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Closure of A Priori Knowability Under A Priori Knowable Material Implication

Heylen, Jan (2014) Closure of A Priori Knowability Under A Priori Knowable Material Implication. Erkenntnis, 80 (2). pp. 359-380.

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Abstract

The topic of this article is the closure of a priori knowability under a priori knowable material implication: if a material conditional is a priori knowable and if the antecedent is a priori knowable, then the consequent is a priori knowable as well. This principle is arguably correct under certain conditions, but there is at least one counterexample when completely unrestricted. To deal with this, Anderson proposes to restrict the closure principle to necessary truths and Horsten suggests to restrict it to formulas that belong to less expressive languages. In this article it is argued that Horsten’s restriction strategy fails, because one can deduce that knowable ignorance entails necessary ignorance from the closure principle and some modest background assumptions, even if the expressive resources do not go beyond those needed to formulate the closure principle itself. It is also argued that it is hard to find a justification for Anderson’s restricted closure principle, because one cannot deduce it even if one assumes very strong modal and epistemic background principles. In addition, there is an independently plausible alternative closure principle that avoids all the problems without the need for restriction.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Heylen, Janjan.heylen@kuleuven.be0000-0002-2809-3320
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: 16735
Journal or Publication Title: Erkenntnis
Publisher: Springer Netherlands
DOI or Unique Handle: 10.1007/s10670-014-9647-4
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Logic
Date: 2014
Page Range: pp. 359-380
Volume: 80
Number: 2
URI: https://philsci-archive.pitt.edu/id/eprint/16735

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