Deductively Definable Logies of Induction

Journal of Philosophical Logic 39 (6):617 - 654 (2010)
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
Keywords Bayesianism  Confirmation  Induction  Non-probabilistic
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