可能有很多算术句子Gödel

IF 0.8 1区哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE

Philosophia Mathematica Pub Date : 2021-02-01 DOI:10.1093/philmat/nkaa041

Kaave Lajevardi;Saeed Salehi

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引用次数: 1

摘要

我们认为，在通常的假设下，对于服从Gödel第一不完备定理的足够强的算术理论，人们不可能不得体地谈论该理论的Gödel句。原因是，在不违反Gödel定理要求的情况下，如果理论是不可靠的，那么可以有一个真句和一个假句，每一个都可证明地等同于它自己在理论中的不可证明性。

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There May Be Many Arithmetical Gödel Sentences

We argue that, under the usual assumptions for sufficiently strong arithmetical theories that are subject to Gödel's First Incompleteness Theorem, one cannot, without impropriety, talk about the Gödel sentence of the theory. The reason is that, without violating the requirements of Gödel's theorem, there could be a true sentence and a false one each of which is provably equivalent to its own unprovability in the theory if the theory is unsound.

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来源期刊

Philosophia Mathematica HISTORY & PHILOSOPHY OF SCIENCE-

CiteScore

1.70

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Philosophia Mathematica is the only journal in the world devoted specifically to philosophy of mathematics. The journal publishes peer-reviewed new work in philosophy of mathematics, the application of mathematics, and computing. In addition to main articles, sometimes grouped on a single theme, there are shorter discussion notes, letters, and book reviews. The journal is published online-only, with three issues published per year.