Kim Jun Young

Leibniz's famous proposition that God has created the best of all possible worlds holds a significant place in his philosophical system. However, the precise manner in which God determines which world is the best remains somewhat ambiguous. Leibniz suggests that a form of "Divine mathematics" is employed to construct and evaluate possible worlds. In this paper, I uncover the underlying mechanics of Divine mathematics by formally reconstructing it. I argue that Divine mathematics is a one-player combinatorial game, in which God's goal is to find the best combination among many possibilities. Drawing on the combinatorial theory, I provide new solutions to some puzzles of compossibility.

In this article, I examine Leibniz’s criticism of Spinoza’s notion of priority by nature based on the first proposition in Spinoza’s Ethics. Leibniz provides two counterexamples: first, the number 10’s being 6+3+1 is prior by nature to its being 6+4; second, a triangle’s property that two internal angles are equal to the exterior angle of the third is prior by nature to its property that the three internal angles equal two right angles. Leibniz argues that Spinoza’s notion cannot capture these priority relations. Although this text has received some scholarly attention, Leibniz’s objection in this text has not been fully explained yet. I argue that evaluating Leibniz’s objection relies on how to understand Spinoza’s notion of conception: first, whether conception is co-extensive with inherence and causation; second, whether conception is mental.

How are pictures to be individuated from other kinds of representations, such as linguistic representations? The traditional view is that a picture represents what it represents because it resembles it. Thus, the so-called “resemblance” theory has been the dominant view in understanding pictorial representation. More recently, however, the basis of this view has been brought into question; several philosophers have tried to provide the right theory of pictorial (or iconic) representations. Flint Schier is one of them. He tries to explain pictorial representations in terms of what he calls “natural generativity” in his book, Deeper Into Pictures. In this paper, I will raise a new problem that has never been debated before. Specifically, I will argue that Flint Schier’s individuation of iconic systems is problematic. I will show a counterexample to his method of individuation and argue that he cannot avoid the problem without abandoning one of the core claims of his theory.