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8. Theoretical Computer Science, Operations Research and Optimization

The Paradox of Knowability in Epistemic Temporal Logic

Alexandru Dragomir
University of Bucharest & Institute for Logic and Data Science, Bucharest, Romania

Abstract:

The Knowability Thesis states that all truths are knowable, and it constitutes one of the main tenets of semantic anti-realism. The Omniscience Thesis states that all truths are already known, and it is obviously false. These two theses have very intuitive translations in the language of modal epistemic logic. The Paradox of Knowability (also known as the Church-Fitch Paradox) is the derivation of the obviously false Omniscience Thesis from the intuitive Knowability Thesis, using the axioms and inference rules of modal epistemic logic. Edgington (1985) solved the paradox by offering a new interpretation of the Knowability Thesis in which all factual (non-epistemic) truths are indexed to the actual world. The consequence of this indexing is that the derivation of the Omniscience Thesis from the Knowability Thesis is blocked. The aim of my presentation is to propose a semantic interpretation of Edgington's Knowability Thesis in a framework based on Hoshi's (2009) work in Epistemic Temporal Logic and Temporal Public Announcement Logic.