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The undergeneration of permutation invariance as a criterion for logicality

Dutilh Novaes, C., 2014, In : Erkenntnis. 79, 1, p. 81-97

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APA

Dutilh Novaes, C. (2014). The undergeneration of permutation invariance as a criterion for logicality. Erkenntnis, 79(1), 81-97. https://doi.org/10.1007/s10670-013-9469-9

Author

Dutilh Novaes, Catarina. / The undergeneration of permutation invariance as a criterion for logicality. In: Erkenntnis. 2014 ; Vol. 79, No. 1. pp. 81-97.

Harvard

Dutilh Novaes, C 2014, 'The undergeneration of permutation invariance as a criterion for logicality', Erkenntnis, vol. 79, no. 1, pp. 81-97. https://doi.org/10.1007/s10670-013-9469-9

Standard

The undergeneration of permutation invariance as a criterion for logicality. / Dutilh Novaes, Catarina.

In: Erkenntnis, Vol. 79, No. 1, 2014, p. 81-97.

Research output: Contribution to journalArticleAcademicpeer-review

Vancouver

Dutilh Novaes C. The undergeneration of permutation invariance as a criterion for logicality. Erkenntnis. 2014;79(1):81-97. https://doi.org/10.1007/s10670-013-9469-9


BibTeX

@article{1f5da485437d4c40a251ba0af9fde018,
title = "The undergeneration of permutation invariance as a criterion for logicality",
abstract = "Permutation invariance is often presented as the correct criterion forlogicality. The basic idea is that one can demarcate the realm of logic by isolatingspecific entities—logical notions or constants—and that permutation invariancewould provide a philosophically motivated and technically sophisticated criterionfor what counts as a logical notion. The thesis of permutation invariance as acriterion for logicality has received considerable attention in the literature in recentdecades, and much of the debate is developed against the background of ideas put forth by Tarski in a 1966 lecture (Tarski 1966/1986). But as noted by Tarski himself in the lecture, the permutation invariance criterion yields a class of putative ‘logical constants’ that are essentially only sensitive to the number of elements in classes of individuals. Thus, to hold the permutation invariance thesis essentially amounts to limiting the scope of logic to quantificational phenomena, which is controversial at best and possibly simply wrong. In this paper, I argue that permutation invariance is a misguided approach to the nature of logic because it is not an adequate formal explanans for the informal notion of the generality of logic. In particular, I discuss some cases of undergeneration of the criterion, i.e. the fact that it excludes from the realm of logic operators that we have good reason to regard as logical, especially some modal operators.",
author = "{Dutilh Novaes}, Catarina",
year = "2014",
doi = "10.1007/s10670-013-9469-9",
language = "English",
volume = "79",
pages = "81--97",
journal = "Erkenntnis",
issn = "1572-8420",
publisher = "SPRINGER",
number = "1",

}

RIS

TY - JOUR

T1 - The undergeneration of permutation invariance as a criterion for logicality

AU - Dutilh Novaes, Catarina

PY - 2014

Y1 - 2014

N2 - Permutation invariance is often presented as the correct criterion forlogicality. The basic idea is that one can demarcate the realm of logic by isolatingspecific entities—logical notions or constants—and that permutation invariancewould provide a philosophically motivated and technically sophisticated criterionfor what counts as a logical notion. The thesis of permutation invariance as acriterion for logicality has received considerable attention in the literature in recentdecades, and much of the debate is developed against the background of ideas put forth by Tarski in a 1966 lecture (Tarski 1966/1986). But as noted by Tarski himself in the lecture, the permutation invariance criterion yields a class of putative ‘logical constants’ that are essentially only sensitive to the number of elements in classes of individuals. Thus, to hold the permutation invariance thesis essentially amounts to limiting the scope of logic to quantificational phenomena, which is controversial at best and possibly simply wrong. In this paper, I argue that permutation invariance is a misguided approach to the nature of logic because it is not an adequate formal explanans for the informal notion of the generality of logic. In particular, I discuss some cases of undergeneration of the criterion, i.e. the fact that it excludes from the realm of logic operators that we have good reason to regard as logical, especially some modal operators.

AB - Permutation invariance is often presented as the correct criterion forlogicality. The basic idea is that one can demarcate the realm of logic by isolatingspecific entities—logical notions or constants—and that permutation invariancewould provide a philosophically motivated and technically sophisticated criterionfor what counts as a logical notion. The thesis of permutation invariance as acriterion for logicality has received considerable attention in the literature in recentdecades, and much of the debate is developed against the background of ideas put forth by Tarski in a 1966 lecture (Tarski 1966/1986). But as noted by Tarski himself in the lecture, the permutation invariance criterion yields a class of putative ‘logical constants’ that are essentially only sensitive to the number of elements in classes of individuals. Thus, to hold the permutation invariance thesis essentially amounts to limiting the scope of logic to quantificational phenomena, which is controversial at best and possibly simply wrong. In this paper, I argue that permutation invariance is a misguided approach to the nature of logic because it is not an adequate formal explanans for the informal notion of the generality of logic. In particular, I discuss some cases of undergeneration of the criterion, i.e. the fact that it excludes from the realm of logic operators that we have good reason to regard as logical, especially some modal operators.

U2 - 10.1007/s10670-013-9469-9

DO - 10.1007/s10670-013-9469-9

M3 - Article

VL - 79

SP - 81

EP - 97

JO - Erkenntnis

JF - Erkenntnis

SN - 1572-8420

IS - 1

ER -

ID: 9767146