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On the Philosophical Development of Kurt Gödel

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Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer

Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 35))

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Abstract

Gödel first advocated the philosophy of Leibniz and then, since 1959, that of Husserl. Based on research in Gödel’s archive, from which a number of unpublished items are presented, we argue that (1) Gödel turned to Husserl in search of a means to make Leibniz’ monadology scientific and systematic, and (2) This explains Gödel’s specific turn to Husserl’s transcendental idealism as opposed to the realism of the earlier Logical Investigations. We then give three examples of concrete influence from Husserl on Gödel’s writings.

Originally published as van Atten and Kennedy 2003. Copyright © 2003 The Association for Symbolic Logic. Reprinted by permission, which is gratefully acknowledged.

An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-3-319-10031-9_13

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Notes

  1. 1.

    As introductions to phenomenology, we recommend Husserl’s The Idea of Phenomenology (Husserl 1999) – as we will see, a ‘momentous lecture’ according to Gödel – and Kockelmans’ annotated edition of Husserl’s article for the Encyclopædia Britannica (Kockelmans 1994), an article that Gödel also studied. The first is work from before, the second from after the appearance of the less transparent Ideas I (Husserl 1976a). For an accessible historical treatment, see Spiegelberg (1983), a work of which Gödel owned and read the earlier, second edition from 1965.

  2. 2.

    The Grandjean questionnaire, printed in Wang (1987, 18, 20).

  3. 3.

    ‘Die Systeme der großen Denker’, taught by Moritz Schlick, WS 24/25; ‘Übersicht über die Hauptprobleme der Philosophie I’ (‘Overview of the main problems in philosophy I’), by Heinrich Gomperz, WS 24/25, and its sequel in SS 25, ‘Übersicht über die Hauptprobleme der Philosophie II’ (‘Overview of the main problems in philosophy II’); ‘Philosophische Übungen’ (‘Philosophical exercises’), by Rudolf Carnap, SS 28; no data on SS 29 and WS 29/30 available. Source: Universitätsarchiv Wien, as reprinted in Schimanovich-Galidescu (2002, 145–146). These are the ‘inskribierte Vorlesungen’; he may have attended courses for which he did not register, such as Schlick’s ‘Logik und Erkenntnistheorie’ (‘Logic and Theory of knowledge’), WS 25 (Schimanovich-Galidescu 2002, 135).

  4. 4.

    Husserl criticised Schlick’s discussion in the introduction to the second edition of the Logical Investigations (Husserl 1984b, 535–536); Schlick replied in the second edition of the Erkenntnislehre of 1925 (Schlick 1925, 127–128n3).

  5. 5.

    On Kaufmann, see Stadler (1997). His correspondence with Husserl is in Husserl (1994, 4).

  6. 6.

    Edmund and Malvine Husserl to Husserl’s former student Roman Ingarden, July 10, 1935 (Husserl 1994, 3:302).

  7. 7.

    References of the form ‘Gödel Papers x/y, z’ refer to item z in folder y in box x of the Gödel Papers in the Firestone Library, Princeton.

  8. 8.

    For example, those of Köhler (2002b, 341–386) and Hintikka (1998). For specific criticism of the latter interpretation, see van Atten (2001).

  9. 9.

    For further discussion of problems with Gödel’s arguments, see Köhler (2002b, 341–386). We entirely disagree, however, with the positive interpretation developed there, in Sect. 4.3, of Gödel as a conventionalist of a particular kind: we claim this is neither historically nor systematically correct.

  10. 10.

    This remark echoes the final paragraph of the Russell paper, e.g., ‘How can one expect to solve mathematical problems systematically by mere analysis of the concepts occurring if our analysis so far does not even suffice to set up the axioms?’ (Gödel 1994, 152).

  11. 11.

    Gödel’s emphasis on simplicity has to do with a particular moral and aesthetic view of the world which finds its inspiration in Leibniz, an important issue which we have not pursued in this paper.

  12. 12.

    The phrase we have omitted from the quotation, ‘Phenomenology does not give a theory’, we take to mean that phenomenology is primarily a method (to isolate what is intuitively given), and not itself a theory. As Husserl said,

    If philosophy has any stock whatever of ‘essentially necessary’ fundamentals in the genuine sense which, according to their essence, can therefore be grounded only by an immediately presentive intuition, then the controversy concerning them is decided not only independently of any philosophical science, but of the idea of such a science and of the latter’s allegedly legitimated theoretical content. (Husserl 1983, 34) (‘Hat überhaupt Philosophie einen Bestand an “prinzipiellen” Grundlagen in dem echten Sinne, die also ihrem Wesen nach nur durch unmittelbar gebende Anschauung begründet werden können, so ist ein Streit, der diese betrifft, in seiner Entscheidung unabhängig von aller philosophischen Wissenschaft, von dem Besitz ihrer Idee und ihres angeblich begründeten Lehrgehaltes’, Husserl 1950c, 41/Husserl 1976a, 40. Gödel owned Husserl 1950c, but the preferred edition [now] is its revision Husserl 1976a. For convenience, we will always mention the page numbers in both editions.)

    Of course, when applying this method one obtains propositions, and it is in this sense that Husserl presents, in Sect. 60 of the Cartesian Meditations, ‘metaphysical results’ (‘metaphysische Ergebnisse’). See also Brainard’s discussion of this point (Brainard 2002, Sect. 2.1).

  13. 13.

    [​​[Addition MvA: Now Toledo (2011, 200).]​​]

  14. 14.

    Note that this alteration is not present in the version Wang gives in Wang (1996, 202). However, Wang mentions the idea in Wang (1987, 174).

  15. 15.

    A concise encapsulation of how Gödel’s concept of rationalism had evolved under Husserl’s influence (from ‘deciding’ philosophical propositions to ‘clarifying’ them) can be seen from the following note to himself (Gödel Papers, 12/43, 060571), likely from after 1961: ‘Perhaps phenomenology combined with foundational research will someday decide clarify those questions in an absolutely convincing manner.’

  16. 16.

    Am Prinzip aller Prinzipien: daß jede originär gebende Anschauung eine Rechtsquelle der Erkenntnis sei, daß alles, was sich uns in der ‘Intuition’ originär (sozusagen in seiner leibhaften Wirklichkeit) darbietet, einfach hinzunehmen sei, als was es sich gibt, aber auch nur in den Schranken, in denen es sich da gibt, kann uns keine erdenkliche Theorie irre machen. Sehen wir doch ein, daß eine jede ihre Wahrheit selbst wieder nur aus den originären Gegebenheiten schöpfen könnte. Jede Aussage, die nichts weiter tut, als solchen Gegebenheiten durch bloße Explikation und genau sich anmessende Bedeutungen Ausdruck zu verleihen, ist also wirklich … ein absoluter Anfang, im echten Sinne zur Grundlegung berufen, principium. (Husserl 1950c, 52/Husserl 1976a, 51)

  17. 17.

    As Kant wrote in the Critique of Pure Reason (A761/B789), ‘Scepticism is thus a resting-place for human reason, where it can reflect upon its dogmatic wanderings and make survey of the region in which it finds itself, so that for the future it may be able to choose its path with more certainty. But it is no dwelling-place for permanent settlement’ (Kant (1781–1787a) 1965a); ‘So ist der Skeptizismus ein Ruheplatz für die menschliche Vernunft, da sie sich über ihre dogmatische Wanderung besinnen und den Entwurf von der Gegend machen kann, wo sie sich befindet, um ihren Weg fernerhin mit mehrerer Sicherheit wählen zu können, aber nicht ein Wohnplatz zum beständigen Aufenthalte’ (Kant (1781–1787b) 1996).

  18. 18.

    Tait (1986, Sect. 7) raises the same objection. Maddy’s set theoretic realism, on the other hand, is one attempt to bring mathematical objects ‘into the world we know’ (Maddy 1990, 48) by reconstructing the perception of mathematical objects along causal lines. Thus ‘set(s) participate in the generation of … perceptual beliefs in the same way that my hand participates in the generation of my belief that there is a hand before me when I look at it in a good light’ (Maddy 1990, 58). Whether or not Maddy is proposing the reduction of mathematical terms to physical ones in that work – and we think it can be argued that she is – we note that her proposal falls into the category of moves to which, we are suggesting, Gödel would have been opposed. We hasten to add that Maddy readily acknowledges this point of disagreement between herself and Gödel, and she is aware that her naturalist interpretation of Gödel’s remarks would not have been his own, as we have noted above.

  19. 19.

    Note Gödel. Of course I don’t wish by that to claim that naïve thought already grasps objective being correctly on all points, as ontological metaphysics often seems to suppose.

  20. 20.

