On the Innocence and Determinacy of Plural Quantification

Florio, Salvatore; Linnebo, Øystein

doi:10.1111/nous.12091

Cited by 18 publications

(10 citation statements)

References 31 publications

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“…There is a parallel argument in Florio and Linnebo (2016). Florio and Linnebo are tentative but come close to biting the bullet:…”

Section: Jones's Commitment To Plural Realismmentioning

confidence: 99%

Should a higher-order metaphysician believe in properties?

Liggins

2021

Synthese

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In this paper I take second order-quantification to be a sui generis form of quantification, irreducible to first-order quantification, and I examine the implications of doing so for the debate over the existence of properties. Nicholas K. Jones has argued that adding sui generis second-order quantification to our ideology is enough to establish that properties exist. I argue that Jones does not settle the question of whether there are properties because—like other ontological questions—it is first-order. Then I examine three of the main arguments for the existence of properties. I conclude that sui generis second-order quantification defeats the “one over many” argument and that, coupled with second-order predication, it also defeats the reference and quantification arguments.

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“…There is a parallel argument in Florio and Linnebo (2016). Florio and Linnebo are tentative but come close to biting the bullet:…”

Section: Jones's Commitment To Plural Realismmentioning

confidence: 99%

Should a higher-order metaphysician believe in properties?

Liggins

2021

Synthese

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“…But this tacit assumption has recently been challenged by Florio and Linnebo (2016). According to their observation, besides Boolos's canonical semantics, there is another non-standard Henkin semantics for plural logic.…”

Section: Alternativementioning

confidence: 99%

Nominalism and Mathematical Objectivity

Luo

2022

Axiomathes

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We observe that Putnam’s model-theoretic argument against determinacy of the concept of second-order quantification or that of the set is harmless to the nominalist. It serves as a good motivation for the nominalist philosophy of mathematics. But in the end it can lead to a serious challenge to the nominalist account of mathematical objectivity if some minimal assumptions about the relation between mathematical objectivity and logical objectivity are made. We consider three strategies the nominalist might take to meet this challenge, and we argue that all these strategies are untenable.

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“…14 Thanks to Mary Leng for suggesting this way of putting it.15 It is sometimes suggested that our grasp of plural logic will deliver the required combinatorial concept. But the same question arises: what allows us to grasp full plural logic, rather than Henkin plural logic?Florio and Linnebo (2016) develop this criticism elegantly.…”

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confidence: 99%

Mathematical Internal Realism

Button¹

2022

Engaging Putnam

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Our modelist might do better to focus on definitional equivalence instead of isomorphism (see Button & Walsh 2018: § §5.1-5.2); but this would not change the dialectic. 6 Button & Walsh (2018: ch.6) coined the term, and go into more detail. 7 The remainder of this section presents the central problem I extract from Putnam's (1980) invocation of the Löwenheim-Skolem Theorem. (Admittedly, Putnam raised the issue in a more "objectual" than "conceptual" key; but see footnote 1, above.) Dummett (1963: 192) raised a similar problem, focussing on Gödelian incompleteness. For more, see Button & Walsh (2018: ch.7). 45 Cf. Button (2013, 217). 46 Cf. Meadows (2013, 539-40). 47 Putnam (1980. 48 At this point, the modelist might start to say things like: maybe I don't even understand (at all) the worry that I am "trapped" in M! At that point, I feel we have earned the right to walk away from the modelist. Of course, there is more to say about such ineffable scepticism; but for more, see Button & Walsh (2018: ch.9, §11.6). 49 Cf. Button & Walsh (2018: §11.6) on "indefinite extensibility" in this context.

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On the Innocence and Determinacy of Plural Quantification

Cited by 18 publications

References 31 publications

Should a higher-order metaphysician believe in properties?

Should a higher-order metaphysician believe in properties?

Nominalism and Mathematical Objectivity

Mathematical Internal Realism

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