Generalized logical consequence: Making room for induction in the logic of science [Book Review]

Journal of Philosophical Logic 31 (3):245-280 (2002)
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We present a framework that provides a logic for science by generalizing the notion of logical (Tarskian) consequence. This framework will introduce hierarchies of logical consequences, the first level of each of which is identified with deduction. We argue for identification of the second level of the hierarchies with inductive inference. The notion of induction presented here has some resonance with Popper's notion of scientific discovery by refutation. Our framework rests on the assumption of a restricted class of structures in contrast to the permissibility of classical first-order logic. We make a distinction between deductive and inductive inference via the notions of compactness and weak compactness. Connections with the arithmetical hierarchy and formal learning theory are explored. For the latter, we argue against the identification of inductive inference with the notion of learnable in the limit. Several results highlighting desirable properties of these hierarchies of generalized logical consequence are also presented



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Samir Chopra
Brooklyn College (CUNY)

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References found in this work

The logic of scientific discovery.Karl Raimund Popper - 1934 - New York: Routledge. Edited by Hutchinson Publishing Group.
Fact, Fiction, and Forecast.Nelson Goodman - 1973 - Cambridge: Harvard University Press.
Logical foundations of probability.Rudolf Carnap - 1950 - Chicago]: Chicago University of Chicago Press.
Scientific reasoning: the Bayesian approach.Peter Urbach & Colin Howson - 1993 - Chicago: Open Court. Edited by Peter Urbach.

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