In Physics, Aristotle starts his positive account of the infinite by raising a problem: “[I]f one supposes it not to exist, many impossible things result, and equally if one supposes it to exist.” His views on time, extended magnitudes, and number imply that there must be some sense in which the infinite exists, for he holds that time has no beginning or end, magnitudes are infinitely divisible, and there is no highest number. In Aristotle's view, a plurality cannot escape having bounds if all of its members exist at once. Two interesting, and contrasting, interpretations of Aristotle's account can be found in the work of Jaako Hintikka and of Jonathan Lear. Hintikka tries to explain the sense in which the infinite is actually, and the sense in which its being is like the being of a day or a contest. Lear focuses on the sense in which the infinite is only potential, and emphasizes that an infinite, unlike a day or a contest, is always incomplete.
Recent work by analytic philosophers on the Trinity takes a mysterious 5th-century document as its starting point, accepting widespread but inaccurate narratives about the history of Trinity theories. This article summarizes the Platonic influence on ancient theologies and describes the rise of transcendent triads, and eventually the idea of a tripersonal God. Recent Trinity theories (positive mysterianism, Trinity monotheism, relative-identity approaches, and “social” theories) are explained as built to respond in various ways to a type of anti-trinitarian argument. But since each recent application of logic and metaphysics to the theology of the Trinity is problematic, it is argued that another look at the minority unitarian report is warranted.