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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.

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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.

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.

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