RUSSELL AND RAMSEY ON THE PROBLEM OF PARADOXES

被引:5
作者
Ladov, Vsevolod A. [1 ]
机构
[1] Tomsk State Univ, Tomsk, Russia
来源
VESTNIK TOMSKOGO GOSUDARSTVENNOGO UNIVERSITETA-FILOSOFIYA-SOTSIOLOGIYA-POLITOLOGIYA-TOMSK STATE UNIVERSITY JOURNAL OF PHILOSOPHY SOCIOLOGY AND POLITICAL SCIENCE | 2018年 / 43卷
关键词
Russell; Ramsey; paradox; logic; mathematics; semantics; set; statement; self-reference;
D O I
10.17223/1998863X/43/9
中图分类号
C [社会科学总论];
学科分类号
03 ; 0303 ;
摘要
The problem of logical paradoxes is considered in the article. At the beginning of the 20th century, the problem was presented by Bertrand Russell and Frank Ramsey. Russell thought of all paradoxes as similar to each other. Ramsey asserted that they made up two completely different groups. In the second half of the 20th century, Ramsey's point of view was dominant. Graham Priest, a modern Australian logician, affirms that Russell was right and Ramsey was wrong for all paradoxes have a similar structure and one way of solution. The author of the article asserts that in this discussion one cannot decide on the winner because paradoxes are similar in one relation and different in another. All paradoxes are similar concerning the structure and the way to solve them. Russell was right in this relation. However, all paradoxes are different concerning the foundation they are built on, and Ramsey was right in this relation. Paradoxes have different foundations because difficulties in some of them arise in relation to logical and mathematical concepts, but difficulties in other paradoxes arise in relation to the clarification of meanings of linguistic expressions in which concepts of thought are presented. For example, Russell's paradox can be included in the first group of paradoxes because of the problem with the concept of the set of all sets. The Burali-Forti paradox can also be included in this group because of the problem with the concept of the set of all ordinal numbers. Other paradoxes have some problems with either words that express concepts or statements that express propositions. That is way these paradoxes should be included in the second group of paradoxes. The Liar paradox is one of the most characteristic examples in this case. In this paradox, we have a problem with an utterance of a citizen of Crete. Alfred Tarski emphasised the linguistic character of the paradox. In the formulation of the paradox, Tarski spoke about sentences of language. Sentences are more distinct linguistic essences than utterances.
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页码:101 / 110
页数:10
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