experience and infinity in kant and husserl

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EXPERIENCE AND INFINITY IN KANT AND HUSSERLAuthor(s): László TengelyiSource: Tijdschrift voor Filosofie, 67ste Jaarg., Nr. 3 (DERDE KWARTAAL 2005), pp. 479-500Published by: Peeters Publishers/Tijdschrift voor FilosofieStable URL: http://www.jstor.org/stable/40889889 .

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Tijdschrifi voor Filosofie, 68/2005, p. 479-500

EXPERIENCE AND INFINITY IN KANT AND HUSSERL1

by László Tengelyi (Wuppertal)

Kants Copernican revolution is often considered as a turning towards human finitude. Heidegger was the first to interpret Kant this way, famously asserting that the Critique of Pure Reason raises, above all "the question of the finitude in human being".2 It is, however, obvious that the idea of infinity plays an equally important role in the critical philosophy as well. Cassirer repeatedly called attention to this fact in his debate with Heidegger in Davos.3 But Heidegger himself saw that the idea of infinity was implied in the analysis of human finitude. Yet it is not easy to see how precisely, in Kant, the perception of finitude and the idea of infinity belong together.

We may find an answer to this question if we consider the relationship between experience and infinity in the doctrine of the antinomy of pure reason. We shall see that Kant holds infinity to be a mere idea, which, however, has an indispensable regulative function in experience.

László TENGELYI, born in 1954 in Budapest, Hungary, is Professor of Philosophy at the Bergische Universität Wuppertal in Germany. He has recently published a book with the title The Wild Region of Life-History in Northwestern University Press.

1 I would like to express my special thanks to Professor Géza Kállay for linguistic corrections and stylistic suggestions. 2 M. HEIDEGGER, Kant und das Problem der Metaphysik, Frankfurt am Main, V. Klostermann, 1973 (19291), P. 211.

3 Ibid., p. 247-250.



480 LászlóTENGELYI

It will be instructive to compare Kant at this point with Husserl, who, drawing upon the notion of regulative principle elaborated in the Critique of Pure Reason, defines the concept of a thing as an "Idea in a Kantian sense". In spite of the common notion of a regulative idea, the difference between the two thinkers remains substantial: Kant puts his own conception in the service of an attempt to justify his distinction between the 'thing in itself and 'appearance'; Husserl, on the contrary, conceives of things as Ideas in a Kantian sense precisely in order to overcome this opposition. How can the common notion of a regulative idea serve for two purposes which are so different from, or even opposed to, each other? The following considerations are designed to give an answer to this question. We may assume that the difference between the two philosophers arises from two different notions of infinity: whereas Kant has a potential infinity in view, rejecting for principal reasons any idea of an infinity actually existing, Husserl, who had first been the as- sistant of Karl Weierstrass in Berlin and became later a colleague of Georg Cantor in Halle, relies upon a scientifically established form of actual, but nevertheless open infinity.

I. Infinity as a Regulative Principle of Experience in Kant

In the Critique of Pure Reason the point of departure for Kant is that although infinity falls outside of the realm of possible experience, it cannot be totally divorced from the process of experience. In contra- distinction with other ideas that point to experientially unavailable objects like mind or God, the idea of infinity cannot entirely be separated from experience (from the phenomena) because infinity is to

designate the unconditional whole, the absolute totality, which is con- stantly sought for in the synthesis of phenomena, and, thus, of experience. Kant calls such an idea a 'cosmical concept' (Weltbegriffi, because it underlies the very notion of the world-whole.4 In a word, then,

4 1. KANT, Kritik der reinen Vernunft (hereafter abridged as "Kr Ar. VT), A 407; in English: I. KANT,

Critique of Pure Reason, tr. by N. KEMP SMITH, New York, St Martins Press, 1965 (first edition:



EXPERIENCE AND INFINITY IN KANT AND HUSSERL 48 1

infinity is considered as a cosmical concept in the Critique of Pure Reason.

