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The Oxford Handbook of Philosophy of Mathematics and Logic$
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Stewart Shapiro

Print publication date: 2005

Print ISBN-13: 9780195148770

Published to Oxford Scholarship Online: July 2005

DOI: 10.1093/0195148770.001.0001

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Logical Consequence, Proof Theory, and Model Theory

Logical Consequence, Proof Theory, and Model Theory

Chapter:
(p.651) Logical Consequence, Proof Theory, and Model Theory
Source:
The Oxford Handbook of Philosophy of Mathematics and Logic
Author(s):

Stewart Shapiro (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0195148770.003.0021

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

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