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Deductively Definable Logics of Induction

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Abstract

A broad class of inductive logics that includes the probability calculus is defined by the conditions that the inductive strengths [A|B] are defined fully in terms of deductive relations in preferred partitions and that they are asymptotically stable. Inductive independence is shown to be generic for propositions in such logics; a notion of a scale-free inductive logic is identified; and a limit theorem is derived. If the presence of preferred partitions is not presumed, no inductive logic is definable. This no-go result precludes many possible inductive logics, including versions of hypothetico-deductivism.

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  1. Center for Philosophy of Science, Department of History and Philosophy of Science, University of Pittsburgh, Pittsburgh, PA, USA

    John D. Norton

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  1. John D. Norton
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Correspondence to John D. Norton.

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Norton, J.D. Deductively Definable Logics of Induction. J Philos Logic 39, 617–654 (2010). https://doi.org/10.1007/s10992-010-9146-2

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