Modal-Epistemic Arithmetic and the problem of quantifying in

Synthese 190 (1):89-111 (2013)
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Abstract

The subject of this article is Modal-Epistemic Arithmetic (MEA), a theory introduced by Horsten to interpret Epistemic Arithmetic (EA), which in turn was introduced by Shapiro to interpret Heyting Arithmetic. I will show how to interpret MEA in EA such that one can prove that the interpretation of EA is MEA is faithful. Moreover, I will show that one can get rid of a particular Platonist assumption. Then I will discuss models for MEA in light of the problems of logical omniscience and logical competence. Awareness models, impossible worlds models and syntactical models have been introduced to deal with the first problem. Certain conditions on the accessibility relations are needed to deal with the second problem. I go on to argue that those models are subject to the problem of quantifying in, for which I will provide a solution.

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Jan Heylen
KU Leuven

Citations of this work

Conceptos de cognoscibilidad.Jan Heylen & Felipe Morales Carbonell - 2023 - Revista de Humanidades de Valparaíso 23:287-308.
The epistemic significance of numerals.Jan Heylen - 2014 - Synthese 198 (Suppl 5):1019-1045.
Proof systems for BAT consequence relations.Pawel Pawlowski - 2018 - Logic Journal of the IGPL 26 (1):96-108.

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References found in this work

Knowledge and its limits.Timothy Williamson - 2000 - New York: Oxford University Press.
The Philosophy of Philosophy.Timothy Williamson - 2007 - Malden, MA: Wiley-Blackwell.
Knowledge and Its Limits.Timothy Williamson - 2000 - Philosophy 76 (297):460-464.
Knowledge and its Limits.Timothy Williamson - 2000 - Tijdschrift Voor Filosofie 64 (1):200-201.

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