Abstractionism and Mathematical Singular Reference†

Assadian, Bahram

doi:10.1093/philmat/nkz003

Philosophia Mathematica

2019

DOI: 10.1093/philmat/nkz003

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Abstractionism and Mathematical Singular Reference†

Bahram Assadian

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2024

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Cited by 4 publications

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“…SeeDummett, 1981a (chaps 7 and 14),Dummett, 1981b (chaps 18-0), and Dummett, 1991 (chaps 15-18),Wright (1983),Wright (1995) andWright (1998). 9 For discussions, see for example,Ebert (2015) andAssadian (2019).…”

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confidence: 99%

Thin entities

Eklund

2022

Theoria

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Oystein Linnebo's book Thin Objects is partly devoted to defending the view that some objects are "thin" in that their existence does not impose any substantive demands on the world. In this paper, I discuss the concern that the defense relies on there being entities that serve as the referents of predicates. Linnebo thus seems to assume the thinness of those entities. In the course of my discussion, I also discuss what Linnebo says about the role of criteria of identity in his discussion of reference and existence.

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Thin entities

Eklund

2022

Theoria

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How Do We Semantically Individuate Natural Numbers?†

Buijsman

2021

Philosophia Mathematica

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How do non-experts single out numbers for reference? Linnebo has argued that they do so using a criterion of identity based on the ordinal properties of numerals. Neo-logicists, on the other hand, claim that cardinal properties are the basis of individuation, when they invoke Hume’s Principle. I discuss empirical data from cognitive science and linguistics to answer how non-experts individuate numbers better in practice. I use those findings to develop an alternative account that mixes ordinal and cardinal properties to provide a detailed (though not conclusively proven) answer to the question: how do we in fact semantically individuate numbers?

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Abstraction, truth, and free logic

Assadian

2024

The Philosophical Quarterly

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Abstractionism is the view that Fregean abstraction principles underlie our knowledge of the existence of mathematical objects. It is often assumed that the abstractionist proof for the existence of such objects requires ‘negative free logic’ in which all atomic sentences with empty terms are false. I argue that while negative free logic is not indispensably needed for the proof of abstract existence, there is a motivation for it—along broadly Fregean lines. The standard motivation for negative semantics rests on the explanation of truth in terms of reference. This line of reasoning, however, is not available in a context in which the reference of abstract terms must be proved, and not presupposed. I reverse the direction of explanation, thereby offering a novel motivation, Truth Priority, for the use of negative semantics. Some of the implications of Truth Priority for the abstractionist conception of ontology and reference will also be explored.

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Abstractionism and Mathematical Singular Reference†

Cited by 4 publications

References 31 publications

Thin entities

Thin entities

How Do We Semantically Individuate Natural Numbers?†

Abstraction, truth, and free logic

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