I argue that Leibniz’s doctrine of sensory representation is intended in part to close an explanatory gap in his philosophical system. Unlike the twentieth century explanatory gap, which stretches between neural states on one side and phenomenal character on the other, Leibniz’s gap lies between experiences of secondary qualities like color and taste and the objects that cause them. The problem is that the precise arrangement and distribution of such experiences can never be given a full explanation. In response, Leibniz (...) appeals to representation. I argue that the sense in which Leibnizian sensations are representations is too weak to close his explanatory gap. In the end, he must appeal to the doctrine of the best possible world. (shrink)

Ockham’s approach to the problem of the instant of change as it is found in the Summa logicae i, chapter 5, and ii, chapter 19, is usually described as “purely logical,” narrowing the treatment of “begins” and “ceases” to simplistic cases. The aim of this paper is to complement our knowledge of Ockham’s position on the problem of the instant of change by analysing the treatment of the problem he gives in his questions on the Physics 98-101. In these passages, (...) Ockham adopts a “physical approach” in order to deal with problems related to the continuity of alteration and the production of the form of the mix from elementary qualities. To solve these problems, he is compelled to give up one of the most important claims at the basis of the logical approach that he adopted in the Summa logicae, namely that the distinction between permanent and successive entities is not relevant in the assignment of truth-conditions to propositions containing the aspectual verbs “beginning” and “ceasing.”. (shrink)

Standard definitions of causal closure focus on where the causes in question are. In this paper, the focus is changed to where they are not. Causal closure is linked to the principle that no cause of another universe causes an event in a particular universe. This view permits the one universe to be affected by the other via an interface. An interface between universes can be seen as a domain that violates the suggested account of causal closure, suggesting a view (...) in which universes are causally closed whereas interfaces are not. On this basis, universes are not affected by other universes directly but rather indirectly. (shrink)

In his highly perceptive, if underappreciated introduction to Wittgenstein’s Tractatus, Russell identifies a “lacuna” within Wittgenstein’s theory of number, relating specifically to the topic of transfinite number. The goal of this paper is two-fold. The first is to show that Russell’s concerns cannot be dismissed on the grounds that they are external to the Tractarian project, deriving, perhaps, from logicist ambitions harbored by Russell but not shared by Wittgenstein. The extensibility of Wittgenstein’s theory of number to the case of transfinite (...) cardinalities is, I shall argue, a desideratum generated by concerns intrinsic, and internal to Wittgenstein’s logical and semantic framework. Second, I aim to show that Wittgenstein’s theory of number as espoused in the Tractatus is consistent with Russell’s assessment, in that Wittgenstein meant to leave open the possibility that transfinite numbers could be generated within his system, but did not show explicitly how to construct them. To that end, I show how one could construct a transfinite number line using ingredients inherent in Wittgenstein’s system, and in accordance with his more general theories of number and of operations. (shrink)

In this paper, I aim to shed light on the use of transcendental deductions, within demonstrations of aspects of Wittgenstein's early semantics, metaphysics, and philosophy of mathematics. I focus on two crucial claims introduced by Wittgenstein within these transcendental deductions, each identified in conversation with Desmond Lee in 1930-31. Specifically, the claims are of the logical independence of elementary propositions, and that infinity is a number. I show how these two, crucial claims are both demonstrated and subsequently deployed by Wittgenstein (...) within a series of transcendental deductions, a series which begins with extensionalism as a generalized condition of sense on propositions, and in the context of which are then derived various, further, significant and unobvious presuppositions generated by that generalized condition of sense. In addition to clearing up deductions of these two, aforementioned claims, I also elucidate deductions of the subsistence of objects, and of logical space as an infinite totality. (shrink)