No, there are good reasons to reject the law of excluded middle other than that particular flavor of relativism. I think the jury’s still out on whether anything of worth can come out of paraconsistent logic (or intuitionism that disallows the law for infinite sets, or other such logics) but trying to reject the principle of explosion and resolving the liar’s paradox seem like the sorts of things a professional logician might reasonably spend time on.
I completely agree. But do you think it’s reasonable for economists to reject the results of other economists on the grounds that the result depends on the law of the excluded middle?
Speaking for myself, I wouldn’t have a problem with an intuitionist/constructivist economist who rejected the formal deductive validity of proof that relied on the LoXM. But it wouldn’t follow from that that the predictions the other economist were wrong, and frankly thats the criteria by which economic theories should be evaluated anyway since perfect deductive validity isn’t important when your axioms aren’t always true either.
As a point of historical curiosity, I’d be interested to know if there ever was an explicitly constructivist economist.
Of course there are. If I understand the abstract correctly, this paper argues for a particular formalization of game theory (often a branch of economics) on the grounds that the players (intuitionistically) play strategies that are computable from only a bounded amount of lookahead.
No, there are good reasons to reject the law of excluded middle other than that particular flavor of relativism. I think the jury’s still out on whether anything of worth can come out of paraconsistent logic (or intuitionism that disallows the law for infinite sets, or other such logics) but trying to reject the principle of explosion and resolving the liar’s paradox seem like the sorts of things a professional logician might reasonably spend time on.
I completely agree. But do you think it’s reasonable for economists to reject the results of other economists on the grounds that the result depends on the law of the excluded middle?
Speaking for myself, I wouldn’t have a problem with an intuitionist/constructivist economist who rejected the formal deductive validity of proof that relied on the LoXM. But it wouldn’t follow from that that the predictions the other economist were wrong, and frankly thats the criteria by which economic theories should be evaluated anyway since perfect deductive validity isn’t important when your axioms aren’t always true either.
As a point of historical curiosity, I’d be interested to know if there ever was an explicitly constructivist economist.
Does this guy count?
Er, this constructivism not this one.
Of course there are. If I understand the abstract correctly, this paper argues for a particular formalization of game theory (often a branch of economics) on the grounds that the players (intuitionistically) play strategies that are computable from only a bounded amount of lookahead.
www.math.wisc.edu/~lempp/conf/wroc/stecher.pdf
Not sure that justifies an “Of course there are”, but very nice find.
Rule 34!
If I couldn’t find one, I’d have been compelled to become one.
Please, no constructivist economics porn. It’s bad enough there’s that Austrian school slashfic.