The view that mathematics deals with ideal objects to which we have epistemic access by a kind of perception has troubled many thinkers. Using ideas from Husserl’s phenomenology, I will take a different look at these matters. The upshot of this approach is that there are non-material objects and that they can be recognized in a process very closely related to sense perception. In fact, the perception of physical objects may be regarded as a special case of this more universal (...) way of recognizing objects of any kind. (shrink)

In the Transcendental Aesthetic of the Critique of Pure Reason, Immanuel Kant famously claims that we have an a priori intuition of space as an ‘infinite given magnitude’. Later on, in the Transcendental Analytic, he seems to add that the intuition of space presupposes a synthetic activity of the transcendental imagination. Several authors have recently pointed out that these two claims taken together give rise to two problems. First, it is unclear how the transcendental imagination of a finite mind could (...) ever result in the intuition of an entity that is infinitely large. Second, Kant claims that our intuition of space has a ‘whole-prior-to-its-parts’ structure, such that its parts are given only as limitations of the whole, while synthesis is compositional and has a ‘parts-prior-to-their-whole’ structure, because it consists in first running through and then taking together the parts of a sensible manifold. I will solve these two problems by showing that Kant thought that synthesis does not always have a compositional structure but that there is also a form of ‘decomposing’ synthesis, which has a whole-prior-to-its-parts structure. Building on similarities between Kant, Edmund Husserl and G. W. F. Hegel, I will argue that infinite space is given to us in intuition by precisely such an activity of decomposition, one that allows us to differentiate between finite spatial objects and the unlimited phenomenal horizon in which they appear. (shrink)

There are three theories in the epistemology of modality that have received sustained attention over the past 20 years: conceivability-theory, counterfactual-theory, and deduction-theory. In this paper we argue that all three face what we call the problem of modal epistemic friction. One consequence of the problem is that for any of the three accounts to yield modal knowledge, the account must provide an epistemology of essence. We discuss an attempt to fend off the problem within the context of the internalism (...) versus externalism debate about epistemic justification. We then investigate the effects that the PMEF has on reductive and non-reductive theories of the relation between essence and modality. (shrink)

El Repertorio bibliográfico sobre Martin Heidegger que se presenta a continuación, reúne la información obtenida de las más de 240 revistas de filosofía disponibles en la Hemeroteca de la Pontificia Universidad Católica del Perú. El Repertorio incluye referencias bibliográficas completas de los artículos, reseñas, estudios críticos, traducciones y otros documentos que abordan la obra del importante pensador alemán hasta el año 2010.

This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics.

The following text is divided in four parts. The first presents the inner relation between the phenomenological concept of intentionality and space in a general mathematical sense. Following this train of though the second part brie_ly characterizes the use of the geometrical concept of manifold (Mannigfaltigkeit) in Husserl’s work. In the third part we present some examples of the use of the concept in Husserl’s analyses of space, time and intersubjectivity, pointing out some dif_iculties in his endeavor. In the fourth (...) and _inal part we offer some points of coincidence between phenomenology and category theory suggesting that the latter can work as a formal frame for ontology in the former. Our thesis is that intentionality operates in different levels as a morphism, functor and natural transformation. (shrink)

I draw on Carl Stumpf’s essay “Psychologie und Erkenntnistheorie”, and his precocious On the Psychological Origin of the Idea of Space, to set out a charge he raises against Kant’s fo...

This paper is concerned with the reappraisal of Husserl’s ontology and epistemology, sketched in book one of Ideen. The main issue is Husserl’s theory of essence and essential insight. I present the fundamental distinction between facts and essences, and, over and above it, Husserl’s defense of an a priori knowledge based on essential insight as well as his partition of the whole realm of a priori knowledge into a formal set of material, regional ontologies. I will show how the theory (...) of essential insight presented in Ideen gives rise to several criticisms, namely those made by Neo-Kantians, like Rickert and Natorp. In the last part, I will show how the mathematical concept of an invariant under a group of variations was the leading case for Husserl’s mature notion of eidetic insight. (shrink)

Topology has been characterized as an unsuitable mathematical framework for the investigation of geometric-perceptual phenomena. This has been attributed to the highly abstract nature of topology leading to failures in tasks such as making distinctions between geometrical figures (e.g., a cube versus a sphere) in which the human perceptual system succeeds easily. An alternative thesis is proposed on both philosophical and empirical grounds. The present analysis applies the Müller-Lyer (ML) illusion as a method of investigation to examine the suitability of (...) topology in raising questions about geometric-perceptual phenomena and formulating potential answers to these questions. Not only will it be concluded that topology is a suitable mathematical framework in which one can formulate relevant questions and potential answers with respect to perceptual phenomena such as the ML illusion, it will also be discussed that topology will not be replaced by other means of spatial representation consistent with the findings that indicate its contributions to our daily spatial behavior along with other means such as Euclidean geometry. In addition, the analysis will be discussed with respect to two relevant themes: 1) the implications of the proposed view in relation to Husserl’s phenomenology and 2) the effect of developmental stages and education that may change the involvement of topology in such perceptual responses over time. (shrink)

