Zur Verallgemeinerung logischer Begriffe: Das Beispiel von partieller Implikation und partieller Äquivalenz

(Wissenschaftstheorie, Englisch)

ccording to Carnap, deductive logic may be regarded as the theory of the relation of logical consequence, and inductive logic as the theory of another concept which is likewise objective and logical, viz., degree of confirmation (Carnap 1962, p. 43). As is well known, in the preface to the second edition of his Logical Foundations of Probability (1962), Carnap distinguishes two concepts of confirmation: Firmness and increase in firmness. According to the firmness-based account, a proposition A confirms another proposition B iff the posterior probability of B given A exceeds the posterior of non-B given A. On the other hand, A incrementally confirms B iff the posterior probability of B given A exceeds the posterior probability of B given non-A. While the majority of accounts purporting to explicate the notions of partial entailment or partial equivalence focus on the incremental concept of confirmation, it seems clear that what Carnap had in mind is much more akin to the firmness-based account. Based on a set of adequacy constraints I prove a representation theorem to the effect that, given these constraints, the posterior-based account is uniquely determined (up to ordinal equivalence) as the only account that satisfies all desiderata.

In my talk I also consider various arguments that have been leveled for the incremental conception, and hence against Carnap's initial suggestion and I show in what way they are ill-founded. Consequently, in addition to defending Carnap's initial suggestion on partial entailment, I advocate a hitherto unaccounted probabilistic generalization of logical equivalence that at the same time is a promising contribution to the highly topical discussion on probabilistic measures of coherence.

Chair: Christine Schurz

Zeit: 16:00-16:30, 12. September 2013 (Donnerstag)

Ort: HS 105

Michael Schippers

(University of Oldenburg, Department of Philosophy, Deutschland)

Michael Schippers (M.Ed.) studied Philsophy and Mathematics at the Universities of Osnabrück and Oldenburg (Germany). He is currently working on a PhD-thesis on probabilistic measures of coherence within the DFG-funded priority program "New Frameworks of Rationality".

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Letzte Aktualisierung: 2013-02-14.