Burt Hopkins

The article explores the relationship between the philosopher and historian of mathematics Jacob Klein’s account of the transformation of the concept of number coincident with the invention of algebra and Husserl’s early investigations of the origin of the concept of number and his late account of the Galilean impulse to mathematize nature. Klein’s research is shown to present the historical context for Husserl’s twin failures in the Philosophy of Arithmetic, to provide a psychological foundation for the proper concept of number and to show how this concept of number functions as the mathematical foundation of universal arithmetic. The argument is advanced that one significant result of bringing together Klein’s and Husserl’s thought on these issues is the need to fine-tune Husserl’s Crisis project of desedimenting the mathematization of nature. Specifically, Klein’s research shows that “a ‘sedimented’ understanding of numbers” “is superposed upon the first stratum of ‘sedimented’ geometrical ‘evidences’” uncovered by Husserl’s fragmentary analyses of geometry in the Crisis. In addition, then, to the task of “the intentional-historical reactivation of the origin of geometry” recognized by Husserl as intrinsic to the reactivation of the origin of mathematical physics, Klein discloses a second task, that of “the reactivation” of the “complicated network of sedimented significances” that “underlies the ‘arithmetical’ understanding of geometry.”

This paper offers both a phenomenologically psychological and phenomenologically transcendental account of the constitution of the unconscious. Its phenomenologically psychological portion is published here as Part I, while its phenomenologically transcendental portion will be published in the next volume of this journal as Part II. Part I first clarifies the issues involved in Husserl's differentiation of the respective contents and methodologies of psychological and transcendental phenomenology. On the basis of this clarification I show that, in marked contrast to the prevailing approach to the unconscious in the phenomenological literature, an approach that focuses on the emotive and aesthetic factors in the descriptive account of the constitution of an unconscious, there are cognitive factors that have yet to be descriptively accounted for by phenomenological psychology. Part I concludes with a phenomenologically psychological account of the role these cognitive factors play in the constitution of an unconscious. Part II will show how Jung's claims regarding a dimension of unconscious contents that lacks genealogical links to consciousness proper, that is, the "collective unconscious, " can be phenomenologically accounted for if Jung's methodological differentiation of empirical and interpretative approaches to the unconscious is attended to and such attention is guided by the phenomenologically transcendental critique of the emotive and aesthetic limitations of both the Freudian and heretofore Husserlian accounts of the descriptive genesis of something like an unconscious.

De acuerdo con la así llamada concepción platonista de la naturaleza de las entidades matemáticas, las afirmaciones matemáticas son análogas a las afirmaciones acerca de objetos físicos reales y sus relaciones, con la diferencia decisiva de que las entidades matemáticas no son ni físicas ni espacio temporalmente individuales, y, por tanto, no son percibidas sensorialmente. El platonismo matemático es, por lo tanto, de la misma índole que el platonismo en general, el cual postula la tesis de un mundo ideal de entidades –eídē– que a la vez están separadas (chōristón) y son el fundamento cognitivo y ontológico del mundo real de cosas físicas que poseen propiedades espacio-temporales. Mientras que la no-identidad entre la concepción platonista de las entidades matemáticas y el platonismo del Platón “histórico” es frecuentemente reconocida tácita o explícitamente tanto por sus defensores como por sus críticos, su conexión conla crítica del Aristóteles “histórico” a la filosofía de Platón frecuentemente no es reconocida. Este artículo llama la atención sobre la conexión de Aristóteles con el así llamado platonismo tradicionalmente concebido y reconstruye un aspecto crucial de su crítica a la tesis originaria del chōrismós platónico que se pierde de vista a menos que se reconozca el objetivo verdadero de su crítica, la descripción platónica igualmente originaria de los números eidéticos.---“The Source of Platonism in the Philosophy of Mathematics Revisited: Aristotle’s Critique of Eidetic Numbers”. According to the so-called Platonistic conception of the nature of mathematical entities, mathematical statements are analogous to statements about real physical objects and their relations, with the one decisive difference that mathematical entities are neither physical nor individuated spatio-temporally and, thus, not perceived sensuously. Mathematical Platonism is therefore of a piece with Platonism in general, which posits the thesis of an ideal world of entities –eídē– that are both separate (chōristón) from and the cognitive and ontological foundations of the real world of physical things possessing spatio-temporal properties. While the non-identity of the Platonistic conception of mathematical entities with the Platonism of the “historical” Plato is usually either tacitly or explicitly acknowledged by its defenders and critics alike, its connection with the “historical” Aristotle’s critique of Plato’s philosophy usually goes unacknowledged. This paper both calls attention to Aristotle’s connection with the so-called Platonism traditionally conceived and reconstructs a crucial aspect of his critique of the original Platonic chōrismós thesis, an aspect that is missed unless the true target of this critique, the equally original Platonic account of eidetic numbers, is recognized.