    Die in der idealist. Phil. behandelte Reflexion auf das Subjekt (d.h. Ihr II Thema d. Denkens), die Unterscheidung von Reflexionsstufen etc. scheint mir sehr interessant u. wichtig. Ich halte es sogar für durchaus möglich, daß dies ‘der’ Weg zur richtigen Metaphysik ist. Die damit verbundene (in Wahrheit aber davon ganz unabhängige) Ablehnung der objektiven Bedeutung des Denkens kann ich aber nicht mitmachen. Ich glaube nicht, daß irgend ein Kantsches oder positivistisches Argument oder die Antinomien d. Mengenl., oder die Quantenmechanik bewiesen hat, daß der Begriff des objektiven Seins (gleichgültig ob für Dinge oder abstrakte Wesenheiten) sinnlos oder widerspruchsvoll ist. [footnote: Damit will ich natürlich nicht behaupten, daß schon das naive Denken das objektive Sein in allen Punkten richtig erfaßt, wie die ontol. Metaphysik vielfach anzunehmen scheint.] Wenn ich sage, daß man eine Theorie der Klassen als objektiv existierender Gegenstände entwickeln kann (oder soll), so meine ich damit durchaus Existenz im Sinne der ontol. Metaphysik, womit ich aber nicht sagen will, daß die abstrakten Wesenheiten in der Natur vorhanden sind. Sie scheinen vielmehr eine zweite Ebene der Realität zu bilden, die uns aber ebenso objektiv. u. von unserem Denken unabhängig gegenübersteht wie die Natur. (Gödel 2003, 502, 504)

  21. 21.

    In this section we are much indebted to Beiser (2002), Wartenberg (1992), and the various entries on idealism in Ritter (1971).

  22. 22.

    In the literature, there are two terminological traditions. One uses ‘ideal’ to qualify the objects in the independent realm; the other uses it to qualify the objects that are dependent on that realm. We will adhere to the first usage. Compare, for example, Beiser (2002, 6) and Wartenberg (1992, 104).

  23. 23.

    Given the explanation of the contrast that follows, it is not likely that ‘objective idealism’ here specifically means that of Schelling and Hegel, it seems also to include Husserl’s transcendental idealism.

  24. 24.

    William Howard tells the following story from 1972 or 1973 (Shell-Gellasch 2003, 40–41):

    Because Gödel had repeatedly asked me to describe my experiences during meditation, I finally suggested that maybe he would like to learn how to do T[ranscendental] M[editation]. He said no, and I asked why not. Gödel replied, ‘The goal of Maharishi’s system of meditation is to erase thoughts, whereas the goal of German Idealism is to construct an object.’

    In saying this, he became quite forceful, holding out his hand – palm and fingers upward – as if he were grasping an object. I think what Gödel meant was that the goal was to build a mental structure. I tried to explain that it was not the purpose of TM to erase thoughts; but his mind was made up.

    The explanation of Gödel’s phrase ‘constructing an object’ here is a delicate matter, and Howard’s explanation may not be sufficient; but Gödel’s gesture is very telling.

  25. 25.

    [​​[Addition MvA: In an email of March 15, 2013, William Howard explains to me:

    When I said, in my interview with Amy, that I thought that what Gödel meant was that the goal was to build a mental structure, what I had in mind was a combination of two things:

    1. 1.

      what I had been able to learn about German Idealism (including some passages from Schelling, and what I had been able to get out of Kant’s Critique of Pure Reason,

    2. 2.

      what I had learned from studying the writings of Gurdjieff and Ouspensky (this preceded my TM adventure; it is where I first learned about the various states of consciousness and is the reason that I took up TM).

    …

    When I said ‘mental structure’, I had in mind what Gurdjieff described as a product of ‘inner work’. He certainly regarded such a structure as being objective. Not that I consider myself an expert on Gurdjieff. Also, I would not normally cite him in a philosophical discussion, but at least you can see what was on my mind at the time.

    As prof. Howard mentioned, Gödel did not want to learn TM. But, Howard tells me in an email of March 9, 2013,

    I had been going to TM retreats every few weeks, and I was asked if I would give a talk. This was early in 1973. I prepared a 2-page outline, to be handed out at the talk. Caroline Underwood, the secretary at the Institute, typed it up and made mimeographed copies for me;

    …

    Caroline Underwood (above) was so fascinated with the material that she had typed up for me, and my explanation of it, that she joined the TM organization a couple of months later. I was pretty surprised, since she was a ‘no nonsense’ type of person (had been an officer in the Navy, I think).

    (Quoted by permission of William Howard.)]​​]

  26. 26.

    Ferner ist nun aber auch die kantische Objektivität des Denkens insofern selbst nun wieder subjektiv, als nach Kant die Gedanken, obschon allgemeine und notwendige Bestimmungen, doch ‘nur unsere’ Gedanken und von dem, was das Ding ‘an sich’ ist, durch eine unübersteigbare Kluft unterschieden sind. Dagegen ist die wahre Objektivität des Denkens diese, dass die Gedanken nicht bloss unsere Gedanken, sondern zugleich das Ansich der Dinge und des Gegenständlichen überhaupt sind. (Hegel (1830) 1906, IV, 2, Sect. 41, Zusatz 2)

  27. 27.

    The annotation between brackets is by the editors of Gödel 1995 and refers to p. 29 of Gödel’s manuscript, which is printed on p. 258 of Gödel 1995.

  28. 28.

    As an aside, we suggest that the views Gödel expounds in this paper on the history of philosophy since the Renaissance and the division of world views according to their optimism or pessimism, where idealism and theology are on the optimistic side, may have been inspired by a paper by Heimsoeth that he knew, ‘Leibniz’ Weltanschauung als Ursprung seiner Gedankenwelt’, Heimsoeth 1916, esp. 370, 72, 76, and by Heimsoeth’s book Die sechs großen Themen der abendländischen Metaphysik (Heimsoeth 1934), on which Gödel made 29 pages of notes, perhaps in 1962 (see p. 27), in which one finds ‘p. 19–70 = Opt[imismus]-Pess[imismus]’. The notes and the reference to the paper on Leibniz are in ‘idealis[ische] Ph[ilosophie].’ (Gödel Papers, 9c/23)

  29. 29.

    Anderseits haben aber eben wegen der Unklarheit und im wörtlichen Sinn Unrichtigkeit vieler Kantscher Formulierungen sich ganz entgegengesetzte philosophische Richtungen aus [dem] Kantschen Denken entwickelt, von denen aber keine dem Kantschen Denken in seinem Kern wirklich gerecht wurde. Dieser Forderung scheint mir erst die Phänomenologie zu genügen, welche ganz im Sinne Kants sowohl dieselben Salto mortale des Idealismus in eine neue Metaphysik als auch die positivistische Ablehnung jeder Metaphysik vermeidet. (Gödel *1961/?, 386)

  30. 30.

    Gödel’s term in the German original, ‘Salto mortale’ will have been a reference to Friedrich Heinrich Jacobi (1743–1819), who argued that in the end all knowledge can only be grounded by making an un-reasonable ‘salto mortale’ or leap of faith, a leap which he valued positively and considered the proper response to scepticism. The term became famous because of the ensuing ‘Pantheism controversy’ in which, among others, Jacobi, Mendelssohn, Kant, Herder, Goethe and Hamann took part. See Beiser (1987, Chap. 2) for further discussion.

  31. 31.

    [​​[Addition MvA: Revealing about Husserl’s personal situation and the mentality with which he faces it is his letter to Mahnke of April 23, 1921 (Husserl 1994, 3:430): ‘Unfortunately I (who as you know am Lutheran, but of Jewish origin) could not become member of the FichtegesellschaftFootnote 32 and I deplore the intrusion of anti-semitism into philosophy(!). But no one can keep me from working, according to my weak powers, in Christian spirit and for Fichte and for German Idealism.’ (‘Leider konnte ich (der ich wie Sie wissen zwar Lutheraner, aber jüdischer Abstammung bin) der Fichtegesellschaft nicht beitreten und beklage das Eindringen des Antisemit[ismus] in die Philosophie (!). Niemand kann mich aber hindern, nach schwächen Kräften im christlichen Geist und für Fichte und den deutschen Idealismus zu wirken.’)]​​]

  32. 32.

    [​​[Addition MvA: The Fichtegesellschaft was a political-philosophical society founded in 1914. In November 1917, Husserl gave three appreciative lectures on Fichte’s ideal of humanity (Husserl 1987, 267–293, English translation Husserl 1995); he repeated those in January and November 1918.]​​]

  33. 33.

    Mochten Kant und die weiteren deutschen Idealisten für eine wissenschaftlich strenge Verarbeitung der sie machtvoll bewegenden Problemmotive auch wenig Befriedigendes und Haltbares bieten: die diese Motive wirklich nachzuverstehen und sich in ihren intuitiven Gehalt einzuleben vermögen, sind dessen sicher, daß in den idealistischen Systemen völlig neue, und die allerradikalsten Problemdimensionen der Philosophie zutage drängen und daß erst mit ihrer Klärung und mit der Ausbildung der durch ihre Eigenart geforderten Methode der Philosophie ihre letzten und höchsten Ziele sich eröffnen. (Husserl 1987, 309)

  34. 34.

    From his notes, it is clear that Gödel read Husserl’s texts mainly in the Husserliana series; by 1961, eight volumes had appeared, of which Ideas I was the third (Husserl 1950c).

  35. 35.

    So begreift es sich, daß die Phänomenologie gleichsam die geheime Sehnsucht der ganzen neuzeitlichen Philosophie ist … Und erst recht erschaut sie Kant, dessen größte Intuitionen uns erst ganz verständlich werden, wenn wir uns das Eigentümliche des phänomenologischen Gebietes zur vollbewußten Klarheit erarbeitet haben. Es wird uns dann evident, daß Kants Geistesblick auf diesem Felde ruhte, obschon er es sich noch nicht zuzueignen und es als Arbeitsfeld einer eigenen strengen Wesenswissenschaft nicht zu erkennen vermochte. (Husserl 1950c, 148/Husserl 1976a, 133)

  36. 36.

    ein Versuch …, den tiefsten Sinn Kant’schen Philosophierens wahrzumachen.