In the doctrine of antinomies, however, the term world' is provided with two different meanings. In its broader sense this expression indeed signifies the unconditional whole or absolute totality of experience. Kant expressively says that "it is just the explication of this very whole that is demanded in the transcendental problems of reason", as they arise in the doctrine of antinomies.5 In its narrower sense, the term world' is opposed to 'nature'. The word 'nature' is taken to designate the universe as "a dynamic whole" permeated with causal relationships.6 The distinction between 'world' and 'nature' corresponds to the dual- ity of mathematical and dynamical categories. The term 'world' refers to the mathematical whole of experience; the term 'nature', on the contrary, refers to its dynamic totality.

The reader of the doctrine of antinomies may first have the impression that 'infinity', together with its opposite, 'finitude', is a possible feature of the 'world' only in so far as this term is taken in its narrower sense. What is infinity, indeed, if not a quantitative, i. e. mathematical characteristic of the absolute whole of experience? If this impression were correct, then infinity would characterize the universe only as far as it is localized in space and time. From this there would only be one more step to the conclusion that, for Kant, infinity rests on intuitive bearers. This would already be true even if only space and time were taken into account. If the relationship between the idea of infinity and the physical universe were equally reflected upon, one would be tempted to speak of an empirical substratum of infinity - as if the question could be decided simply by an inquiry into physical reality.

All this is, however, a mere appearance. In reality, Kant is far from being simply concerned with space and time, or even with the physical

London, Macmillan, 1929). The original page numbers, which are referred to here and thereafter, are indicated on the margins of the English text.

5 1. Kant, KrAr.V, A 484. 6l.KANT,KrJ.r.V,A4l8i




universe in the doctrine of antinomies. What the antithetic of pure reason is all about is rather the concept of unconditional whole or absolute totality. Space, time and universe can only be the bearers of the categorial determination of infinity, if they are considered as unconditional wholes or absolute totalities, which, as such, do not depend on any further condition. It is solely the notion of the unconditional whole or absolute totality which underlies the interpretation of infinity in the Critique of Pure Reason.

From this it follows that the question of infinity has an impact on all the four antinomies. It is, in other words, the concept of world in its broader and not in its narrower sense which is involved in this question.

In this respect, it is of great significance that Kant distinguishes the notion of an infinite whole from the concept of a maximum. The two concepts are clearly different from each other, because a multiplicity of given units which it contains can never attain a maximal magnitude, "since one or more units can always be added to it".7 Consequently, "no multiplicity is the greatest".8 Therefore, Kant defines infinity in another way: he means by it a multiplicity which - "in relation to any assign- able unit" - "is greater than all number[s]".9 This is, as he says, the mathematical concept of infinity.10 He adds, however, that this does not exclude the possibility of a transcendental concept of infinity: that concept is based on the insight that "the successive synthesis of units re- quired for the enumeration of a quantum {Durchmessung des Quantums) can never be completed".11

This transcendental concept sharply separates infinity from experience. The course of experience is submitted to what may be designated as the rule of successive synthesis.12 It is only step by step, proceeding from

7 1. Kant, KrAr.V, A 431. 8 1. Kant, KrAr. V, A 431. 9 1. Kant, Àr.^r.K, A 432. 10 1. Kant, KrAr. V, A 432, n. 11 1. Kant, KrAr.V, A 432. 12 1. KANT, KrAr.V, A 500: "[...] die empirische Synthesis [ist] [...] notwendig sukzessiv."



EXPERIENCE AND INFINITY IN KANT AND HUSSERL 483

one experience to another, that reason may go forward here. However, if infinity, as its transcendental definition suggests, is to be encountered only where a successive synthesis 'can never be completed', then there is an obvious gap between experience and infinity.

