Spinoza, Leibniz and the Debate over the Possibility of Two Substances Sharing the Same Attribute: A Contribution to the History of Logic and Metaphysics in the 17th Century

This paper sets out to examine and respond to Leibniz's objection to E1p2 and E1p5. The objection is well known: it is false, according to Leibniz, that two substances of different attributes have nothing in common (i. e., E1p2) and, consequently, that in nature there cannot be two or more substances of the same attribute (i. e., E1p5). Here I claim that E1p2, and therefore E1p5, resist Leibniz's objection. To do so, I first address the meaning and function of E1p2 in order to determine two possible contexts in which the demonstration is valid: the context delimited by the Cartesian doctrine of the principal attribute, and the scholastic context of the logical doctrine of essential diversity. Second, I examine Leibniz's objection, by which I determine more precisely the epistemic framework of both E1p2d and Leibniz's objection. Third, I propose a critical analysis of Leibniz's objection to show that, although this objection has some semblance of validity, if we consider only what Spinoza stated in the definitions and axioms prior to E1p2, it entails a contradiction. Finally, I indicate the most difficult point in the proof of E1p2 in order to propose a small rectification that renders it immune to Leibniz's objection.