2018
DOI: 10.1080/00455091.2017.1344502
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Modal structuralism simplified

Abstract: Since Benacerraf’s ‘What Numbers Could Not Be, ’ there has been a growing interest in mathematical structuralism. An influential form of mathematical structuralism, modal structuralism, uses logical possibility and second order logic to provide paraphrases of mathematical statements which don’t quantify over mathematical objects. These modal structuralist paraphrases are a useful tool for nominalists and realists alike. But their use of second order logic and quantification into the logical possibility operato… Show more

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Cited by 5 publications
(3 citation statements)
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“…(ii) How about dispensing with second-order logic by making the relations and properties in (M) fixed? For instance, let us follow Berry (2018) and paraphrase ϕ as 27 :…”
Section: Alternativementioning
confidence: 99%
See 1 more Smart Citation
“…(ii) How about dispensing with second-order logic by making the relations and properties in (M) fixed? For instance, let us follow Berry (2018) and paraphrase ϕ as 27 :…”
Section: Alternativementioning
confidence: 99%
“…PA ♢ comes by combing four first-order axioms of PA with □ ,s P(0) ∧ ( ∀x)( ∀y)(P(x) ∧ s(x, y) → P(y) → (∀x)( (x) → P(x)). 28 It is worth mentioning that Berry (2018) motivates her simplified modal structuralism as an alternative to Hellman's canonical modalism in order to solve the quantifying in problem and the incompossible problem. So there is no problem for her to take some mathematical facts for granted, but this is not available to a nominalist.…”
Section: Alternativementioning
confidence: 99%
“…Some restriction of the usual comprehension axiom will be needed to accommodate Armstrong's contention that there are no uninstantiated properties. For a version of modal structuralism that does not require second order quantification, see Berry (2018). The parenthetical "and perhaps more than sufficient" is there to indicate that Armstrong's was an inexact conception of truthmaking, to use Kit Fine's terminology-see (2017).…”
Section: Armstrong's Entailment Principlementioning
confidence: 99%