Sound and Fury

Signifying nothing

My favourite tautologies

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So today I was reading Artificial Intelligence and Scientific Method and Gillies mentions that (p \rightarrow q) \vee (q \rightarrow p) is a logical truth; a tautology in classical logic (but not in intuitionistic logic). I was interested by that and check that it is indeed the case by writing out the truth table. I didn’t bother to actually find a proof, but contented myself with the fact that the truth table + the fact that the propositional calculus is sound and complete is kind of a proof. Then I thought what are some other cool tautologies. Here are a couple I remembered.

  • \neg p \rightarrow (p \rightarrow q)
  • ( ( p \rightarrow q) \wedge (\neg p \rightarrow q ) ) \rightarrow q

Then I thought. Hmm. I’m a geek. But I’m still enamoured of this ability to put \LaTeX code in my wordpress posts so I thought I’d write about it…


Written by Seamus

March 7, 2008 at 3:20 pm

Posted in LaTeX, maths, philosophy

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