The problem of 'space' in Frege's ontology a transcentental inquiry

Abstract

This thesis is an attempt to evaluate Frege's ontology of numbers in a critical way in view of Kant's transcendental philosophy. Despite the significant divergences between Kant and Frege, these two philosophers will be taken in continuity. It is shown that these divergences originate mostly from Frege's way of misevaluating Kant's system. The main problem of the thesis is the "space" of the objective thoughts in Frege's system. The most important conceptual similarities between Kant and Frege are the relations between object and concept, and concept and judgement. For both, arithmetical objects are neither empirical nor sensible and these objects do not exist by themselves. Numbers, as arithmetical objects, are found in Number concepts. Objects and concepts are found in judgements. Both Kant and Frege attempt to secure an objective status for natural numbers. In Frege's system, neither the formation nor the space of objects is mentioned. He does not consider 'synthesis' or 'unity' which are crucial for the formation of objects in Kant's system and to the objective thoughts, Frege does not assign a space. Frege's ontology does not provide a medium for connecting the objective thoughts either. Thus Frege's system is ontologically incomplete.