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

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)

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)

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)

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)