3 ms·
I am assuming that we are talking about taking the law of excluded middle out from classical logic, where all the other things independent from that law still h
by stiff 14y ago
I am assuming that we are talking about taking the law of excluded middle out from classical logic, where all the other things independent from that law still hold, and I think implication being material is independent.
- DanWaterworth 14y agoI mean material implication as in: In propositional logic, material implication is a valid rule of replacement which is an instance of the connective of the same name. It is the rule that states that "P implies Q" is logically equivalent to "not-P or Q". http://en.wikipedia.org/wiki/Implication http://en.wikipedia.org/wiki/Implication
- stiff 14y agoYes 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.
- DanWaterworth 14y agoOK, but we're not talking about classical logic, otherwise the question about whether the law of the excluded middle is derivable is uninteresting.
- stiff 14y agoWell, 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.
- DanWaterworth 14y agoI 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.
- stiff 14y agoThis 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.
- DigitalTurk 14y agoActually, 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.