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Switch to: References
Citations of:
Numbers in presence and absence: a study of Husserl's philosophy of mathematics
Hingham, MA: Distributors for the U.S. and Canada, Kluwer Boston (1982)
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This book offers an historically-informed critical assessment of Dummett's account of abstract objects, examining in detail some of the Fregean presuppositions whilst also engaging with recent work on the problem of abstract entities. |
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This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what (...) |
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(2009). The Importance of Number in Husserl's Early Theory of Time-Constitution. Journal of the British Society for Phenomenology: Vol. 40, Husserl's Lectures on Internal Time-Conciousness, pp. 188-206. |
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This paper reconstructs and critically analyzes Husserl’s philosophical engagement with symbolic technologies—those material artifacts and cultural devices that serve to aid, structure and guide processes of thinking. Identifying and exploring a range of tensions in Husserl’s conception of symbolic technologies, I argue that this conception is limited in several ways, and particularly with regard to the task of accounting for the more constructive role these technologies play in processes of meaning-constitution. At the same time, this paper shows that a critical (...) |
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This article develops a critical investigation of the epistemological core of Hilbert's foundational project, the so-called the finitary attitude. The investigation proceeds by distinguishing different senses of 'number' and 'finitude' that have been used in the philosophical arguments. The usual notion of modern pure mathematics, i.e. the sense of number which is implicit in the notion of an arbitrary finite sequence and iteration is one sense of number and finitude. Another sense, of older origin, is connected with practices of counting (...) |
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The question of the psychologism of the theory of number developed by Husserl in his Philosophy of Arithmetic has long been debated, but it cannot be considered fully resolved. In this paper, I address the issue from a new point of view. My claim is that in the Philosophy of Arithmetic, Husserl made, albeit indirectly, a series of arguments that are worth reconstructing and clarifying since they are useful in shedding some light on the psychologism issue. More specifically, I maintain (...) |
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The paper examines the roots of Husserlian phenomenology in Weierstrass's approach to analysis. After elaborating on Weierstrass's programme of arithmetization of analysis, the paper examines Husserl's Philosophy of Arithmetic as an attempt to provide foundations to analysis. The Philosophy of Arithmetic consists of two parts; the first discusses authentic arithmetic and the second symbolic arithmetic. Husserl's novelty is to use Brentanian descriptive analysis to clarify the fundamental concepts of arithmetic in the first part. In the second part, he founds the (...) |
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Evidence is the very core of Husserlian phenomenology, with the term “evidence” signifying for Husserl the phenomenological perspective on the question of truth. In contrast to the conventional philosophical understanding of “truth” in mainly epistemological terms, Husserl’s notion of “evidence”, as elaborated in his Logical Investigations (1900–1), is more essentially ontological, pointing to the way in which a phenomenon becomes clear to us in its constitution. Husserl’s main point in the Sixth Investigation was that we can “see” how evidence functions (...) |
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Few have entertained the idea that Georg Cantor, the creator of set theory, might have influenced Edmund Husserl, the founder of the phenomenological movement. Yet an exchange of ideas took place between them when Cantor was at the height of his creative powers and Husserl in the throes of an intellectual struggle during which his ideas were particularly malleable and changed considerably and definitively. Here their writings are examined to show how Husserl's and Cantor's ideas overlapped and crisscrossed in the (...) |
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This paper argues that frege did not significantly influence husserl's departure from psychologism by (1) examining husserl's early logical reflections, Especially those concerning the meaning of the term ""vorstellung"," and (2) determining which parts of husserl's "philosophy of arithmetic", Criticized for its psychologism by frege, Were psychologistic and when husserl rejected them. It concludes that the logical writings show an independent movement toward a non-Psychologistic position and that the psychologism of "philosophy of arithmetic" was abandoned by 1891 apart from any (...) |
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In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended. |
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The recent move to naturalize phenomenology through a mathematical protocol is a significant advance in consciousness research. It enables a new and fruitful level of dialogue between the cognitive sciences and phenomenology of such a nuanced kind that it also prompts advancement in our phenomenological analyses. But precisely what is going on at this point of ‘dialogue’ between phenomenological descriptions and mathematical algorithms, the latter of which are based on dynamical systems theory? It will be shown that what is happening (...) |
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The current resurgence of interest in cognition and in the nature of cognitive processing has brought with it also a renewed interest in the early work of Husserl, which contains one of the most sustained attempts to come to grips with the problems of logic from a cognitive point of view. Logic, for Husserl, is a theory of science; but it is a theory which takes seriously the idea that scientific theories are constituted by the mental acts of cognitive subjects. (...) |
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In this talk I present the main results from Anta (2021), namely, that the theoretical division between Boltzmannian and Gibbsian statistical mechanics should be understood as a separation in the epistemic capabilities of this physical discipline. In particular, while from the Boltzmannian framework one can generate powerful explanations of thermal processes by appealing to their microdynamics, from the Gibbsian framework one can predict observable values in a computationally effective way. Finally, I argue that this statistical mechanical schism contradicts the Hempelian (...) |
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The aim of this work is to elucidate the meaning of 'infinity' from a phenomenological perspective, especially within the framework of Husserl’s theory of knowledge and perception. In the first chapter I firstly sketch the basics of Husserl’s phenomenology of knowledge. Thereafter I delve into the questions concerning the reduction to the 'reellen Bestand', which is hold to be the ground of verification of purports in the "Logical Investigations". I then propose an interpretation of the categorial intuition as directed to (...) |
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In 1913, in a draft for a new Preface for the second edition of the Logical Investigations, Edmund Husserl reveals to his readers that "The source of all my studies and the first source of my epistemological difficulties lies in my first works on the philosophy of arithmetic and mathematics in general", i.e. his Habilitationsschrift and the Philosophy of Arithmetic: "I carefully studied the consciousness constituting the amount, first the collective consciousness (consciousness of quantity, of multiplicity) in its simplest and (...) |
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