Burt Hopkins’s (Università Ca' Foscari Venezia, Department of Philosophy and Cultural Heritage) main research interest is the philosophical foundation of the transformation of knowledge that began in the 16th century with the philosophical advent of modernity. He has written three books, most recently The Origin of the Logic of Symbolic Mathematics: Jacob Klein and Edmund Husserl (2011) and The Philosophy of Husserl (2010), and edited two others. He has published over sixty articles and given over 100 lectures on contemporary European philosophy (especially the phenomenology of Edmund Husserl, Martin Heidegger, and Jacob Klein), Plato, early modern philosophy, and philosophy and depth psychology. He is founding co-editor of The New Yearbook for Phenomenology and Phenomenological Philosophy. Hopkins’s current research continues the tradition of transcendental phenomenology and is focused on the critique of symbolic reason.
“Jacob Klein on Simon Stevin’s Symbolic Breakdown of the Ancient Distinction between Discrete and Continuous Magnitude”
I examine Klein’s argument that the new symbolic number concept [Zahl-Begriff] permits Stevin to address the consequences of the schism between the actual understanding of number [Zahl] and the understanding clinging to the traditional number concept [Anzahl-Begriff], as a definite amount of definite objects. According to Klein, these consequences include Stevin’s rejection of the ancient distinction between discrete and continuous magnitude and the traditional appellations of absurd or surd or irrational (i.e., un-speakable) numbers [Zahlen]. According to Klein, Stevin attacks these traditional appellations with the thesis that there are no absurd, irrational, irregular, inexplicable, or surd numbers, which supports the claim that incommensurability does not cause the incommensurable terms to be surds.
- Mardi 23 mai 2017, 17h - EHESS (Salle AS1_24, 1er sous-sol) – 54, bld Raspail 75006 Paris
“Jacob Klein’s on John Wallis’s Symbolic Realization Number as Dimensionless Magnitude”
I examine Klein’s argument that it is only in terms of a symbolic reinterpretation of the mode of being of ancient numbers, understood as definite amounts of definite objects [Anzahlen], that Wallis’s account of the universality of arithmetic as a general theory of ratios, which depends on the homogeneity of all numbers, can be understood. A major consequence of Wallis’s reinterpretation is that the object of arithmetic and logistic in their algebraic expansion is now determined as number [Zahl], and this means as a symbolically conceived ratio. Not only is this conception of number, as ratio, consonant with that of algebra as a general theory of proportions and ratios, but, also, as the material of arithmetic and logistic, its being no longer presents any problem, since, unlike the problematical mode of being of the ancient material (ὕλη), its mode of being is immediately graspable in the notation. Thus Klein argues that unlike the pure units that make up the material of ancient number (ἀριθμός), the mode of being of which can be subject to dispute because it can be conceived of as formations that are either independent orobtained by abstraction (ἀφαίρεσις), in Wallis’s Mathesis Universalis the being of numbers [Zahlen]—its symbolic character as dimensionless—is indisputable.
- Mardi 30 mai 2017, 17h - EHESS (Salle AS1_24, 1er sous-sol) – 54, bld Raspail 75006 Paris
“The Phenomenological Context of Jacob Klein’s Philosophy of Mathematics”
Leo Strauss’s famous remark, that there’s barely a sentence in Klein’s work whose meaning wasn’t influenced by his association with Martin Heidegger and Edmund Husserl, is as true as it is misleading. It’s true, because the phenomenological philosophy of Husserl and Heidegger informed both the content and the context of Klein’s philosophical development. It’s misleading, however, because Klein’s work on the origin of modern algebra can only be understood as a fundamental critique of major presuppositions guiding both Heidegger’s and Husserl’s phenomenologies. In the case of Heidegger, the presupposition is that ancient Greek philosophy was basically ontology, the inquiry into the intelligibility and nature of the things that exist, beings. Klein argues that this view of ancient Greek philosophy is basically Aristotelian and therefore elides ancient Greek philosophy’s more original origin in Plato’s and the Pre-Socratics’ preoccupation with the problem of the one and many in nature and number. In the case of Husserl, Klein’s work criticizes the presupposition behind his theory of intentionality, that general ontology provides the answer to the question of the meaning of being. Klein’s work does so by showing that the meaning of general ontology is inseparable from historically dated presuppositions stemming from 16th and 17th century philosophy and mathematics, presuppositions that occlude the intelligibility of non-formalized structures of being.
- Mardi 6 juin 2017, 17h - EHESS (Salle AS1_23, 1er sous-sol) – 54, bld Raspail 75006 Paris
“Jacob Klein on the Philosophy of the History of the Exact Sciences”
In this lecture I will discuss Klein’s argument that mathematics as a science lacks the conceptual resources to investigate its own history, because the formality of its concepts are not historically datable within the context of mathematical science. The conclusion he draws from this will also investigated, that the history in question only emerges as a problem on the basis of philosophical investigations into the foundations of mathematics, which are historically datable. Finally, the implications of Klein’s conclusion, that the proper discipline of the history of mathematics is the history of the philosophy of the philosophy of the foundations of mathematics, will be discussed and critically assessed.
- Mardi 13 juin 2017, 13h à 15h - EHESS (Salle AS1_08, 1er sous-sol) – 54, bld Raspail 75006 Paris