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What Do We Mean? Semantics, Practices and Pluralism
Abstract: In this informal talk, I will revisit some longstanding issues in philosophical logic in the light of some contemporary developments.
The longstanding issues? (1) Michael Dummett’s challenge in The Logical Basis of Metaphysics to the effect that to get anywhere in fundamental issues of metaphysics we would do well to attend to the fundamental commitments of our theory of meaning—and that those concerns lead to the conclusion that we can find common ground in intuitionistic logic, not classical logic. (2) The issue of pluralism (or monism) about logical consequence. Contemporary work in logic is filled with a range of different (and seemingly opposed) accounts of what follows from what. Many different kinds of logical pluralism have arisen to attempt to make sense of the diversity of logical analyses, and just as many defences of logical monism have been offered.
The contemporary developments? The rise of dependent type theory in computer science and the consequent rise of proof assistants in the formalisation of mathematics. Different proof assistants (Agda, Idris, Lean, Isabelle, Coq) make different choices in the formal representation of mathematical reasoning, but the predominant choice of these proof assistants is to represent proofs constructively, in what amounts to intuitionistic logic and not classical logic.
https://consequently.org/presentation/2024/what-do-we-mean-arche/
Abstract: In this informal talk, I will revisit some longstanding issues in philosophical logic in the light of some contemporary developments.
The longstanding issues? (1) Michael Dummett’s challenge in The Logical Basis of Metaphysics to the effect that to get anywhere in fundamental issues of metaphysics we would do well to attend to the fundamental commitments of our theory of meaning—and that those concerns lead to the conclusion that we can find common ground in intuitionistic logic, not classical logic. (2) The issue of pluralism (or monism) about logical consequence. Contemporary work in logic is filled with a range of different (and seemingly opposed) accounts of what follows from what. Many different kinds of logical pluralism have arisen to attempt to make sense of the diversity of logical analyses, and just as many defences of logical monism have been offered.
The contemporary developments? The rise of dependent type theory in computer science and the consequent rise of proof assistants in the formalisation of mathematics. Different proof assistants (Agda, Idris, Lean, Isabelle, Coq) make different choices in the formal representation of mathematical reasoning, but the predominant choice of these proof assistants is to represent proofs constructively, in what amounts to intuitionistic logic and not classical logic.
https://consequently.org/presentation/2024/what-do-we-mean-arche/