Conditional Excluded Middle without the Limit Assumption
نویسندگان
چکیده
منابع مشابه
Conditional Excluded Middle without the Limit Assumption
But Lewis famously objects that counterfactually supposing that a given line had been more than an inch long will not yield an A-world minimally different from i. ‘‘Just as there is no shortest possible length above 1¢¢,’’ he writes, ‘‘so there is no closest world to ours among the worlds with lines more than an inch long’’ (1973a, 20–21; see also 1981b, 228–230). Lewis and Stalnaker also agree...
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But Lewis famously objects that counterfactually supposing that a given line had been more than an inch long will not yield an A-world minimally different from i. “Just as there is no shortest possible length above 1′′,” he writes, “so there is no closest world to ours among the worlds with lines more than an inch long” (a, –; see also b, –). Lewis and Stalnaker also agree abo...
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We prove that if a Π2 sentence is provable in a certain theory of higher order arithmetic without the law of the excluded middle then it is uniformly provable in the weak classical theory RCA0. Applying the contrapositive of this result, we give three examples where results of reverse mathematics can be used to show nonexistence of proofs in certain intuitionistic systems.
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ژورنال
عنوان ژورنال: Philosophy and Phenomenological Research
سال: 2011
ISSN: 0031-8205
DOI: 10.1111/j.1933-1592.2011.00507.x