  37. 37.

    die ganze Phänomenologie [ist] nichts anderes als die erste streng wissenschaftliche Gestalt dieses Idealismus.

  38. 38.

    For examples from correspondence and work, see Kern (1964, 28–33).

  39. 39.

    Gedanken ohne Inhalt sind leer. (Kant (1781–1787b) 1996, A51/B75)

  40. 40.

    It seems that Gödel made a much more intensive study of German Idealism than Husserl ever had; Footnote 41 compare the amount of material in the relevant folders in the Gödel Nachlaß (Gödel Papers, 9b/16, 9b/17, 9b/18, and 9c/23) with the remark by Boehm (Boehm 1968, 50n1). Footnote 42 (Boehm is of course right when he goes on to point out that lack of direct acquaintance with a body of philosophical work does not imply a judgment on the quality of one’s critique of it.) In passing, we note that Gödel closely studied the section ‘‹Kant und die Philosophie des Deutschen Idealismus›’ (‘‹Kant and the philosophy of German Idealism›’) in Husserl’s First Philosophy (Husserl 1956a, 395ff.). Conversely, Husserl was well-read on British empiricism, of which in particular Hume was important to him: Hume’s Treatise on Human Nature is the most heavily annotated book in Husserl’s library, and Husserl, in his transcendental phase, has a very high opinion of Hume (e.g., Husserl 1954, 91; Husserl 1956a, 156–157). Gödel, on the other hand, seems never to have studied the British empiricists that carefully. Robin Rollinger pointed out to us that this means that, via Husserl, Hume had a considerable indirect influence on Gödel. Indeed, Köhler (2002b, 359–360) has drawn attention to the similarity of two passages in Gödel and Hume.

  41. 41.

    [​​[Addition MvA: Husserl wrote to E.P. Welch on June 17/21, 1933 that ‘even the great Idealists after Kant I have come to know only through fragments, hence I have never studied them intensively’ (Spiegelberg 1981, 183) (‘auch die grossen Idealisten nach Kant habe ich nur in Bruchstücken kennen gelernt, also nie eingehend studiert’, Husserl 1994, VI:460).]​​]

  42. 42.

    [​​[Addition MvA: Boehm remarks there that Husserl had read in detail of Kant only the main works, of Fichte only the ‘popular’ writings, of Schelling perhaps nothing, of Hegel some 50 pages.]​​]

  43. 43.

    This draft is a reply to Rota’s review of Husserl’s The Crisis of the European Sciences and Transcendental Phenomenology (Husserl 1954), intended for Scientific American, sent to Gödel by Rota on July 11, 1972. It must have been written somewhere in the period July–September 1972, as Gödel sent the final version (omitting the passages we quote) on September 15, 1972 (Gödel Papers, 2c/141, 012030). Incidentally, that final version differs in letter but not in spirit from Rota’s rendition of it in Rota (2000), a circumstance that Rota hints at by next presenting as a quotation what is really a gloss on the final paragraph of Gödel’s paper from around 1961 (Gödel *1961/?, 374–387).

  44. 44.

    Es bedarf einer Wissenschaft vom Seienden in absolutem Sinn. Diese Wissenschaft, die wir Metaphysik nennen, erwächst aus einer ‘Kritik’ der natürlichen Wissenschaften auf Grund der in allgemeinen Erkenntniskritik gewonnenen Einsicht in das Wesen der Erkenntnis und der Erkenntnisgegenständlichkeit nach ihren verschiedenen Grundgestaltungen, in den Sinn der verschiedenen fundamentalen Korrelationen zwischen Erkenntnis und Erkenntnisgegenständlichkeit. (Husserl 1950b, 23)

  45. 45.

    Prinzipiell entspricht (im Apriori der unbedingten Wesensallgemeinheit) jedem ‘wahrhaft seienden’ Gegenstand die Idee eines möglichen Bewusstseins, in welchem der Gegenstand selbst originär und dabei volkommen adequat erfaßbar ist. Umgekehrt, wenn diese Möglichkeit gewährleistet ist, ist eo ipso der Gegenstand wahrhaft seiend. (Husserl 1950c, 349/Husserl 1976a, 329)

  46. 46.

    Les perfections de Dieu sont celles de nos ames, mais il les possede sans bornes. (Leibniz (1710) 1885, 27)

  47. 47.

    Kein gewöhnlicher ‘Realist’ ist je so realistisch und so concret gewesen als ich, der phänomenologische ‘Idealist’ (ein Wort, das ich übrigens nicht mehr gebrauche). (Husserl 1994, 7:16)

  48. 48.

    Vernunft verweist auf Möglichkeiten der Bewährung, und diese letztlich auf das Evident-Machen und Evident-Haben. (Husserl 1950a, 92)

  49. 49.

    Gödel will have read this in the 1965 edition of Spiegelberg (1983), where it occurs on p. 84. The passage is from a letter from Husserl to Lévy-Bruhl, March 11, 1935: ‘die Methode … durch die ich gegen den schwächlichen Mystizismus und Irrationalismus eine Art Überrationalismus begründen will, der den alten Rationalismus als unzulänglich überschreitet und doch seine innerste Intentionen rechtfertigt’ (Husserl 1994, 7:164).

  50. 50.

    Die Phänomenologie als Eidetik … ist rationalistisch; sie überwindet aber den beschränkten dogmatischen Rationalismus durch den universalsten der auf die transzendentale Subjektivität, auf Ich, Bewußtsein und bewußte Gegenständlichkeit einheitlich bezogenen Wesensforschung. (Husserl 1962, 301)

  51. 51.

    Ohne in allgemeinen Zügen mir über Sinn, Wesen, Methoden, Hauptgesichtspunkte einer Kritik der Vernunft ins Klare zu kommen, ohne einen allgemeinen Entwurf für sie ausgedacht, entworfen, festgestellt und begründet zu haben, kann ich wahr und wahrhaftig nicht leben. (Husserl 1956b, 297)

  52. 52.

    Concerning this, Gödel marked some of the relevant passages in his own copy of the Logical Investigations. This was a 1968 reprint of the second (B1) edition; it had not appeared in the Husserliana series yet. Before 1968 he must have studied a copy of another edition. In his own copy, the footnote on p. 354 to the last line of Sect. 4, is marked by a large exclamation mark on the left, and underlined as follows:

    Die sich in diesem Paragraphen schon aussprechende Opposition gegen die Lehre vom ‘reinen’ Ich billigt der Verf., wie aus den oben zitierten \(\underline{\mathit{Ideen}}\) ersichtlich ist, nicht mehr. (vgl. a.a.O., §57, S. 109; §80, S. 159.) (Husserl 1973c, 542n1) Footnote 53

    Correspondingly, on the preceding page (353),

    Das phänomenologisch reduzierte Ich ist also nichts Eigenartiges, das über den mannigfaltigen Erlebnissen schwebte, sondern es ist einfach mit ihrer eigenen Verknüpfungseinheit identisch. (Husserl 1973c, 542n1) Footnote 54

    is marked by a large question mark in the margin. And a passage in Ideas I is underlined as follows:

    In den ‘Log. Unters.’ vertrat ich in der Frage des reinen Ich eine Skepsis, die ich im Fortschritte meiner Studien nicht festhalten konnte. Die Kritik, die ich gegen Natorps gedankenvolle ‘Einleitung in die Psychologie’ richtete (II1, S. 340f.), ist also in einem Hauptpunkte nicht triftig. (Husserl 1950c, 138/Husserl 1976a, 124) Footnote 55

    On p. 4 of the first four inside pages of his copy of Ideas I, among the notes is one in which Gödel refers to this footnote.

  53. 53.

    The opposition to the doctrine of a ‘pure’ ego, already expressed in this paragraph, is one that the author no longer approves of, as is plain from his \(\underline{\mathit{Ideas}}\) cited above.

  54. 54.

    The phenomenologically reduced ego is therefore nothing peculiar, floating above many experiences: it is simply identical with their own interconnected unity.

  55. 55.

    In the \(\underline{\mathit{Logische}\ \mathit{Untersuchungen}}\) [Logical Investigations] I advocated a skepticism with respect to the question about the pure Ego, but which I could not adhere to asmy studies progressed. The criticism which I directed against Natorp’s thoughtful Einleitung in die Psychologie [Introduction to Psychology] is, as I now see, not well-founded in one of its main contentions. (Husserl 1983, 133)

  56. 56.

    [​​[Addition MvA: Now Toledo 2011, 200.]​​]

  57. 57.

    On the other hand, at one point Gödel said to Wang that ‘Husserl aimed at absolute knowledge, but so far this has not been attained.’ (Wang 1996, 291; see also 169)

  58. 58.

    For an intellectual-psychological biography of Husserl, see Wetz (1995).

  59. 59.

