Since the end of the last century, there has been several ambitious attempts to naturalize Husserlian phenomenology by way of mathematization. To justify themselves in view of Husserl’s adamant antinaturalism, many of these attempts appeal to the new physico-mathematical tools that were unknown in Husserl’s time and thus allegedly make his position outdated. This paper critically addresses these mathematization proposals and aims to show that Husserl had, in fact, sufficiently good arguments that make his antinaturalistic position sound even today. The (...) starting point of the discussion presented in this paper is the mathematization project introduced by Jean-Michel Roy, Jean Petitot, Bernard Pachoud, and Francisco Varela in their introduction to the book Naturalizing Phenomenology. This proposal was followed by a number of critiques but also by several alternative naturalization attempts clearly inspired by Roy et al.’s ambitious project. The review of some of Husserl’s important arguments often overlooked or misinterpreted by both the naturalization advocates and their critics leads the author of the paper to the twofold conclusion which, on the one hand, explores the deeper reasons for the impossibility of a physical and mathematical treatment of phenomenology, on the other hand, clarifies the sense in which such treatments are possible, namely by way of restriction of the variety of experiential aspects that undergo naturalization and substitution of the aspects amenable to the direct mathematization for the directly unmathematizable ones. In the fourth section of this paper, the author attempts to demonstrate that, contrary to widespread belief, Husserl’s arguments are not obsolete by the standards of the contemporary physico-mathematical approaches employed in the mathematization of phenomenology and indeed stand the test of time. (shrink)

Brouwer and Weyl recognized that the intuitive continuum requires a mathematical analysis of a kind that set theory is not able to provide. As an alternative, Brouwer introduced choice sequences. We first describe the features of the intuitive continuum that prompted this development, focusing in particular on the flow of internal time as described in Husserl's phenomenology. Then we look at choice sequences and their logic. Finally, we investigate the differences between Brouwer and Weyl, and argue that Weyl's conception of (...) choice sequences is defective on several counts. (shrink)

Even though Husserl and Brouwer have never discussed each other's work, ideas from Husserl have been used to justify Brouwer's intuitionistic logic. I claim that a Husserlian reading of Brouwer can also serve to justify the existence of choice sequences as objects of pure mathematics. An outline of such a reading is given, and some objections are discussed.

Edmund Husserl has argued that we can intuit essences and, moreover, that it is possible to formulate a method for intuiting essences. Husserl calls this method 'ideation'. In this paper I bring a fresh perspective to bear on these claims by illustrating them in connection with some examples from modern pure geometry. I follow Husserl in describing geometric essences as invariants through different types of free variations and I then link this to the mapping out of geometric invariants in modern (...) mathematics. This view leads naturally to different types of spatial ontologies and it can be used to shed light on Husserl's general claim that there are different ontologies in the eidetic sciences that can be systematically related to one another. The paper is rounded out with a consideration of the role of ideation in the origins of modern geometry, and with a brief discussion of the use of ideation outside of pure geometry. (shrink)

When did the concept of model begin to be used in mathematics? This question appears at first somewhat surprising since “model” is such a standard term now in the discourse on mathematics and “modelling” such a standard activity that it seems to be well established since long. The paper shows that the term— in the intended epistemological meaning—emerged rather recently and tries to reveal in which mathematical contexts it became established. The paper discusses various layers of argumentations and reflections in (...) order to unravel and reach the pertinent kernel of the issue. The specific points of this paper are the difference in the epistemological concept to the usually discussed notions of model and the difference between conceptions implied in mathematical practices and their becoming conscious in proper reflections of mathematicians. (shrink)

In the 1930s Otto Selz developed a novel approach to the psychology of perception which he called “synthetic psychology of wholes”. This “synthetic psychology” is based on a phenomenological description of the structural relationships between elementary items building up integral wholes. The present article deals with Selz’s account of spatial cognition within this general framework. Selz Zeitschrift für Psychologie, 114, 351–362 argues that his approach to spatial cognition delivers answers to the long-discussed question of the epistemological status of the laws (...) of geometry. More specifically he tries to derive the Euclidean axioms from the structural laws valid for phenomenal space. After a brief description of the discussion of the status of geometry in the 1920s/1930, the present article explains Selz’s understanding of “phenomenology”. Section 4 then deals with Selz’s attempt to derive the Euclidean laws from the structural phenomenological laws of space. Selz’s attempted derivation suffers from some formal shortcomings, which however can be repaired. The question arises, though, whether the necessary improvements do not rely upon more intricate geometric intuitions and thus render Selz’s attempt to base geometry upon the phenomenology of spatial cognition circular. (shrink)

On an ordinary view of the relation of philosophy of science to science, science serves only as a topic for philosophical reflection, reflection that proceeds by its own methods and according to its own standards. This ordinary view suggests a way of writing a global history of philosophy of science that finds substantially the same philosophical projects being pursued across widely divergent scientific eras. While not denying that this view is of some use regarding certain themes of and particular time (...) periods, this essay argues that much of the epistemology and philosophy of science in the early twentieth century in a variety of projects looked to the then current context of the exact sciences, especially geometry and physics, not merely for its topics but also for its conceptual resources and technical tools. This suggests a more variable project of philosophy of science, a deeper connection between early twentieth-century philosophy of science and its contemporary science, and a more interesting and richer history of philosophy of science than is ordinarily offered.Author Keywords: Rudolf Carnap; C. I. Lewis; Oskar Becker; History of philosophy of science. (shrink)

