This paper examines the role that Leibniz’s philosophy played in the debate between the Idealists and their opponents at the turn of the twentieth century. While it is Russell’s The Philosophy of Leibniz (1900) which is most frequently referred to in this context, this paper focuses on John Dewey’s Leibniz’s New Essays which was written twelve years earlier, during the Hegelian phase of Dewey’s career. It is important to shift our attention to Dewey’s commentary not only because it has been almost entirely neglected, but also because it provides a broader perspective on the role of the Leibnizian system in one of the leading debates in the history of philosophy, namely the debate over the intelligibility of the idea of internal relations. In particular, Dewey’s book reveals Leibniz’s involvement in the emergence of the notion of organism which was at the heart of the debate.

In the essay “Principia Calculi rationalis” Leibniz attempts to prove the theory of the syllogism within his own logic of concepts. This task would be quite easy if one made unrestricted use of the fundamental laws discovered by Leibniz, e.g., in the “General Inquiries” of 1686. In the essays of August 1690, Leibniz had developed some similar proofs which, however, he considered as unsatisfactory because they presupposed the unproven law of contraposition: “If concept A contains concept B, then conversely Non-B contains Non-A”. The proof in “Principia Calculi rationalis” appears to reach its goal without resorting to this law. However, it contains a subtle flaw which results from failing to postulate that the ingredient concepts have to be “possible”, i.e. self-consistent. Once this flaw is corrected, it turns out that the proof – though formally valid – would not have been approved by Leibniz because, again, it rests on an unproven principle even stronger than the law of contraposition.