Skip to main content
SpringerLink
Log in
Book cover

Essays on Husserl's Logic and Philosophy of Mathematics pp 147–168Cite as

The Brentanist Philosophy of Mathematics in Edmund Husserl’s Early Works

  • Chapter
  • First Online:

Part of the book series: Synthese Library ((SYLI,volume 384))

Abstract

A common analysis of Edmund Husserl’s early works on the philosophy of logic and mathematics presents these writings as the result of a combination of two distinct strands of influence: on the one hand a mathematical influence due to his teachers is Berlin, such as Karl Weierstrass, and on the other hand a philosophical influence due to his later studies in Vienna with Franz Brentano. However, the formative influences on Husserl’s early philosophy cannot be so cleanly separated into a philosophical and a mathematical pathway. Growing evidence indicates that a Brentanist philosophy of mathematics was already in place before Husserl. Rather than an original combination at the confluence of two different streams, his early writings represent an elaboration of topics and problems that were already being discussed in the School of Brentano within a pre-existing framework. The traditional account understandably neglects Brentano’s own work on the philosophy of mathematics and logic, which can be found mostly in his unpublished manuscripts and lectures, and various works by Brentano’s students on the philosophy of mathematics which have only recently emerged from obscurity. Husserl’s early works must be correctly placed in this preceding context in order to be fully understood and correctly assessed.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    See i.a. Miller 1982, 4; Haddock 1997, 127: “Über den Begriff der Zahl and later Philosophie der Arithmetik are in some sense the result of such a marriage between the mathematician formed under the guidance of Weierstrass and the philosopher formed in the school of the philosopher-psychologist Brentano,” Centrone 2010, 5: “From Weierstrass, one could say, Husserl inherits the project of founding analysis on a restricted number of simple and primitive concepts, and from Brentano he inherits the method for identifying these primitive concepts, namely by describing the psychological laws that regulate their formation.”

  2. 2.

    Hartimo 2006, 319: “The paper examines the roots of Husserlian phenomenology in Weierstrass’s approach to analysis.… Husserl’s novelty is to use Brentanian descriptive analysis to clarify the fundamental concepts of arithmetic in the first part.”

  3. 3.

    For a first outline of the idea of a Brentanist philosophy of mathematics, see Ierna 2011a.

  4. 4.

    E.g. Frege 1884; Kronecker 1887; Dedekind 1888.

  5. 5.

    Albertazzi et al. 1996, 3 ff.; Schuhmann 2004, 278.

  6. 6.

    Moran 2000, 24 “one can speak loosely of a ‘Brentano school’.”

  7. 7.

    Albertazzi et al. 1996, 6.

  8. 8.

    Stumpf 2008.

  9. 9.

    Ierna 2005.

  10. 10.

    Husserl 2005.

  11. 11.

    Ehrenfels’ Dissertation and an introductory article are forthcoming in Meinong Studies 8 (Ehrenfels 2017, Ierna 2017).

  12. 12.

    Beiträge zur Variationsrechnung, Husserl 1883.

  13. 13.

    Schuhmann 1977, 7. It is often repeated in the secondary literature that Husserl worked for Weierstrass as an “assistant.” The source for this nugget of information is Malvine Husserl’s brief biographical sketch of Edmund Husserl, written in 1940. Karl Schuhmann, the editor of this text, however, indicates that this expression could not have meant any kind of “official or semi-official function” and that Malvine Husserl probably anachronistically projected the more recent institution of assistantships back on Husserl’s Berlin period (Schuhmann 1988, 121, n. 33).

  14. 14.

    Husserl 1891, 5 n.; 1970, 12 n., see manuscript Q 3, 1, quoted in Ierna 2006, 36 f.

  15. 15.

    Cf. Miller 1982, 1–4.

  16. 16.

    Spalt 1991, 351 f., also see 355; compare Kline 1972, 953; for a more extensive account, see Ierna 2006, specifically 40 f.

  17. 17.

    See Ierna 2006, 38 ff. and 46 ff.

  18. 18.

    Husserl 1887, 8; 1970, 295.

  19. 19.

    Husserl 1887, 12; 1970, 297.

  20. 20.

    Königsberger 1874, 1.

  21. 21.

    Husserl 1887, 58 f.; 1970, 334; Bolzano 1889, 2 f.

  22. 22.

    Husserl 1887, 13; 1970, 289; Bolzano 1889, 3.

  23. 23.

    Bolzano 1889, 4 f.

  24. 24.

    Husserl 1891, 246–250; 1970, 218–221; also see Ierna 2003.

  25. 25.

    Husserl 1900, § 70.

  26. 26.

