Arithmetic is Necessary

IF 0.7 1区哲学 0 PHILOSOPHY

JOURNAL OF PHILOSOPHICAL LOGIC Pub Date : 2024-06-05 DOI:10.1007/s10992-024-09760-9

Zachary Goodsell

引用次数: 0

Abstract

(Goodsell, Journal of Philosophical Logic, 51(1), 127-150 2022) establishes the noncontingency of sentences of first-order arithmetic, in a plausible higher-order modal logic. Here, the same result is derived using significantly weaker assumptions. Most notably, the assumption of rigid comprehension—that every property is coextensive with a modally rigid one—is weakened to the assumption that the Boolean algebra of properties under necessitation is countably complete. The results are generalized to extensions of the language of arithmetic, and are applied to answer a question posed by Bacon and Dorr (2024).

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算术是必要的

(Goodsell, Journal of Philosophical Logic, 51(1), 127-150 2022）在一个可信的高阶模态逻辑中确立了一阶算术句子的非偶然性。在这里，同样的结果是通过明显较弱的假设得出的。最值得注意的是，刚性理解的假设--即每个属性都与模态上的刚性属性同源--被弱化为必然性下属性的布尔代数是可数完备的这一假设。这些结果被推广到算术语言的扩展中，并被应用于回答培根和多尔（2024）提出的一个问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

JOURNAL OF PHILOSOPHICAL LOGIC PHILOSOPHY-

CiteScore

2.50

自引率

20.00%

发文量

期刊介绍： The Journal of Philosophical Logic aims to provide a forum for work at the crossroads of philosophy and logic, old and new, with contributions ranging from conceptual to technical. Accordingly, the Journal invites papers in all of the traditional areas of philosophical logic, including but not limited to: various versions of modal, temporal, epistemic, and deontic logic; constructive logics; relevance and other sub-classical logics; many-valued logics; logics of conditionals; quantum logic; decision theory, inductive logic, logics of belief change, and formal epistemology; defeasible and nonmonotonic logics; formal philosophy of language; vagueness; and theories of truth and validity. In addition to publishing papers on philosophical logic in this familiar sense of the term, the Journal also invites papers on extensions of logic to new areas of application, and on the philosophical issues to which these give rise. The Journal places a special emphasis on the applications of philosophical logic in other disciplines, not only in mathematics and the natural sciences but also, for example, in computer science, artificial intelligence, cognitive science, linguistics, jurisprudence, and the social sciences, such as economics, sociology, and political science.