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The development of mathematics and the birth of phenomenology

Mirja Hartimo

In Phenomenology and mathematics. London: Springer. pp. 107--121 (2010)

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No Magic: From Phenomenology of Practice to Social Ontology of Mathematics.Mirja Hartimo & Jenni Rytilä - 2023 - Topoi 42 (1):283-295.details The paper shows how to use the Husserlian phenomenological method in contemporary philosophical approaches to mathematical practice and mathematical ontology. First, the paper develops the phenomenological approach based on Husserl's writings to obtain a method for understanding mathematical practice. Then, to put forward a full-fledged ontology of mathematics, the phenomenological approach is complemented with social ontological considerations. The proposed ontological account sees mathematical objects as social constructions in the sense that they are products of culturally shared and historically developed practices. (...) Download Export citation Bookmark
Intuitionism in the Philosophy of Mathematics: Introducing a Phenomenological Account.Philipp Berghofer - 2020 - Philosophia Mathematica 28 (2):204-235.details 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 (...) Download Export citation Bookmark 6 citations
Is Husserl’s Antinaturalism up to Date? A Critical Review of the Contemporary Attempts to Mathematize Phenomenology.Andrij Wachtel - 2022 - Husserl Studies 38 (2):129-150.details 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appeal to the new physico-mathematical tools that were unknown in Husserl’s time and thus allegedly make his position outdated.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 (...) Download Export citation Bookmark
Husserl’s Foundation of the Formal Sciences in his “Logical Investigations”.Henning Peucker - 2012 - Axiomathes 22 (1):135-146.details This article is composed of three sections that investigate the epistemological foundations of Husserl’s idea of logic from the Logical Investigations . First, it shows the general structure of this logic. Husserl conceives of logic as a comprehensive, multi-layered theory of possible theories that has its most fundamental level in a doctrine of meaning. This doctrine aims to determine the elementary categories that constitute every possible meaning (meaning-categories). The second section presents the main idea of Husserl’s search for an epistemological (...) Download Export citation Bookmark 1 citation
Husserl: ¿Fenomenología de la matemática?Miguel Hernando Guamanga - 2021 - Eidos: Revista de Filosofía de la Universidad Del Norte 36:170-192.details 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: (...) Download Export citation Bookmark

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