Misuse of the Material Conditional

I'm going to start off easy.  First, check out the wikipedia entry on the Material Conditional.

Note that there are two usages:

As a truth function, and

As a formal connective

Now, note that the truth table for one has p->q being true for all conditions except where p is true and q is false.

And then, note that the material conditional p->q as a formal connective:

can be considered as a symbol of a formal theory, taken as a set of sentences, satisfying all the classical inferences involving ->, in particular the following characteristic rules:

Modus ponens;

Conditional proof;

Classical contraposition;

Classical reductio ad absurdum.

Now, I take the use in a modus tollens to be precisely the same sort of use as in modus ponens.  You can try to argue differently, but that would put a bit of a hole into modus tollens, and how it is generally shown to relate to modus ponens.

Finally, note the truth table at the SEP entry on Conditionals.  In the Non-Truth-Functional Interpretation truth table, A->B is true when A is true and B is true, false when A is true and B is false and could be true or false when A is false (so we simply don't know).

This does not correlate with what WLC stated in his answer in his Q&A Formulating the Moral Argument (see my earlier take on this here).  He got it wrong because he tried to use the Material Conditional as a truth function when he clearly should have used it as a formal connective.  Anyone who has subsequently or coincidentally followed him on this is also wrong.

---

One of the objections I got to the argument above was a little confused.  The objector complained that 1) WLC “intends the argument to be interpreted subjunctively” and 2) “(t)he truth table (Craig) gives is for the indicative mood”.

So, which is it?  Why give a truth table for the indicative mood if WLC intends the argument to be taken subjunctively?  Why not present the argument subjunctively if he meant it to be taken subjunctively?  And what does he think he's doing changing what is claimed by some to be a material conditional (which I think it probably is, but not with the truth functionality interpretation) into a counterfactual (conditional)?

If he wants to be using a counterfactual condition, and to be using the subjunctive ... he should use the subjunctive.  It's not hard, even I could do it (although I think the major premise that follows is false, because the protasis is true while the apodosis is false):

• If WLC's god were not to exist, then objective moral duties and values would not exist
• But objective moral duties and values do exist
• Therefore, WLC's god exists.

See the "were not to"?  This is a calling card of the counterfactual.

If WLC did intend to use the subjunctive mood and create a counterfactual conditional, then all talk about the material conditional as a truth function (the sin committed by the various people who thus motivated me to write this piece) is misguided. 

See also philosophical treatments of the counterfactual conditional.