

I've railed elsewhere about the fact that WLC's morality argument is posed confusingly; in modus tollens form rather than the (more standard) modus ponens form.  To clarify, the argument:

• If P then Q
• P
• Therefore, Q

is more straightforward than:

• If not Q then not P
• P
• Therefore, Q

So, why use the latter rather than the former?

I've also pointed out that WLC himself torpedoes his own argument when appealing to vacuous truth (which he calls "trivial truth", perhaps because it thus seems as if he is referring to a Nils Bohr quotation).

What I have come to realise is not only that WLC possibly was aware of what he was doing when he presented his argument in the form that he did, but also that the problem that he was trying to avoid possibly applies to all arguments for the existence of god.

You see, if WLC had presented the moral argument in the standard modus ponens form, it would look like this:

• If objective moral values and duties exist then god exists 
• Objective moral values and duties do exist
• Therefore, god exists

The issue that WLC was aware of, I think, is that people who are not theists are not as enamoured with "objective moral values and duties" as theists are.  Sure, we agree that if a god of the sort that WLC believes in were to exist, then it would follow that objective moral values and duties would exist, somehow rooted in the existence of that god.  But this is just saying "if a god existed, then the sort of objective moral values and duties that only would exist if a god existed would exist" and non-theists simply do not believe that "the sort of objective moral values and duties that would only exist if a god existed" exist.

So, for us, "objective moral values and duties" of the sort that WLC is referring to constitutes an empty category and therefore it becomes perfectly clear that the major premise of the modus ponens is only vacuously true.  The argument becomes:

• If the sort of objective moral values and duties that would only exist if a god existed existed then a god would exist
• The sort of objective moral values and duties that would only exist if a god existed do exist
• Therefore, a god does exist

We can live with the major premise, since it's vacuously true, but we disagree with the minor premise.

Now, the thing with the vacuously true premise is that it effectively begs the question.  The (actually empty) category that is in question is assumed to not be empty on the basis of an assumption that the conclusion is true.  This is the case, even when you shuffle the terms around and present your argument in modus tollens form.

The trick the WLC then plays, by shuffling his terms around, is to imply that the major premise of his modus tollens is vacuously true:

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.

Again, can you see?  WLC is pointing out that he is begging the question here (see WLC Being a Duffer for more).  His argument only works for theists who have already committed to the truth of what he is ostensibly trying to prove.  It's a worthless argument.

If an argument is begging the question in its modus ponens form then the argument is begging the question in all correctly stated equivalent forms, including the modus tollens form, such as WLC's stripped down version:

• If god did not exist then objective moral values and duties would not exist
• Objective moral values and duties do exist
• Therefore, god exists

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My other realisation was that this applies to all arguments for god.  If you shuffle the terms around and find that there is begging of the question happening in one (correctly stated) form of the argument, then it's happening in all correctly stated forms of the argument.

This is not a huge realisation on my part, since I thought that was the case in an informal way.  It's just nice to know that it can be shown formally.

Of course, if there is an argument for god which does not include any begging of the question, you are welcome to present your case.