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An argument against Nominalism

Ferrari, Francesco Maria (2021) An argument against Nominalism. [Preprint]

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Abstract

Nominalism in formal ontology is still the thesis that the only acceptable domain of quantification is the first-order domain of particulars. Nominalists may assert that second-order well-formed formulas can be fully and completely interpreted within the first-order domain, thereby avoiding any ontological commitment to second-order entities, by means of an appropriate semantics called ``substitutional". In this paper I argue that the success of this strategy depends on the ability of Nominalists to maintain that identity, and equivalence relations more in general, is first-order and invariant. Firstly, I explain why Nominalists are formally bound to this first-order concept of identity. Secondly, I show that the resources needed to justify identity, a certain conception of identity invariance, are out of the nominalist's reach.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Ferrari, Francesco Mariaferrarifram@gmail.com0000-0002-1648-4180
Keywords: Formal Ontology; Extensionality; Identity; Logicality; Nominalism.
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
Depositing User: Dr. Francesco Maria Ferrari
Date Deposited: 24 Nov 2021 19:14
Last Modified: 24 Nov 2021 19:14
Item ID: 19916
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
Date: 19 November 2021
URI: http://philsci-archive.pitt.edu/id/eprint/19916

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