# Burt Hopkins

Burt Hopkins, professor of Philosophy, Seattle University. His 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.

### Conférences

#### Husserl and Jacob Klein on Symbolic Cognition

I argue that Klein’s philosophical analysis of Viète’s invention of symbolic cognition is conceptually invisible to Husserl’s logical account of symbolic cognition, because the mode of concept formation involved in the genesis of the symbolic concept of number behind this innovation is presupposed rather than accounted for by Husserl’s account. I support my argument by making salient the two fundamental presuppositions inseparable from Husserl’s theory : 1) the formal isomorphism between positive integers beginning with two and symbolic numerals and 2) the a-historicity of the formality constitutive of the concept of number. I conclude by attempting to characterize the enduring phenomenological significance of the problematical status of these presuppositions.

*Mardi 3 mai 2016 de 17h à 19h - EHESS (salle 1) - 190-198, avenue de France 75013 Paris.*

#### The Role of ‘Intentionality’ in Jacob Klein’s Account of the Historicity of the Concept of Number

I claim that Jacob Klein argues that the transformation of the concept of number from its ancient Greek to its modern conceptuality establishes that the distinction between a purely conceptual mode of cognition and a non-conceptual intuitive mode of cognition is unique to modernity. I claim that Klein maintains that this distinction was, in effect, first formulated by Descartes. Because of this, Edmund Husserl’s theory of intentionality (prior to his taking up the problem of the historicity of intentional meaning in his late work), which trades on this distinction, had to be ruled out by Klein as being too modern to be of assistance in providing an account of the origin of the distinction between the symbolic mode of concept-formation and the pre-modern, non-symbolic mode of concept-formation that it superseded. This, I submit, is the reason behind not only Klein’s use of the term ‘conceptuality’ instead of ‘intentionality’ to characterize concept-formation both in general and with regard to the specific differences between ancient and modern modes, but also the reason why, when it came to articulating these differences, he employed the scholastic Eustachias’ formulation of the distinction between first and second intentions.

*Mardi 10 mai 2016 de 15h à 17h - CAK (salle des séminaires 5e étage) - 27, rue Damesme 75013 Paris.*

#### From General Method to General Object: Jacob Klein on Viète’s Transformation of Ancient Analysis

I argue that to account for the origin of the general concept of mathematical object, Jacob Klein’s philosophical analysis attempts to reconstruct a strand in the history of mathematics, namely, François Viète’s appropriation and transformation of ancient geometrical and arithmetic analysis in his analytical art. On the basis of mathematically historical evidence, I claim that Klein’s argument attempts to show that in the part of the analytical procedure of Viète’s logistice speciosa he called “zetetic,” Viète’s calculations operate on mathematical concepts whose ontological status is identifiable with neither ancient numbers nor ancient magnitudes. Because of this, Klein argues that these concepts represent the first appearance of the modern concept of number, the symbolic structure that underlies symbolic calculi.

*Jeudi 19 mai 2016 de 10h à 13h - CAK (salle des séminaires 6e étage) - 27, rue Damesme 75013 Paris.*

#### Klein on the Role of Rhetoric in Shaping the Reception and Self-Understanding of Viète’s Algebra

I argue that Jacob Klein philosophical-historical research on the origin of algebra adumbrates the role of 16 th century rhetoric in facilitating the collapse of the ancient mathematical distinction between “theorem” and “problem.” I reconstruct Klein’s account and amplify and develop it in light of the contemporary researches of Giovanna Cifoletti on the rhetorical context of the development and self-understanding of algebra in 16 th century France. Specifically, I argue that Cifoletti’s account of the inseparability of rhetoric and the logic of algebra on the one hand, and that of the dialectical art of thinking and algebra on the other, is prefigured in Klein’s account of François Viète’s creation of the first symbolic algebra.

*Mardi 24 mai 2016 de 17h à 19h - EHESS (salle 3) - 190-198, avenue de France 75013 Paris.*