Layers of Logical Consequence Logical consequence as epistemically model-theoretic and metaphysically proof-theoretic

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Grace Field

Abstract

Model-theory and proof-theory are two long-standing alternative descriptions of logical consequence. Proof-theory characterises truth in terms of logical implication. Namely, according to proof-theory, the statement ‘A implies B’ is true iff there exists a proof from A to B. In contrast, model-theory characterises truth based on possible states of the world. By model-theory, ‘A implies B’ is true iff for any model m, if m satisfies A then m satisfies B. In this paper I argue that we can reconcile the views, by making an appropriate distinction between epistemic nature and metaphysical nature. Namely, I will argue that we can view logical consequence as epistemically model-theoretic and metaphysically prooftheoretic.

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