Predication and Computable Concepts

Max Freund


By constructing an formal semantic interpretation (and employing results from computability theory in its construction), we show that predication can be consistently assumed to be a semi-computable concept, relative to the formal system LC, when restricted in its application to fully computable or semi-computable concepts. Within the context of the same formal system, we also prove that a contradiction ensues if it is held that predication is a fully computable. If predication is assumed to be a semi-computable concept applicable to any concept (computable or otherwise), we show that a consequence follows within LC that would contradict a well established result from computability theory. System LC is a conceptualist second order logical formal system for reasoning with computable concepts. It also contains an axiom assigning correlates to semi-computable concepts, which is justified on the basis of Church’s thesis and a discussion concerning the relationship between computable concepts and Turing machines.


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