Logical Consequence, Proof Theory, and Model Theory

Stewart Shapiro

in The Oxford Handbook of Philosophy of Mathematics and Logic

Published in print March 2005 | ISBN: 9780195148770
Published online July 2005 | e-ISBN: 9780199835560 | DOI:

Series: Oxford Handbooks in Philosophy

Logical Consequence, Proof Theory, and Model Theory

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This chapter provides broad coverage of the notion of logical consequence, exploring its modal, semantic, and epistemic aspects. It develops the contrast between proof-theoretic notion of consequence, in terms of deduction, and a model-theoretic approach, in terms of truth-conditions. The main purpose is to relate the formal, technical work in logic to the philosophical concepts that underlie reasoning.

Keywords: logic; consequence; semantics; epistemology; proof theory; deduction; model theory; truth-conditions

Chapter.  9244 words. 

Subjects: Philosophy of Mathematics and Logic

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