This gap accounts for the fact that reason is as soon entangled in contradictions as it tries to grasp the unconditional whole of experience. Kant takes the actual situation of experience as his starting-point for an inquiry into the conditions which are indispensable for the different characteristics of this very situation. These conditions are arranged into four heterogeneous series, according to the four groups of categories. First, spatio-temporal series, secondly, more and more elementary con- stituents of complex appearances are envisaged; thirdly, causal chains are considered, in which we stumble, fourthly, again and again upon con- tingency, without coming across any existence which might be called necessary. All of these four series prove to be sources of conflict and antinomy as soon as we try to encompass them by means of a regress- ive synthesis. In all the four cases, however, the real difficulty arises from the gap between experience and infinity. Reason has to surpass every limited totality of conditions, since there is no sufficient reason to assume that any member of the considered series could radically differ from the others and might therefore be the bearer of the unconditional. As we have seen, infinity cannot be identified with the concept of a maximum, and it remains especially irreducible to the actually or momentar- ily greatest totality of conditions, which has just been attained but may still be surmounted. In quest of the unconditional whole, reason necessarily transcends all finite totalities. However, an infinite totality can never be attained by means of a successive synthesis.

That is why reason inevitably gets into contradiction with itself. On the one hand, it is, by its very nature, in search of the unconditional whole of experience. This search compelis it to surmount all finite totalities. On the other hand, in experience reason is necessarily submitted to the rule of successive synthesis. However, this rule blocks its road towards infinity. Here it becomes clear that the conflict of reason with itself is engendered by the collision of two principles or laws: the




requirement of absolute totality comes into antagonism with the rule of successive synthesis. That is why Kant speaks of antinomy, meaning by this word the antithetic of two laws of reason.

It is not by accident that the term 'antinomy is often used by Kant in the singular. Antinomies in the plural share their common mechanism of coming into being - it is this mechanism that the singular form of the term designates. The contradictions reason gets into with itself do not arise from the peculiarities of space and time. These contradictions are not connected to the special characteristics of the universe, either, or to the qualities of the dynamic whole of nature inter- woven by causal interconnections. The real antinomy in all antinomies is a consequence of the gap between experience and infinity. This is the ultimate ground of the transcendental illusion reason falls victim to when it hopes, again and again, to discover the unconditional whole, the absolute totality of experience in the necessarily incomplete - and, therefore, conditioned - series of conditions, getting thereby into contradiction - in a way into the contradiction - with itself.

Let us consider the mechanism that generates this contradiction somewhat more closely! It is, as Kant says, "a certain transcendental illusion", which "has mocked [reason] with a reality where none is to be found".13 Everything begins here with the incapacity of reason to encompass the absolute totality of the different series of conditions by means of a successive synthesis. It is added, however, that reason finds itself misled by "a quite natural illusion".14 What does this natural illusion consist in? The answer is clear: it is said to be an illusion to think that all series of conditions are "in themselves in their totality either finite or infinite".15 Kant calls this illusion 'transcendental', because he considers it not only as natural, but as necessary as well. It seems indeed to be necessary to think that a series of conditions of an actual

13 1. Kant, KrAr.V, A 50'. 14 1. KANT,^r.^.r.V:,A500. 15 1. Kant, Kr.dr.V, A 505.




situation is in itself either finite or infinite. Yet, Kant tries to unmask this necessity as an illusion. He says: the world "exists in itself neither as an infinite whole nor as a finite whole."16 He adds: "What we have here said of the first cosmological idea [...], applies also to all the others."17

These considerations provide a clue to the solution of the antinomies. This clue is to be seen in the statement that "the world is not an unconditioned whole".18 In this statement two different thoughts may be discerned:

(1) Kant forms here a concept of the world which is clearly different from the notion of the totality of things. In the Critique of Pure Reason the world proves to be an open whole of a never entirely accomplished synthesis, rather than the sum-total of ready-made things.