    See Cantor 1883.

  27. 27.

    Also see Haddock 2006 and Ierna 2012.

  28. 28.

    Husserl 1983, 95 f.

  29. 29.

    Husserl 1900, 156 n. 2.

  30. 30.

    Frege 1884.

  31. 31.

    Kronecker 1887.

  32. 32.

    Dedekind 1888.

  33. 33.

    While we can (and should) distinguish Husserl’s three early works on the philosophy of mathematics, i.e. his (unpublished, lost) habilitation work, the partial print thereof by the same title Über den Begriff der Zahl, and the Philosophie der Arithmetik, here we will discuss his early position as a comprehensive whole. Various historical sub-periodizations can be found in Miller (1982), Willard (1984), and Ierna (2005).

  34. 34.

    Husserl 1887, 7; 1970, 294.

  35. 35.

    Husserl uses Anzahl (“amount”) interchangeably with Zahl (“number”), so the straightforward translation of Anzahl with “cardinal number” is not entirely uncontroversial or unproblematic.

  36. 36.

    Husserl 1891, 49, 59, 66 n., 241.

  37. 37.

    Stumpf 1883, 96.

  38. 38.

    Husserl 1887, 24; 1970, 307.

  39. 39.

    Husserl 1891, Ch. 8.

  40. 40.

    If we combine this with his 1887 habilitation thesis that “In the proper sense we cannot count beyond three,” then the only numbers, properly speaking, would be two and three.

  41. 41.

    Husserl 1891, 225, 1970, 201.

  42. 42.

    Husserl 2005, also see Husserl 2002, 295; Ierna 2005, § 3.2.

  43. 43.

    Husserl 1891, 290.

  44. 44.

    Husserl 1891, 297.

  45. 45.

    We find a first definition in Stumpf 1883, 101, which was underlined by Husserl in his personal copy, conserved at the Husserl Archives Leuven with signature BQ 472, and then a more extensive discussion in Stumpf 1890, 64 ff.

  46. 46.

    See Schuhmann 1977, 16. The manuscript has the signature K I 50/47. A picture of the first page of the manuscript (with title and date) can be found in Sepp 1988, 157. The surrounding pages in the manuscript contain excerpts and critical discussions of Riemann and Helmholtz, which also were the topic of Husserl’s early lectures at Halle.

  47. 47.

    Also see Ierna 2005, 7.

  48. 48.

    Stumpf’s habilitation work has only recently been published (Stumpf 2008) and I discuss its main points more extensively elsewhere (Ierna 2011a and esp. Ierna 2015). Since it cannot yet be conclusively established that Husserl had access to this material, the notions shared between Stumpf’s and Husserl’s habilitation works at least suggest a shared background in Brentano.

  49. 49.

    I will not go into Stumpf’s discussions of space and geometry or the theory of probability here, which would go well beyond the scope of the present contribution.

  50. 50.

    Husserl 2005; Ierna 2005, 2009.

  51. 51.

    Ehrenfels’ Dissertation and an introductory article are forthcoming in Meinong Studies 8 (Ehrenfels 2017, Ierna 2017).

  52. 52.

    Brentano 1874, vi.

  53. 53.

    The following discussion of Brentano’s theories is partially based on Ierna 2006 and Ierna 2011a.

  54. 54.

    Brentano 1874, 29, 34.

  55. 55.

    Brentano 1874, 86.

  56. 56.

    Brentano 1874, 93.

  57. 57.

    Stumpf 2008, 18–2.

  58. 58.

    Stumpf 2008, 19–1.

  59. 59.

    Stumpf 2008, 19–3.

  60. 60.

    Stumpf 2008, 24–2.

  61. 61.

    Husserl 1891, 215; 1970, 193.

  62. 62.

    Brentano EL 80/13060, quoted from Rollinger 2009, 81 f.

  63. 63.

    Husserl 2002, 296.

  64. 64.

    Husserl 1887, 50 f.; 1970, 328.

  65. 65.

    see Brentano 1884/85, Y 2, 107 ff.

  66. 66.

    Stumpf 2008, 24–1. Echoed by Husserl: “In the proper sense one can hardly count beyond three” (Husserl 1887, Theses; 1970, 339)

  67. 67.

    Husserl 1891, 215; 1970, 193.

  68. 68.

    Brentano 1884/85, Y 2, 32.

  69. 69.

    Brentano 1884/85, Y 2, 28 f.

  70. 70.

    Brentano 1884/85, Y 2, 47.

  71. 71.

    E.g. Brentano 1884/85, Y 2, 29.

  72. 72.

    Stumpf 1886/87, Q 11/II, 504. Translation from Rollinger 1999, 301.

