TWO REFORMULATIONS OF THE VERIFICATIONIST THESIS IN EPISTEMIC TEMPORAL LOGIC THAT AVOID FITCH’S PARADOX by Alexandru DRAGOMIR

RRFA-VIII-1-2014-06.Dragomir

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Author: Alexandru DRAGOMIR

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.

Keywords : Fitch’s paradox, knowability, dynamic epistemic logic, epistemic
logic, epistemic temporal logic, protocols

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