Tuesday, December 07, 2004

Reppert's Proof That Bill Clinton Was Right

Victor Reppert sends this logical tidbit:

1. Going to class is pointless.
2. An unsharpened pencil is pointless.
Therefore, 3. Going to class is an unsharpened pencil.

The Clintonian thesis Reppert had in mind was presumably the one to the effect that "It all depends on what the meaning of 'is' is." Both premises in the above 'argument' feature the 'is' of predication, while the conclusion sports an 'is' of identity. And if I may read into Reppert's laconic e-mail message a bit, he is suggesting that the formal fallaciousness of the pencil argument derives from the shift from predication statements to an identity statement.

This suggests the following rule: One cannot validly infer an identity statement from a premise set none of whose members is an identity statement. Call this Reppert's Rule. Is it true? Consider the following argument:

4. Socrates is Socrates-identical.
5. The teacher of Plato is Socrates-identical.
6. Therefore, Socrates is the teacher of Plato.

(4) and (5) are both predications, not identity statements: both appear to predicate a property, the property of Socrates-identity, of their subjects. And yet the argument is valid. We appear to have a counterexample to Reppert's Rule.

Of course, there is something fishy about haecceity-properties such as Socrates-identity pace Alvin Plantinga. (I have a blog post in the works on this very topic). But what about this argument:

7. Socrates and the teacher of Plato exemplify all the same (non-haecceity) properties.
8. If x and y exemplify all the same (non-haecceity) properties, then x = y.
9. Therefore, Socrates is the teacher of Plato.

This is a valid argument in which the conclusion, but neither premise, is an identity statement. So this appears to be a clear counterexample to Reppert's Rule.

So what is wrong with the pencil argument? Classically, it can be viewed as falling afoul of one or the other of two rules. First, it contains an undistributed middle term. With a little massaging, the argument assumes this form:

Every S is M
Every P is M
Ergo, Every S is P. This form is easily shown to be invalid.

Second, and more to the point, the pencil argument involves the informal fallacy of equivocation: 'Pointless' is being used in two senses. Interestingly enough, this so-called informal fallacy can be depicted as a formal fallacy, namely the dreaded quaternio terminorum, or four-term fallacy:

Every S is M
Every P is N
Ergo, Every S is P.

Here there is a lack of a middle term as opposed to an undistributed middle term.

So how should we diagnose the pencil argument? I would say it commits the four-term fallacy, or equivalently, it involves an equivocation. As far as I can see, however, the problem is not that 'is' in the conclusion is the 'is' of identity while instances of 'is' in the premises are instances of the 'is' of predication.

Clinton was right in the central ontological pronouncement of his presidency: Much depends on what the meaning of 'is' is -- but not the validity/invalidity of the pencil argument.