Abstract

Kant distinguishes between intuitions and concepts in his formal logic and this distinction corresponds to the one made in type-theoretic languages. Independently, his theory of things in themselves can be explicated by the use of type-theoretic language. The two themes come together in Kant's criticism of Leibniz. Kant criticizes Leibniz in two ways: Leibniz took appearances to represent things in themselves; and Leibniz did not distinguish concepts from intuitions. On this essay's explication, both are ways of saying Leibniz rejected type-theoretic distinctions, and it is true he did. Kant's theory of things in themselves does suit his major purposes in epistemology and ethics and in differentiating himself from Leibniz and Berkeley. ;J. H. Lambert is rather unfamiliar so a general introduction is included. He is a mathematician, experimentalist, linguist and philosopher who worked on logic in the Leibnizian tradition and corresponded with Kant. His logic is largely algebraic but has some beginnings of type-theoretic distinctions. He does see substance as what is behind properties and he describes a substance as a "thing in itself." His account of things in themselves is similar in some ways to Kant's but is not critical. Overall, he seems to have contributed to many of Kant's ideas on the structure of knowledge but he completely missed any notion of a critical limitation of knowledge. He does raise the question of justifying claims to a priori non-analytic knowledge, but explicitly declines to give an answer. ;Leibniz's logic is algebraic, both formally and in his philosophy. This explains why he rejects substances as substrate or as the thing behind the properties and instead, after about 1690, sees substances as an "enduring law" relating the properties of a thing. This notion of substance as enduring law unifies his metaphysics, ethics, and physics, and is the basis for his arguments against Descartes. His algebraic logic also explains his difficulties with the logic of relations. He never considered relations eliminable or insignificant but he failed to find a technical treatment of them. ;This essay looks at Leibniz's, Lambert's, and Kant's views on reference and how those views affect their metaphysics, particularly their ideas of substance, individuals, and things in themselves. The main purpose is to give background and an explication of Kant's theory of things in themselves. ;First the logical issue is stated by use of formal languages. The relevant alternatives are type-theoretic and algebraic languages. The first have individual constants which refer to individuals and predicate constants which correspond to universals. These two types of constants are distinguished by the syntax, or grammar, of the languages. Algebraic languages make no such distinction. The two sorts of languages can be translated into each other but there is a difference as to what sentences are provable. In type-theoretic languages with identity, sentences of the form "c=c" are provable. The translates of these sentences into algebraic languages with identity are not provable. This difference is important to the account of Kant's theory of things in themselves.