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.

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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.

WLC's Mistake in Formulating the Moral Argument

Actually, there is more than one mistake that WLC made in his formulation of the moral argument and there is more than one mistake that WLC made in his Q&A response, Formulating the Moral Argument.  I've addressed the moral argument a few times already; in The Modified William Lane Craig Moral Proof, The Logic of an Apologist, WLC3: When Morality Arguments are Bad, The Moral Argument in Graphical Form and WLC Being a Duffer.

In the first, I show how the same argument can be used to argue for the existence of a god via the existence of Kim Kardashian (if there is a better way to highlight how trivial an argument is, I'd like to know it).  I'll get to the second in a moment.  In the third, I summarise the first and second arguments and go into a little detail as to why I think WLC's formulation of the moral argument is questionable. In the fourth I demonstrated, in a diagram, the circularity of the moral argument.

The fifth is more about his Q&A response to a question about … well, it should be reasonably clear already -  it's the formulation of the moral argument, which I too questioned in The Logic of an Apologist.

Now, The Logic of an Apologist got some attention recently at Craig-Land, in a thread dedicated to lampooning my arguments, eventually focussing in on the moral argument and my assertion that WLC presents the moral argument oddly and, as I interpreted it in WLC3: When Morality Arguments are Bad, deceptively.

There's a bit of noise in the discussion, but through it is an interaction between me and the thread's originator, λ-calculus, that I want to use as my launch-pad to discussing WLC's errors.  Reasonably late in the thread (post #86) I challenged λ-calculus to answer the question I effectively posed in The Logic of an Apologist: why did WLC formulate the moral argument the way he did, if not to deceive?  I also reframed the question, to make it easier for him: Why did he word it in the form (~A->~B;B;∴A) rather than in the form (A->B;A;∴B)?

Someone else immediately chimed in and referred to WLC's Q&A response, Formulating the Moral Argument.  And this led me to take another look at the piece that was the inspiration for WLC Being a Duffer.

What a treasure trove!

My original comment on it was that WLC effectively torpedoes his own argument, but that is only one of many problems.  Here are the ones that I have identified:

Problem 1 - Equivocation on the term "objective"

This is a problem with the content of the argument.  By "objective" WLC really means "absolute", as opposed to "relative".  But he equivocates, perhaps unintentionally, when he tries to persuade atheists to accept that there is such a thing as "objective moral values and duties".  We can use metrics, generally agreed principles and cool reason to work out this action is better or worse than that action - that would be objective - rather than letting ourselves be swayed by personal opinion, hyperbole and how we felt on the day - which would be subjective.  When WLC gives examples of "objective values" saying this or that is "simply wrong", you can tell that he's really talking about absolute morality, rather than objective morality - or he wouldn't be raising emotive topics like rape or torturing children for fun.

Problem 2 - Equivocation on the term "conditional"

This is a problem with his explanation for formulating the argument the way he did.  He writes "Since, as our truth table reveals, the whole conditional statement comes out true if the consequent is true, then it doesn’t matter whether the antecedent clause is true or false."

Here he is mixing up what is known as a material conditional with what is known as a conditional sentence.  He's helped in this in that the terms both contain the word "conditional" and they can be symbolised the same way (A->B).  Wikipedia will explain the potential for confusion better than I:

The material conditional is used to form statements of the form p->q (termed a conditional statement) which is read as "if p then q" or "p only if q". It is conventionally compared to the English construction "If...then...". However, unlike the English construction, the material conditional statement p->q does not specify a causal relationship between p and q. It is merely to be understood to mean "if p is true, then q is also true" such that the statement p->q is false only when p is true and q is false.

These are quite different understandings of the construction "if … then …".

Problem 3 - Equivocation on the term "true"

When, in general parlance, we say that something is "true", we do not mean that it is "trivially true" or "vacuously true" - we mean that it is actually true such that its negation is not true.  WLC is equivocating by presenting as "true" something which is only vacuously true.

Problem 4 - Lack of specificity to morality (if Problem 2 is ignored)

This argument works (to the extent that it works) with anything, including the existence of Kim Kardashian.  It's not really a moral argument at all.

Problem 5 - Triviality due to negation (if Problems 1, 2 and 3 are ignored)

WLC himself points out that, from his point of view, his first premise is trivially true - because he believes that his god does exist.  But this isn't actually just from his (or any other theist's) point of view.  In terms of the argument, if it were to succeed, it makes its major premise trivial.

There may well be other problems, feel free to point them out.