Abstract
This essay was written when I was studying mathematics in Göttingen in 1954–55 with a fellowship from the German Academic Exchange Service (DAAD). At that time my background in philosophy was limited to a one semester course that is compulsory for all students in Norwegian universities. However, Professor Arne Næss liked the essay and suggested that I submit it as a Master’s Thesis in philosophy at the University of Oslo. He also arranged to have it published in the monograph series of the Norwegian Academy of Science and Letters, where it appeared in 1958. I am indebted to Arne Næss for taking this interest in my work, and also to the German Academic Exchange Service for their support.
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Notes
Originally published as Husserl und Frege, ein Beitrag zur Beleuchtung der Entstehung der phänomenologischen Philosophie, Oslo: Aschehoug, 1958. Translation by Claire Ortiz Hill.
Edmund Husserl, Philosophie der Arithmetik, Halle: Pfeffer, 1891. Cited in the text as PA.
Edmund Husserl, Logical Investigations, New York: Humanities Press, 1970 (1900–1901). Cited in the text as LI.
See for example LI, 263; ID § 18 as cited in note 6.
For example Werner Illemann, Die vorphänomenologische Philosophie Edmund Husserls und ihre Bedeutung für die phänomenologische, Dissertation, Leipzig, 1932, p. 70.
Edmund Husserl, Ideas: General Introduction to Pure Phenomenology, New York: Colliers, 1962 (1913). Cited in the text as ID.
Although there are many phenomenological features also in the Philosophie der Arithmetik. See for example Husserl’s own statements LI, 204 n.; 449 n. and many others.
See for example LI, 248–66.
Gottlob Frege, “Review of E.G. Husserl, Philosophie der Arithmetik I”, anthologized in Frege’s Collected Papers on Mathematics, Logic and Philosophy, Oxford: Blackwell, 1984, pp. 195–209. Cited as FR are the pages of the original German article as given in the margins of the 1984 translation.
Franz Hildebrand, Göttingische gelehrte Anzeigen, Band 17 (1893), pp. 175–80
A. Elsas, Philosophische Monatshefte, XXX, Band (1894), pp. 437–40
W. Heinrich, Vierteljahrsschrift für wissenschaftliche Philosophie, Neunzehnter Jahrgang (1895), pp. 436–39.
Benno Erdmann, Logik, Halle: Niemeyer, 1892.
Gottlob Frege, Grundgesetze der Arithmetic, vol. I & II, Jena: Pohle, 1893 – 1903. The English translation of volume I: Basic Laws of Arithmetic, Berkeley: University of California Press, 1964 is cited as BL following the German pagination included in the translation.
Gottlob Frege, Begriffsschrift, Halle, 1879.
Gottlob Frege, Die Grundlagen der Arithmetik, Breslau: Marcus, 1884. The English translation: Foundations of Arithmetic, Oxford: Blackwell, 1986, 2nd ed. rev. is cited in the text as FA.
“Function and Concept”, “On Concept and Object”, and “On Sense and Reference” are anthologized in Translations from the Philosophical Writings of Gottlob Frege, Oxford: Blackwell, 1980, 3rd ed., cited in the text as GB.
Arthur North Whitehead and Bertrand Russell, Principia Mathematica, vol. 1, 2nd ed., Cambridge: Cambridge University Press, 1950 (1910), p. VIII.
Bertrand Russell, Introduction to Mathematical Philosophy, London: Allen & Unwin, 1919, p. 25 n. 2.
Ernst Schröder, Vorlesungen über die Algebra der Logik (exakte Logik), I. Band, Leipzig: Teubner, 1890, II. Band erster Teil, Leipzig, 1891. Later: III. Band. Algebra und Logik der Relative, erster Teil, Leipzig, 1895. The remaining parts of the work were published after Schröder’s death. Husserl reviewed the first volume in the Göttingische gelehrte Anzeigen.
Marvin Farber, The Foundation of Phenomenology, Cambridge, MA, Harvard University Press, 1943, pp. 16–17.
E.W. Beth, Les fondements logiques des Mathematics, 2nd ed., Paris: Louvain, 1955, p. 119.
