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As anyone who has watched the original Star Trek series knows, Mr Spock was big on logic. He was also big on labeling the behaviour of humans "illogical". For example, consider this quote: May I say that I have not enjoyed serving under Humans. I find their illogic and foolish emotions a constant irritant. Season 3, episode 7 ("Day of the Dove") Now it's true that humans do make logical errors from time to time. For example suppose Tom is considering hiring a contractor. A friend recommends asking for references because "Good contractors provide references." Sure enough, the contractor provides references and Tom hires them. Unfortunately the work is poor, and Tom complains, "I thought good contractors provide references!?" But it's not just in the case of formal errors of logic that people's arguments and behaviour are termed "illogical"—or more commonly "irrational". For example, purchasing and selling decisions ...

Contrary to the assertion of the scandalous propaganda on the left, Santa Claus does indeed exist. And I can prove it. Start with proposition A: A . If A is true, then Santa Claus exists. Now, suppose A were true. Then it would follow that if A is true, then Santa Claus exists , and again since we're supposing A is true, it would follow that Santa Claus exists. So we've shown that if A is true, then Santa Claus exists . But that is proposition A, so we've proven that proposition A is true. So that means that Santa Claus exists! (A remarkable conclusion given my recent post on things that probably don't exist .) The only trouble is that the reasoning above lets you prove anything (e.g. that penguins rule the universe ). It's an example of Curry's paradox , which can't be easily explained away, and is the subject of ongoing research by logicians. Bah humbug! Still not convinced? Thomas Aquinas to the rescue! Well, actually, his modern admirers. Aquinas came u...

A recent article by philosopher Steven Hales is titled " You Can Prove a Negative " (a slightly different version of the article is available as a pdf file ). Hales argues that the "principle of folk logic" saying you can't prove a negative is just plain wrong . He points out that " any claim can be expressed as a negative, thanks to the rule of double negation." So it's easy to come up with examples of proving a negative. Hales goes on to say that "Some people seem to think that you can’t prove a specific sort of negative claim, namely that a thing does not exist." He counters this with an example of a valid proof that something doesn't exist: 1. If unicorns had existed, then there is evidence in the fossil record. 2. There is no evidence of unicorns in the fossil record. 3. Therefore, unicorns never existed. Of course, the difficulty here is with the truth of the premises (1 and 2). In particular, it could be that we just haven...