Burt Hopkins

Jacob Klein’s own account of the change from the ancient to the modern mode of thinking presented in his seminal Greek Mathematical Thought and the Origin of Algebra included the observation that it did not consider the larger perspective of this change. The discussion to follow proposes to view the larger perspective of this transition through the lens provided by the Kantian concept of a “critique” of pure reason. By asking and attempting to answer the question of whether Klein’s account of what he calls the “symbolic abstraction” responsible for the genesis of the modern concept of number can be seen as what Kant characterizes as an “assessment” of pure reason, it is my intent to venture a prolegomenon to a critique of what, following Klein, I want to argue is most properly called “symbolic reason.”

Straipsnyjc svarstornas Algio Micklino atsakas huscrliSkosios fcnorncnologijos kritikarns. Autorius iSrySkina tris svarbiausius IJusscrlio kritikq argurnen- tus: 1 .IHusscrlio fcnorncnologija yra toli graiu nc "rnohlas bc jokiq ikankstiniy prielaidq", ji suponuo- ja dckartiSkqj teiginj, jog bliti rciSkia "hliti paiintu". 2.1-Tusserlio tciginj apic fcnorncnologines duotics apo- diktiSkurnq susilpnina jo patics patcikiarni tokios duo- tics apra5yrnai. IS ju, prieSingai Husserlio ketinirnarns. i6aiSkcja fenorncnologincs rcflcksijos ncpajcgurnas "susidoroti" tiek su retencine 1;iikines patirties di- rncnsija, tiek su radikalia Kito patirtics kitokybe. 3.Husscrlio rnctodui ir rnqstyrnui apskritai budingas eurocentrizrnas ir episterninis irnpcrializrnas - visus kultlirinius ir istorinills skirturnus jis susurnuojn savo fenornenologijoje, kuriy traktuoja kaip slaptq graiko- curopictiSko.jo irnogaus llikcsi.iij iksipildyrnn. Algiui Micktinui svarbiausias klausirnns yra Sis: Koclkl reiketq intcrpretuoti Husserli blitent iitaip? Micktinas, Husscrlio rnokiniy Eugcno Finko ir Lud- wigo Landgrebe's rnokinys, gcrai suvokc, jog ypa- tingas Husscrlio raSyrno stilius nesyk yra veikiau su- trrlkdes nei pacle,jysvisu radikalurnu atsiskleisti svar- biausiorns Mol\qto.jo @valgorns ir atradirnarns. Tatiau jam Sis triikurnas visuornct atrodes ncrciksrningas ly- ginant su rniliiniiku potcncialu, kuris Siuosc atradi- rnuose gltidi. laukdarnas tolcsnio iiplctojirno. Hus- scrlio filosofija Micktinui yra tarsi jminirno laukiantis rnjsliy rinkinps, ir Si jrninirnq jis laiko prasrningesniu uidaviniu ui pastangas padcrnonstruoti huserliSkos fenornenologijos nenuoscklurnus ir silpnqsiasvietas. Savo darbuose Micktinas parodo. jog, ncpaisant kri- tikq iipuoliu, Husscrlio fcnorncnologinio rnctodo vi- suotinurnas ir fundamentalurnas iilicka ncpancigti. Raktiniai iodiiai: fi.nornenologija, refleksijn, skirtis, jk~~orner~ns, ~~~~enntnn.spn.snrrli.s, pntirtis

This book reassesses the phenomenological `controversy' between Husserl and Heidegger over the proper status of the phenomenon of intentionality. It seeks to determine whether Heidegger's hermeneutical critique of intentionality is sensitive to Husserl's reflective account of its `Sachen selbst'. Hopkins argues that Heidegger's critique is directed toward the `cogito' modality of intentionality, and therefore, passes over its `non-actional', or `horizonal', dimension in Husserl's phenomenology. As a result of this, he concludes that Heidegger misinterprets Husserl's account of the intentional `immanence' exhibited by phenomenological reflection. On the basis of these findings, Hopkins suggests that the phenomenological methodology, operative in the so-called hermeneutic critique of transcendental consciousness, itself involves transcendental `presuppositions' that are most appropriately characterized in terms of intentional, and reflective, phenomena.

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, together with 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. This context establishes that Husserl’s failures are ultimately rooted in the historical transformation of number documented in Klein’s research, from its premodern meaning as the unity of a multitude of determinate objects to its modern meaning as a symbolic representation with no immediate relation to a concrete multiplicity. The argum...

Two of Husserl’s most important, though fragmentary texts from the final phase of his thought, The Crisis of European Sciences and Transcendental Phenomenology and “The Origin of Geometry as an Intentional-Historical Problem,” focus on the themes of history and the life-world. It is well known that prior to these works Husserl sought to establish transcendental phenomenology as both a factually and an historically pure eidetic science. Thus the interpreter of the whole of Husserl’s thought is faced with the question of whether his later focus on history and the life-world represents a significant departure from his previous thought. In what follows, I shall defend the thesis that it does not. Specifically, I shall argue that the completion of Husserl’s project of realizing the goal of First Philosophy in transcendental phenomenology renders necessary the turn both to history and to the life-world. In connection with this, I shall argue further that the peculiar phenomenological character of this necessity demands that the ‘concepts’ of history and life-world operative in Husserl’s last texts are taken to be inseparably rooted in a more original phenomenon. Husserl conceives this more original phenomenon as the crisis situation of the exemplars of European humanity, the philosophers, who, as the “functionaries of mankind” are faced with the “breakdown” situation of our time, with the “breakdown” of science itself.

Many of the contributions to this volume are based on research originally presented at the historic first meeting in the United States of Japanese and American phenomenologists that took place at Seattle University in the Summer of 1991. In addition, other contributions have been added in order to supplement and complement the themes of the work presented at this meeting. Owing both to the vagaries of fate and the finitude of time, the publication of these essays has taken much longer than was originally intended. Nevertheless, this delay is more than offset by the inclusion in one volume of both phenomenological thematics and phenomenological authors who do not usually appear together.

The paper argues that the ontology of Self behind Descartes’s paradigmatic modern account of passion is an obstacle to interpreting properly the account Socrates gives in the Symposium of the truth of Eros’s origin, nature, and gift to the philosophical initiate into his truth. The key to interpreting this account is located in the relation between Eros and the arithmos-structure of the community of kinds, which is disclosed in terms of the Symposium’s dramatic mimesis of the two Platonic sources of being, the One Itself and the indeterminate dyad. This interpretation’s focus is the vulgar and philosophical dimensions of the phallic pun at the beginning of the dialogue. Both dimensions of the dialogue’s opening joke manifest the appearance of Eros in the dialogue as a distorted imitation of the koinonia of the greatest kinds: Being, Rest, Motion, the Same, and the Other.

This essay articulates obstacles to an interpretation of the whole proper to Plato’s philosophy that are rooted in the general methodical principle of traditional hermeneutics, and then addresses them by a novel hermeneutic application of Husserl’s transcendental and eidetic reductions. This application involves disclosing the transcendental phenomena of the texts of Plato’s dialogues on the basis of the former and articulating their phenomenological essence in accord with the latter. A meta-hermeneutical argument for what Plato himself might have thought is then ventured, which takes as its point of departure both the transcendental phenomena of his texts and Aristotle’s report that eide for him were in some sense arithmoi.

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

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.

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.

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

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..

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