An introduction to transcendental exposition of Skolem paradox

In the present thesis, we carry out a transcendental investigation of Skolem paradox. Skolem paradox is a paradox at the junction point of symbolic logic, axiomatic set theory and philosophy. Skolem paradox is generally understood as a model theoretic paradox which undermines the realist approach to these areas. In order to show why this paradox doesn't pose a threat to the realist approach to these areas, we begin with clarifying the crucial assumptions on which such an understanding relies. According to our investigation, first of these assumptions is that the elements of formal language is constituted just by listing and enumerating its symbols with the help of recursive functions defined in syntactical manner. Second of these assumptions is that the axiomatic approach is only way to understand the set theoretic notions such as the universe of sets and uncountability. As for the second assumption we argue, in relation to Kant's transcendental thought, that cognition of the universe of sets is necessary to the set theoretic discourse. From Kantian point of view the universe of sets is the formal whole of reason and we determine the schemata of reason on which constitution of the formal whole depends. As for the first assumption we claim that cognition and constitution of the representation of Cantor's diagonal argument depend on the same schemata of reason. We conclude that these schemata provide in a manner objectivity and absoluteness to the universe of sets. In view of our investigation we obtain an interpretation of Skolem paradox in relation to Lövenheim-Skolem Theorem. According to this interpretation Lövenheim-Skolem Theorem implies two different points of view about the universe of sets and if these points of view are differentiated Skolem paradox doesn't pose a threat to the realist approach.