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Truth and existence

Heylen, Jan and Horsten, Leon (2017) Truth and existence. Thought: A Journal of Philosophy, 6 (2). pp. 106-114.


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Halbach has argued that Tarski biconditionals are not ontologically conservative over classical logic, but his argument is undermined by the fact that he cannot include a theory of arithmetic, which functions as a theory of syntax. This article is an improvement on Halbach's argument. By adding the Tarski biconditionals to inclusive negative free logic and the universal closure of minimal arithmetic, which is by itself an ontologically neutral combination, one can prove that at least one thing exists. The result can then be strengthened to the conclusion that infinitely many things exist. Those things are not just all Gödel codes of sentences but rather all natural numbers. Against this background inclusive negative free logic collapses into noninclusive free logic, which collapses into classical logic. The consequences for ontological deflationism with respect to truth are discussed.

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Item Type: Published Article or Volume
Heylen, Janjan.heylen@kuleuven.be0000-0002-2809-3320
Horsten, Leonleon.horsten@uni-konstanz.de0000-0003-3610-9318
Keywords: disquotational theory of truth; Tarski biconditionals; ontological deflationism; inclusive negative free logic; universal closure of arithmetic; nominalism; finitism
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
Depositing User: Dr. Jan Heylen
Date Deposited: 18 Jan 2022 05:20
Last Modified: 18 Jan 2022 05:20
Item ID: 20114
Journal or Publication Title: Thought: A Journal of Philosophy
Official URL:
DOI or Unique Handle:
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
Date: 2017
Page Range: pp. 106-114
Volume: 6
Number: 2

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