This paper provides a rational reconstruction of a Platonic trope bundle theory that is a live alternative to contemporary bundle theories. According to the theory, Platonic particulars are composed of what Plato calls images of Forms; contemporary metaphysicians call these tropes. Tropes are dependent on Forms and the Receptacle, while trope bundles are structured by natural kinds using the Phaedo's principles of inclusion and exclusion and the Timaeus’ geometrised elements, as well as by co-location in the Receptacle. Key elements of (...) discussion include persistence and abundance of Plato's tropes. The resulting theory is compared with contemporary trope bundle theories. (shrink)

This paper offers a reconstruction of Xenocrates’ theory of indivisibles which would not commit him to the idea of ‘jerky motion’ criticized by Aristotle in Physica VI, yet would perfectly square with Plato’s Timaeus, the basis of Xenocrates’ canon. Relying on Alexander’s, Porphyry’s, and Themistius’s accounts of his theory, as well on a detailed analysis of De lineis insecabilibus, I suggest that Xenocrates’ minima, contrary to what Aristotle implies, are not to be understood as more or less stable particulars, like (...) tiny chunks of matter, moving about or leaping in physical space from point A to point B. Yet Xenocrates’ minima do remain ‘physical’ and ‘corporeal’ in a more Platonic sense of these words, not presupposing any kind of leaping, jumping, or jerking. This explains why Xenocrates associated the sensible realm with one of the three Fates, namely Clotho. (shrink)

At 47e–53c of the Timaeus Plato presents his most detailed metaphysical analysis of particulars. We are told about the construction of the physical universe, the ways we can and cannot talk about the phenomena produced, and about the two causes – Necessity and Intelligence – which govern the processes and results of production. It seems to me that we are told too much and too little: too much, because we have two accounts of the generation of phenomenal particulars – one, (...) the ‘formal account’, which makes use of the receptacle, Forms and form-copies, and a second, the ‘geometrical account’, which appeals to geometrical shapes, the Demiurge and, apparently, matter; too little, because there is insufficient guidance as to how to relate the two accounts. (shrink)

At 47e–53c of the Timaeus Plato presents his most detailed metaphysical analysis of particulars. We are told about the construction of the physical universe, the ways we can and cannot talk about the phenomena produced, and about the two causes – Necessity and Intelligence – which govern the processes and results of production. It seems to me that we are told too much and too little: too much, because we have two accounts of the generation of phenomenal particulars – one, (...) the ‘formal account’, which makes use of the receptacle, Forms and form-copies, and a second, the ‘geometrical account’, which appeals to geometrical shapes, the Demiurge and, apparently, matter; too little, because there is insufficient guidance as to how to relate the two accounts. (shrink)

In Plato’s Timaeus, two different theories – the Receptacle theory and the geometrical particle theory – are presented to explain change in the natural world. In this paper, I argue that there is tension between the two theories. After examining several possible solutions for this tension, I conclude that Plato does not present it as something ready to be solved within the dialogue but, rather, as something to be understood in a way that maintains both theories. Finally, I also argue (...) that the contrast between the two theories in the Timaeus derives from a similar contrast in the Phaedo. (shrink)

In the Timaeus, Plato’s Timaeus offers an account of the sensible world in terms of “images” of forms. Often, images are taken to be particulars: either objects or particular property instances (tropes). Contrary to this trend, I argue that images are general characteristics which are immanent in the receptacle, or bundles of such characteristics. Thus, the entire sensible world can be analysed in terms of immanent general characteristics, the receptacle, and forms. Hence, for Timaeus, fundamentally, there are no sensible particulars. (...) I end by arguing that my interpretation is compatible with Timaeus’ construction of sensible entities from triangles. (shrink)

A complete philosophy of mathematics must address Paul Benacerraf’s dilemma. The requirements of a general semantics for the truth of mathematical theorems that coheres also with the meaning and truth conditions for non-mathematical sentences, according to Benacerraf, should ideally be coupled with an adequate epistemology for the discovery of mathematical knowledge. Standard approaches to the philosophy of mathematics are criticized against their own merits and against the background of Benacerraf’s dilemma, particularly with respect to the problem of understanding the distinction (...) between pure and applied mathematics and the effectiveness of applied mathematics in the natural sciences and engineering. The evaluation of these alternatives provides the basis for articulating a philosophically advantageous Aristotelian inherence concept of mathematical entities. An inherence account solves Benacerraf’s dilemma by interpreting mathematical entities as nominalizations of structural spatiotemporal properties inhering in existent spatiotemporal entities. (shrink)