For all its diversity, contemporary discourse about the Other shares the following suppositions: the Other in its radicality eludes the economy of the logic of the Same; it is beyond Being; its alterity is tied to the infinite in a manner that exceeds the ambit of thematization; and the problem it presents to philosophy is novel, in the precise sense that the dominant logic of the Western tradition, the so-called “logic of the Same” , is incapable of recognizing the full depth of the problem of the Other. In what follows I will engage critically each of these suppositions, to the end of answering the question whether contemporary discourse about the Other is determined by a two-fold one-sidedness, characterized by its thoroughly modern presuppositions about the nature of the Self and logic and by its positing of the kath auto status of the Other as something that is either completely unrelated to the Same or, granting the necessity of recognizing some kind of relation to the Same, something that has absolute priority over the Same. My answer to this question will be “yes.” I will endeavor to demonstrate the two-fold one-sidedness belonging to these suppositions by first returning to the original discussion of the Other in the Western tradition, Plato’s account of the dialogue between the philosophical Stranger from Elea and the mathematician Theaetetus in the Sophist

La manière dont Jacob Klein rend compte de l’historicité propre aux unités de base de la signification dans la pensée de la Grèce ancienne ainsi que de l’Europe moderne est présentée et étudiée en relation au « sens de l'être » dans la pensée phénoménologique heideggerienne et à la conception husserlienne de la signification ontologique instrumentale du calcul symbolique. Sur le fond des reconstructions kleiniennes des nombres éidétiques dans le Sophiste de Platon et de l’ontologie cartésienne des objets mathématiques indéterminés, deux affirmations se trouvent avancées, à savoir (1) que la composition « artithmologique » de l'être dans le Sophiste de Platon représente un défi par rapport au caractère prétendument fondamental du « sens » dans l’historicité heideggerienne de l’être et (2) que la constitution de la conceptualité propre aux unités de base du calcul symbolique excède celle de la conception husserlienne de leur « simple » instrumentalité

_ Source: _Volume 46, Issue 2, pp 205 - 220 I investigate the phenomenological significance of Husserl’s appeal to the “numerical identity” of _irreality_ as it appears in recollected manifolds of lived-experience in his mature account of the transcendental constitution of transcendence and find it wanting. I show that what is at stake for Husserl in this appeal is the descriptive mark that exhibits the distinction between a unit of meaning as it is constituted in psychologically determined lived-experience and as it is constituted in lived-experience that is determined transcendentally. In other words, I show that numerical identity functions for Husserl as the criterion that signals transcendental psychologism has been overcome. I then present the argument that it has not been overcome in Husserl’s investigations, because the collective unity characteristic of numerical unity is presupposed by those investigations rather than made evidentially manifest and articulated.

As the founder of phenomenology, Edmund Husserl has been hugely influential in the development of contemporary continental philosophy. In _The Philosophy of Husserl_, Burt Hopkins shows that the unity of Husserl’s philosophical enterprise is found in the investigation of the origins of cognition, being, meaning, and ultimately philosophy itself. Hopkins challenges the prevailing view that Husserl’s late turn to history is inconsistent with his earlier attempts to establish phenomenology as a pure science and also the view of Heidegger and Derrida, that the limits of transcendental phenomenology are historically driven by ancient Greek philosophy. Part 1 presents Plato’s written and unwritten theories of _eidê_ and Aristotle’s criticism of both. Part 2 traces Husserl’s early investigations into the formation of mathematical and logical concepts and charts the critical necessity that leads from descriptive psychology to transcendentally pure phenomenology. Part 3 investigates the movement of Husserl’s phenomenology of transcendental consciousness to that of monadological intersubjectivity. Part 4 presents the final stage of the development of Husserl’s thought, which situates monadological intersubjectivity within the context of the historical _a priori_ constitutive of all meaning. Part 5 exposes the unwarranted historical presuppositions that guide Heidegger’s fundamental ontological and Derrida’s deconstructive criticisms of Husserl’s transcendental phenomenology. _The Philosophy of Husserl_ will be required reading for all students of phenomenology.

