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neglects Brentano’s own work on the philosophy of mathematics and logic, which can be found mostly in his unpublished manuscripts and lectures, and various works by Brentano’s students on the philosophy of mathematics which have only recently emerged from obscurity.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.
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Notes
- 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.
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.
For a first outline of the idea of a Brentanist philosophy of mathematics, see Ierna 2011a.
- 4.
- 5.
- 6.
Moran 2000, 24 “one can speak loosely of a ‘Brentano school’.”
- 7.
Albertazzi et al. 1996, 6.
- 8.
Stumpf 2008.
- 9.
Ierna 2005.
- 10.
Husserl 2005.
- 11.
- 12.
Beiträge zur Variationsrechnung, Husserl 1883.
- 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.
- 15.
Cf. Miller 1982, 1–4.
- 16.
- 17.
See Ierna 2006, 38 ff. and 46 ff.
- 18.
- 19.
Husserl 1887, 12; 1970, 297.
- 20.
Königsberger 1874, 1.
- 21.
- 22.
- 23.
Bolzano 1889, 4 f.
- 24.
- 25.
Husserl 1900, § 70.
- 26.
See Cantor 1883.
- 27.
- 28.
Husserl 1983, 95 f.
- 29.
Husserl 1900, 156 n. 2.
- 30.
Frege 1884.
- 31.
Kronecker 1887.
- 32.
Dedekind 1888.
- 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.
- 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.
Husserl 1891, 49, 59, 66 n., 241.
- 37.
Stumpf 1883, 96.
- 38.
- 39.
Husserl 1891, Ch. 8.
- 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.
- 42.
- 43.
Husserl 1891, 290.
- 44.
Husserl 1891, 297.
- 45.
- 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.
Also see Ierna 2005, 7.
- 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.
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.
- 51.
- 52.
Brentano 1874, vi.
- 53.
- 54.
Brentano 1874, 29, 34.
- 55.
Brentano 1874, 86.
- 56.
Brentano 1874, 93.
- 57.
Stumpf 2008, 18–2.
- 58.
Stumpf 2008, 19–1.
- 59.
Stumpf 2008, 19–3.
- 60.
Stumpf 2008, 24–2.
- 61.
- 62.
Brentano EL 80/13060, quoted from Rollinger 2009, 81 f.
- 63.
Husserl 2002, 296.
- 64.
- 65.
- 66.
- 67.
- 68.
Brentano 1884/85, Y 2, 32.
- 69.
Brentano 1884/85, Y 2, 28 f.
- 70.
Brentano 1884/85, Y 2, 47.
- 71.
- 72.
- 73.
Stumpf 1887, Q 14, 86 ff.
- 74.
Stumpf 1887, Q 14, 114a.
- 75.
- 76.
- 77.
See Ierna 2006 for a more detailed reconstruction of the provenance and role of these concepts in Husserl’s early works.
- 78.
Stumpf 1939.
- 79.
From the conclusion to Ierna 2015.
- 80.
Ehrenfels 1891, 291 f.
- 81.
Op. cit., 295.
- 82.
Husserl 1891, 91.
- 83.
Op. cit., 186.
- 84.
His much later work on the law of primes based on the concept of Gestalt is less relevant in this context.
- 85.
Husserl 1956, 294.
- 86.
Husserl 1994, 158.
- 87.
Husserl 2005, 297.
- 88.
Husserl 1994, 158.
- 89.
Husserl 1983, 154–214.
- 90.
See Ierna 2005, 47–48, n. 170.
- 91.
Husserl 1994, 158.
- 92.
Husserl 1983, 175.
- 93.
Op. cit., 42 f.
- 94.
Schuhmann & Schuhmann 2001.
- 95.
Also see Ierna 2011b.
- 96.
Husserl 1994, 160.
- 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.
Husserl 1970, 357.
- 99.
Husserl 2005, 301.
- 100.
Op. cit., 307.
- 101.
Husserl 1994, 161.
- 102.
Husserl 1891, 323.
- 103.
Husserl 1994, 161.
- 104.
See Husserl 1900, 175.
- 105.
Husserl 2001, 247–248.
- 106.
Op. cit., 52.
- 107.
Op. cit., 102.
- 108.
Op. cit., 252.
- 109.
Op. cit., 86 f.
- 110.
Op. cit., 100.
- 111.
- 112.
Husserl 2001, 309. Husserl elsewhere (318) suggests that instead of Verknüpfung we could also say Operation.
- 113.
Op. cit., 311.
- 114.
Op. cit., 311 f.
- 115.
Op. cit., 314 f.
- 116.
Op. cit., 315.
- 117.
Something Husserl apparently didn’t fully appreciate yet in 1891, 292–294.
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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.
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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
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