    Ich arbeite, nun schon das zehnte Jahr, mit Aufwand aller Kräfte an einer systematischen Begründung der Phänomenologie, bzw. der phänomenologischen Theorie und Kritik der gesammten Vernunft. Ich glaube, die wesentlichen Schwierigkeiten überwunden zu haben. (Husserl 1994, 5:206)

  60. 60.

    Incidentally, the Paris Lectures and the Cartesian Meditations are not the same work; the latter is a much worked out version of the former. They are, however, published together in Husserliana, Cartesianische Meditationen und Pariser Vorträge (Husserl 1950a), which Gödel owned. Perhaps Gödel mentioned this title to Wang and the ‘und’ got lost in the note-taking.

  61. 61.

    Gödel continues:

    At one point there existed a five hundred page manuscript on this investigation (mentioned in letters to Ingarden, with whom he wished to publish the manuscript). This manuscript has apparently been lost, perhaps when Husserl’s works were taken to Louvain in 1940. It is possible that this and other works were removed.

    (See also Wang 1996, 320.) Gödel has made similar remarks about manuscripts disappearing, e.g., some of Leibniz’, which have sometimes been dismissed as symptoms of a possible mental instability on Gödel’s part. But in this case, Gödel was completely correct, and by way of proof he pointed Sue Toledo (n.d., 9)Footnote 62 to the following statement of Husserl’s former student Roman Ingarden from 1962:

    Thus in 1927 Husserl proposes to me also that I should ‘adjust’ a great bundle of manuscripts (consisting probably of 600–700 sheets of paper) on the original constitution of time, which he had written in Bernau in 1917–1918. He gave me a completely free hand with the editing of the text, his only condition being that the work should be published under our two names. I could not, however, accept his proposition, first of all because I was convinced that Husserl would have done the work much better himself at the time. To tell the truth, I now regret my decision. Judging by what he told me on the context of his study, it was certainly his most profound and perhaps most important work … As it happened, the work has not been edited at all, and what is worse nobody seems to know where the manuscript is. (Ingarden 1962, 157n4)

    Apparently unbeknown to Ingarden, after his declining Husserl’s proposition, the task was accepted by Husserl’s assistant Eugen Fink. However, he hardly worked on it and in 1969 he gave the manuscript to the Husserl Archive in Leuven. It was published only in 2001 (Husserl 2001a).

  62. 62.

    [​​[Addition MvA: Now Toledo (2011, 200).]​​]

  63. 63.

    [​​[Addition MvA: Now Toledo (2011, 200).]​​]

  64. 64.

    [​​[Addition MvA:Now Toledo (2011, 202).]​​]

  65. 65.

     ‘objektive’, in jenem Sinn der für Jedermann daseienden, sich als wie sie ist in intersubjektiver Erkenntnisgemeinschaft ausweisenden. (Husserl 1974, 247)

  66. 66.

    For an account of the later Weyl’s disagreements with Husserl, see Bell (2003).

  67. 67.

    [​​[Correction MvA: The request, dated December 18, 1929, is for Vol. 4, which includes the Dissertatio de arte combinatoria of 1666.]​​]

  68. 68.

    In a letter to Gödel of July 26, 1954 (Gödel Papers, 2c/141, 011919), Nicholas Rescher recalls that as a Princeton graduate student he had noticed that Gödel borrowed most of the books on Leibniz available at the Firestone Library at some point between 1946 and 1948.

  69. 69.

    We are thankful to Arthur Collins for urging us to be explicit about these two contrary tendencies.

  70. 70.

    Mahnke had studied mathematics with Hilbert and philosophy with Husserl in Göttingen from 1902 till 1906. He obtained his Doktorat in 1922 with Husserl in Freiburg, and his Habilitation in Greifswald in 1926. In 1927 he succeeded Heidegger in Marburg, when the latter came to Freiburg to succeed Husserl. In 1939, he died in a car accident. (Cristin and Sakai 2000, 323–325; Husserl 1994, 3:453, 57)

  71. 71.

    Ich selbst bin eigentlich Monadologe. (Husserl 1994, 3:408)

  72. 72.

    Of the literature on this connection, we would in particular like to mention van Breda (1967), Ehrhardt (1967), Cristin (1990) and Cristin and Sakai (2000).

  73. 73.

    [​​[Correction of the translation, MvA: after ‘such an interpretation’, add ‘or a similar one’.]​​]

  74. 74.

    Leibniz meinte in seinem genialen Aperçu einer Monadenlehre: nach seinem letzten wahren Sein reduziere sich alles Seiende auf Monaden … Es könnte am Ende sein, daß eine transzendental-philosophisch begründete Weltbetrachtung gerade eine solche oder ähnliche Interpretation als schlechtsinnige Notwendigkeit forderte. (Husserl 1956a, 71–72)

  75. 75.

    So führt die Phänomenologie auf die von Leibniz in genialem aperçu antizipierte Monadologie. (Husserl 1959, 190) See also Husserl (1956a, 196–197) and Husserl (1973b, 7).

  76. 76.

    Er selbst ist ja durchaus ein Schauer, nur daß leider überall die theoretische Einzelanalyse und Einzelausführung fehlt, ohne die Geschautes eben nicht zur Wissenschaft werden kann. Husserl to Mahnke, January 5, 1917 (Husserl 1994, 3:407–408).

  77. 77.

    Da das monadisch konkrete ego das gesamte wirkliche und potentielle Bewußtseinsleben mit befaßt, so ist es klar, daß das Problem der phänomenologischen Auslegung dieses monadischen ego (das Problem seiner Konstitution für sich selbst) alle konstitutiven Probleme überhaupt in sich befassen muß. In weiterer Folge ergibt sich die Deckung der Phänomenologie dieser Selbstkonstitution mit der Phänomenologie überhaupt. (Husserl 1950a, 102–103)

  78. 78.

    There are differences between Husserl’s interpretation of the monad and Mahnke’s. Husserl’s assistant Eugen Fink wrote a draft of a discussion of these, see Husserl (1994, 3:519–520).

  79. 79.

    Perhaps of relevance for the question whether Husserl ever imagined the possibility of incompleteness as proved, during his lifetime, by Gödel, a fact never known to Husserl, is the following passage in Mahnke’s book from 1917, which Husserl marked in his copy:

    That not all, even rather few, manifolds in the outside world have the property of being definite, is obvious. But also concerning formal mathematics it is still a great question whether its totality is a heap of infinitely many different and unrelated theories of manifolds, or rather can be organised into one big, definite system. The concept of mathematics seems to demand that the latter is the case; yet, a proof is still to be found. (‘Dass nicht alle, ja sogar nur herzlich wenige Mannigfaltigkeiten der wirklichen Welt diese Eigenschaft der Definitheit haben, liegt auf der Hand. Aber auch in der formalen Mathematik ist noch eine grosse Frage, ob ihre Gesamtheit ein beziehungsloses Nebeneinander von unendlich vielen verschiedenen Mannigfaltigkeitslehren ist oder vielmehr selbst in ein einziges, grosses definites System geordnet werden kann. Der Begriff der Mathematik scheint zu erfordern, dass das letztere der Fall ist. Doch steht der Nachweis dafür noch aus’, Mahnke 1917, 32.)

    There has been much discussion whether Gödel’s incompleteness theorems are fatal to Husserl’s philosophy of mathematics as expounded in Formal and Transcendental Logic (Husserl 1974). Cavaillès (Cavaillès 1947, 71ff.) may have been the first to raise that question. However, the surprising thing is that Husserl’s former student Felix Kaufmann did not raise it in 1931. On January 15, 1931, Kaufmann participated in a meeting of the Wiener Kreis where Gödel presented his Incompleteness Theorems. Exchanges between Kaufmann and Gödel on that occasion have been recorded as well (Stadler 1997, 278–280). At that very time, Kaufmann was corresponding with Husserl, reporting on his study of Formal and Transcendental Logic, and on his work on an article ‘Logische Prinzipienfragen in der mathematischen Grundlagenforschung’ (‘Principal questions of logic in foundational research in mathematics’) (Husserl 1994, 4:179–181). If Kaufmann had been aware of the potential problem for Formal and Transcendental Logic, he surely would have told Husserl. For a convincing reply to the charge that the Incompleteness Theorems are fatal to Husserl’s philosophy of mathematics, see Lohmar 1989, Chap. 11.

  80. 80.

    [​​[Addition MvA: Now Toledo (2011, 201).]​​]

  81. 81.

    Cette pensée de moy, qui m’apperçois des objets sensibles, et de ma propre action qui en resulte, adjoute quelque chose aux objets des sens. Penser à quelque couleur et considerer qu’on y pense, ce sont deux pensées tres differentes, autant que la couleur même differe de moy qui y pense. Et comme je conçois que d’autres Estres peuvent aussi avoir le droit de dire moy, ou qu’on pourroit le dire pour eux, c’est par là que je conçois ce qu’on appelle la substance en general, et c’est aussi la consideration de moy même, qui me fournit d’autres notions de metaphysique, comme de cause, effect, action, similitude, etc., et même celles de la Logique et de la Morale. Ainsi on peut dire qu’il n’y a rien dans l’entendement, qui ne soit venu des sens, excepté l’entendement même, ou celuy qui entend. (Leibniz 1875–1890, 6:502)

  82. 82.