John Wild, “Husserl’s Critique of Psychologism”, Philosophical Essays in Memory of Edmund Husserl, ed. Marvin Farber, Cambridge, MA: Harvard University Press, 1940, p. 42.
Emmanuel Levinas, La théorie de Vintuition dans la phénoménologie de Husserl, Thesis, Paris: Alcan, 1930, p. 33.
Farber, The Foundation..., pp. 55–58.
Alonzo Church has corrected the most important of these inaccuracies in his review of the book in the Journal of Symbolic Logic, vol. 9(1944), pp. 63–65.
Andrew Osborn, Edmund Husserl and his Logical Investigations, 2nd ed., Cambridge MA, 1949.
See for example Jan Patocka’s bibliography in Revue internationale de Philosophie, tome I (1938–39), pp. 374–97.
Since the definitions in this work are built step by step on a small number of undefined basic concepts, and given in a highly formal logical terminology, precise reproduction of these definitions would require several pages and interfere with this work in form and content. All necessary information about the definitions will be given in the section below called “Posing the Problem”.
G.H. von Wright provides clear and easily readable reasons for these statements in “The Logical Problem of Induction”, Acta Philosop-hica Fennica, Fasc. III, Oxford, 1941, 2nd ed. rev. The truth of the statements is naturally dependent on how the words and expressions figuring in the assertions are defined. Especially important are the words which we have placed in quotation marks, and which we use throughout the study in the sense given in von Wright’s work.
These remarks are based on the author’s impression after reading works in history and the natural sciences. Historical research involves observations based on empirical study as examined by Ottar Dahl in his work Om årsaksproblemer i historisk forskning (On causal problems in historical research), Oslo: Universitetsforlaget, 1956.
However, such a work would naturally presuppose the truth of a series of general conditionals from many different branches of science (for example on how “sources” are viewed).
For example, we are confident that the difficulties Husserl encountered while working on the second volume of the Philosophy of Arithmetic along with reflections and other “unavailable” events in Husserl’s intellectual life are sufficient to explain his development.
Since in this work we assume that the reader already has confidence in this “causal law”, and since we do not wish to try to increase this confidence, we are only formulating it explicitly in order to make the connection clearer in the work. “Causal laws” are not generally explicitly formulated in historical works (Ottar Dahl, op. cit. p. 143), and according to Aristotle there is no reason to do so, for a line of reasoning is clear if it lacks only premises in which one has a great deal of confidence (Aristotle, Topica, 8 Chap. 12, 162b, freely cited). In this work we have omitted most such ancillary premises without saying anything.
It is obviously possible that Husserl also encountered other difficulties of this kind prior to 1900. When we concentrate on the difficulties which he encountered while working on the Philosophy of Arithmetic, the reason is that, as we will see, Frege’s arguments reached him precisely while he was dealing with these difficulties.
It is obviously not impossible that by appealing to other “causal laws” we could instill confidence that Frege also played a significant role in other changes in Husserl’s philosophy from 1891–1900. But the following is valid for all the “causal laws” we know: if they can be used to instill confidence that Frege may have been significant for such a change, the causal law this work is based on can do the same. As far as we know our study is for this reason complete in this respect.
Edmund Husserl, “Der Folgerungskalkül und die Inhaltslogik”, Vierteljahrsschrift für wissenschaftliche Philosophie, 15 Jahrgang (1891), pp. 351–356.
Edmund Husserl, “Antwort an die vorstehende Erwiderung des Herrn Voigt”, Vierteljahrsschrift ftir wissenschaftliche Philosophie, 17 Jahrgang (1893), p. 511.
Edmund Husserl, “Bericht über deutsche Schriften zur Logik aus dem Jahre 1894”, Archiv für systematische Philosophie (Neue Folge der Philosophischen Monatshefte) III. Band (1897), pp. 216–44; “Bericht über deutsche Schriften zur Logik in den Jahren 1895–98”, this same Journal IX. Band (1903), pp. 393–408, and pp. 523–543 and X. Band (1904), pp. 101–25. (Frege is not mentioned in these surveys, apparently because his German language works in these years are limited to brief commentaries on his own works and the works of others).
