Burt Hopkins

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.