Essay of little or no significance #2: what follows from what?

"What the Tortoise Said to Achilles" is a short essay by Lewis Caroll, published in 1895. It playfully explores one of the most fundamental questions of reasoning: what follows from what? Certainly the philosopher in me is always very interested in what a statement implies.

I recently learnt the phrases “Voy a clase” (“I’m going to class”) and “Me voy de clase” (“I’m leaving class”). The information that those statements provide is quite clear, but there is more to them than meets the eye. The first, for example, tells you not only that I am going to class but also that I am not currently at class; the second tells you not only that I am leaving class but also that I am currently in class. So far so trivial, perhaps, but it reminds me of another much more powerful example.

Suppose Epimenides, a Cretan philosopher, once said "Cretans never tell the truth." Was his statement true or false? It would seem his statement cannot be true, because if Epimenides was telling the truth then that itself would make his statement false. So Epimenides’ statement must be false. But here’s the interesting part (no, really): for his statement to be false there must have existed at least one Cretan (including himself) who once said something true. And if it’s not fascinating that such an innocuous looking statement can guarantee the existence of truth-telling Cretans, I don’t know what is.