T. Parent
Nazarbayev University
If a semantically open language has no constraints on self-reference, one can prove an absurdity. The argument utilizes co-referring names 'a0' and 'a1', and the definition of a functional expression 'The reflection of x = y'. The definition enables a type of self-reference without deploying any semantic terminology--yet given that a0= a1, the definition implies the that 'a0' = 'a1', which is absurd. In truth, however, 'the reflection of x = y' expresses an ill-defined function. And since there is a general ban on ill-defined functions, there is no real cause for concern. Still, the moral would be that the prohibition on ill-defined functions entails that self-reference cannot be unconstrained, even in a semantically open language.
Keywords Self-Reference  Circularity  Paradox  Yablo, Stephen  Tarski, Alfred  Godel, Kurt  Classical Logic
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References found in this work BETA

On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.
On the Plurality of Worlds.Allen Stairs - 1988 - Philosophy and Phenomenological Research 49 (2):333-352.

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