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)

It is pointed out that the Higgs field may be supplanted by an ordinary Klein-Gordon field conformally coupled to the space-time curvature, and with very small, real, rest mass. Provided there is a bare cosmological constant of order of its square mass, this field can induce spontaneous symmetry breaking with a mass scale that can be as large as the Planck-Wheeler mass, but may be smaller. It can thus play a natural role in grand unified theories. In the theory (...) presented here the physical cosmological constant is small, being of order of the squared mass, and can meet observational constraints without having to be cancelled accurately. The physical gravitational constant differs somewhat from the coupling constant in Einstein's equation, and is temperature dependent in the broken symmetry regime. Symmetry restoration occurs at high temperature. (shrink)

: Through a close reading of Klein and Irigaray's work on the mother-daughter relationship via the Electra myth, Jacobs diagnoses what she considers a fundamental problem in psychoanalytic and feminist psychoanalytic theory. She shows that neither thinker is able to theorize the mother-daughter relationship on a structural level but is only able to describe its symptoms. Jacobs makes a crucial distinction between description and theory and argues that the need to go beyond description and phenomenology toward the creation of (...) a structural theory is the only way that feminist philosophy and psychoanalysis can avoid reproducing the terms of the male imaginary. The essay concludes by arguing that theorization of the mother-daughter relationship can only be achieved if we analyze manifestations of the mother-daughter relationship in clinical, cultural, and mythical material through the framework of a foreclosed or absent underlying maternal law. (shrink)

Through a close reading of Klein and Irigaray's work on the mother-daughter relation’ ship via the Electra myth, Jacobs diagnoses what she considers a fundamental problem in psychoanalytic and feminist psychoanalytic theory. She shows that neither thinker is able to theorize the mother-daughter relationship on a structural level but is only able to describe its symptoms. Jacobs makes a crucial distinction between description and theory and argues that the need to go beyond description and phenomenology toward the creation of (...) a structural theory is the only way that feminist philosophy and psychoanalysis can avoid reproducing the terms of the male imaginary. The essay concludes by arguing that theorization of the mother-daughter relationship can only be achieved if we analyze manifestations of the mother-daughter relationship in clinical, cultural, and mythical material through the framework of a foreclosed or absent underlying maternal law. (shrink)

Through a close reading of Klein and Irigaray's work on the mother-daughter relation’ ship via the Electra myth, Jacobs diagnoses what she considers a fundamental problem in psychoanalytic and feminist psychoanalytic theory. She shows that neither thinker is able to theorize the mother-daughter relationship on a structural level but is only able to describe its symptoms. Jacobs makes a crucial distinction between description and theory and argues that the need to go beyond description and phenomenology toward the creation of (...) a structural theory is the only way that feminist philosophy and psychoanalysis can avoid reproducing the terms of the male imaginary. The essay concludes by arguing that theorization of the mother-daughter relationship can only be achieved if we analyze manifestations of the mother-daughter relationship in clinical, cultural, and mythical material through the framework of a foreclosed or absent underlying maternal law. (shrink)

I present two of Jacob Klein’s chief discoveries from a perspective of peculiar fascination to me: the enchanting (to me) contemporaneous significance, the astounding prescience, and hence longevity, of his insights. The first insight takes off from an understanding of the lowest segment of the so-called DividedLine in Plato’s Republic. In this lowest segment are located the deficient beings called reflections, shadows, and images, and a type of apprehension associatedwith them called by Klein “image-recognition” (εἰκασία). The second (...) discovery involves a great complex of notions from which I will extract one main element:the analysis of what it means to be a number and what makes possible this kind of being, and, it turns out, all Being. (shrink)

I present two of Jacob Klein’s chief discoveries from a perspective of peculiar fascination to me: the enchanting (to me) contemporaneous significance, the astounding prescience, and hence longevity, of his insights. The first insight takes off from an understanding of the lowest segment of the so-called DividedLine in Plato’s Republic. In this lowest segment are located the deficient beings called reflections, shadows, and images, and a type of apprehension associatedwith them called by Klein “image-recognition” (εἰκασία). The second (...) discovery involves a great complex of notions from which I will extract one main element:the analysis of what it means to be a number and what makes possible this kind of being, and, it turns out, all Being. (shrink)

What is at stake for Jacob Klein in François Vieta’s analytical art is the birth of both the “modern concept of ‘number’ [Zahl], as it underlies symbolic calculi” and the expanded, in contrast to ancient Greek science, scope of the generality of mathematical science itself. Of the former, Klein writes that it “heralds a general conceptual transformation which extends over the whole of modern science”. The latter, he says, lends the “treatment” [πραγματεία] at issue in the ancient (...) Greek mathematical idea of a “‘general treatment’ [καθόλου πραγματεία]” “a completely new sense” “within the system of ‘science.’” The generality of this new sense will concern both the method and object of science in what will come to be known as universal mathematics. This transformation of the basic concept and scope, initially of mathematics and then of “the system of knowledge in general”, “concerns first and foremost the concept of ἀριθμόσ itself”. As a result of “its transfer into a new conceptual dimension” —i.e., into the dimension in which both “the concept of ‘number’ [Zahl]... is itself... as is that which it means” “symbolic in nature”—a transfer that “becomes visible” “for the first time in Vieta’s ‘general analytic,’” there follows “a thoroughgoing modification of the means and aims of science.” Klein maintains that what this modification involves is “best characterized by a phrase... in which Vieta expresses the ultimate problem, the problem proper, of his ‘analytical art’: ‘Analytical art appropriates to itself by right the proud problem of problems, which is: TO LEAVE NO PROBLEM UNSOLVED’.”. (shrink)

By examining Klein’s discussion of the difference between Plato and Aristotle regarding the ontology of number, this article aims to spells out the significanceof that debate both in itself and for the development of the later mathematical sciences. This is accomplished by explicating and expanding Klein’s account of the differences that exist in the understanding of number presented by these two thinkers. It is ultimately argued that Klein’s analysis can be used to show that the transition from (...) the ancient to the modern number concept has some roots in this disagreement between Plato and Aristotle regarding number. This, in turn, sets up that dispute as an essential part of the background to the more general break between ancient and modern conceptuality, the uncovering of whichis Klein’s main concern. (shrink)

By examining Klein’s discussion of the difference between Plato and Aristotle regarding the ontology of number, this article aims to spells out the significanceof that debate both in itself and for the development of the later mathematical sciences. This is accomplished by explicating and expanding Klein’s account of the differences that exist in the understanding of number presented by these two thinkers. It is ultimately argued that Klein’s analysis can be used to show that the transition from (...) the ancient to the modern number concept has some roots in this disagreement between Plato and Aristotle regarding number. This, in turn, sets up that dispute as an essential part of the background to the more general break between ancient and modern conceptuality, the uncovering of whichis Klein’s main concern. (shrink)

By examining Klein’s discussion of the difference between Plato and Aristotle regarding the ontology of number, this article aims to spells out the significanceof that debate both in itself and for the development of the later mathematical sciences. This is accomplished by explicating and expanding Klein’s account of the differences that exist in the understanding of number presented by these two thinkers. It is ultimately argued that Klein’s analysis can be used to show that the transition from (...) the ancient to the modern number concept has some roots in this disagreement between Plato and Aristotle regarding number. This, in turn, sets up that dispute as an essential part of the background to the more general break between ancient and modern conceptuality, the uncovering of whichis Klein’s main concern. (shrink)