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Is there a logic of confirmation transfer? (English) Zbl 0972.03006

Summary: This article begins by exploring a lost topic in the philosophy of science: the properties of the relations “evidence confirming \(h\) confirms \(h'\)” and, more generally, “evidence confirming each of \(h_1, h_2,\dots, h_m\) confirms at least one of \(h_1',h_2',\dots, h_n'\)”. The Bayesian understanding of confirmation as positive evidential relevance is employed throughout. The resulting formal system is, to say the least, oddly behaved. Some aspects of this odd behaviour the system has in common with some of the non-classical logics developed in the twentieth century. One aspect – its “parasitism” on classical logic – it does not, and it is this feature that makes the system an interesting focus for discussion of questions in the philosophy of logic. We gain some purchase on an answer to a recently prominent question, namely, what is a logical system? More exactly, we ask whether satisfaction of formal constraints is sufficient for a relation to be considered a (logical) consequence relation. The question whether confirmation transfer yields a logical system is answered in the negative, despite confirmation transfer having the standard properties of a consequence relation, on the grounds that validity of sequents in the system is not determined by the meanings of the connectives that occur in formulas. Developing the system in a different direction, we find it bears on the project of “proof-theoretic semantics”: conferring meaning on connectives by means of introduction (and possibly elimination) rules is not an autonomous activity, rather it presupposes a prior, non-formal, notion of consequence. Some historical ramifications are also addressed briefly.

MSC:

03A05 Philosophical and critical aspects of logic and foundations
03B30 Foundations of classical theories (including reverse mathematics)
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