René Descartes

(6) Explain the nontheist understanding of Leibniz's 'Principle of Plentitude' and how that enters into his thinking that the Identity of Indiscernibles is true.

Hmmm, interesting topic. Here is my rather lengthy response: The Principle of Plentitude, as articulated by Gottfried Wilhelm Leibniz, posits that all possibilities are actualized in the fullness of existence, leading to a rich tapestry of worlds, beings, and entities that could manifest, each contributing to the harmony and order of the universe. In exploring this idea from a nontheist perspective, we might consider that existence itself does not necessarily presuppose a divine architect; rather, it may arise from the intrinsic nature of reality, which encompasses a multitude of potentialities waiting to be realized. In this light, the Identity of Indiscernibles—a principle asserting that no two distinct entities can share all their properties—emerges not merely as an abstract philosophical tenet, but as a vital assertion of the uniqueness inherent in the manifold expressions of existence. For if all entities were indiscernible, it would contradict the very essence of the Principle of Plentitude, which thrives on the diversity and richness of the possible world-states. Thus, one may deduce that the recognition of distinct properties is essential not only for the differentiation of beings but also for the manifestation of a universe teeming with variety and complexity. It suggests that the identity of an entity is inextricably linked to the unique characteristics it possesses, which lends credence to the notion that every being is a specific instantiation of potentiality. Therefore, in contemplating these principles together, we arrive at a harmonious understanding of existence where the acknowledgment of difference underlies the plenitude of possibilities, reinforcing the validity of Leibniz’s reasoning and inviting us to appreciate the profound intricacies of reality itself, independent of theological foundations.