- 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
This article advances an unabashedly partisan view of how best to “relevantize” a logic. The view is laid out as informally as possible, given the technical nature of the subject matter. Here, “relevantizing” is understood as the project of formulating a decent system of logic that does not endorse Lewis's First Paradox: A, ¬A:B. Such a system will be paraconsistent, in that it will allow for distinct inconsistent theories (within a given language). But it will not be dialetheist. That is, it will not allow for true contradictions. Dialetheism does not follow from (though, in order to avoid trivialization, it requires) a refusal to infer whatever one pleases from a contradiction.
Neil Tennant is Distinguished Humanities Professor at The Ohio State University. His publications include Anti‐realism in Logic (Oxford University Press, 1987) and The Taming of the True (Oxford University Press, 1997).
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