Eve explains why requiring all proof to be recursively, discursively priced is a form of skepticism that is simply a denial of reason. There is a real sort of skeptical attitude which is the thirst for truth, but there is also simply the refusal to believe something which lazily uses the impossible standard Eve very clearly describes.
Charles Dodgson, probably better known to most by his pen name Lewis Carroll and his books Alice In Wonderland and Through the Looking Glass, was a logician and mathematician at Oxford University. The Alice books are actually wonderfully full of logical puzzles and paradoxes, and I have heard the claim made that the reason that everyone in Wonderland is insane, is precisely because they are all perfectly logical, within their own parameters.
I want to talk about something else today, though. At one point, Dodgson wrote a short dialogue between swift-footed Achilles and the Tortoise, sometime after Achilles, impossibly, has caught up with the Tortoise and is riding on his back. For some reason, the conversation has turned to a discussion of the modus ponens, the logical validity of which Achilles is trying to persuade the Tortoise.
Modus ponens is one of the most basic valid argument…
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