  73. 73.

    Stumpf 1887, Q 14, 86 ff.

  74. 74.

    Stumpf 1887, Q 14, 114a.

  75. 75.

    Stumpf 1886/87, Q 11/II, 494.

  76. 76.

    Husserl 1887, 41 f.; 1970, 321.

  77. 77.

    See Ierna 2006 for a more detailed reconstruction of the provenance and role of these concepts in Husserl’s early works.

  78. 78.

    Stumpf 1939.

  79. 79.

    From the conclusion to Ierna 2015.

  80. 80.

    Ehrenfels 1891, 291 f.

  81. 81.

    Op. cit., 295.

  82. 82.

    Husserl 1891, 91.

  83. 83.

    Op. cit., 186.

  84. 84.

    His much later work on the law of primes based on the concept of Gestalt is less relevant in this context.

  85. 85.

    Husserl 1956, 294.

  86. 86.

    Husserl 1994, 158.

  87. 87.

    Husserl 2005, 297.

  88. 88.

    Husserl 1994, 158.

  89. 89.

    Husserl 1983, 154–214.

  90. 90.

    See Ierna 2005, 47–48, n. 170.

  91. 91.

    Husserl 1994, 158.

  92. 92.

    Husserl 1983, 175.

  93. 93.

    Op. cit., 42 f.

  94. 94.

    Schuhmann & Schuhmann 2001.

  95. 95.

    Also see Ierna 2011b.

  96. 96.

    Husserl 1994, 160.

  97. 97.

    Husserl 1970, 344. This is from his treatise on Semiotik, which was meant as an appendix to the Philosophie der Arithmetik as a whole, also see 358, 368.

  98. 98.

    Husserl 1970, 357.

  99. 99.

    Husserl 2005, 301.

  100. 100.

    Op. cit., 307.

  101. 101.

    Husserl 1994, 161.

  102. 102.

    Husserl 1891, 323.

  103. 103.

    Husserl 1994, 161.

  104. 104.

    See Husserl 1900, 175.

  105. 105.

    Husserl 2001, 247–248.

  106. 106.

    Op. cit., 52.

  107. 107.

    Op. cit., 102.

  108. 108.

    Op. cit., 252.

  109. 109.

    Op. cit., 86 f.

  110. 110.

    Op. cit., 100.

  111. 111.

    Husserl 2002, 296 f.; compare Haddock 2006, 194.

  112. 112.

    Husserl 2001, 309. Husserl elsewhere (318) suggests that instead of Verknüpfung we could also say Operation.

  113. 113.

    Op. cit., 311.

  114. 114.

    Op. cit., 311 f.

  115. 115.

    Op. cit., 314 f.

  116. 116.

    Op. cit., 315.

  117. 117.

    Something Husserl apparently didn’t fully appreciate yet in 1891, 292–294.

References

  • L. Albertazzi, M. Libardi, R. Poli (eds.), The School of Franz Brentano (Kluwer, Dordrecht, 1996)

    Google Scholar 

  • B. Bolzano, Paradoxien des Unendlichen (Mayer & Müller, Berlin, 1889)

    Google Scholar 

  • F. Brentano, Psychologie vom empirischen Standpunkte (Duncker & Humblot, Leipzig, 1874)

    Google Scholar 

  • F. Brentano, Die elementare Logik und die in ihr nötigen Reformen I. Manuscript Y 2, Vienna 1884/85

    Google Scholar 

  • G. Cantor, Grundlagen einer allgemeinen Mannichfaltigkeitslehre. Ein mathematisch-philosophischer Versuch in der Lehre des Unendlichen (Teubner, Leipzig, 1883)

    Google Scholar 

  • S. Centrone, Logic and Philosophy of Mathematics in the Early Husserl (Springer, Dordrecht, 2010)

    Book  Google Scholar 

  • R. Dedekind, Was sind und was sollen die Zahlen? (Vieweg & Sohn, Braunschweig, 1888)

    Google Scholar 

  • G. Frege, Grundlagen der Arithmetik. Eine logisch mathematische Untersuchung über den Begriff der Zahl (Koebner, Breslau, 1884)

    Google Scholar 

  • G.R. Haddock, Husserl’s relevance for the philosophy and foundations of mathematics. Axiomathes 1–3, 125–142 (1997)

    Article  Google Scholar 

  • G.R. Haddock, Husserl’s philosophy of mathematics: Its origin and relevance. Husserl Stud. 22, 193–222 (2006)

    Article  Google Scholar 

  • M. Hartimo, Mathematical roots of phenomenology: Husserl and the concept of number. Hist. Philos. Log. 27, 319–337 (2006)

