Claire Murphy

Nicholas of Cusa develops an account of the elements of the material world that (like many of his philosophical views) is syncretistic, mystical, and even, at times, seemingly contradictory. On the one hand, Cusanus believes we have Aristotelian precedent for thinking matter is infinitely divisible; on the other hand, he holds that the human mind comprehends reality as a whole, and material things in particular, in a mathematical manner, and that our mathematical analysis of the elements that constitute material bodies cannot proceed ad infinitum. This paper investigates the seeming tension between these views and finds a resolution in Cusanus’s discussion of the quaternarium, or fourfold oneness, according to which the human mind knows all things. In particular, Cusanus says, we understand the composition of the elements according to a fourfold structure that mirrors the structure of all reality as it relates to its first divine principle. While the mathematical concepts of the human mind will, of course, fall short of those of the divine mind, nonetheless our human number is a reflection of the divine, and thus our mathematical knowledge of the world truly reflects something of its reality.

Pierre Duhem’s 1905 essay “Physics of a Believer” is generally read as proposing a neat separation between metaphysics and physics as two fields that have little to nothing in common: some things will be the subject of metaphysics and some of physics, but nothing will fall under the purview of both. In this article, I advance a more nuanced interpretation of Duhem’s understanding of the differences between physics and metaphysics by drawing on his notion of “common sense” and highlighting the historical (particularly Aristotelian) influences at work in Duhem’s thought on this question. I argue that Duhem’s own distinction between physics and metaphysics is subtler than the received view, framing metaphysics and physics as two distinctive fields of inquiry that nonetheless both begin from sensed phenomena and common-sense principles that are eminently certain but characteristically imprecise.