Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th–16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science — in which the symbolic "form" of a mathematical statement is completely inseparable from its "content" of physical meaning. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.

The Meno, one of the most widely read of the Platonic dialogues, is seen afresh in this original interpretation that explores the dialogue as a theatrical presentation. Just as Socrates's listeners would have questioned and examined their own thinking in response to the presentation, so, Klein shows, should modern readers become involved in the drama of the dialogue. Klein offers a line-by-line commentary on the text of the Meno itself that animates the characters and conversation and carefully probes each significant (...) turn of the argument. "A major addition to the literature on the Meno and necessary reading for every student of the dialogue."--Alexander Seasonske, Philosophical Review "There exists no other commentary on Meno which is so thorough, sound, and enlightening."-- Choice Jacob Klein was a student of Martin Heidegger and a tutor at St. John's College from 1937 until his death. His other works include Plato's Trilogy: Theaetetus, the Sophist, and the Statesman, also published by the University of Chicago Press. (shrink)

This article argues that Epictetus employs the terms orexis and hormê in the same manner as the older Stoics. It then shows, on the basis of this claim, that the older Stoics recognized a distinction between dispositional and occurrent forms of motivation. On this account of Stoic theory, intentional action is in each instance the product of two forms of cognition: a value ascription that attributes goodness or badness to some object, conceiving of its possession as beneficial or harmful to (...) the agent, together with a situational judgment about appropriate action. The resulting interpretation suggests that the Stoic theory of motivation as a whole — and not merely the Stoic analysis of the pathê — has the basic shape of a practical syllogism, with more psychological depth than commentators have recognized. (shrink)

I argue that comparisons of Stoic virtue to stochastic skills — now standard in the secondary literature on Stoicism — are based on a misreading of the sources and distort the Stoic position in two respects. In paradigmatic stochastic skills such as archery, medicine, or navigation the value of the skill’s external end justifies the existence and practice of the skill and constitutes an appropriate focus of rational motivation. Neither claim applies to virtue as the Stoics understand it. The stochastic (...) model of virtue almost certainly originated with Carneades and should be distinguished clearly from the Stoic account. Doing so clarifies the Stoic position and shows that it anticipates what Thomas Hurka calls a modern view of value. (shrink)

According to the Stoics, the psychology of adult human beings is unified in a striking sense: each of the soul's perceptive, discursive, and motivational functions belongs to the single faculty of reason. Reason, in turn, is constituted by a set of conceptions (ennoiai) and preconceptions (prolêpseis) acquired on the basis of experience. The few secure sources that bear on this theory in the early Stoa suggest that certain of these empirically acquired conceptions function, somehow, as a criterion of truth in (...) human perception and rational cognition generally. The conceptions associated with this cognitive role are sometimes said to be shared or common (koinai).These tenuous but intriguing claims are the focus of .. (shrink)