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41. New Yearbook for Phenomenology and Phenomenological Philosophy: Volume > 11
Edward C. Halper Klein on Aristotle on Number
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Jacob Klein raises two important questions about Aristotle’s account of number: (1) How does the intellect come to grasp a sensible as an intelligible unit? (2) What makes a collection of these intelligible units into one number? His answer to both questions is “abstraction.” First, we abstract (or, better, disregard) a thing’s sensible characteristics to grasp it as a noetic unit. Second, after counting like things, we again disregard their other characteristics and grasp the group as a noetic entity composed of “pure” units. As Klein explains them, Aristotle’s numbers are each “heaps” of counted units; in contrast, each of Plato’s numbers is one. This paper argues that Klein is right to understand a noetic unit existing in the sensible entity, but that his answer to the second question is not consonant with Aristotle’s insistence that Plato cannot account for the unity of a number, whereas he can. Slightly modifying Klein’s analysis, I show that Aristotle’s numbers are each one.
42. New Yearbook for Phenomenology and Phenomenological Philosophy: Volume > 11
Burt Hopkins The Philosophical Achievement of Jacob Klein
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Jacob Klein’s account of the original phenomenon of formalization accomplished by the innovators of modern mathematics, when they transformed the Greek arithmos into the modern concept of number, and his suggestion that the essential structure of this historically located formalization has become paradigmaticfor the concept formation of non-mathematical concepts (and therefore the most salient characteristic of the “modern consciousness”), is situated within the context of Husserl’s and Heidegger’s understanding of formalization. I show that from the perspective of Klein’s account of formalization the questions thatinform Husserl’s and Heidegger’s phenomenological responses to the problem of formalization are derivative, insofar as both phenomenologists presuppose that the essence of formalization is something that is knowable independent of its historicity. I then show that Klein’s philosophical achievement consists in his account of formalization and the formality of the concepts that it generates as being ungraspable so long as thinking approaches them as something is knowable, independent of its historicity.
43. New Yearbook for Phenomenology and Phenomenological Philosophy: Volume > 11
Andrew Romiti Jacob Klein on the Dispute Between Plato and Aristotle Regarding Number
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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.
44. New Yearbook for Phenomenology and Phenomenological Philosophy: Volume > 11
Joseph Cosgrove On the Mathematical Representation of Spacetime: A Case Study in Historical–Phenomenological Desedimentation
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This essay is a contribution to the historical phenomenology of science, taking as its point of departure Husserl’s later philosophy of science and Jacob Klein’s seminal work on the emergence of the symbolic conception of number in European mathematics during the late sixteenth and seventeenth centuries. Sinceneither Husserl nor Klein applied their ideas to actual theories of modern mathematical physics, this essay attempts to do so through a case study of the conceptof “spacetime.” In §1, I sketch Klein’s account of the emergence of the symbolic conception of number, beginning with Vieta in the late sixteenth century. In §2,through a series of historical illustrations, I show how the principal impediment to assimilating the new symbolic algebra to mathematical physics, namely, thedimensionless character of symbolic number, is overcome via the translation of the traditional language of ratio and proportion into the symbolic language of equations. In §§3–4, I critically examine the concept of “Minkowski spacetime,” specifically, the purported analogy between the Pythagorean distance formula and the Minkowski “spacetime interval.” Finally, in §5, I address the question of whether the concept of Minkowski spacetime is, as generally assumed, indispensable to Einstein’s general theory of relativity.
45. New Yearbook for Phenomenology and Phenomenological Philosophy: Volume > 11
Daniele De Santis Phenomenological Kaleidoscope: Remarks on the Husserlian Method of Eidetic Variation
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The main goal of this article is to examine Edmund Husserl’s method of “eidetic variation”—that is, to examine the way this method is supposed to work in connection with the notion of “similarity” (Ähnlichkeit). Unlike most interpretations, it will be suggested that similarity represents the leading methodologicalprinciple of eidetic variation. We will argue, therefore, that, on the one hand, this method is rooted in the sphere of association and passivity while, on the otherhand, it is constituted by the transposition of a passive synthesis into an active operation. After having introduced and discussed a twofold notion of phantasy(as “localized phantasy” and as “pure phantasy”) as well as a twofold concept of eidos (as “hen epi pollon” and as “pure eidos”), the extent to which for Husserl there cannot be any eidetic variation without a monadology will be shown.
46. New Yearbook for Phenomenology and Phenomenological Philosophy: Volume > 11
R. Matthew Shockey Heidegger on Understanding One’s Own Being
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One of the characteristics that define us as Dasein, according to Heidegger, is that our being is at issue for us. Most readers interpret this to mean that we each, as individuals situated in the world with others, face the questions of who, how, and whether to be within our unique situations. Yet what Heidegger identifies as Dasein’s being is a general structure—care—that is the same for all individuals. Adapting and modifying John Haugeland’s account of understanding as projecting entities upon their constitutive ontological possibilities, I argue that it is this general, ontological structure that Heidegger means to say is at issue for us, and that understanding ourselves in terms of it is a condition of possibility of understanding ourselves as particular individuals faced with the questions of who, how, and whether to be in our respective situations. I then show how this allows us to begin to address Heidegger’s view of the role philosophy plays in an individual’sexistence as it makes explicit the ontological structure which she normally only tacitly understands.
47. New Yearbook for Phenomenology and Phenomenological Philosophy: Volume > 11
Richard F. Hassing History of Physics and the Thought of Jacob Klein
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Aristotelian, classical, and quantum physics are compared and contrasted in light of Jacob Klein’s account of the algebraicization of thought and the resultingdetachment of mind from world, even as human problem-solving power is greatly increased. Two fundamental features of classical physics are brought out: species-neutrality, which concerns the relation between the intelligible and the sensible, and physico-mathematical secularism, which concerns the question of the difference between mathematical objects and physical objects, and whether any differences matter. In contrast to Aristotelian physics, which is species-specific, classical physics is species-neutral. In contrast to both Aristotelian and quantum physics, classical physics assumes that any differences between mathematical objects and physical objects make no difference for the conduct of physics. Aristotle’s act and potency, and Heisenberg’s uncertainty principle are discussed as counterexamples to the physico-mathematical secularism of classical physics. The algebraicization of thought in conjunction with the disposition and program for the mastery of nature leads to the homogenization of heterogeneities in both mathematics and physics, and, therewith, to confusion concerning the meaning of human being and our place in the whole.
48. New Yearbook for Phenomenology and Phenomenological Philosophy: Volume > 11
Eva Brann Jacob Klein’s Two Prescient Discoveries
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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.
49. New Yearbook for Phenomenology and Phenomenological Philosophy: Volume > 2
Karl Schuhmann Introduction Husserl's "Marperger Lecture" from July 6, 1898
50. New Yearbook for Phenomenology and Phenomenological Philosophy: Volume > 2
Edmund Husserl, Hans Reiner On the Psychological Justification of Logic (1900)