(2) However, it must be added that, in Kant's eyes, this new concept of the world is at the same time the ultimate justifying instance of the distinction between the 'thing in itself and 'appearance'. In the Critique of Pure Reason it is emphasized that the world as an open whole of successive syntheses does not exist in itself That is why it may be said to be, in itself, neither a finite, nor an infinite whole. Both alternatives can only be denied because the world is precisely not a 'thing in itself. Here an inquiry into the structural differences between 'what is a world* and 'what is a thing is clearly initiated. But Kant's main aim remains to draw the conclusion that the world of experience is a world of appearances and "appearances in general are nothing outside our representations".19

These reflections do not leave the concept of infinity untouched, either. For sure, the definition of this concept remains unmodified, but its role, and its relationship with experience, appears in a new light. As

16 1. KANT,Ar.¿¿r.K,A5O5. 17 1. KANT,A>.¿¿r.K,A5O5. 18 1. Kant, KrAr.V, A 505. 19 1. Kant, Ar.¿¿r.K, A 506.




we have seen, infinity can only be encountered where a successive synthesis 'can never be completed'. Consequently, infinity can have no place in the world of appearances, which is nothing else but an open whole of successive syntheses. Therefore, the concept of infinity, just as well as the notion of unconditional whole, designates a mere idea, which "serves as a rule" , and not as a "constitutive principle", in experience.20 The gap between experience and infinity is in a certain sense bridged by this regulative function. Infinity serves here as a regulative principle of successive syntheses in experience. As Kant says, it is "a principle of the greatest possible continuation and extension of experience, allowing no empirical limit to hold as absolute".21 Such a principle is designed to put a stop to the deceptive tendency of reason to search for the absolute totality of experience in the necessarily incomplete - and, therefore, conditioned - series of conditions.

As a regulative principle the notion of infinity obtains a certain field of application in experience. However, there is great emphasis on the observation that infinity can never be considered as a constitutive principle of experience. From this observation, an important consequence may be drawn. According to Kant, infinity (in the sense of absolute totality) is "only produced in the idea" and it is not even to be regarded as "equivalent to thinking an object that cannot be given in experience".22 In other words, nothing corresponds to this idea; it is a mere idea without any bearing on objects. What has an objective reality in the world of appearances is "successive infinite and never whole'.10 Obviously, the expression 'successive infinite' signifies here the same as the expression "potentially infinite" in another passage of the Critique of Pure Reason^ The necessarily incomplete series of conditions, which are considered in the doctrine of antinomies, are always finite, even if

20 1. Kant, KrAr. V, A 508-509. 21 1. Kant, Är.^r.VT, A 509. 22 1. Kant, KrAr.V, A 510. ™ I. Kant, Kr.d.r.V, A 524. 24 1. Kant, ATr.ár.VÍ, A 418.




they can always be supplemented by new members. Consequently, they are what may be described as 'successive' or 'potential' infinite. But Kant clearly sees that, they "cannot, therefore, exhibit an [actually] infinite multiplicity".25

By way of a summary one may say that it is not without reason that the idea of infinity is generated in the human mind, but the reason in question does not reside in the objective reality of this idea. On the contrary, infinity is a mere idea without objective reality; yet, as a regulative principle, it has a function in experience. The upshot is that, according to Kant, the idea of infinity has a purpose, although it has no object. If we compare this position with the great systems of early modern metaphysics, in which infinity certainly has a constitutive role, we may find indeed appropriate to say that Kant's Copernican revolution is a turn to human finitude. Infinity in the Critique of Pure Reason is dissolved as an illusion, even if its idea is a necessary rule of experience and, thereby, also an evidence for reason's spontaneity.

II. Husserl's Notion of a Thing as an Idea in a Kantian Sense

In Ideas Pertaining to Pure Phenomenology and Phenomenological Philosophy, as well as in the new elaboration of the Sixth Logical Investigation from the summer of 1913, Husserl draws upon Kant's conception of a regulative principle. However, his way of relying upon this conception shows no sign of orthodoxy. He diverges from Kant at the outset by defining the thing itself (we may even say: the thing in itself) as an "Idea in a Kantian sense".26

25 1. Kant, Kr.dr.V, A 418. 26 E. HUSSERL, Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie, vol. I,

