Logical paradoxes solution in semantically closed language

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Transliteration of original Title: 
Reshenie logicheskikh paradoksov v semanticheski zamknutom yazyke
Author(s): 
Vsevolod Ladov
Tomsk Scientific Center, Siberian Branch, Russian Academy of Sciences
Issue number: 
No.2 (Vol.52)
Pages: 
104-119
Abstract: 

The author considers the following question: is a consistent semantically closed language possible? The negative answer is the orthodox answer in the logic of the 20th century. It was presented in Russell’s theory of types and Tarski’s semantic theory of metalanguages. Nevertheless, contemporary logicians and philosophers of language return to this problem time and again, pointing to its relevance in various aspects. In particular, it is asserted that semantically closed language is a very important tool for expressing logical and philosophical ideas. In logic of the 20th century, the problem of semantically closed language was discussed in connection with the problem of logical paradoxes. Russell and Tarski saw a fundamental cause of paradoxes in the phenomenon of self-reference that arises in semantically closed language. Accordingly, a solution for paradoxes was seen in eliminating the cause, that is, in prohibiting semantically closed language by means of a hierarchy of logical types of classes (Russell) or a hierarchy of metalanguages (Tarski). However, some contemporary logicians criticize the hierarchical approach, whose main argument consists in asserting that the approach was wrong in its diagnosis of the cause of paradoxes. This author does not try to correct the diagnostics of the hierarchical approach by identifying another cause of paradoxes. Instead, the author recognizes that a general solution of the problem of paradoxes cannot be given, a priori, by eliminating what fundamentally generates them. In this article, a new “ad hoc solution” of the problem is offered that rests upon an empirical method of identifying and eliminating paradoxes. A specific characteristic of the method is admitting the existence of consistent semantically closed language.

Keywords: 
semantically closed language, self-reference, paradoxes, truth, Russell, Tarski, hierarchical approach, semantic incorrectness, ad hoc solution of logical paradoxes
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DOI: 
10.5840/eps201752233
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