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Philosophy of Arithmetic

January 31, 2023

Philosophy of Arithmetic: Psychological and Logical Investigations (German: Philosophie der Arithmetik. Psychologische und logische untersuchungen) is an 1891 book about the philosophy of mathematics by the philosopher Edmund Husserl. Husserl's first published book, it is a synthesis of his studies in mathematics, under Karl Weierstrass, with his studies in philosophy and psychology, under Franz Brentano, to whom it is dedicated, and Carl Stumpf.

Philosophy of Arithmetic
AuthorEdmund Husserl
Original titlePhilosophie der Arithmetik
TranslatorDallas Willard
LanguageEnglish
SubjectPhilosophy of mathematics
PublisherKluwer Academic Publishers
Publication date
1891
Published in English
2003
Media typePrint (Hardcover)
Pages580
ISBN1-4020-1546-1
OCLC52858552
510/.1 22
LC ClassQA9 .H813 2003

Structure

The Philosophy of Arithmetic constitutes the first volume of a work which Husserl intended to comprise two volumes, of which the second was never published. Comprehensively it would have encompassed four parts and an Appendix.

The first volume is divided in two parts, in the first of which Husserl purports to analyse the "Proper concepts of multiplicity, unity and amount" (Die eigentliche Begriffe von Vielheit, Einheit und Anzahl) and in the second "The symbolic amount-concepts and the logical sources of amount-arithmetic" (Die symbolischen Anzahlbegrife und die logischen Quellen der Anzahlen-Arithmetik).

Content

The basic issue of the book is a philosophical analysis of the concept of number, which is the most basic concept on which the entire edifice of arithmetic and mathematics can be founded. In order to proceed with this analysis, Husserl, following Brentano and Stumpf, uses the tools of psychology to look for the "origin and content" of the concept of number. He begins with the classical definition, already given by Euclid, Thomas Hobbes and Gottfried Wilhelm Leibniz, that "number is a multiplicity of unities" and then asks himself: what is multiplicity and what is unity? Anything that we can think of, anything we can present, can be considered at its most basic level to be "something". Multiplicity is then the "collective connection" of "something and something and something etc." In order to get a number instead of a mere quantity, we can also think of these featureless, abstract "somethings" as "ones" and then get "one and one and one etc." as basic definition of number in abstracto. However, these are just the proper numbers, i.e. number which we can conceive of properly, without the help of instruments or symbols. Psychologically we are limited to just the very first few numbers if we want to conceive of them properly, with higher numbers our short term memory is not enough to think of them all together, but still as identical to themselves and different from all others. Hence, Husserl says, we have to move on to the analysis of symbolically conceived numbers, which are effectively those that are used in mathematics.

History

The book is a product of Husserl's years of study with Weierstrass (in Berlin) and his student Leo Königsberger (in Vienna) on the mathematical side and his studies with Brentano (in Vienna) and Stumpf (in Halle) on the psychological/philosophical side. The book is mostly based on his habilitationsschrift of 1887 "On the Concept of Number" (Über den Begriff der Zahl). Husserl also lectured on the concept of number between 1889 and 1891, much in the same vein. He continued working on the second volume up to at least 1894.

Gottlob Frege was critical of Philosophy of Arithmetic, and accused Husserl of relying too much on the metaphysical and not enough on the logical aspects of mathematics. Frege’s criticisms influenced negatively the young mathematician’s career as a professor. Husserl’s Logical Investigations secured his reputation ten years later, but Frege and others never accepted Husserl as a practitioner of true logic.

Editions

The original edition: 

 Philosophie der Arithmetik Psychologische und logische untersuchungen, von Dr. E. G. Husserl. 1. bd. 1891, xvi, 324 p. 23 cm. LC Classification: QA9 .H8 Dewey Class No.: 510.1 Other System No.: OCLC 4787664

Husserliana edition: 

 Philosophie der Arithmetik Psychologische und logische untersuchungen - mit ergänzenden Texten (1890-1901) Series: Husserliana - Edmund Husserl Gesammelte werke, Vol. XII Husserl, Edmund Ed. Eley, Lothar 1970, 585 p., Hardcover ISBN 90-247-0230-5

Official English translation of the Husserliana edition: 

 Philosophy of Arithmetic Psychological and Logical Investigations - with Supplementary Texts from 1887-1901 Series: Edmund Husserl Collected Works, Vol. X Husserl, Edmund Tr. Willard, Dallas 2003, 580 p., Hardcover ISBN 1-4020-1546-1

