Is English consequence compact?

被引：1

作者：

Paseau, A. C. ^{[1
]}

Griffiths, Owen ^{[2
]}

机构：

[1] Univ Oxford, Wadham Coll, Oxford OX1 3PN, England

[2] Univ Cambridge, Fac Philosophy, Sidgwick Ave, Cambridge CB3 9DA, England

来源：

THOUGHT-A JOURNAL OF PHILOSOPHY | 2021年 / 10卷 / 03期

关键词：

compactness; first-order logic; logic; logical consequence; philosophy of logic; second-order logic; validity;

D O I：

10.1002/tht3.492

中图分类号：

B [哲学、宗教];

学科分类号：

01 ; 0101 ;

摘要：

By mimicking the standard definition for a formal language, we define what it is for a natural language to be compact. We set out a valid English argument none of whose finite subarguments is valid. We consider one by one objections to the argument's logical validity and then dismiss them. The conclusion is that English-and any other language with the capacity to express the argument-is not compact. This rules out a large class of logics as the correct foundational one, for example any sound and complete logic, and in particular first-order logic. The correct foundational logic is not compact.

引用

页码：188 / 198

页数：11

共 26 条

[1]

[Anonymous], 1985, PHILOS LINGUISTICS

[2]

Barwise J., 1977, Studies in logic and the foundations of mathematics, V90, P5, DOI DOI 10.1016/S0049-237X(08)71097-8

[3]

Beall J.C., 2006, LOGICAL PLURALISM

[4] 2ND-ORDER LOGIC [J].