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Early Writings in the Philosophy of Logic and Mathematics

Early Writings in the Philosophy of Logic and Mathematics
Author: Edmund Husserl
Publisher: Springer
Total Pages: 0
Release: 2011-02-04
Genre: Philosophy
ISBN: 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 Along with these texts we have included a number of unpublished manuscripts from the same period and dealing with the same or closely related topics.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.


Collected Works

Collected Works
Author: Edmund Husserl
Publisher:
Total Pages: 505
Release: 1994
Genre:
ISBN: 9789024723423

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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
Total Pages: 250
Release: 2010-05-06
Genre: Philosophy
ISBN: 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.


Essays on Husserl's Logic and Philosophy of Mathematics

Essays on Husserl's Logic and Philosophy of Mathematics
Author: Stefania Centrone
Publisher: Springer
Total Pages: 541
Release: 2017-09-07
Genre: Philosophy
ISBN: 9402411321

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Essays on Husserl’s Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl’s work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl’s by considering their reception and elaboration by some of his disciples and followers, such as Oskar Becker and Jacob Klein, as well as their influence on some of the most significant logicians and mathematicians of the past century, such as Luitzen E. J. Brouwer, Rudolf Carnap, Kurt Gödel and Hermann Weyl. Most of the papers consider Husserl and another scholar – e.g. Leibniz, Kant, Bolzano, Brentano, Cantor, Frege – and trace out and contextualize lines of influence, points of contact, and points of disagreement. Each essay is written by an expert of the field, and the volume includes contributions both from the analytical tradition and from the phenomenological one.


Philosophy of Mathematics in the Twentieth Century

Philosophy of Mathematics in the Twentieth Century
Author: Charles Parsons
Publisher: Harvard University Press
Total Pages: 365
Release: 2014-03-10
Genre: Philosophy
ISBN: 0674419499

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In these selected essays, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the past century: Brouwer, Hilbert, Bernays, Weyl, Gödel, Russell, Quine, Putnam, Wang, and Tait.


Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century
Author: Paolo Mancosu
Publisher: Oxford University Press, USA
Total Pages: 290
Release: 1999
Genre: Matematik
ISBN: 0195132440

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1. Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century p. 8 1.1 The Quaestio de Certitudine Mathematicarum p. 10 1.2 The Quaestio in the Seventeenth Century p. 15 1.3 The Quaestio and Mathematical Practice p. 24 2. Cavalieri's Geometry of Indivisibles and Guldin's Centers of Gravity p. 34 2.1 Magnitudes, Ratios, and the Method of Exhaustion p. 35 2.2 Cavalieri's Two Methods of Indivisibles p. 38 2.3 Guldin's Objections to Cavalieri's Geometry of Indivisibles p. 50 2.4 Guldin's Centrobaryca and Cavalieri's Objections p. 56 3. Descartes' Geometrie p. 65 3.1 Descartes' Geometrie p. 65 3.2 The Algebraization of Mathematics p. 84 4. The Problem of Continuity p. 92 4.1 Motion and Genetic Definitions p. 94 4.2 The "Causal" Theories in Arnauld and Bolzano p. 100 4.3 Proofs by Contradiction from Kant to the Present p. 105 5. Paradoxes of the Infinite p. 118 5.1 Indivisibles and Infinitely Small Quantities p. 119 5.2 The Infinitely Large p. 129 6. Leibniz's Differential Calculus and Its Opponents p. 150 6.1 Leibniz's Nova Methodus and L'Hopital's Analyse des Infiniment Petits p. 151 6.2 Early Debates with Cluver and Nieuwentijt p. 156 6.3 The Foundational Debate in the Paris Academy of Sciences p. 165 Appendix Giuseppe Biancani's De Mathematicarum Natura p. 178 Notes p. 213 References p. 249 Index p. 267.


Principia Mathematica

Principia Mathematica
Author: Alfred North Whitehead
Publisher:
Total Pages: 688
Release: 1910
Genre: Logic, Symbolic and mathematical
ISBN:

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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
Total Pages: 219
Release: 2019-10-05
Genre: Philosophy
ISBN: 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.


Philosophical Papers: Volume 1, Mathematics, Matter and Method

Philosophical Papers: Volume 1, Mathematics, Matter and Method
Author: Hilary Putnam
Publisher: Cambridge University Press
Total Pages: 380
Release: 1979-04-30
Genre: Mathematics
ISBN: 9780521295505

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This volume deals with the philosophy of mathematics and of science and the nature of philosophical and scientific enquiry.