RESUMEN La fenomenología de Husserl está inmersa en un entramado de regresiones y revisiones conceptuales que dificultan la identificación de una estructura sistémica. Los conceptos característicos de la fenomenología carecen de univocidad y no son propios de algunas obras de Husserl. Philosophie der Arithmetik ilustra el problema referido. ¿Puede inscribirse esta obra dentro de la categoría de texto fenomenológico? ¿Es posible hablar de una fenomenología de la matemática en Husserl? y ¿qué sentido tendría esto? Los objetivos del presente ensayo son: (...) primero, analizar la dificultad que tiene Philosophie der Arithmetik para responder a las inquietudes de la filosofía de las matemáticas, y segundo, proponer la posibilidad de una fenomenología de la matemática condicionada a la clarificación conceptual y al estudio crítico de la influencia de la tradición analítica sobre la filosofía de las matemáticas. ABSTRACT Husserl's phenomenology is immersed in a network of regressions and conceptual revisions that hinder the identification of a systemic structure. The characteristic concepts of phenomenology fall short of uniqueness and are not appropriate for some of Husserl's works. Philosophie der Arithmetik illustrates the aforementioned problem. Can this work be classified under the category of phenomenological texts? Is it possible to talk about a phenomenology of mathematic in Husserl? And what would be the point of this? The objectives of the present essay are: first, to analyze the difficulty that Philosophie der Arithmetik has responding to the concerns of the philosophy of mathematics, and second, to propose the possibility of a phenomenology of mathematics, conditioned to conceptual clarification and critical study of the influence of the analytical tradition on the philosophy of mathematics. (shrink)

The aim of this paper is to establish a phenomenological mathematical intuitionism that is based on fundamental phenomenological-epistemological principles. According to this intuitionism, mathematical intuitions are sui generis mental states, namely experiences that exhibit a distinctive phenomenal character. The focus is on two questions: what does it mean to undergo a mathematical intuition and what role do mathematical intuitions play in mathematical reasoning? While I crucially draw on Husserlian principles and adopt ideas we find in phenomenologically minded mathematicians such as (...) Hermann Weyl and Kurt Gödel, the overall objective is systematic in nature: to offer a plausible approach towards mathematics. (shrink)

This paper explicates Husserl’s usage of what he calls “radical Besinnung” in Formale und transzendentale Logik. Husserl introduces radical Besinnung as his method in the introduction to FTL. Radical Besinnung aims at criticizing the practice of formal sciences by means of transcendental phenomenological clarification of its aims and presuppositions. By showing how Husserl applies this method to the history of formal sciences down to mathematicians’ work in his time, the paper explains in detail the relationship between historical critical Besinnung and (...) transcendental phenomenology. Ultimately the paper suggests that radical Besinnung should be viewed as a general methodological framework within which transcendental phenomenological descriptions are used to criticize historically given goal-directed practices. (shrink)

Husserl’s official account of essence is modal. It is also, I submit, incompatible with the role that essence is supposed to play, especially relative to necessity, in his overall philosophy. In the Husserlian framework, essence should rather be treated as a non-modal notion. The point, while not generally acknowledged, has been made before (by Kevin Mulligan for one); yet the arguments given for it, though perhaps sound, are not Husserlian. In this paper I present a thoroughly Husserlian argument for that (...) claim, as well as a Husserlian essentialist account of necessity. I also discuss the role of grounding within the account. (shrink)