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Apophatic Finitism and Infinitism

Heylen, Jan (2019) Apophatic Finitism and Infinitism. Logique et Analyse, 247. pp. 319-337.


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This article is about the ontological dispute between finitists, who claim that only finitely many numbers exist, and infinitists, who claim that infinitely many numbers exist. Van Bendegem set out to solve the 'general problem' for finitism: how can one recast finite fragments of classical mathematics in finitist terms? To solve this problem Van Bendegem comes up with a new brand of finitism, namely so-called 'apophatic finitism'. In this article it will be argued that apophatic finitism is unable to represent the negative ontological commitments of infinitism or, in other words, that which does not exist according to infinitism. However, there is a brand of infinitism, so-called 'apophatic infinitism', that is able to represent both the positive and the negative ontological commitments of apophatic finitism. Unfortunately, apophatic finitism cannot adopt that way without losing the ability to represent the positive ontological commitments of infinitism.

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Item Type: Published Article or Volume
Heylen, Janjan.heylen@kuleuven.be0000-0002-2809-3320
Keywords: Finitism Infinitism Apophatic finitism Apophatic infinitism Ontological commitments
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
Depositing User: Dr. Jan Heylen
Date Deposited: 28 May 2020 14:16
Last Modified: 28 May 2020 14:16
Item ID: 17244
Journal or Publication Title: Logique et Analyse
Publisher: Peeters
DOI or Unique Handle:
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
Date: 2019
Page Range: pp. 319-337
Volume: 247

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