A Formal Analysis of Selected Proofs by Aquinas for the Uniqueness of God

Abstract

In the current article I present and comment on fragments of Leibniz’s Remarks on Benedict de Spinoza’s Ethics (part I, Of God). Emphasis is put on Spinoza’s and Leibniz’s remarks on substance and attribute. I guide the reader through Leibniz’s reconstruction of the proof for theorem 2 from the first part of his Ethics and Leibniz’s criticism concerning it. The importance of theorem 2 lies in that it is used by Spinoza in the proof for pantheism (expressed in theorem 14). Another thing worth considering is Leibniz’s critical remarks related to Spinoza’s argument for the existence of a substance (theorem 7). I reconstruct part of both Spinoza’s and Leibniz’s reasoning using modalities. I also reconstruct Spinoza’s proof for the uniqueness of a substance presented by theorem 8. Finally, I recall main features of the Leibnizian concept of substance pointing at the disagreement between both philosophers concerning extension.