Husserliana, 111/ 1, ed by K. SCHUHMANN, The Hague, M. Nijhoff, 1976 (hereafter quoted as Ideen 7), § 143, p. 330. f. Cf. E. HUSSERL, Logische Untersuchungen. Ergänzungsbandy Erster Teil: Entwürfe zur Umarbeitung der VI. Untersuchung und zur Vorrede für die Neuauflage der Logischen Untersuchungen (Sommer 1913), ed. by U. Melle, Husserliana, vol. XX/1, Dordrecht/Boston/London, Kluwer, 2002 (hereafter abridged as "Entwürfe"), p. 197: "Danach ist Wirklichkeit eines Dinges eine 'Idee' in Kantschem




What is meant here by the expression the 'thing (in) itself? The answer is in Husserl the same as in Kant: the opposite of 'appearance'. However, Husserl interprets the opposition between thing and appearance not in the same way as Kant. What he means by appearance is a profile', an 'aspect' or a 'perspective abridgment' {Abschattung, perspek- tivische Verkürzung) of the thing itself. That is why he claims that to grasp an appearance is to grasp the thing itself from a specific perspective, under one of its possible aspects. Phenomenology maintains that appearances manifest the thing itself in its bodily presence. This is considered by Husserl as part and parcel of the meaning of perceptual experience. If there is still a fundamental difference between the thing (in itself) and appearance, this difference results solely from the fact that appearances (in the sense of profiles or aspects of a thing) necessarily remain characterized by one-sidedness and indeterminacy.27 It must clearly be seen that a whole series of different aspects belongs to one and the same thing. Therefore, each single appearance is only a partial aspect of the thing itself. The discovery of such partial aspects may be viewed as an endless process.

No great distance is marked by these thoughts from the Kantian interpretation of appearance. Undoubtedly, we find no comparable analysis of perception in the Critique of Pure Reason. Yet, it is clear that,

Sinn, Korrelat der 'Idee' eines 'gewissen, aber im voraus nie vollbestimmten, vielmehr unendlich vieldeutigen Wahrnehmungsverlaufs, eines ins Unendliche erweiterungsfähigen [...]." What is meant by ' Wirklichkeit eines Dinges (reality of a thing) in this quotation becomes clear from another passage: "Nur aktuelle Erfahrung kann sozusagen aus den unendlich vielen und unendlich vieldeutigen bloßen Möglichkeiten die eine, einzige Wirklichkeit 'des' Dinges, des 'an sich' völlig bestimmten, heraus- schneiden." (Ibid., p. 198.) We may elicit from these two passages that an Idea in a Kantian sense is the idea of a thing in its particular reality, i. e. of "the" thing, "as far as it is entirely determined 'in itself". The thing in this sense of the word is not identical with the real, but necessarily incomplete object which, just like the phenomenal object in Kant, is never given as a whole in experience. For a similar interpretation of the term 'Idea in a Kantian sense' in Husserl see R. Bernet, Conscience et existence, Paris, PUF, 2004, p. 161: "L'Idée au sens kantien est [...] l'idée de la chose-en-soi [...]." Cf. R. BERNET, La vie du sujet, Paris, PUF, 1994, p. 130: "La chose-en-soi n'est pas donnée sous la forme d'un objet réel, mais d'une idée."

27 E. Husserl, Ideen /, § 138, p. 319.




according to Kant, appearances are not so much isolated sense-data as rather special aspects of an object which is not exhausted by them. Here, however, the analogy comes to an end. For Kant adds that no such aspect reflects in any faithful manner what the object as a thing in itself may be. But this is precisely the view which is challenged in Husserl's phenomenology.28

1.

From the perspective of the present discussion, it is important to decide whether or not a thing (in) itself can be conceived of as the sum- total of its appearances (i.e. of its partial aspects). Kants answer to this question is unequivocally in the negative, because, according to him, the absolute totality of all partial aspects of a thing cannot be present in experience, except as a rule regulating the gaining of experience. But a rule of this kind is not to be confused with a given thing.

