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Publication Details

Synonymity and Extensional Isomorphism

(Original title: Synonymita a extenzionálna izomorfia)
Filozofia, 24 (1969), 4, 378-398.
Type of work: Papers and Discussions
Publication language: Slovak
In this paper several definitions of synonymity are being constructed and analysed, according to which two arbitrary extensional isomorphic expressions are synonymous. The definitions and reflections connected with them are being relativized with regard to the extensional language / (and to the language J’ which is its extension) which is a language of a simple theory of types. The concept of extensional isomorphism is exactly defined in Definition 12. In other words, two arbitrary, correctly formed expressions W1 and W2 in which no variables occur, are extensionally isomorphic if and only if (i) W1 denotes the same object as W2, (ii) W1, W2 have the same logical structure and (iii) corresponding primitive expressions of the expressions W1 and W2 denote the same objects. The exact definition also refers to the forms of the language ] (or J’), which means that in the present work the synonymity of forms (of the variables and expressions in which free variables occur) is also being taken into account. According to the first of the definitions under study, the expressions W1 and W2 are synonymous if and only if they are extensionally isomorphic; according to the other definitions, the expressions W1, W2 are synonymous even when W1 can be transformed, by means of replacements of its certain sub-expressions by other expressions, to the expressions W2 or, at least, to some expression V which is extensionally isomorphic with W2. By imposing different conditions on the expressions which may be mutually replaced in the transformation of the expression W1 to W2 or V, a whole scale of definitions can be obtained which meet different intuitive and theoretical demands made upon the synonymity of linguistic expressions (e. g., one may exchange logically or definitionally equivalent expressions). Various possibilities of formulating these conditions are suggested in the present paper.
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