Here I reexamine Duhem's question of the continuity between medieval dynamics and early modern conservation theories. I concentrate on the heavens. For Aristotle, the motions of the heavens are eternally constant (and thus mathematizable) because an eternally constant divine Reason is their mover. Duhem thought that impetus and conservation theories, by extending sublunar mechanics to the heavens, made a divine renewer of motion redundant. By contrast, I show how Descartes derives his law of conservation by extending Aristotelian celestial dynamics to (...) the earth. Descartes argues that motion is intrinsically linear, not circular. But he agrees that motion is mathematically intelligible only where divine Reason moves bodies in a constant and eternal motion. Descartes strips bodies of active powers, leaving God as the only natural mover; thus both celestial and sublunar motions are constant, and uniformly mathematizable. The law of conservation of the total quantity of motion is an attempt to harmonize the constancy derived a priori with the phenomenal inconstancy of sublunar motions. (shrink)

Any comprehensive interpretation of the "Theaetetus" has to provide answers to, among others, two very general questions concerning that dialogue: "What is Plato's relation to the problems faced in the "Theaetetus"?" and "What is the significance of the absence of the Forms from the discussion of the "Theaetetus", given their undoubted relevance to the topic of the dialogue, i.e. knowledge?" Predominantly, the answer given to the first question in the literature has been that the problems are those that Plato is (...) trying to tackle and the one to the second question, when it has been addressed at all, that the Forms are left out of the discussion because Plato no longer thought them relevant, either for having abandoned or seriously revised them, by the time of writing the "Theaetetus". In this study of the Wax Block and the Aviary models of judgment that occur in the second part of the "Theaetetus" as part of its discussion of the problem of false judgment, I argue that the problems faced there actually arise because of the neglect of Forms. The discussion of the second part is, I contend, carried out on a materialist ontology, an ontology assumed because it suits the definition of knowledge as true judgment which inaugurates that part of the dialogue, an ontology in no way subscribed to by Plato. The Wax Block is, I explain, a materialist model and fails in the case of judgments about numbers for treating them on a par with material subjects, ignoring their intelligible status. In particular, it fails to distinguish judging 5 and 7 to be 11 from judging 12 to be 11 because of its neglect of Forms; Plato would distinguish those judgments by distinguishing 5 and 7 from 12 with help from his part-whole analysis, to which the Forms are essential. (shrink)

This paper shows how the universals of category theory in mathematics provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. The paper also shows how the always-self-predicative universals of category theory provide the "opposite bookend" to the never-self-predicative universals of iterative set theory and thus that the paradoxes arose from having (...) one theory (e.g., Frege's Paradise) where universals could be either self-predicative or non-self-predicative (instead of being always one or always the other). (shrink)

The Parmenides poses the question for what entities there are Forms, and the criticism of Forms it contains is commonly supposed to document an ontological reorientation in Plato. According to this reading, Forms no longer express the excellence of a given entity and a Socratic, ethical perspective on life, but come to resemble concepts, or what concepts designate, and are meant to explain nature as a whole. Plato’s conception of dialectic, it is further suggested, consequently changes into a value-neutral method (...) directed at tracing the interrelation of such Forms, an outlook supposedly documented in certain passages on method from the Sophist and the Statesman as well. -/- The article urges that this reading is untenable. For in the Parmenides the question for what entities one should posit Forms is left open, and the passages on method from the Sophist and Statesman neither encourage a non-normative ontology nor a value-neutral method of inquiry. What the three dialogues encourage us to do is rather to set common opinions about the relative worth and value of things aside when conducting ontological inquiries; and this attitude, the article concludes, demonstrates a close kinship, rather than a significant difference, between Plato’s Socrates and his Eleatic philosophers. (shrink)