Husserl seriously considers Kant's insight into the regulative function of a mere idea. He entirely relies upon Kant in saying that the only kind of infinity which characterizes the course of experience is "the endless- ness in proceeding".29 Moreover, Husserl undertakes to show in detail how, in every perceptual situation, the course of further experience is pre-delineated and how the integral structure of such pre-delineations is summarized in the concept of a concrete thing. Here, once again, phenomenology draws upon the Critique of Pure Reason, which clearly indicates how the concept of a thing serves as "a rule for intuitions".30

28 There is a difference between Kant's and Husserl's concept of experience as well. Science is inte- grated into what Kant calls 'experience'. Accordingly, in the Critique of Pure Reason regulative ideas are related to scientifically organized experience. On the contrary, what Husserl has in view is rather a perceptual experience that is presupposed by sciences. It is this perceptual experience which an 'Idea in a Kantian sense' is related to.

29 1. Kant, KrAr. V, A 25 and E. Husserl, Ideen /, § 149, p. 346. 30 See I. Kant, KrAr. V, A 106 and E. Husserl, Ideen /, § 149, p. 346.




In spite of all the common features, however, phenomenology and Kantianism are, to be sure, separated by a whole range of differences even on this elementary level. The most important of these distinctive features is that Husserl attributes a proper intentionality to intuition in general and to perception in particular, whereas for Kant it is only a concept of understanding which lends to perception - and to intuition as such - the reference to an object. However, such differences, be they as fundamental as the example of intentionality suggests, are of minor significance for our present purposes.31 Husserl is led by the idea of pre-delineations in perceptual situations to form the phenomenological concept of horizon. By means of this concept he is able to restate Kant's tenet according to which the world of appearances is not an unconditional whole. The notion of the world as a universal horizon may be regarded as a phenomenological version of this Kantian tenet.

Yet, Husserl distances himself from Kant on a decisive point when he identifies the thing (in) itself with the sum-total of its appearances (appearance interpreted here as partial aspect or profile). What makes this divergence from Kant possible? The answer is to be sought for in Husserl's interpretation of what is meant here by csum-total' According to the Critique of Pure Reason^ a sum- to tal of appearances is always characterized as a 'successive infinite'. Husserl, on the contrary, has a "continuum of appearances" in view, pointing out the "omnilateral infinity" of this continuum.32 It is precisely this omnilaterally infinite continuum of appearances which, in his opinion, amounts to the adequate givenness of the thing itself.

From a Kantian point of view it might be objected that such a continuum, in its turn, can never be given in experience. This objection is, however, only an apparent one, since Husserl by no means argues for

31 For further differences see L. Tengelyi, 'Husserls Begriff des Horizontes', in: R. Elm (Hrsg.), Horizonte des Horizontbegriffi. Hermeneutische, phänomenologische und interkulturelle Studien, Sankt

Augustin, Academia Verlag, 2004, p. 144 f. and p. 148 f. 32 E. Husserl, Ideen /, § 143, p. 331.




the givenness of a continuum in experience. He very well admits that the omnilaterally infinite continuum of partial aspects is nothing but a mere idea with only a regulative function in experience. As far as the applicability of infinity to experience is concerned, he entirely agrees with Kant; that is why he evokes, in this context, an Idea in a Kantian sense'. What he considers as a given is not the omnilaterally infinite continuum of appearances itself, but only the idea of this continuum.33 However, in opposition to Kant, he claims that this idea has not only a purpose but also an object^ and that its object is not only potentially but - as every continuum - actually infinite. That is why it may be identified with the thing itself in its adequate givenness.

Here Husserl largely relies on the concepts of continuum and infinity, as they have been elaborated in 19th century mathematics. In the tradition of European philosophy the notion of actual infinity had been rejected since Aristotle. Aristotle's main proposition on this topic was formulated in mediaeval Latin as infinitum actu non datur. Although actual infinity as a characteristic of God was already rehabilitated as early as in scholasticism, and although it was later even applied to the world by a whole series of thinkers from Nicolaus Cusanus and Giordano Bruno to Spinoza and Leibniz, it did not allow for any further articulation. It was considered as unique and indivisible, consisting of no parts and admitting no measurement.34 It is this noble yet unar- ticulated notion of actual infinity that Kant is confronted with, and he clearly rejects it, because he sees in it a source of antinomies. It is only after his death that new tendencies in the interpretation of actual infinity emerge. A break-through manifests itself with Bernhard Bolzano, Karl Weierstrass, Richard Dedekind and, especially, with Georg Cantor. 19th century set theory marks a new era by establishing a firm ground for the reinterpretation of actual infinity. The decisive step is taken by Cantor, who is just as erudite in the philosophical tradition, as he is a

