Why mathematical logic?: Philosophy Forums

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Why mathematical logic?

ottological
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Posted 10/12/09 - 09:03 AM:	#11
lullus wrote: Why is that mathematical logic works? I mean that when you conclude something from abstract reasoning why is that result true in the real world? It seems like any attempt to show that, without a doubt, mathematical logic is a valid way to work.. must use mathematical logic to prove that. In exactly the same was as assuming the Bible is true leads to the conclusion that God exists. Well, I think you are really asking how we know mathematical logic is sound--that is, how we know that we cannot prove false conclusions from true premises. The answer is that we can prove that various mathematical logics are sound. However, these proofs of soundness are not carried out in any mathematical logic. Instead, we prove the soundness of a mathematical logic in metalogically (i.e., in ordinary language). I suppose one could object to this method of proof by asking how we know our informal logic is correct, but that seems to me to be an untenable point of view.

Legion
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Posted 10/13/09 - 04:50 AM:	#12
Maybe it’s because natural systems and formal systems are both (in their own ways) systems of entailment. X entails Y In this statement, X and Y could be propositions of a formal system or phenomena of a natural system.
We sense. We reason. We predict. We don't always get those right.

lullus
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