This paper seeks to highlight the importance of spatial cognition in Bergson’s Données immédiates by engaging with Robert Watt’s reconstruction of Bergson’s argument that every idea of number involves the idea of space. We focus on the second stage of Watt’s reconstruction, where Bergson argues that only space can provide the distinction required for our counting of otherwise identical items. Watt bases his reconstruction on a premise regarding the possibility that identical objects, in the absence of spatial distinction, might remain (...) identical across different “temporal locations”. Our paper raises the prospect that Bergson is committed to a stronger thesis, namely one implying that identical objects would necessarily remain indistinguishable without the intervention of space. The paper thus concludes by emphasizing the indispensability of space for knowledge according to Bergson. (shrink)

In his commentary on Euclid, Proclus develops what he takes to be an important Platonic critique of the epistemology of abstraction. As I argue, his argument closely reflects terminology and concepts from Plato’s Philebus. Both emphasize the priority—in reality and in our awareness—of the precise over the imprecise. Specifically, Proclus’s famous notion of the psychical “projection” of intermediate mathematical entities, while having no technically exact precedent in Plato, finds a conceptual neighbor in the Philebus’s suggestion that philosophical arithmeticians “posit” pure (...) units for counting. Likewise, for both our self-engagement in mathematical thinking serves to clarify the independence of the precise sciences—both in their content and in their practice—from perception. Thus, as I argue, Plato and Proclus, with their different terms and nuances, develop a shared conception scientific inquiry in which an activity of “creative discovery” plays a central role. (shrink)

This study examines Plato's dialogue on the good life and argues, most centrally, that the "pleasures of learning" exemplify, for Socrates, the possibility of good becoming or change.

In the 'Hippias Major' Socrates uses a counter-example to oppose Hippias‘s view that parts and wholes always have a "continuous" nature. Socrates argues, for example, that even-numbered groups might be made of parts with the opposite character, i.e. odd. As Gadamer has shown, Socrates often uses such examples as a model for understanding language and definitions: numbers and definitions both draw disparate elements into a sum-whole differing from the parts. In this paper I follow Gadamer‘s suggestion that we should focus (...) on the parallel between numbers and definitions in Platonic thought. However, I offer a different interpretation of the lesson implicit in Socrates‘s opposition to Hippias. I argue that, according to Socrates, parts and sum-wholes may share in essential attributes; yet this unity or continuity is neither necessary, as Hippias suggests, nor is it impossible, as Gadamer implies. In closing, I suggest that this seemingly minor difference in logical interpretation has important implications for how we should understand the structure of human communities in a Platonic context. (shrink)

In his Euclid commentary, Proclus states that mathematical objects have a status in between Platonic forms and sensible things. Proclus uses geometrical examples liberally to illustrate his theory but says little about arithmetic. However, by examining Proclus’s scattered statements on number and the traditional sources that influenced him (esp. the Philebus), I argue that he maintains an analogy between geometry and arithmetic such that the arithmetical thinker projects a “field of units” to serve as the bearers of number forms. I (...) argue that this conception of a “multitude,” wherein each unit differs in no way from the others, implies that Platonists need not recognize unqualifiedly what would become the principle of the identity of indiscernibles. I argue that Cratylus 432c in particular provides support for a reading of Plato as consistently thinking beyond the principle of identity. I conclude by drawing out an important epistemological and ethical lesson from this reading. (shrink)

In his Euclid commentary, Proclus states that mathematical objects have a status in between Platonic forms and sensible things. Proclus uses geometrical examples liberally to illustrate his theory but says little about arithmetic. However, by examining Proclus’s scattered statements on number and the traditional sources that influenced him, I argue that he maintains an analogy between geometry and arithmetic such that the arithmetical thinker projects a “field of units” to serve as the bearers of number forms. I argue that this (...) conception of a “multitude,” wherein each unit differs in no way from the others, implies that Platonists need not recognize unqualifiedly what would become the principle of the identity of indiscernibles. I argue that Cratylus 432c in particular provides support for a reading of Plato as consistently thinking beyond the principle of identity. I conclude by drawing out an important epistemological and ethical lesson from this reading. (shrink)