“If . . . a proof that there are no proofs is nonsensical, so is a proof that there are proofs. Reason is our starting point. There can be no question either of attacking or defending it.”

– Miracles

“Reasoning is never, like poetry, judged from the outside at all. The critique of a chain of reasoning is itself a chain of reasoning: the critique of a tragedy is not itself a tragedy.”

– A Preface to “Paradise Lost”

I have often used Professor Kirke’s argument (from The Lion, the Witch, and the Wardrobe by C. S. Lewis) as an excellent example of a valid, deductive argument.

There are only three possibilities. Either your sister is telling lies, or she is mad,  or she is telling the truth. You know she doesn’t tell lies and it is obvious that she is not mad. For the moment then and unless any further evidence turns up, we must assume that she is telling the truth.

This argument can be analyzed in a number of profitable ways for the student of logic. We could symbolize it most directly as an extended Disjunctive Syllogism, in this form:

(L v M) v T     ~L • ~M     .:  T

We could also cast it (with minor editing) as an extended modus tollens, and so on. But for those who have not studied propositional logic, it might be clearer simply to consider this in terms of a genus and species chart, as follows:

Lucy claims to have gone to Narnia

Lucy’s claim is false       Lucy’s claim is true

Lucy is telling lies      Lucy is mad                                         .

The dividing principles should be clear. Lucy claims to have gone to Narnia. Her claim is either false or true. If her claim is false, then she either knows that it is false, or she does not. If it is false and she knows it, then she is telling lies. If it is false but she does not know it, then she is mad.

The Professor argues that Lucy’s claim is true by stating that there are only three final possibilities, as the chart shows, then removing two of them. Those who are familiar with the writings of C. S. Lewis will recognize this argument form. Consider this section from Lewis’s Mere Christianity, where Lewis is arguing that Jesus must be God:

We are faced, then, with a frightening alternative. This man we are talking about either was (and is) just what He said or else a lunatic, or something worse. Now it seems to me obvious that He was neither a lunatic nor a fiend: and consequently, however strange or terrifying or unlikely it may seem, I have to accept the view that He was and is God.

Apparently, Lewis desired his young readers of the Narnian Chronicles to learn logic, and particularly this form of argument, so that they would be able to analyze it in a much more serious form when they got around to reading his more theological literature.  And I say, the sooner the better.