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Modal-Epistemic Arithmetic and the Problem of Quantifying In

Heylen, Jan (2013) Modal-Epistemic Arithmetic and the Problem of Quantifying In. Synthese, 190 (1). pp. 89-111.

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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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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Heylen, Janjan.heylen@kuleuven.be0000-0002-2809-3320
Keywords: Heyting Arithmetic; Epistemic Arithmetic; Modal-Epistemic Arithmetic; awareness models; impossible worlds models; syntactical models; logical omniscience; quantifying in; Stewart Shapiro; Leon Horsten
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Logic
Depositing User: Dr. Jan Heylen
Date Deposited: 20 Dec 2019 17:29
Last Modified: 20 Dec 2019 17:29
Item ID: 16737
Journal or Publication Title: Synthese
DOI or Unique Handle: https://doi.org/10.1007/s11229-012-0154-3
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Logic
Date: 2013
Page Range: pp. 89-111
Volume: 190
Number: 1
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/16737

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