Two Reformulations of the Verificationist Thesis in Epistemic Temporal Logic that Avoid Fitch’s Paradox

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Abstract
1) We will begin by offering a short introduction to Epistemic Logic and presenting Fitch’s paradox in an epistemic‑modal logic. (2) Then, we will proceed to presenting three Epistemic Temporal logical frameworks creat‑ ed by Hoshi (2009) : TPAL (Temporal Public Announcement Logic), TAPAL (Temporal Arbitrary Public Announcement Logic) and TPAL+P ! (Temporal Public Announcement Logic with Labeled Past Operators). We will show how Hoshi stated the Verificationist Thesis in the language of TAPAL and analyze his argument on why this version of it is immune from paradox. (3) Edgington (1985) offered an interpretation of the Verificationist Thesis that blocks Fitch’s paradox and we will propose a way to formulate it in a TAPAL‑based lan‑ guage. The language we will use is a combination of TAPAL and TPAL+P ! with an Indefinite (Unlabeled) Past Operator (TAPAL+P !+P). Using indexed satisfi‑ ability relations (as introduced in (Wang 2010 ; 2011)) we will offer a prospec ‑ tive semantics for this language. We will investigate whether the tentative re‑ formulation of Edgington’s Verificationist Thesis in TAPAL+P !+P is free from paradox and adequate to Edgington’s ideas on how „all truths are knowable“ should be interpreted.
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Archival date: 2017-12-20
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References found in this work BETA
Reasoning About Knowledge.Fagin, Ronald; Y. Halpern, Joseph; Moses, Yoram & Vardi, Moshe
Knowledge and Belief.Hintikka, Jaakko
Dynamic Epistemic Logic.van Ditmarsch, Hans; van Der Hoek, Wiebe & Kooi, Barteld
Modal Logic.Blackburn, Patrick; de Rijke, Maarten & Venema, Yde

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2017-12-20

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