    Article  Google Scholar 

  • A. Höfler, Besprechung von Kerry, ‘Über Anschauung und ihre psychische Verarbeitung’, Husserl, Philosophie der Arithmetik, von Ehrenfels, ‘Zur Philosophie der Mathematik’, Zeitschrift für Psychologie und Physiologie der Sinnesorgane VI (1894)

    Google Scholar 

  • E. Husserl, Beiträge zur Variationsrechnung, Vienna 1883, Unpublished dissertation

    Google Scholar 

  • E. Husserl, Über den Begriff der Zahl: Psychologische Analysen, Heynemann’sche Buchdruckerei (F. Beyer), Halle (1887)

    Google Scholar 

  • E. Husserl, Philosophie der Arithmetik. Psychologische und Logische Untersuchungen (C.E.M. Pfeffer (Robert Stricker), Halle, 1891)

    Google Scholar 

  • E. Husserl, Logische Untersuchungen. Erster Theil: Prolegomena zur Reinen Logik (Niemeyer, Halle, 1900)

    Google Scholar 

  • E. Husserl, Persönliche Aufzeichnungen. Philos. Phenomenol. Res. XVI, 293–302 (1956)

    Article  Google Scholar 

  • E. Husserl, in Philosophie der Arithmetik. Mit ergänzenden Texten (1890–1901), ed. by L. Eley Husserliana XII. (Nijhoff, Den Haag, 1970)

    Google Scholar 

  • E. Husserl, Studien zur Arithmetik und Geometrie, ed. by I. Strohmeyer Husserliana XXI (Nijhoff, Den Haag, 1983)

    Google Scholar 

  • E. Husserl, Briefwechsel. in Die Brentanoschule, vol. I, ed. by K. Schuhmann, E. Schuhmann (Kluwer, Dordrecht, 1994)

    Google Scholar 

  • E. Husserl, in Logik: Vorlesung 1896 ed. by E. Schuhmann, Husserliana, Materialienbände I. (Kluwer, Dordrecht, 2001)

    Google Scholar 

  • E. Husserl, in Logische Untersuchungen (Ergänzungsband: Erster Teil), ed. by U. Melle, Husserliana XX/1. (Kluwer, Dordrecht, 2002)

    Google Scholar 

  • E. Husserl, Lecture on the Concept of Number (WS 1889/90). C. Ierna (ed. & tr.), The new yearbook for phenomenology and phenomenological philosophy V (2005)

    Google Scholar 

  • C. Ierna, Husserl and the infinite. Studia phaenomenologica III No. 1–2 (2003), 179–194

    Google Scholar 

  • C. Ierna, The beginnings of Husserl’s Philosophy (Part 1: From Über den Begriff der Zahl to Philosophie der Arithmetik). The new yearbook for phenomenology and phenomenological philosophy V (2005), 1–56

    Google Scholar 

  • C. Ierna, The beginnings of Husserl’s Philosophy (Part 2: Philosophical and mathematical background). The new yearbook for phenomenology and phenomenological philosophy VI (2006), 23–71

    Google Scholar 

  • C. Ierna, Husserl et Stumpf sur la Gestalt et la fusion. Philosophiques 36(2), 489–510 (2009)

    Article  Google Scholar 

  • C. Ierna, Brentano and mathematics. Rev. Roum. Philos. 55(1), 149–167 (2011a)

    Google Scholar 

  • C. Ierna, Der Durchgang durch das Unmögliche. An Unpublished Manuscript from the Husserl-Archives. Husserl Stud. 27(3), 217–226 (2011b)

    Article  Google Scholar 

  • C. Ierna, La notion husserlienne de multiplicité : au-delà de Cantor et Riemann. Methodos 12 (2012)

    Google Scholar 

  • C. Ierna, Carl Stumpf’s philosophy of mathematics, in Philosophy from an Empirical Standpoint: Essays on Carl Stumpf, ed. by D. Fisette, R. Martinelli (Rodopi, Amsterdam, 2015)

    Google Scholar 

  • C. Ierna, On Christian von Ehrenfels’ Dissertation, Meinong Studies 8 (2017)

    Google Scholar 

  • M. Kline, Mathematical Thought, vol 1 (Oxford University Press, New York, 1972)

    Google Scholar 

  • L. Königsberger, Vorlesungen über die Theorie der elliptischen Functionen nebst einer Einleitung in die allgemeine Functionenlehre, vol 1 (Teubner, Leipzig, 1874)

    Google Scholar 

  • L. Kronecker, Über den Zahlbegriff. Crelle’s J. Reine Angew. Math. 101, 337–355 (1887)