Bibliography

  • Walter Biemel, ‘The decisive phases in the development of Husserl’s philosophy’, in: R.O. Elveton, editor, The Phenomenology of Husserl, Selected critical readings (Chicago: Quadrangle Books, 1970), (Tr. by Elveton, R.O.).
  • Francesco Dentoni, Alle radici della fenomenologia (Roma: Abete, 1978).
  • Hans-Martin Gerlach and Hans Rainer Sepp, editors, Husserl in Halle, Daedalus (Europäisches Denken in Deutscher Philosophie) 5 (Frankfurt a. M.: Peter Lang GmbH, 1994).
  • Burt Hopkins, ‘Authentic and Symbolic Numbers in Husserl’s Philosophy of Arithmetic ’, in The New Yearbook for Phenomenology and Phenomenological Philosophy II (2002), 39–71.
  • Edmund Husserl, ‘Persönliche Aufzeichnungen’, in Philosophy and Phenomenological Research XVI (1956), (Ed. W. Biemel).
  • Edmund Husserl, ‘Erinnerungen an Franz Brentano’, in: T. Nenon and H.R. Sepp, editors, Husserliana XXV (Den Haag: Nijhoff, 1987).
  • Malvine Husserl, ‘Skizze eines Lebensbildes von Edmund Husserl’, in Husserl Studies 5 (1988), 105–125, (ed. Karl Schuhmann).
  • Carlo Ierna, ‘Husserl and the Infinite’, in Studia Phaenomenologica III:1–2 (2003), 179–194 [1].
  • Carlo Ierna, “The Beginnings of Husserl’s Philosophy. Part 1: From Über den Begriff der Zahl to Philosophie der Arithmetik”, in The New Yearbook for Phenomenology and Phenomenological Philosophy V (2005), 1-56.
  • J. Philip Miller, Numbers in Presence and Absence, Phaenomenologica 90 (Den Haag: Nijhoff, 1982).
  • Jitendra Nath Mohanty, ‘Husserl, Frege and the Overcoming of Psychologism’, in: Kah Kyung Cho, editor, Philosophy and Science in phenomenological Perspective, Phaenomenologica 95 (Dordrecht/Boston/Lancaster: Nijhoff, 1984), 143–152.
  • Jitendra Nath Mohanty, ‘The Development of Husserl’s thought’, in: B.M. Smith and D.W. Smith, editors, The Cambridge Companion to Husserl (Cambridge: Cambridge University Press, 1995).
  • Robin D. Rollinger, Meinong and Husserl on Abstraction and Universals, Studien zur Österreichischen Philosophie XX (Amsterdam – Atlanta: Rodopi, 1993).
  • Robin D. Rollinger, Husserl’s Position in the School of Brentano, Phaenomenologica 150 (Dordrecht: Kluwer, 1999).
  • Roger Schmit, Husserls Philosophie der Mathematik (Bonn: Bouvier, 1981).
  • Karl Schuhmann, Husserl – Chronik (Denk- und Lebensweg Edmund Husserls), Husserliana Dokumente I (Den Haag: Nijhoff, 1977).
  • Dallas Willard, Logic and the Objectivity of Knowledge (Athens (Ohio): Ohio University Press, 1984).

