Burt Hopkins

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’.”

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

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.

The dissertation endeavors to study the controversial relationship of the phenomenologies of Husserl and Heidegger by investigating their respective treatments of intentionality. Husserl's reflective and Heidegger's hermeneutical accounts of intentionality are brought into bold phenomenal relief in order to secure the phenomenal basis underlying their conflicting views of both the character and status of this phenomenon. Specifically, the study discusses Husserl's reflective exhibition of intentionality in terms of its manifestation of the phenomenally original essence of lived-experiences, and Heidegger's immanent critique of the same in terms of its manifestation of phenomenally derivative understanding of Being. ;The discussion shows that Husserl finds the reflective securing of intentionality to manifest the most original phenomenal manifestation of die Sachen selbst, while Heidegger finds the hermeneutical securing of the same to manifest the temporalization of Dasein's being-in-the-world. The issues underlying the discrepancies of these two phenomenological findings are brought into relief with a discussion of the philosophical "prerogatives" of each thinker's understanding of phenomenology. These issues emerge in terms of the Heideggerian 'prerogative' of the hermeneutical advance regard toward Being, and the Husserlian 'prerogative' of the reflective seeing of the phenomenological regard. The study finds that the unavoidable opposition of the phenomenal content of these issues has its basis in the character and status each accords to the essence of the phenomenon of "reflection." The study concludes with a consideration of the phenomenal warrant of what comes forward as die Sachen selbst of the Husserlian 'prerogative' of the ontologically neutral reflective uncovering of the phenomenon of transcendental subjectivity and the Heideggerian 'prerogative' of the hermeneutical disclosure of the ontico-ontological disclosedness of the unreflective phenomenon of Being

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...

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

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.

“Back to Husserl: Reclaiming the Traditional Philosophical Context ofthe Phenomenological ‘Problem’ of the Other: Leibniz’s Monadology”. The internalmotivation that led Husserl to revise his early view of the pure Ego as empty ofessential content is traced to the end of explicating his reformulation of phenomenologyas the egology of the concrete transcendental Ego. The necessity ofrecasting transcendental phenomenology as a transcendental idealism that followsfrom this reformulation is presented and the appearance of transcendentalsolipsism of this idealism exposed as unfounded. That the ground of this exposureis Husserl’s phenomenological appropriation of Leibniz’s metaphysical insightsinto the problem of accounting for the plurality of monads, and, therefore, not theCartesian problem of the other mind, is presented as the key to reclaiming thetraditional philosophical context of the phenomenological problem of 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.

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.

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.

This paper offers both a phenomenologically psychological and a phenomenologically transcendental account of the constitution of the unconscious. Its phenomenologically psychological portion was published in the previous volume of this journal as Part I, while its phenomenologically transcendental portion is published here as Part II. Part I first clarified the issues involved in Husserl's differentiation of the respective contents and methodologies of psychological and transcendental phenomenology. On the basis of this clarification it showed 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 (rooted in Freud's theory of repression) in the descriptive account of the constitution of an unconscious, there are cognitive factors (rooted in Jung's theory of apperception) that have yet to be descriptively accounted for by phenomenological psychology. Part I concluded with a phenomenologically psychological account of the role these cognitive factors play in the constitution of an unconscious. Part II shows how Jung's claims regarding a dimension of unconscious contents that lacks genealogical links to consciousness proper, i. e., the so-called "collective unconscious," can be phenomenologically accounted for if: (1) Jung's methodological differentiation of empirical and interpretative (hermeneutically phenomenological) approaches to the unconscious is attended to and; (2) 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.