Logic and Philosophy of Mathematics in the Early Husserl
Logic and Philosophy of Mathematics in the Early Husserl

Author: Stefania Centrone

Publisher: Springer Science & Business Media

Published: 2010-05-06

Total Pages: 250

ISBN-13: 9048132479

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Logic and Philosophy of Mathematics in the Early Husserl focuses on the first ten years of Edmund Husserl’s work, from the publication of his Philosophy of Arithmetic (1891) to that of his Logical Investigations (1900/01), and aims to precisely locate his early work in the fields of logic, philosophy of logic and philosophy of mathematics. Unlike most phenomenologists, the author refrains from reading Husserl’s early work as a more or less immature sketch of claims consolidated only in his later phenomenology, and unlike the majority of historians of logic she emphasizes the systematic strength and the originality of Husserl’s logico-mathematical work. The book attempts to reconstruct the discussion between Husserl and those philosophers and mathematicians who contributed to new developments in logic, such as Leibniz, Bolzano, the logical algebraists (especially Boole and Schröder), Frege, and Hilbert and his school. It presents both a comprehensive critical examination of some of the major works produced by Husserl and his antagonists in the last decade of the 19th century and a formal reconstruction of many texts from Husserl’s Nachlaß that have not yet been the object of systematical scrutiny. This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to analytical philosophers and phenomenologists with a background in standard logic.

Early Writings in the Philosophy of Logic and Mathematics
Early Writings in the Philosophy of Logic and Mathematics

Author: Edmund Husserl

Publisher: Springer

Published: 2011-02-04

Total Pages: 0

ISBN-13: 9789048142668

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The primary intent of this volume is to give the English reader access to all the philosophical texts published by Husserl between the appearance of his first book, Philosophie der Arithmetik, and that of his second book, Logische Untersuchungen- roughly, from 1890 through 1901. Along with these texts we have included a number of unpublished manuscripts from the same period and dealing with the same or closely related topics. A few of the texts here translated (the review of Pahigyi, the five "report" articles of 1903-1904, the "notes" in Lalande's Vocabulaire, and the brief discussion. article on Marty of 1910) obviously fall outside this time period, so far as their publication dates are concerned; but in content they seem clearly confined to it. The final piece translated, a set of personal notes that date from 1906 through 1908, provides insight into how Husserl experienced his early labors and their results, and into how he saw their relation to work before him: a phenomenological critique of reason in all of its forms. Thus the texts here translated - which obviously are to be read in conjunction with his first two books - cover the progression of Husserl's Problematik from the relatively narrow one of clarifying the epistemic structure of general arithmetic, to the all-encompassing one of establishing in principle, through phenomenological research, the line between legitimate and illegitimate claims to know or to be rational, regardless of the domain concerned.

Philosophy of Arithmetic
Philosophy of Arithmetic

Author: Edmund Husserl

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 558

ISBN-13: 9401000603

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This volume is a window on a period of rich and illuminating philosophical activity that has been rendered generally inaccessible by the supposed "revolution" attributed to "Analytic Philosophy" so-called. Careful exposition and critique is given to every serious alternative account of number and number relations available at the time.

The Origin of the Logic of Symbolic Mathematics
The Origin of the Logic of Symbolic Mathematics

Author: Burt C. Hopkins

Publisher: Indiana University Press

Published: 2011-09-07

Total Pages: 593

ISBN-13: 0253005272

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Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts—especially mathematical concepts and the process of mathematical abstraction that generates them—have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.

Introduction to Logic and Theory of Knowledge
Introduction to Logic and Theory of Knowledge

Author: Edmund Husserl

Publisher: Springer Science & Business Media

Published: 2008-08-26

Total Pages: 500

ISBN-13: 1402067275

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Claire Ortiz Hill The publication of all but a small, unfound, part of the complete text of the lecture course on logic and theory of knowledge that Edmund Husserl gave at Göttingen during the winter semester of 1906/07 became a reality in 1984 with the publication of Einleitung in die Logik und Erkenntnistheorie, Vorlesungen 1906/07 edited by 1 Ullrich Melle. Published in that volume were also 27 appendices containing material selected to complement the content of the main text in significant ways. They provide valuable insight into the evolution of Husserl’s thought between the Logical Investigations and Ideas I and, therefore, into the origins of phenomenology. That text and all those appendices but one are translated and published in the present volume. Omitted are only the “Personal Notes” dated September 25, 1906, November 4, 1907, and March 6, 1908, which were translated by Dallas Willard and published in his translation of Husserl’s Early 2 Writings in the Philosophy of Logic and Mathematics. Introduction to Logic and Theory of Knowledge, Lectures 1906/07 provides valuable insight into the development of the ideas fun- mental to phenomenology. Besides shedding considerable light on the genesis of phenomenology, it sheds needed light on many other dimensions of Husserl’s thought that have puzzled and challenged scholars.

