Metalogic and the Overgeneration Argument

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Metalogic and the Overgeneration Argument. / Florio, Salvatore; Incurvati, Luca.

In: Mind, Vol. 128, No. 511, 07.2019, p. 761–793.

Research output: Contribution to journalArticlepeer-review

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Florio, S & Incurvati, L 2019, 'Metalogic and the Overgeneration Argument', Mind, vol. 128, no. 511, pp. 761–793. https://doi.org/10.1093/mind/fzy059

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Author

Florio, Salvatore ; Incurvati, Luca. / Metalogic and the Overgeneration Argument. In: Mind. 2019 ; Vol. 128, No. 511. pp. 761–793.

Bibtex

@article{a1c74721df3b4e398c0f6b005c32be73,
title = "Metalogic and the Overgeneration Argument",
abstract = " A prominent objection against the logicality of second-order logic is the so-called Overgeneration Argument. However, it is far from clear how this argument is to be understood. In the first part of the article, we examine the argument and locate its main source, namely the alleged entanglement of second-order logic and mathematics. We then identify various reasons why the entanglement may be thought to be problematic. In the second part of the article, we take a metatheoretic perspective on the matter. We prove a number of results establishing that the entanglement is sensitive to the kind of semantics used for second-order logic. These results provide evidence that, by moving from the standard set-theoretic semantics for second-order logic to a semantics which makes use of higher-order resources, the entanglement either disappears or may no longer be in conflict with the logicality of second-order logic.",
author = "Salvatore Florio and Luca Incurvati",
year = "2019",
month = jul,
doi = "10.1093/mind/fzy059",
language = "English",
volume = "128",
pages = "761–793",
journal = "Mind",
issn = "0026-4423",
publisher = "Oxford University Press",
number = "511",

}

RIS

TY - JOUR

T1 - Metalogic and the Overgeneration Argument

AU - Florio, Salvatore

AU - Incurvati, Luca

PY - 2019/7

Y1 - 2019/7

N2 - A prominent objection against the logicality of second-order logic is the so-called Overgeneration Argument. However, it is far from clear how this argument is to be understood. In the first part of the article, we examine the argument and locate its main source, namely the alleged entanglement of second-order logic and mathematics. We then identify various reasons why the entanglement may be thought to be problematic. In the second part of the article, we take a metatheoretic perspective on the matter. We prove a number of results establishing that the entanglement is sensitive to the kind of semantics used for second-order logic. These results provide evidence that, by moving from the standard set-theoretic semantics for second-order logic to a semantics which makes use of higher-order resources, the entanglement either disappears or may no longer be in conflict with the logicality of second-order logic.

AB - A prominent objection against the logicality of second-order logic is the so-called Overgeneration Argument. However, it is far from clear how this argument is to be understood. In the first part of the article, we examine the argument and locate its main source, namely the alleged entanglement of second-order logic and mathematics. We then identify various reasons why the entanglement may be thought to be problematic. In the second part of the article, we take a metatheoretic perspective on the matter. We prove a number of results establishing that the entanglement is sensitive to the kind of semantics used for second-order logic. These results provide evidence that, by moving from the standard set-theoretic semantics for second-order logic to a semantics which makes use of higher-order resources, the entanglement either disappears or may no longer be in conflict with the logicality of second-order logic.

U2 - 10.1093/mind/fzy059

DO - 10.1093/mind/fzy059

M3 - Article

VL - 128

SP - 761

EP - 793

JO - Mind

JF - Mind

SN - 0026-4423

IS - 511

ER -