Dear Colleague: Your letter shook me so profoundly that I was unable to answer it as soon as I should have. I am continuously concerned with it in my thoughts. Judge for yourself whether I have not inflicted more pain on myself than on you, and whether I may not ethically regard this guilt towards you and blame towards myself as stemming from the best conscience, something I have had to accept, and still must accept, as my fate. Clarifing the matter requires that I lay out a part of my life history. I had quickly realized that the project for Parts II and III of my Ideas was inadequate, and in an effort (beginning in the autumn of l9l2) to improve them and to shape in a more concrete and differentiated fashion the horizon of the problems they disclosed, I got involved in a new, quite far-ranging investigations. (These included the phenomenology of the person and personalities of a higher order, culture, the human environment in general; the transcendental phenomenology of “empathy” and the theory of transcendental intersubjectivity, the “transcendental aesthetic” as the phenomenology of the world purely as the world of experience, time and individuation, the phenomenology of association as the theory of the constitutive achievements of passivity, the phenomenology of the logos, the phenomenological problematic of “metaphysics,” etc.) These investigations stretched on all through the workfilled Freiburg years, and the manuscripts grew to an almost unmanageable extent. As the manuscripts grew so too did the ever greater the apprehension about whether, in my old age, I would be able to bring to completion what had been entrusted to me. This impassioned work led to repeated setbacks and repeated states of depression. In the end what I was left with was an allpervasive basic mood of depression, a dangerous collapse of confidence in myself. It was in this period that Heidegger began to mature -— for a number of..

The paper argues for three things. First, that the abstract concepts of ancient Greek and modern mathematics are fundamentally different. The general treatment of mathematical things in ancient Greek mathematics manifestly does not presuppose a general mathematical object, while in modern mathematics the generality of the method presupposes precisely such a general mathematical object. Two, that this difference in abstract concepts of mathematics makes a difference in our understanding of a discipline other than mathematics, specifically, in the discipline of history. And, three, that what is at issue in this difference is whether it is necessary for human beings to understand themselves from the perspective of history in order to understand themselves properly as human

Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts—especially mathematical concepts and the process of mathematical abstraction that generates them—have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge

Burt C. Hopkins - Husserl, Heidegger, and the Space of Meaning: Paths Toward Transcendental Philosophy - Journal of the History of Philosophy 40:2 Journal of the History of Philosophy 40.2 271-273 Book Review Husserl, Heidegger, and the Space of Meaning: Paths Toward Transcendental Philosophy Steven Galt Crowell. Husserl, Heidegger, and the Space of Meaning:Paths Toward Transcendental Philosophy. Evanston, IL: Northwestern University Press, 2001. Pp. xvii + 323. Cloth, $79.95. Paper, $27.95. The "space of meaning" announced in the title of the present collection of essays has both a historical and systematic referent. Historically, it refers to the fact that it is now "possible to recognize that what has distinguished philosophy in the twentieth century is not that it has concerned itself with language, but that, whether through the prism of language or not, it has concerned itself with meaning". Systematically, it refers to the issues that emerge when the project of transcendental phenomenology is explored in a manner that..

La manière dont Jacob Klein rend compte de l’historicité propre aux unités de base de la signification dans la pensée de la Grèce ancienne ainsi que de l’Europe moderne est présentée et étudiée en relation au « sens de l'être » dans la pensée phénoménologique heideggerienne et à la conception husserlienne de la signification ontologique instrumentale du calcul symbolique. Sur le fond des reconstructions kleiniennes des nombres éidétiques dans le Sophiste de Platon et de l’ontologie cartésienne des objets mathématiques indéterminés, deux affirmations se trouvent avancées, à savoir (1) que la composition « artithmologique » de l'être dans le Sophiste de Platon représente un défi par rapport au caractère prétendument fondamental du « sens » dans l’historicité heideggerienne de l’être et (2) que la constitution de la conceptualité propre aux unités de base du calcul symbolique excède celle de la conception husserlienne de leur « simple » instrumentalité.

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’.”

James F. Sheridan Allegheny College As we come to the end of the century, an attentive student of con temporary European philosophy will no doubt be startled by a volume titled Husserl in Contemporary Context. Such philosophers are most likely to believe that Hussed has now been declared II classical" rather than a contemporary thinker or, worse, simply old fashioned. Access to Hussed today will most likely come through the allegedly definitive critiques of his work by Heidegger and Derrida and to a lesser extent through the readings of his work by Levinas and Merleau Ponty although Merleau-Ponty himself has been declared old fashioned by some postmodems. Hence, if by II contemporary" one understands the problematic set by the work of the late Heidegger, Derrida, Foucault, et. al., Hussed's work seems strange indeed in such a contemporary context, seems better understood as the last gasp of philosophy dominated by metaphysics and thus fit only for inclusion in courses in the history of philosophy.