    C’est aussi par la connoissance des vérités necessaires et par leurs abstractions que nous sommes élevés aux Actes Reflexifs, qui nous font penser à ce qui s’appelle Moy et a considérer que ceci ou cela est en nous: et c’est ainsi qu’en pensant à nous, nous pensons à l’Etre, à la Substance, au simple et au composé, à l’immateriel et à Dieu même; en concevant que ce qui est borné en nous, est en lui sans bornes. Et ces Actes Reflexifs fournissent les objets principaux de nos raisonnemens. (Théodicée, Préface, 4a.) (Leibniz 1991, 111)

  83. 83.

    van Atten, Horsten, and Rucker, ‘Evolving a mind’, in progress.

  84. 84.

    [​​[Addition MvA: I hope that one day we will finish that paper.]​​]

  85. 85.

    See also the paragraph on p. 189 of Wang 1974, that ends ‘It is my impression that Gödel proposes to answer it by phenomenological considerations’, and Wang’s draft for From Mathematics to Philosophy, ‘II Fassung Further revisions of the chapter on set theory’, p. 3 (Gödel Papers, box 20), where Gödel rewrote a passage as follows: ‘The observations in this and the last paragraph are meant to be the beginning of a descriptive analysis of our in part subconscious thinking process about sets and thereby of the objective ideas we have in mind when we use the term set’ [emphasis ours]. For further discussion of the relation between Husserl’s correlation thesis and the ontology of mathematics, see van Atten (2001) and van Atten (2002).

  86. 86.

    Similarly, Gödel marked, by a stenographical note ‘wichtig’ (‘important’), underlining, and vertical lines in the margin, the paragraph where Husserl reaffirms the noetic-noematic correlation and its universal importance beginning, in the edition that he owned (Husserl 1950c), on p. 330, line 31 and continuing on 331 until line 17 (Husserl 1976a, 311 line 25–312 line 11; 1983, 323 line 26–324 line 10).

  87. 87.

    Føllesdal stresses these in his introduction to Gödel’s paper from around 1961, although he certainly also touches on themes in transcendental phenomenology on p. 369 and 372 (Gödel 1995).

  88. 88.

    In recent years, Richard Tieszen has done much to make these Husserlian themes accessible to those interested in Gödel. See, e.g., Tieszen (2002).

  89. 89.

    See, for example, the account by Conrad-Martius in van Breda and Taminiaux (1959), a book that Gödel knew, as there are reading notes in Gödel (Papers, 9c/22, 050111) (although not to this paper in particular). See also Kuhn et al. (1975).

  90. 90.

    [​​[Addition MvA: Now Toledo (2011, 202).]​​]

  91. 91.

    On p. 237 of Gödel’s copy of the Crisis (Husserl 1954), there are many underlinings in the passage where Husserl describes how already in the 5th and 6th Logical Investigations the problematic of the noetic-noematic correlation comes close to the surface. Husserl therefore concludes: ‘Thus, in that work lie the first, albeit very imperfect, beginnings of “phenomenology”.’ [‘So liegen in diesem Werke in der Tat die ersten, freilich sehr unvollkommenen Anfänge der “Phänomenologie”.’]

  92. 92.

    [​​[Correction of the translation, MvA: insert ‘indeed’.]​​]

  93. 93.

    The conversations Kreisel is here referring to will have been the same ones as those in the background of his letter to Gödel of September 6, 1965 that we mentioned in Sect. 6.3.2.

  94. 94.

    Robert Tragesser suggested to us that Husserl in turn may well have taken Kant’s discussion in the ‘Amphiboly’ section of the Critique of Pure Reason as a model, for example the comparison of Leibniz with Locke on B327.

  95. 95.

    Gegensätze wie die zwischen Rationalismus (Platonismus) und Empirismus, Relativismus und Absolutismus, Subjektivismus und Objektivismus, Ontologismus und Transzendentalismus, Psychologismus und Antipsychologismus, Positivismus und Metaphysik, teleologischer und kausalistischer Weltauffassung. (Husserl 1962, 300)

  96. 96.

    Überall berechtigte Motive, überall aber Halbheiten oder unzulässige Verabsolutierungen von nur relativ und abstraktiv berechtigten Einseitigkeiten. (Husserl 1962, 300)

    Robert Sokolowski has remarked: ‘Husserl acknowledges a debt to Leibniz in regard to mathesis universalis [and much more, as we have seen above], but Leibniz’s hope of reconciling conflicting points of view, in science and politics, may also be at work in phenomenology, with similar deep-seated limitations.’ In a footnote to this passage, he refers to Mahnke (Mahnke 1925) and adds: ‘Probably the greatest weakness is the conviction that agreement of minds pacifies human affairs’ (Sokolowski 1973, 320). At the same time, we are reminded of Borges: ‘The metaphysicians of Tlön … know that a system is naught but the subordination of all the aspects of the universe to one of those aspects – any one of them. (Borges 1998, 74)

  97. 97.

    Note MvA and JK. Concerning this last remark, see our discussion of Gödel’s attitude toward Kant’s idealism in Sect. 6.3.2.

  98. 98.

    [​​[Addition MvA: In the postscript to a recent reprint of Parsons (1995), Parsons refers to this suggestion and comments that ‘their conjecture fits well with what we know about Gödel’s temperament, but I think it likely that he also had not, to his own satisfaction, sufficiently integrated what he was deriving from Husserl with his earlier ideas’ (Parsons 2014, 196). Gödel’s draft remark is rather tentative, and it seems to me that, to make it, one needs not so much to have achieved sufficient integration as to harbour enough hope for it. But I certainly agree with Parsons’ suggestion as such; see Sect. 6.7 of the present chapter.]​​]

  99. 99.

    Warren Goldfarb (Gödel 1995, 324) thinks that Gödel was overestimating the extent to which positivist dogmas remained orthodoxy in 1959, but even so it is not likely that a phenomenological view would have been welcomed by philosophers of mathematics at the time.

  100. 100.

    Eberhard defends ‘nicht sinnliche Anschauung’ (‘non-sensuous intuition’). That he means ‘intellektuelle Anschauung’ (‘intellectual intuition’) is clear from his explanation (Kant (1790) 1998, Stück III, Nr.2, S. 281–282). See also Gawlina (1996, 193–194).

  101. 101.

    Über eine Entdeckung nach der alle neue Kritik der reinen Vernunft durch eine ältere entbehrlich gemacht werden soll (Kant (1790) 1998).

  102. 102.

    Husserl never discussed Eberhard in his manuscripts (including his published work), although he has read at least Kant’s side of the polemic, as is witnessed by his pencil lines and marginal comments in one of his editions of Kant’s writings. We are grateful to Robin Rollinger at the Husserl Archive in Leuven for investigating this for us.

  103. 103.

    [​​[Addition MvA: I have now come to think that, on the one hand, a foundation of classical mathematics in which intuition of the objects is central, such as Gödel’s, is indeed forced to take recourse to Kantian ideas also in that (non-physical) context; but that, on the other hand, Husserl’s doctrine of purely categorial objects as developed after Ideas I precludes doing just that. See van Atten (2010, 78–79) for further discussion (Sect. 12.3 of the reprint in this volume).]​​]

  104. 104.

    Aber als ‘Idee’ (im Kantischen Sinn) ist gleichwohl die volkommene Gegebenheit vorgezeichnet. (Husserl 1950c, 351/Husserl 1976a, 331)

  105. 105.

    Note MvA and JK. The ‘epistemic essence’ is like the sense but includes aspects of evidence.

  106. 106.

    Wo die gebende Anschauung eine transzendierende ist, da kann das Gegenständliche nicht zu adäquater Gegebenheit kommen; gegeben sein kann nur die Idee eines solchen Gegenständlichen, bzw. seines Sinnes und seines ‘erkenntnismäßigen Wesens’ und damit eine apriorische Regel für die eben gesetzmäßigen Unendlichkeiten inadäquater Erfahrungen. (Husserl 1950c, 352/Husserl 1976a, 332)

  107. 107.

    Jede Seinsart, wir haben das schon mehrfach betonen müssen, hat wesensmäßig ihre Gegebenheitsweisen und damit ihre Weisen der Erkenntnismethode. Wesentliche Eigentümlichkeiten derselben als Mängel behandeln, sie gar in der Art zufälliger, faktischer Mängel ‘unserer menschlichen’ Erkenntnis anrechnen, ist Widersinn. (Husserl 1950c, 191/1976a, 176)

  108. 108.

    A different question is whether Husserl’s intended non-revisionism is indeed forced by his philosophical premises; for an argument that it is not, see van Atten (2002).

  109. 109.

    As far as the integration of phenomenology with monadology is concerned, one finds optimism about it in the essays by Mahnke (1917) and Cristin (1990), and those by Cristin and Poser in Cristin and Sakai (2000) and Mertens (2000), on the other hand, has argued that a phenomenological monadology is impossible in principle.

  110. 110.

    Kreisel complains about this in his letter to Gödel of April 12, 1969 (Gödel Papers, 2a/92, 011266).

  111. 111.

    [​​[Addition MvA: But now see van Atten (2014) (Sect. 11.3.5.6 in this volume).]​​]

  112. 112.

    Note MvA and JK. Of Church’s manuscript for his talk at the International Congress of Mathematicians, Moscow 1966, published in its proceedings in 1968 (Church 1968).

  113. 113.