    Google Scholar 

  • E. Mach, Beiträge zur Analyse der Empfindungen (Gustav Fischer, Jena, 1886)

    Google Scholar 

  • J. P. Miller, Numbers in Presence and Absence, Phaenomenologica 90 (Nijhoff, Den Haag, 1982)

    Google Scholar 

  • D. Moran, Introduction to Phenomenology (Routledge, London, 2000)

    Book  Google Scholar 

  • R. Rollinger, Husserl’s Position in the School of Brentano, Phaenomenologica 150 (Kluwer, Dordrecht, 1999)

    Google Scholar 

  • R. Rollinger, Brentano’s logic and Marty’s early philosophy of language. Brentano Studien XII, 77–98 (2009)

    Google Scholar 

  • K. Schuhmann, Husserl-Chronik (Denk- und Lebensweg Edmund Husserls) (Nijhoff, Den Haag, 1977)

    Book  Google Scholar 

  • K. Schuhmann, Malvine Husserls “Skizze eines Lebensbildes von E. Husserl”. Husserl-Studies 5, 105–125 (1988)

    Article  Google Scholar 

  • K. Schuhmann, Brentano’s impact on twentieth-century philosophy, in The Cambridge Companion to Brentano, ed. by D. Jacquette (Cambridge University Press, Cambridge, 2004), pp. 277–297

    Google Scholar 

  • E. Schuhmann, K. Schuhmann, Husserls Manuskripte zu seinem Göttinger Doppelvortrag von 1901. Husserl Stud. 17(2), 87–123 (2001)

    Article  Google Scholar 

  • H. R. Sepp (ed.), Edmund Husserl und die Phänomenologische Bewegung. Zeugnisse in Text und Bild (Alber, Freiburg München, 1988)

    Google Scholar 

  • D. Spalt, Die mathematischen und philosophischen Grundlagen des Weierstraßschen Zahlbegriffs zwischen Bolzano und Cantor. Arch. Hist. Exact Sci. 41(4), 311–362 (1991)

    Google Scholar 

  • C. Stumpf, Tonpsychologie, vol 1 (Hirzel, Leipzig, 1883)

    Google Scholar 

  • C. Stumpf, Tonpsychologie, vol 2 (Hirzel, Leipzig, 1890)

    Google Scholar 

  • C. Stumpf, Vorlesungen über Psychologie, manuscript Q 11/I, Halle WS 1886/87 (unpublished lecture notes)

    Google Scholar 

  • C. Stumpf, Logik und Enzyklopädie der Philosophie, manuscript Q 14, Halle SS 1887 (unpublished lecture notes)

    Google Scholar 

  • C. Stumpf, Erkenntnislehre (Barth, Leipzig, 1939)

    Google Scholar 

  • C. Stumpf, in Über die Grundsätze der Mathematik, ed by W. Ewen (Königshausen & Neumann, Würzburg, 2008)

    Google Scholar 

  • C. von Ehrenfels, Zur Philosophie der Mathematik. Vierteljahrsschrift für wissenschaftliche Philosophie 15, 285–347 (1891)

    Google Scholar 

  • C. von Ehrenfels’, Größenrelationen und Zahlen: eine psychologische Studie, ed. by C. Ierna, Meinong Studies 8 (2017)

    Google Scholar 

  • D. Willard, Logic and the Objectivity of Knowledge (Ohio University Press, Athens, 1984)

    Google Scholar 

  • K. Zindler, Beiträge zur Theorie der mathematischen Erkenntnis. Sitzungsberichte der Wiener Akademie. Philos-Histor. Abth., Bd. 118 (1889)

    Google Scholar 

Download references

Acknowledgements

This chapter is an outcome of the project "From Logical Objectivism to Reism: Bolzano and the School of Brentano" P401 15-18149S (Czech Science Foundation), realised at the Institute of Philosophy of the Czech Academy of Sciences.

Author information

Authors and Affiliations

  1. Faculty of Philosophy, University of Groningen, Groningen, The Netherlands

    Carlo Ierna

  2. Institute of Philosophy, Czech Academy of the Sciences, Prague, Czech Republic

    Carlo Ierna

Authors
  1. Carlo Ierna
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Carlo Ierna .

Editor information

Editors and Affiliations

  1. Institut für Philosophie, Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany

    Stefania Centrone

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Ierna, C. (2017). The Brentanist Philosophy of Mathematics in Edmund Husserl’s Early Works. In: Centrone, S. (eds) Essays on Husserl's Logic and Philosophy of Mathematics. Synthese Library, vol 384. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1132-4_7

Download citation

Publish with us

Policies and ethics

Search

Navigation