January 31, 2023
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Philosophy of Arithmetic Psychological and Logical Investigations German Philosophie der Arithmetik Psychologische und logische untersuchungen is an 1891 book about the philosophy of mathematics by the philosopher Edmund Husserl Husserl s first published book it is a synthesis of his studies in mathematics under Karl Weierstrass with his studies in philosophy and psychology under Franz Brentano to whom it is dedicated and Carl Stumpf Philosophy of ArithmeticAuthorEdmund HusserlOriginal titlePhilosophie der ArithmetikTranslatorDallas WillardLanguageEnglishSubjectPhilosophy of mathematicsPublisherKluwer Academic PublishersPublication date1891Published in English2003Media typePrint Hardcover Pages580ISBN1 4020 1546 1OCLC52858552Dewey Decimal510 1 22LC ClassQA9 H813 2003 Contents 1 Structure 2 Content 3 History 4 Editions 5 BibliographyStructure EditThe Philosophy of Arithmetic constitutes the first volume of a work which Husserl intended to comprise two volumes of which the second was never published Comprehensively it would have encompassed four parts and an Appendix The first volume is divided in two parts in the first of which Husserl purports to analyse the Proper concepts of multiplicity unity and amount Die eigentliche Begriffe von Vielheit Einheit und Anzahl and in the second The symbolic amount concepts and the logical sources of amount arithmetic Die symbolischen Anzahlbegrife und die logischen Quellen der Anzahlen Arithmetik Content EditThe basic issue of the book is a philosophical analysis of the concept of number which is the most basic concept on which the entire edifice of arithmetic and mathematics can be founded In order to proceed with this analysis Husserl following Brentano and Stumpf uses the tools of psychology to look for the origin and content of the concept of number He begins with the classical definition already given by Euclid Thomas Hobbes and Gottfried Wilhelm Leibniz that number is a multiplicity of unities and then asks himself what is multiplicity and what is unity Anything that we can think of anything we can present can be considered at its most basic level to be something Multiplicity is then the collective connection of something and something and something etc In order to get a number instead of a mere quantity we can also think of these featureless abstract somethings as ones and then get one and one and one etc as basic definition of number in abstracto However these are just the proper numbers i e number which we can conceive of properly without the help of instruments or symbols Psychologically we are limited to just the very first few numbers if we want to conceive of them properly with higher numbers our short term memory is not enough to think of them all together but still as identical to themselves and different from all others Hence Husserl says we have to move on to the analysis of symbolically conceived numbers which are effectively those that are used in mathematics History EditThe book is a product of Husserl s years of study with Weierstrass in Berlin and his student Leo Konigsberger in Vienna on the mathematical side and his studies with Brentano in Vienna and Stumpf in Halle on the psychological philosophical side The book is mostly based on his habilitationsschrift of 1887 On the Concept of Number Uber den Begriff der Zahl Husserl also lectured on the concept of number between 1889 and 1891 much in the same vein He continued working on the second volume up to at least 1894 Gottlob Frege was critical of Philosophy of Arithmetic and accused Husserl of relying too much on the metaphysical and not enough on the logical aspects of mathematics Frege s criticisms influenced negatively the young mathematician s career as a professor Husserl s Logical Investigations secured his reputation ten years later but Frege and others never accepted Husserl as a practitioner of true logic Editions EditThe original edition Philosophie der Arithmetik Psychologische und logische untersuchungen von Dr E G Husserl 1 bd 1891 xvi 324 p 23 cm LC Classification QA9 H8 Dewey Class No 510 1 Other System No OCLC 4787664 Husserliana edition Philosophie der Arithmetik Psychologische und logische untersuchungen mit erganzenden Texten 1890 1901 Series Husserliana Edmund Husserl Gesammelte werke Vol XII Husserl Edmund Ed Eley Lothar 1970 585 p Hardcover ISBN 90 247 0230 5 Official English translation of the Husserliana edition Philosophy of Arithmetic Psychological and Logical Investigations with Supplementary Texts from 1887 1901 Series Edmund Husserl Collected Works Vol X Husserl Edmund Tr Willard Dallas 2003 580 p Hardcover ISBN 1 4020 1546 1Bibliography EditWalter Biemel The decisive phases in the development of Husserl s philosophy in R O Elveton editor The Phenomenology of Husserl Selected critical readings Chicago Quadrangle Books 1970 Tr by Elveton R O Francesco Dentoni Alle radici della fenomenologia Roma Abete 1978 Hans Martin Gerlach and Hans Rainer Sepp editors Husserl in Halle Daedalus Europaisches Denken in Deutscher Philosophie 5 Frankfurt a M Peter Lang GmbH 1994 Burt Hopkins Authentic and Symbolic Numbers in Husserl s Philosophy of Arithmetic in The New Yearbook for Phenomenology and Phenomenological Philosophy II 2002 39 71 Edmund Husserl Personliche Aufzeichnungen in Philosophy and Phenomenological Research XVI 1956 Ed W Biemel Edmund Husserl Erinnerungen an Franz Brentano in T Nenon and H R Sepp editors Husserliana XXV Den Haag Nijhoff 1987 Malvine Husserl Skizze eines Lebensbildes von Edmund Husserl in Husserl Studies 5 1988 105 125 ed Karl Schuhmann Carlo Ierna Husserl and the Infinite in Studia Phaenomenologica III 1 2 2003 179 194 1 Carlo Ierna The Beginnings of Husserl s Philosophy Part 1 From Uber den Begriff der Zahl to Philosophie der Arithmetik in The New Yearbook for Phenomenology and Phenomenological Philosophy V 2005 1 56 J Philip Miller Numbers in Presence and Absence Phaenomenologica 90 Den Haag Nijhoff 1982 Jitendra Nath Mohanty Husserl Frege and the Overcoming of Psychologism in Kah Kyung Cho editor Philosophy and Science in phenomenological Perspective Phaenomenologica 95 Dordrecht Boston Lancaster Nijhoff 1984 143 152 Jitendra Nath Mohanty The Development of Husserl s thought in B M Smith and D W Smith editors The Cambridge Companion to Husserl Cambridge Cambridge University Press 1995 Robin D Rollinger Meinong and Husserl on Abstraction and Universals Studien zur Osterreichischen Philosophie XX Amsterdam Atlanta Rodopi 1993 Robin D Rollinger Husserl s Position in the School of Brentano Phaenomenologica 150 Dordrecht Kluwer 1999 Roger Schmit Husserls Philosophie der Mathematik Bonn Bouvier 1981 Karl Schuhmann Husserl Chronik Denk und Lebensweg Edmund Husserls Husserliana Dokumente I Den Haag Nijhoff 1977 Dallas Willard Logic and the Objectivity of Knowledge Athens Ohio Ohio University Press 1984 Retrieved from https en wikipedia org w index php title Philosophy of Arithmetic amp oldid 1126208883, wikipedia, wiki, book, books, library,

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