    [​​[Addition MvA: In the context of Husserl’s transcendental idealism, the role of these other criteria is, and can only be, to inform provisional choices, until intuitiveness is arrived at or, in a higher-order intuition, seen to be unattainable. See also Chap. 12, Sect. 12.3 in this volume.]​​]

  114. 114.

    Combined with Gödel’s conviction, expressed in the draft letter to Rota quoted at the end of Sect. 6.6.3, that Husserl was not a revisionist in mathematics, and moreover with Gödel’s continued attempts at defending realism in his conversations with Wang, this is our reason not to believe that, rather than a phenomenologically grounded realism, the 1972 version of the Dialectica paper should be considered Gödel’s final philosophical view, a possibility that Sol Feferman suggested to us. We think that in that paper, Gödel is showing his talent for penetrating a philosophical position that is not his own, as he had done before in his papers on Kant.

References

  • van Atten, M. (2001). Gödel, mathematics, and possible worlds. Axiomathes, 12(3–4), 355–363. Included in this volume as Chap. 7.

    Google Scholar 

  • van Atten, M. (2002). Why Husserl should have been a strong revisionist in mathematics. Husserl Studies, 18(1), 1–18.

    Article  Google Scholar 

  • van Atten, M. (2010). Construction and constitution in mathematics. The New Yearbook for Phenomenology and Phenomenological Philosophy, 10, 43–90. Included in this volume as Chap. 12.

    Google Scholar 

  • van Atten, M. (2014). Gödel and intuitionism. In Dubucs and Bourdeau (2014, pp. 169–214). Included in this volume as Chap. 11.

    Google Scholar 

  • van Atten, M., & Kennedy, J. (2003). On the philosophical development of Kurt Gödel. Bulletin of Symbolic Logic, 9(4), 425–476. Included in this volume as Chap. 6.

    Google Scholar 

  • Becker, O. (1930). Zur Logik der Modalitäten. Jahrbuch für Philosophie und phänomenologische Forschung, 11, 497–548.

    Google Scholar 

  • Beiser, F. (1987). The fate of reason: German philosophy from Kant to Fichte. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Beiser, F. (Ed.). (1992). The Cambridge companion to Hegel. Cambridge: Cambridge University Press.

    Google Scholar 

  • Beiser, F. (2002). German Idealism: The struggle against subjectivism, 1781–1801. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Bell, J. (2003). Hermann Weyl’s later philosophical views: His divergence from Husserl. In Feist (2003, pp. 173–185).

    Google Scholar 

  • Benacerraf, P. (1973). Mathematical truth. Journal of Philosophy, 70, 661–679.

    Article  Google Scholar 

  • Benacerraf, P., & Putnam, H. (Eds.). (1964). Philosophy of mathematics: Selected readings (1st ed.). Cambridge: Cambridge University Press.

    Google Scholar 

  • Benacerraf, P., & Putnam, H. (Eds.). (1983). Philosophy of mathematics: Selected readings (2nd ed.). Cambridge: Cambridge University Press.

    Google Scholar 

  • Bergamini, D., & the editors of Life. (1963). Mathematics. New York: Time.

    Google Scholar 

  • Boehm, R. (1968). Vom Gesichtspunkt der Phänomenologie. Den Haag: Martinus Nijhoff.

    Book  Google Scholar 

  • Borges, J. L. (1998). Collected fictions. London: Penguin.

    Google Scholar 

  • Brainard, M. (2002). Belief and its neutralization: Husserl’s system of phenomenology in Ideas I. Albany: State University of New York Press.

    Google Scholar 

  • van Breda, H. L. (1967). Leibniz’ Einfluß auf das Denken Husserls. In Müller and Totok (1967, pp. 125–145).

    Google Scholar 

  • van Breda, H. L., & Taminiaux, J. (Eds.). (1959). Edmund Husserl: 1859–1959. Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Brouwer, L. E. J. (1975). In A. Heyting (Ed.), Philosophy and foundations of mathematics (Vol. 1 of Collected works). Amsterdam: North-Holland.

    Google Scholar 

  • Buldt, B., Köhler, E., Stöltzner, M., Weibel, P., Klein, C., & DePauli-Schimanovich-Göttig, W. (Eds.). (2002). Kompendium zum Werk (Volume 2 of Kurt Gödel. Wahrheit und Beweisbarkeit). Wien: öbv & hpt.

    Google Scholar 

  • Carr, D., & Casey, E. (Eds.). (1973). Explorations in phenomenology. Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Casula, M. (1975). Die Lehre von der prästabilierten Harmonie in ihrer Entwickelung von Leibniz bis A.G. Baumgarten. Studia Leibnitiana, Supplementa, 14, 397–414.

    Google Scholar 

  • Cavaillès, J. (1947). Sur la logique et la théorie de la science. Paris: Presses Universitaires de France.

    Google Scholar 

  • Church, A. (1968). Paul J. Cohen and the continuum problem. In Petrovsky (1968, pp. 15–20).

    Google Scholar 

  • Cristin, R. (1990). Phänomenologie und Monadologie: Husserl und Leibniz. Studia Leibnitiana, 22(2), 163–174.

    Google Scholar 

  • Cristin, R., & Sakai, K. (Eds.). (2000). Phänomenologie und Leibniz. Freiburg: Alber.

    Google Scholar 

  • Dubucs, J., & Bourdeau, M. (Eds.). (2014). Constructivity and computability in historical and philosophical perspective. Dordrecht: Springer.

    Google Scholar 

  • Ehrhardt, W. (1967). Die Leibniz-Rezeption in der Phänomenologie Husserls. In Müller and Totok (1967, pp. 146–155).

    Google Scholar 

  • Feist, R. (Ed.). (2003). Husserl and the sciences. Ottawa: University of Ottawa Press.

    Google Scholar 

  • Gawlina, M. (1996). Das Medusenhaupt der Kritik: Die Kontroverse zwischen Immanuel Kant und Johann August Eberhard. Berlin: Walter de Gruyter.

    Google Scholar 

  • Gödel, K. (Papers). Firestone library, Princeton. Most citations are of the form ‘Gödel Papers box/folder, item number’.

    Google Scholar 

  • Gödel, K. (1931e). Review of “Zur Logik der Modalitäten”, by Oskar Becker. Monatshefte für Mathematik und Physik, 38, 5–6. Reprinted, with original page numbers in the margin and an English translation, in Gödel (1986, pp. 216–217).

    Google Scholar 

  • Gödel, K. (1932f). Review of “Die intuitionistische Grundlegung der Mathematik”, by Arend Heyting. Zentralblatt für Mathematik und ihre Grenzgebiete, 2, 321–322. Reprinted, with original page numbers in the margin and an English translation, in Gödel (1986, pp. 246–247).

    Google Scholar 

  • Gödel, K. (*1933o). The present situation in the foundations of mathematics. Lecture, published in Gödel (1995, pp. 45–53).

    Google Scholar 

  • Gödel, K. (1944). Russell’s mathematical logic. In Schilpp (1944, pp. 123–153). Reprinted, with original page numbers in the margin, in Gödel (1990, pp. 119–141).

    Google Scholar 

  • Gödel, K. (*1946/9-C1). Some observations about the relationship between theory of relativity and Kantian philosophy. Lecture, published in Gödel (1995, pp. 247–259).

    Google Scholar 

  • Gödel, K. (1947). What is Cantor’s continuum problem? American Mathematical Monthly, 54, 515–525. Reprinted, with original page numbers in the margin, in Gödel (1990, pp. 176–187).

    Google Scholar 

  • Gödel, K. (*1951). Some basic theorems on the foundations of mathematics and their implications. Lecture, published in Gödel (1995, pp. 304–323).

    Google Scholar 

  • Gödel, K. (*1961/?) The modern development of the foundations of mathematics in the light of philosophy. Lecture draft in German, published, with an English translation, in Gödel (1995, pp. 374–387). The English title is Gödel’s.

    Google Scholar 

  • Gödel, K. (1964). What is Cantor’s continuum problem? In Benacerraf and Putnam (1964, pp. 258–273). Revised and expanded version of Gödel 1947. Reprinted, with original page numbers in the margin, in Gödel (1990, pp. 254–270).

    Google Scholar 

  • Gödel, K. (1986). Publications 1929–1936 (Collected works, Vol. 1; S. Feferman, J. Dawson, Jr., S. Kleene, G. Moore, R. Solovay, & J. van Heijenoort, Eds.). Oxford: Oxford University Press.

    Google Scholar 

  • Gödel, K. (1990). Publications 1938–1974 (Collected works, Vol. 2; S. Feferman, J. Dawson, Jr., S. Kleene, G. Moore, R. Solovay, & J. van Heijenoort, Eds.). Oxford: Oxford University Press.

    Google Scholar 

  • Gödel, K. (1995). Unpublished essays and lectures (Collected works, Vol. 3; S. Feferman, J. Dawson, Jr., S. Kleene, G. Moore, R. Solovay, & J. van Heijenoort, Eds.). Oxford: Oxford University Press.

    Google Scholar 

  • Gödel, K. (2003). Correspondence A–G (Collected works, Vol. 4; S. Feferman, J. Dawson, Jr., W. Goldfarb, C. Parsons, & W. Sieg, Eds.). Oxford: Oxford University Press.

