In book IX of the Republic, Socrates offers a strange mathematical calculation, which claims to prove that the tyrant lives exactly 729 times less pleasantly than the king. For the first time, a complete and detailed reconstruction of this difficult text and its underlying structure is offered in the present article. It thereby proves that the distinction between ‘pleasure’ and the ‘image of pleasure’ is one among the keys to understanding the passage. It is furthermore shown how the whole calculation (...) is based on Plato’s ontology of dimensions and therefore proves that this theorem can be taken into account at least already for the time of the Republic. (shrink)

Does the Longer Way, described but not taken in Plato's Republic, provide understanding that justice and other virtues are good? Sarah Broadie argues that it does not, on the grounds that Socrates and the brothers learn about justice's goodness without taking the Longer Way. I argue that Socrates’ arguments for justice's goodness are not so complete as to make it impossible for philosopher-rulers to gain from the Longer Way greater understanding of the same point. My main textual evidence is a (...) passage of Book IX (589b–c), a summary that has been widely underappreciated. (shrink)

Aristotelian ideas have in the past been applied with mixed fortunes to quantum mechanics. One of the most persistent criticisms is that Aristotle’s notions of potentiality and actuality are burdened with a teleological character long ago abandoned in the natural sciences. Recently this criticism has been met with a model of the actualization of quantum potentialities in light of Aristotle’s doctrine of ‘spontaneous events’. This presumably restores the nowadays acceptable idea of efficient causation in place of Aristotle’s original doctrine of (...) the ‘four causes’. In this article I challenge the model by arguing that when properly scrutinized Aristotle’s final cause poses no problems for an Aristotelian reading of quantum mechanics. Final causes in fact provide a better ontology for quantum mechanics than spontaneous causation. The idea of ‘spontaneity’ is unanalyzable and therefore of little use in quantum mechanics. In addition, it is ontologically sterile in the context of quantum measurement, as shown by a historical and conceptual review of the role of efficient causation in experimental physics. (shrink)

I discuss Aristotle’s opening argument against Platonic Forms in _Metaphysics_ A.9, ‘the Razor’, which criticizes the introduction of Forms on the basis of an analogy with a hypothetical case of counting things. I argue for a new interpretation of this argument, and show that it involves two interesting objections against the introduction of Forms as formal causes: one concerns the completeness and the other the adequacy of such an explanatory project.

Plato's Republic critiques Athenian democracy as practised during the Peloponnesian War years. The diseased city Socrates attempts to purge mirrors Athens in crucial particulars, and his proposals should be evaluated as counter-weights to existing institutions and practices, not as absolutes to be instantiated. Plato's assessment of the Athenian polity incorporates two strategies -- one rhetorical, the other argumentative -- both of which I address. Failure to consider Athens a catalyst for Socrates' arguments has led to the misconception that Plato was (...) dogmatically committed to a single political doctrine for all and for all time. (shrink)