Generalized Logical Consequence: Making Room for Induction in the Logic of Science

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...

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Bibliographic Details
Published in:Journal of philosophical logic 2002-06, Vol.31 (3), p.245-280
Main Authors: Chopra, Samir, Martin, Eric
Format: Article
Language:English
Subjects:
Computer science
Constraints on learning
Experiments
Hypotheses
Identification
Inductive reasoning
Inference
Learning
Learning theories
Learning theory
Logic
Logical theorems
Mathematical theorems
Modal realism
Observational terms
Philosophical logics. Philosophy of language
Philosophy
Predicate logic
Scientists
Theory
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Summary: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.
ISSN:0022-3611
1573-0433
DOI:10.1023/A:1015714624624