Este artículo se propone describir el modo de aparecimiento del mundo sensible, entendiéndolo como el primer suelo sobre el cual la vida humana se instala efectivamente entre cosas concretas. Se intentará desvincular este nivel de presencia inmediata y cotidiana del mundo exterior del modo como tradicionalmente se le concibe, a saber, en el sentido de una manifestación “objetual”. En este contexto, se recurrirá a descripciones fenomenológicas de la percepción que tuvieron lugar principalmente en trabajos filosóficos y psicológicos de la primera (...) mitad del siglo XX, y que fueron influenciados por las reflexiones tempranas de Edmund Husserl. (shrink)

. Este artículo se propone discutir las dificultades que pertenecen al ejercicio de pensarnos en cuanto corporales. Guía de estas reflexiones son los índices heideggerianos sobre la corporalidad humana realizados en Zollikoner Seminare. Dichos seminarios advierten que la actual experiencia de nuestro cuerpo, pese a poder ser estimada como inmediata, se halla mediada por nuestros propios supuestos epocales y se enraiza ya en el pensar ontológico de Occidente. Así, este artículo intentará examinar las aporías filosóficas de tal mediación histórico-epocal, exponiendo (...) la reflexión heideggeriana del cuerpo desde el claro del ser como una respuesta a la idea tradicional de subjetividad fundada en la noción de “mera presencia”. (shrink)

The present paper attempts to show that a 1915 article by Erich Kretschmann must be credited not only for being the source of Einstein’s point-coincidence remark, but also for having anticipated the main lines of the logical-empiricist interpretation of general relativity. Whereas Kretschmann was inspired by the work of Mach and Poincaré, Einstein inserted Kretschmann’s point-coincidence parlance into the context of Ricci and Levi-Civita’s absolute differential calculus. Kretschmann himself realized this and turned the point-coincidence argument against Einstein in his second (...) and more famous 1918 paper. While Einstein had taken nothing from Kretschmann but the expression “point-coincidences”, the logical empiricists, however, instinctively dragged along with it the entire apparatus of Kretschmann’s conventionalism. Disappointingly, in their interpretation of general relativity, the logical empiricists unwittingly replicated some epistemological remarks Kretschmann had written before General Relativity even existed. (shrink)

In this paper, I start with the opposition between the Husserlian project of a phenomenology of the experience of time, started in 1905, and the mathematical and physical theory of time as it comes out of Einstein’s special theory of relativity in the same year. Although the contrast between the two approaches is apparent, my aim is to show that the original program of Husserl’s time theory is the constitution of an objective time and a time of the world, starting (...) from the intuitive giveness of time, i.e., from time as it appears. To show this, I stress the structural similarity between Husserl’s original question of time and the problem of a phenomenology of space constitution as it was first developed in the his manuscripts from the nineteenth century, in which we find the threefold question of the origin of our representation of space, of the geometrization of intuitive space, and of the constitution of transcendent world space. Finally, I reconsider some of Husserl’s main theses about the phenomenological constitution of objective time in light of the main results of special relativity time-theory, introducing several corrections to central assumptions that underlie Husserl’s theory of time. (shrink)

The project of a naive physics has been the subject of attention in recent years above all in the artificial intelligence field, in connection with work on common-sense reasoning, perceptual representation and robotics. The idea of a theory of the common-sense world is however much older than this, having its roots not least in the work of phenomenologists and Gestalt psychologists such as Kohler, Husserl, Schapp and Gibson. This paper seeks to show how contemporary naive physicists can profit from a (...) knowledge of these historical roots of their discipline, which are shown to imply above all a critique of the set-theory-based models of reality typically presupposed by contemporary work in common-sense ontology. (shrink)

Ever since its appearance in 1913, Reinach's work on a The A Priori Foundations of the Civil Law has served as the principal representative of phenomenological, aprioristic and ontological/realist approaches to the philosophy of law. This annotated bibliography provides an overview of the reception of Reinach's thinking, which has been of influence also in the realm of speech act theory.

This dissertation engages in a critical analysis of the work of Adolf Reinach in the theory of knowledge and legal philosophy. Reinach had trained as a lawyer and brought that perspective and experience to bear in his phenomenological work on problems in evidence and legal philosophy. His contributions to phenomenology in the early 20th century provide a window into the earliest phases of the development of the phenomenological movement, prior to World War I. This dissertation locates this work in the (...) European intellectual context of the era and finds analogies with key philosophical dilemmas and developments in England during the same period, arguably ones with shared intellectual roots. Valued for his talent as an inspiring university lecturer, Reinach was a central figure in the circle of young scholars who practiced phenomenology in the spirit of the "early" "pre-Ideen" phase of phenomenology. The dissertation Appendices include translations of selected excerpts from the Nachlass. My translation of the obituary Edmund Husserl wrote and published following Adolf Reinach's death in WWI is published separately. Professor Raymond Klibansky was my supervisor and mentor throughout. (shrink)

This paper attempts to explain the emergence of the logical empiricist philosophy of space and time as a collision of mathematical traditions. The historical development of the ``Riemannian'' and ``Helmholtzian'' traditions in 19th century mathematics is investigated. Whereas Helmholtz's insistence on rigid bodies in geometry was developed group theoretically by Lie and philosophically by Poincaré, Riemann's Habilitationsvotrag triggered Christoffel's and Lipschitz's work on quadratic differential forms, paving the way to Ricci's absolute differential calculus. The transition from special to general relativity (...) is briefly sketched as a process of escaping from the Helmholtzian tradition and entering the Riemannian one. Early logical empiricist conventionalism, it is argued, emerges as the failed attempt to interpret Einstein's reflections on rods and clocks in general relativity through the conceptual resources of the Helmholtzian tradition. Einstein's epistemology of geometry should, in spite of his rhetorical appeal to Helmholtz and Poincaré, be understood in the wake the Riemannian tradition and of its aftermath in the work of Levi-Civita, Weyl, Eddington, and others. (shrink)