Edmund Husserl, “Ernst Schröder, Vorlesungen über die Álgebra der Logik (Exakte Logik), I. Band, Leipzig, B.G. Teubner, 1890 (Recension)”, Göttingische gelehrte Anzeigen, Erster Band (1891), pp. 243–78
Edmund Husserl, “Der Folgerungskalkül und die Inhaltslogik”, Vierteljahrsschrift für wissenschaftliche Philosophie, 17 Jahrgang (1893), p. 51.
Edmund Husserl, “A. Voigt’s ‘elementare Logik’ und meine Darlegungen zur Logik des logischen Kalküls”, Vierteljahrsschrift für wissenschaftliche Philosophie, 17 Jahrgang (1893), pp. 111–20, and his “Antwort an die vorstehende Erwiderung des Herrn Voigt” in the same volume, pp. 508–11.
Edmund Husserl, “Psychologische Studien zur elementaren Logik” I–II, Philosophische Monatshefte, XXX, Band (1894), pp. 159–191.
LI, p. 42, cited page 4 of this text.
LI, pp. 262–63. See also Edmund Husserl: “Bericht über deutsche Schriften zur Logik in den Jahren 1895–99”, Archiv für systematische Philosophie, IX Band (1903), pp. 397–400, and his “Philosophie als strenge Wissenschaft”, Logos, Band I (1910–11), p. 319.
Husserl, “Psychologische...”, p. 187.
The appropriateness of Frege’s definition is apparent, among other things, in that the brilliant creator of set theory Cantor defined cardinal numbers in a similar way. In 1902 Russell identified the cardinal number M with the set of all sets equivalent to M in precisely the same way as Frege, and von Neumann used a modified form of Frege’s definition in 1928.
BL pp. ix–x; See also Wilma Papst, Gottlob Frege als Philosoph, Dissertation Berlin, pp. 22–23.
See preface.
Edmund Husserl, Formal and Transcendental Logic, The Hague: Martinus Nijhoff, 1969, p. 87.
This is not an original statement. Jacob Klein said as much in the article “Phenomenology and the History of Science”, Philosophical Essays in Memory of Edmund Husserl, ed. Marvin Farber, Cambridge, MA: Harvard University Press, 1940, p. 146: “Now Husserl’s radical criticism of psychologism implies anything but a simple opposition between neverchanging “abstract” principles and everchanging “empirical” things.”
He rejects, among other things, one of the arguments Frege used, namely the normative character of logic. This is dealt with later on in this study.
Werner Illemann shows this in Die vorphänomenologische Philosophie Edmund Husserls und ihre Bedeutung für die phänomenologische, Dissertation, Leipzig, 1932, p. 41 f.
This “cogito” is one of Husserl’s many points of contact with Descartes. Not without reason did Husserl entitle his first French work Meditations Cartesiennes.
For example in “Philosophie als strenge Wissenschaft”, Logos, Bd. 1(1910–11), p. 295.
Arne Næss, “Husserl on the Apodictic Evidence of Ideal Laws”, Theoria XX (1954), p. 63.
R. Kynast, Das Problem der Phänomenologie, eine wissenschafistheoretische Untersuchung, Breslau: Trewend & Granier, 1917, p. 59.
For example, Wilhelm Reimer, “Der phänomenologische Evi-denzbegriff”, Kant Studien, Band 23 (1919), pp. 290–91.
We hope to come back to this important question in a more epistemologically directed work on the phenomenological method.
Some of Farber’s statements on Frege’s significance for Husserl’s development are more in agreement with the results of this study than the one cited in the preface. See, for example pp. 5, 57–58, 98 of his The Foundation of Phenomenology.
Friedrich Ueberweg, Grundriss der Geschichte der Philosophie, pt 4, Die Deutsche Philosophie des XIX. Jahrhunderts und der Gegenwart, Basel, 1951, p. 506.
Ibid., p. 512.
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Føllesdal, D. (1994). Husserl and Frege: A Contribution to Elucidating the Origins of Phenomenological Philosophy. In: Haaparanta, L. (eds) Mind, Meaning and Mathematics. Synthese Library, vol 237. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8334-3_1
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