    Google Scholar 

  • Gödel, K. (2003a). Correspondence H–Z (Collected works, Vol. 5; S. Feferman, J. Dawson, Jr., W. Goldfarb, C. Parsons, & W. Sieg, Eds.). Oxford: Oxford University Press.

    Google Scholar 

  • Hegel, G. F. W. (1830) 1906. Encyklopädie der philosophischen Wissenschaften im Grundrisse (G. Bolland, Ed.). Leiden: A.H. Adriani.

    Google Scholar 

  • Heimsoeth, H. (1916). Leibniz’ Weltanschauung als Ursprung seiner Gedankenwelt. Kant-Studien, 21, 365–395.

    Google Scholar 

  • Heimsoeth, H. (1934). Die sechs großen Themen der abendländischen Metaphysik (2nd ed.). Berlin: Junker und Dünnhaupt.

    Google Scholar 

  • Heyting, A. (1931). Die intuitionistische Grundlegung der Mathematik. Erkenntnis, 2, 106–115. English translation in Benacerraf and Putnam (1983, pp. 52–61).

    Google Scholar 

  • Hintikka, J. (1998). On Gödel’s philosophical assumptions. Synthese, 114, 13–23.

    Article  Google Scholar 

  • Husserl, E. (1911) 1981. Philosophie als strenge Wissenschaft (W. Szilasi, Ed.). Frankfurt am Main: Vittorio Klostermann. Originally in Logos, 1, 289–341.

    Google Scholar 

  • Husserl, E. (1928). Vorlesungen zur Phänomenologie des inneren Zeitbewußtseins (Jahrbuch für Philosophie und phänomenologische Forschung, 9, pp. 367–498). Halle: Max Niemeyer.

    Google Scholar 

  • Husserl, E. (1950a). Cartesianische Meditationen und Pariser Vorträge (Husserliana, Vol. 1; S. Strasser, Ed.). Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Husserl, E. (1950b). Die Idee der Phanomenologie: Fünf Vorlesungen (Husserliana, Vol. 2; W. Biemel, Ed.). Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Husserl, E. (1950c). Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie: Erstes Buch (Husserliana, Vol. 3; M. Biemel, Ed.). Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Husserl, E. (1954). Die Krisis der europäischen Wissenschaften und die transzendentale Phänomenologie (Husserliana, Vol. 6; W. Biemel, Ed.). Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Husserl, E. (1956a). Erste Philosophie (1923/1924): Erster Teil: Kritische Ideengeschichte (R. Boehm, Ed., Husserliana, Vol. 7). Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Husserl, E. (1956b). Persönliche Aufzeichnungen (W. Biemel, Ed.). Philosophy and Phenomenological Research, 16(3), 293–302.

    Article  Google Scholar 

  • Husserl, E. (1959). Erste Philosophie (1923/1924): Zweiter Teil: Theorie der phänomenologischen Reduktion (Husserliana, Vol. 8; R. Boehm, Ed.). Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Husserl, E. (1962). Phänomenologische Psychologie (Husserliana, Vol. 9; W. Biemel, Ed.). Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Husserl, E. (1973b). Zur Phänomenologie der Intersubjektivität: Dritter Teil (1929–1935) (Husserliana, Vol. 15; I. Kern, Ed.). Den Haag: Martinus Nijhoff.

    Book  Google Scholar 

  • Husserl, E. (1973c). Logical investigations (2nd ed.; J. Findlay, Trans.). London: Routledge/Kegan Paul.

    Google Scholar 

  • Husserl, E. (1973d). Cartesian meditations (D. Cairns, Trans.). Den Haag: Martinus Nijhoff.

    Book  Google Scholar 

  • Husserl, E. (1974). Formale und transzendentale Logik (Husserliana, Vol. 17; P. Janssen, Ed.). Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Husserl, E. (1976a). Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie: Erstes Buch. 1. Halbband: Text der 1.–3. Auflage (Husserliana, Vol. 3/1; K. Schuhmann, Ed.). Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Husserl, E. (1983). Ideas pertaining to a pure phenomenology and to a phenomenological philosophy: First book: General introduction to phenomenology (Edmund Husserl collected works, Vol. 2; F. Kersten, Trans.). Dordrecht: Kluwer.

    Google Scholar 

  • Husserl, E. (1984b). Logische Untersuchungen: Zweiter Band, 2. Teil (Husserliana, Vol. 19/2; U. Panzer, Ed.). Den Haag: Martinus Nijhoff.

    Book  Google Scholar 

  • Husserl, E. (1987). Aufsätze und Vorträge (1911–1921) (Husserliana, Vol. 25; T. Nenon & H. Sepp, Eds.). Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Husserl, E. (1994). Briefwechsel (Husserliana Dokumente, Vols 3/1–3/10; K. Schuhmann & E. Schuhmann, Eds.). Dordrecht: Kluwer. Cited according to volume and page(s).

    Google Scholar 

  • Husserl, E. (1995b). Fichte’s ideal of humanity (three lectures) (J. Hart, Trans.). Husserl Studies, 12, 111–133.

    Google Scholar 

  • Husserl, E. (1999). The idea of phenomenology (Edmund Husserl collected works, Vol. 8; L. Hardy, Trans.). Dordrecht: Kluwer.

    Google Scholar 

  • Husserl, E. (2001a). Logical investigations (2 vols; J. Findlay, Trans.; D. Moran, Ed.). London: Routledge.

    Google Scholar 

  • Husserl, E. (2002a). Logische Untersuchungen: Ergänzungsband. Erster Teil (Husserliana, Vol. 20/1; U. Melle, Ed.). Dordrecht: Kluwer.

    Book  Google Scholar 

  • Ingarden, R. (1962). Edith Stein on her activity as an assistant of Edmund Husserl. Philosophy and Phenomenological Research, 23, 155–175.

    Article  Google Scholar 

  • Kant, I. (1781–1787a) 1965a. Critique of pure reason (N. K. Smith, Trans.). New York: St Martin’s Press.

    Google Scholar 

  • Kant, I. (1781–1787b) 1996. Kritik der reinen Vernunft (W. Weischedel, Ed.). Frankfurt am Main: Suhrkamp.

    Google Scholar 

  • Kant, I. (1790) 1998. Der Streit mit Johann August Eberhard (M. Lauschke, & M. Zahn, Ed.). Hamburg: Meiner.

    Google Scholar 

  • Kennedy, J., & Kossak, R. (Eds.). (2011). Set theory, arithmetic and foundations of mathematics: Theorems, philosophies (Lecture Notes in Logic, Vol. 36). Cambridge: Cambridge University Press.

    Google Scholar 

  • Kern, I. (1964). Husserl und Kant. Den Haag: Martinus Nijhoff.

    Book  Google Scholar 

  • Kockelmans, J. (1994). Edmund Husserl’s phenomenology. West Lafayette: Purdue University Press.

    Google Scholar 

  • Köhler, E. (2002a). Gödel und der Wiener Kreis. In Buldt et al. (2002, pp. 83–108).

    Google Scholar 

  • Köhler, E. (2002b). Gödel’s Platonismus. In Buldt et al. (2002, pp. 341–386).

    Google Scholar 

  • Köhler, E., Weibel, P., Stöltzner, M., Buldt, B., Klein, C., & DePauli-Schimanovich-Göttig, W. (Eds.). (2002). Dokumente und historische Analysen (Volume 1 of Kurt Gödel, Wahrheit und Beweisbarkeit). Wien: öbv & hpt.

    Google Scholar 

  • Kreisel, G. (1965). Mathematical logic. In Saaty (1965, pp. 95–195).

    Google Scholar 

  • Kreisel, G. (1967). Mathematical logic: What has it done for the philosophy of mathematics?” In Schoenman (1967, pp. 201–272).

    Google Scholar 

  • Kreisel, G. (1980). Kurt Gödel: 28 April 1906–14 January 1978. Biographical Memoirs of Fellows of the Royal Society, 26, 149–224.

    Article  Google Scholar 

  • Kuhn, H., Avé-Lallemant, E., & Gladiator, R. (Eds.). (1975). Die Münchener Phänomenologie. Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Leibniz, G. W. (1710) 1885. Essais de theodicée sur la bonté de Dieu, la liberté de l’homme et l’origine du mal. In Leibniz (1875–1890, Vol. 6, pp. 21–375).

    Google Scholar 

  • Leibniz, G. W. (1875–1890). Die philosophischen Schriften von Gottfried Wilhelm Leibniz (7 vols; C. Gerhardt, Ed.). Berlin: Weidmann. Cited according to volume and page(s).

    Google Scholar 

  • Leibniz, G. W. (1989). Philosophical Essays (R. Ariew & D. Garber, Trans., Eds.). Indianapolis: Hackett.

    Google Scholar 

  • Leibniz, G. W. (1991). G.W. Leibniz’s Monadology: An edition for students (N. Rescher, Trans., Ed.). Pittsburgh: University of Pittsburgh Press.

    Google Scholar 

  • Lohmar, D. (1989). Phänomenologie der Mathematik: Elemente einer phänomenologischen Aufklärung der mathematischen Erkenntnis nach Husserl. Dordrecht: Kluwer.

    Book  Google Scholar 

  • Maddy, P. (1990). Realism in mathematics. Oxford: Clarendon Press.

