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, 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.

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.

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.

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