Peirce and Husserl: Mutual Insights on Logic, Mathematics and Cognition
Peirce and Husserl: Mutual Insights on Logic, Mathematics and Cognition

Author: Mohammad Shafiei

Publisher: Springer Nature

Published: 2019-10-05

Total Pages: 222

ISBN-13: 3030258009

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This volume aims to provide the elements for a systematic exploration of certain fundamental notions of Peirce and Husserl in respect with foundations of science by means of drawing a parallelism between their works. Tackling a largely understudied comparison between these two contemporary philosophers, the authors highlight the significant similarities in some of their fundamental ideas. This volume consists of eleven chapters under four parts. The first part concerns methodologies and main principles of the two philosophers. An introductory chapter outlines central historical and systematical themes arising out of the recent scholarship on Peirce and Husserl. The second part is on logic, its Chapters dedicated to the topics from Peirce’s Existential Graphs and the philosophy of notation to Husserl’s notions of pure logic and transcendental logic. The third part includes contributions on philosophy of mathematics. Chapters in the final part deal with the theory of cognition, consciousness and intentionality. The closing chapter provides an extended glossary of central terms of Peirce’s theory of phaneroscopy, explaining them from the viewpoint of the theory of cognition.

Husserl and Mathematics
Husserl and Mathematics

Author: Mirja Hartimo

Publisher: Cambridge University Press

Published: 2021-08-05

Total Pages: 419

ISBN-13: 1108997562

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Husserl and Mathematics explains the development of Husserl's phenomenological method in the context of his engagement in modern mathematics and its foundations. Drawing on his correspondence and other written sources, Mirja Hartimo details Husserl's knowledge of a wide range of perspectives on the foundations of mathematics, including those of Hilbert, Brouwer and Weyl, as well as his awareness of the new developments in the subject during the 1930s. Hartimo examines how Husserl's philosophical views responded to these changes, and offers a pluralistic and open-ended picture of Husserl's phenomenology of mathematics. Her study shows Husserl's phenomenology to be a method capable of both shedding light on and internally criticizing scientific practices and concepts.

Phenomenology and Mathematics
Phenomenology and Mathematics

Author: Mirja Hartimo

Publisher: Springer Science & Business Media

Published: 2010-03-11

Total Pages: 244

ISBN-13: 9048137292

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During Edmund Husserl’s lifetime, modern logic and mathematics rapidly developed toward their current outlook and Husserl’s writings can be fruitfully compared and contrasted with both 19th century figures (Boole, Schröder, Weierstrass) as well as the 20th century characters (Heyting, Zermelo, Gödel). Besides the more historical studies, the internal ones on Husserl alone and the external ones attempting to clarify his role in the more general context of the developing mathematics and logic, Husserl’s phenomenology offers also a systematically rich but little researched area of investigation. This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics. It gathers the contributions of the main scholars of this emerging field into one publication for the first time. Combining both historical and systematic studies from various angles, the volume charts answers to the question "What kind of philosophy of mathematics is phenomenology?"

On Logic and the Theory of Science
On Logic and the Theory of Science

Author: Jean Cavailles

Publisher: MIT Press

Published: 2021-04-27

Total Pages: 143

ISBN-13: 1913029417

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A new translation of the final work of French philosopher Jean Cavaillès. In this short, dense essay, Jean Cavaillès evaluates philosophical efforts to determine the origin—logical or ontological—of scientific thought, arguing that, rather than seeking to found science in original intentional acts, a priori meanings, or foundational logical relations, any adequate theory must involve a history of the concept. Cavaillès insists on a historical epistemology that is conceptual rather than phenomenological, and a logic that is dialectical rather than transcendental. His famous call (cited by Foucault) to abandon "a philosophy of consciousness" for "a philosophy of the concept" was crucial in displacing the focus of philosophical enquiry from aprioristic foundations toward structural historical shifts in the conceptual fabric. This new translation of Cavaillès's final work, written in 1942 during his imprisonment for Resistance activities, presents an opportunity to reencounter an original and lucid thinker. Cavaillès's subtle adjudication between positivistic claims that science has no need of philosophy, and philosophers' obstinate disregard for actual scientific events, speaks to a dilemma that remains pertinent for us today. His affirmation of the authority of scientific thinking combined with his commitment to conceptual creation yields a radical defense of the freedom of thought and the possibility of the new.