    Google Scholar 

  • Mahnke, D. (1917). Eine neue Monadologie (Vol. 39). Kantstudien Ergänzungsheft. Berlin: Reuther & Reichard.

    Google Scholar 

  • Mahnke, D. (1925). Leibnizens Synthese von Universalmathematik und Individualmetaphysik. Pt. 1. Jahrbuch für Philosophie und phänomenologische Forschung, 7, 304–611.

    Google Scholar 

  • Menger, K. (1981). Erinnerungen an Kurt Gödel. Typescript, first published in Köhler et al. (2002, pp. 63–81).

    Google Scholar 

  • Mertens, K. (2000). Husserls Phänomenologie der Monade: Bemerkungen zu Husserls Auseinandersetzung mit Leibniz. Husserl Studies, 17, 1–20.

    Article  Google Scholar 

  • Müller, K., & Totok, W. (Eds.). (1967). Akten des Internationalen Leibniz-Kongresses (14.–19. Nov. 1966) (Studia Leibnitiana, Supplementa, Vol. 1). Wiesbaden: Steiner.

    Google Scholar 

  • Parsons, C. (1995). Platonism and mathematical intuition in Kurt Gödel’s thought. Bulletin of Symbolic Logic, 1(1), 44–74.

    Article  Google Scholar 

  • Parsons, C. (2014). Philosophy of mathematics in the twentieth century: Selected essays. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Petrovsky, I. (Ed.). (1968). Proceedings of the international congress of mathematicians (Moscow 1966). Moscow: Mir.

    Google Scholar 

  • Renouvier, C., & Prat, L. (1899). La nouvelle monadologie. Paris: Colin.

    Google Scholar 

  • Ritter, J. (Ed.). (1971). Historisches Wörterbuch der Philosophie (Vol. 1: A–C). Basel: Schwabe.

    Google Scholar 

  • Rota, G. -C. (2000). Ten remarks on Husserl and phenomenology. In Wiegand (2000, pp. 89–97).

    Google Scholar 

  • Saaty, T. (Ed.). (1965). Lectures on modern mathematics (Vol. 3). New York: Wiley.

    Google Scholar 

  • Saaty, T., & Weyl, F. (Eds.). (1969). The spirit and uses of the mathematical sciences. New York: McGraw-Hill.

    Google Scholar 

  • Schilpp, P. A. (Ed.). (1944). The philosophy of Bertrand Russell (The Library of Living Philosophers, Vol. 5). Evanston: Nortwestern University Press. 3rd ed., New York: Tudor, 1951.

    Google Scholar 

  • Schimanovich-Galidescu, M. -E. (2002). Archivmaterial zu Gödels Wiener Zeit, 1924–1940. In Köhler et al. (2002, pp. 135–147). Wien.

    Google Scholar 

  • Schlick, M. (1925). Allgemeine Erkenntnislehre (2nd ed.). Berlin: Springer.

    Book  Google Scholar 

  • Schoenman, R. (Ed.). (1967). Bertrand Russell: Philosopher of the century. London: George Allen/Unwin.

    Google Scholar 

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

    Book  Google Scholar 

  • Schutz, A. (1966). Collected papers (I. Schutz, Ed., Vol. 3). Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Shell-Gellasch, A. (2003). Reflections of my adviser: Stories of mathematics and mathematicians. Mathematical Intelligencer, 25(1), 35–41.

    Article  Google Scholar 

  • Sokolowski, R. (1973). Logic and mathematics in Husserl’s Formal and transcendental logic. In Carr and Casey (1973, pp. 306–327).

    Google Scholar 

  • Sokolowski, R. (1996). Thoughts on phenomenology and skepticism. In Wachterhauser (1996, pp. 43–51).

    Google Scholar 

  • Spiegelberg, H. (1981). The context of the phenomenological movement. Den Haag: Martinus Nijhoff.

    Book  Google Scholar 

  • Spiegelberg, H. (1983). The phenomenological movement (3rd ed., with the collaboration of K. Schuhmann). Dordrecht: Kluwer.

    Google Scholar 

  • Stadler, F. (1997). Studien zum Wiener Kreis. Frankfurt: Suhrkamp.

    Google Scholar 

  • Tait, W. (1986). Truth and proof: The Platonism of mathematics. Synthese, 69, 341–70.

    Article  Google Scholar 

  • Tieszen, R. (1998). Kurt Gödel’s path from the incompleteness theorems (1931) to phenomenology (1961). Bulletin of Symbolic Logic, 4(2), 181–203.

    Article  Google Scholar 

  • Tieszen, R. (2002). Gödel and the intuition of concepts. Synthese, 133(3), 363–391.

    Article  Google Scholar 

  • Toledo, S. n.d. Notes on conversations with Gödel, 1972–1975. Now published as Toledo 2011.

    Google Scholar 

  • Toledo, S. (2011). Sue Toledo’s notes of her conversations with Gödel in 1972–5. In Kennedy and Kossak (2011, pp. 200–207).

    Google Scholar 

  • Tragesser, R. (1973). On the phenomenological foundations of mathematics. In Carr and Casey (1973, pp. 285–298).

    Google Scholar 

  • Tragesser, R. (1977). Phenomenology and logic. Ithaca: Cornell University Press.

    Google Scholar 

  • Wachterhauser, B. (Ed.). (1996). Phenomenology and skepticism: Essays in honour of James M. Edie. Evanston: Northwestern University Press.

    Google Scholar 

  • Wang, H. (1974). From mathematics to philosophy. London: Routledge/Kegan Paul.

    Google Scholar 

  • Wang, H. (1987). Reflections on Kurt Gödel. Cambridge, MA: MIT.

    Google Scholar 

  • Wang, H. (1996). A logical journey: From Gödel to philosophy. Cambridge, MA: MIT.

    Google Scholar 

  • Wartenberg, T. (1992). Hegel’s idealism: The logic of conceptuality. In Beiser (1992, pp. 102–129).

    Google Scholar 

  • Wetz, F. (1995). Edmund Husserl. Frankfurt: Campus.

    Google Scholar 

  • Weyl, H. (1918). Das Kontinuum: Kritische Untersuchungen über die Grundlagen der Analysis. Leipzig: Veit.

    Google Scholar 

  • Weyl, H. (1955). Erkenntnis und Besinnung: Ein Lebensrückblick. Studia Philosophica, 15, 153–171.

    Google Scholar 

  • Weyl, H. (1969). Insight and reflection. In Saaty and Weyl (1969, pp. 281–301). Translation of Weyl 1955.

    Google Scholar 

  • Wiegand, O. (Ed.) (2000). Phenomenology on Kant, German Idealism, hermeneutics and logic. Dordrecht: Kluwer.

    Google Scholar 

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Acknowledgements

We are grateful to the staff of the Department of Rare Books and Special Collections at the Firestone Library of Princeton University, and to Marcia Tucker of the Library of the Institute for Advanced Study, for facilitating our research, and overall for ensuring such a pleasant stay in the archive; also, we are grateful again to Marcia Tucker and to Phillip Griffiths, Director of the Institute for Advanced Study, for making it possible for private scholars and universities to obtain a microfilm copy of the Gödel Nachlaß, and to the Institute for Advanced Study which kindly granted permission to quote from Gödel’s Nachlaß.

We would also like to express our gratitude to the following people: Mic Detlefsen, for a long conversation on Hao Wang; Markku Roinila, for help on Leibniz; Robin Rollinger, for checking material in the Husserl Archive, for translating from Husserl’s shorthand, and for discussion of idealism; Sue Toledo, for sharing her notes on her conversations with Gödel and for permitting us to quote from them; Robert Tragesser, for his information about Kreisel, discussion, and useful comments; Michel Bourdeau, Arthur Collins, Nico Krijn, Per Martin-Löf, Charles Parsons, Richard Tieszen, Jouko Väänänen, Palle Yourgrau, and Norma Yunez-Naude, for discussion and helpful comments.

We are thankful to Aki Kanamori for his editorial corrections and suggestions.

An early lecture version of this paper was presented in Helsinki, May 2002; a later one at MIT, Berkeley, Stanford, and Leuven, March 2003, and at the first meeting of the Nordic Society for Phenomenology, Helsinki, April 2003. We thank the organisers for giving us these opportunities, and the audiences for their questions and comments.

Mark van Atten wishes to thank the Department of Mathematics at Helsinki University for supporting four visits to Helsinki, between November 2001 and January 2003; the Fund for Scientific Research-Flanders (Belgium) for a grant to visit Princeton; Bas van Fraassen for his invitation to Princeton.

Added to this reprint. William Howard kindly granted permission to quote from the reminiscences he generously shared with me.

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  1. Sciences, Normes, Décision (CNRS/Paris IV), CNRS, Paris, France

    Mark van Atten

  2. Department of Mathematics and Statistics, University of Helsinki and Helsinki Collegium of Advanced Studies, University of Helsinki, Helsinki, Finland

    Juliette Kennedy

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Dedicated to the memory of Karl Schuhmann (1941–2003)

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van Atten, M., Kennedy, J. (2015). On the Philosophical Development of Kurt Gödel. In: Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Logic, Epistemology, and the Unity of Science, vol 35. Springer, Cham. https://doi.org/10.1007/978-3-319-10031-9_6

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