Hermann Weyl was one of the most important figures involved in the early elaboration of the general theory of relativity and its fundamentally geometrical spacetime picture of the world. Weyl’s development of “pure infinitesimal geometry” out of relativity theory was the basis of his remarkable attempt at unifying gravitation and electromagnetism. Many interpreters have focused primarily on Weyl’s philosophical influences, especially the influence of Husserl’s transcendental phenomenology, as the motivation for these efforts. In this article, I argue both that these (...) efforts are most naturally understood as an outgrowth of the distinctive mathematical-physical tradition in Göttingen and also that phenomenology has little to no constructive role to play in them. (shrink)

This dissertation explores and argues for the import of the imagination (Phantasie) in Edmund Husserl's phenomenological method of inquiry. It contends that Husserl's extensive analyses of the imagination influenced how he came to conceive the phenomenological method throughout the main stages of his philosophical career. The work clarifies Husserl's complex method of investigation by considering the role of the imagination in his main methodological apparatuses: the phenomenological, eidetic, and transcendental reductions, and eidetic variation - all of which remained ambiguous despite (...) his extensive programmatic discussions. The work illuminates and clarifies aspects of the Husserlian phenomenological method never before explored. -/- In order to clarify Husserl's eidetic method of inquiry, I propose a new way of thinking about the imagination - as direct intuitive presentation (eigentliche anschauliche Vorstellung) and as horizonal-nexic level of consciousness exhibiting the neutrality, freedom, and possibility as its essential features. Following Husserl's studies of the imagination, I propose a three-level model of consciousness (realizing, imagining, and eidetic) and explore the dynamic flexibility of each level (as horizon within which acts such as judgments or memories can unfold). This model of consciousness allows for a rethinking of the sources and conditions for the possibility of eidetic phenomenological inquiry - topics Husserl was mostly silent about. -/- Through a rethinking of the model of consciousness, I propose a tight and substantial relationship between the natural (everyday) and artificial (methodological, theoretical) attitudes. I argue that the structure and systems of possibilities pertaining to the artificial attitude - i.e., our actual as well as possible methodological tools - are structurally and well as informationally bound to the structure and system of possibilities pertaining to the natural attitude. In order to explore the nature of the relationship between these two attitudes I argue that we must take a closer look at the structure and abilities of imagining consciousness - the sole nexic-horizonal level that can function both naturally and artificially. This insight regarding the nature of consciousness clarifies Husserl's transcendental idealism in its intimate connection to the everyday. Understanding Husserl's philosophical stance is thus purged of all possibility of mistakenly labeling it as entailing immanent detachment, solipsism, or Platonic idealism. (shrink)

Richard Tieszen [Tieszen, R. (2005). Philosophy and Phenomenological Research, LXX(1), 153–173.] has argued that the group-theoretical approach to modern geometry can be seen as a realization of Edmund Husserl’s view of eidetic intuition. In support of Tieszen’s claim, the present article discusses Husserl’s approach to geometry in 1886–1902. Husserl’s first detailed discussion of the concept of group and invariants under transformations takes place in his notes on Hilbert’s Memoir Ueber die Grundlagen der Geometrie that Hilbert wrote during the winter 1901–1902. (...) Husserl’s interest in the Memoir is a continuation of his long-standing concern about analytic geometry and in particular Riemann and Helmholtz’s approach to geometry. Husserl favored a non-metrical approach to geometry; thus the topological nature of Hilbert’s Memoir must have been intriguing to him. The task of phenomenology is to describe the givenness of this logos, hence Husserl needed to develop the notion of eidetic intuition. (shrink)

Before Abraham Robinson and Kurt Gödel became familiar with Paul Cohen’s Results, both logicians held a naïve Platonic approach to philosophy. In this paper I demonstrate how Cohen’s results influenced both of them. Robinson declared himself a Formalist, while Gödel basically continued to hold onto the old Platonic approach. Why were the reactions of Gödel and Robinson to Cohen’s results so drastically different in spite of the fact that their initial philosophical positions were remarkably similar? I claim that the key (...) to these different responses stems from the meanings that Gödel and Robinson gave to the concept of intuition, as well as to the relationship between epistemology and ontology. I also illustrate that although it might initially appear that Gödel’s and Robinson’s positions after Cohen’s results were quite different, this was not necessarily the case. (shrink)