Sunday, March 14, 2010

Carnap Disenchantment

[Sigh, I can never make up my mind about Carnap. I guess I'm feeling anti today]

I understand what it is to say that it's "merely a pragmatic choice" whether to use first order logic with the usual connectives vs. with the sheffer stroke. In both cases you will be expressing truths when you derive things in accordance with the logical laws, so the only harm you can do with choosing the sheffer stroke is make your proofs take longer.

But the "choice" of accepting a weaker vs. stronger and (say) inconsistent logical system, does not have this feature. In one case, you will be deriving truths. In the other case, you will now be deriving some falsehoods/crash your whole language so that none of your sentences are meaningful at all.

So I don't see what Carnap can mean by saying that adopting a system is merely pragmatic choice. Adopting a consistent system is a hard epistemic task! The only pragmatic choice is choosing which system - of a menu of systems of reasoning which are coherent enough to give their terms meaning and count as truth-preserving - to use.

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