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Comment by stiff | Hacker News Reader

Yes I understand, but why do you think it needs justification? As far as I understand this is simply the definition of implication in classical logic, for one it follows from the truth tables of both expressions.

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OK, but we're not talking about classical logic, otherwise the question about whether the law of the excluded middle is derivable is uninteresting.

Well, that's exactly what people were considering and what the article is referring too, a variant of classical logic where everything except the law of excluded middle holds true. I don't think this is uninteresting, which postulates are independent from one another is one of the core problems in logic.

Nice flame, eot.

I didn't mean to flame, I thought we were having an interesting debate. I was under the impression we we're talking about logic systems in general where reductio ad absurdum exists, but the law of the excluded middle doesn't. Anyway, thanks, I learnt much.

This would be a very peculiar logic I think, maybe you just come from a very different background and hence all the hair-splitting was necessary, we just wandered so far away from the original point I lost patience, maybe unnecessarily, in the end it really was an interesting debate for me too.

Actually, I guess he's right.

Arguably, the common sense definition of 'A -> B' is simply modus ponens. That is 'Given A and A->B, it follows that B'. It's then no longer obvious that A -> B is equivalent to ~A v B.

Indeed, implication in IL is different from material implication even though IL has modus ponens.

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