- Series Information
- The Oxford Handbook of Philosophy of Mathematics and Logic
- Notes on the Contributors
- Philosophy of Mathematics and Its Logic: Introduction
- A Priority and Application: Philosophy of Mathematics in the Modern Period
- Later Empiricism and Logical Positivism
- Wittgenstein on Philosophy of Logic and Mathematics
- The Logicism of Frege, Dedekind, and Russell
- Logicism in the Twenty‐first Century
- Logicism Reconsidered
- Intuitionism and Philosophy
- Intuitionism in Mathematics
- Intuitionism Reconsidered
- Quine and the Web of Belief
- Three Forms of Naturalism
- Naturalism Reconsidered
- Nominalism Reconsidered
- Structuralism Reconsidered
- Mathematics—Application and Applicability
- Logical Consequence, Proof Theory, and Model Theory
- Logical Consequence From a Constructivist View
- Relevance in Reasoning
- No Requirement of Relevance
- Higher‐order Logic
- Higher‐order Logic Reconsidered
Abstract and Keywords
In spite of the great advancement of logic in our time and the technical sophistication of disciplines such as model theory and proof theory, the concept of logical consequence—the most basic notion of logic—is still poorly understood. Basic intuitions are often in conflict with each other, and rather few attempts have been made to sort this out in a systematic fashion. This article critically reviews some of the attempts that have been made to articulate intuitions about logical consequence, but the review makes no claim to be comprehensive or to settle the issues. Most attention is given to how the notion of logical consequence may be developed from a constructivist point of view.
Dag Prawitz is Professor of Theoretical Philosophy at Stockholm University, Emeritus (as of 2001). Most of his research is in proof theory, philosophy of mathematics, and philosophy of language. Some early works include Natural Deduction: A Proof‐Theoretical Study (1965), “Ideas and Results in Proof Theory” (Proceedings of the Second Scandinavian Logic Symposium, 1971), and “Philosophical Aspects of Proof Theory” (Contemporary Philosophy, A New Survey, 1981). Some recent ones are “Truth and Objectivity from a Verificationist Point of View” (Truth in Mathematics, 1998), “Meaning and Objectivity” (Meaning and Interpretation, 2002), and replies to critic's in Theoria (1998) (special issue, “The Philosophy of Dag Prawitz”).
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