33 E. Husserl, Ideen /, § 143, p. 331. 34 See e. g. B. SPINOZA, Ethica, Pars I, prop. XV, Schol.




creative mathematician. This decisive step may be said to consist in the separation of what is called the transfinite' from 'absolute infinity'. It is not difficult to indicate the difference. Cantor himself claims that whereas absolute infinity cannot be enlarged or increased, a transfinite multiplicity is always susceptible to augmentation.35 This characteristic leads up to further ones. Whereas no articulation is to be discerned in absolute infinity, because it is unique and indivisible, without parts and measure, a transfinite multiplicity may differ from another one in composition, order and size. Consequently, whereas absolute infinity may be described, in Kantian terms, as an 'unconditioned whole', a transfinite multiplicity cannot be characterized by this expression. Nor can it be designated as an 'absolute totality'. On the contrary, such a multiplicity remains, in spite of its actual infinity, just a relative totality and a principally open whole, precisely because there are other transfinite multiplicities, which differ from it in composition, order and size.36

Husserl is familiar with the two papers in which this distinction is argued for by Cantor; he refers to them as early as in the Philosophy of Arithmetics.07 It is in one of these two papers that the notion of continuum is treated of at length.38 It is not difficult to see that the Cantonan distinction between transfinity and absolute infinity is a pre- requisite of Husserl's attempt to identify the thing (in) itself with the

35 G. CANTOR, Gesammelte Abhandlungen, hrsg. von E. Zermelo, Hildesheim, Georg Olms Verlagsbuchhandlung, 1962 (reprographischer Nachdruck der Erstausgabe von 1932), p. 405; cf. d. 375. r 36 For a more detailed interpretation of the Cantorian distinction between 'absolute infinity' and the 'transfinite' see L. Tengelyi, 'Transfinite Zahl und transzendentaler Schein. Kant und Cantor in der Sicht von Marc Richirs Phänomenologie', in: Aufklärung durch Kritik. Festschrift fur Manfred Baum zum 65. Geburtstag, Hrsg. von D. HüNlNG, K. Michel und A. Thomas, Berlin, Duncker & Humblot, 2004, p. 451-475, especially p. 452-455. 37 E. HUSSERL, Philosophie der Arithmetik, Husserliana, vol. XII, p. 115, n. 2. The two papers in question are 'Grundlagen einer allgemeinen Mannigfaltigkeitslehre' (1883; identical with part 5 of 'Über lineare Punktmannigfaltigkeiten in the Gesammelte Abhandlungen) and 'Mitteilungen zur Lehre vom Transfiniten' (1887).

38 G. CANTOR, 'Grundlagen einer allgemeinen Mannigfaltigkeitslehre', § 10, in: Gesammelte Abhandlungen, op. cit., p. 190-194.




omnilaterally infinite continuum of its partial aspects. Indeed, this identification presupposes different infinite multiplicities of appearances, which do not coalesce into a chaotic mixture. This observation accounts also for one of the most important features of Husserl's approach: it is not the world as a whole but each single thing in its particular reality which is considered by him as an Idea in a Kantian sense.39

Relying upon the new concept of an actual but open infinity, phenomenology marks a turn in the description of thing and world. To be sure, it is by strong ties that, from 1907 on, Husserl's thinking is linked up with Kantian transcendental philosophy. It is the elucidation of transcendental subjectivity which is specified as the ultimate goal of phenomenological investigations. The principle of finite perspective is put to the fore by Husserl in the analysis of space and time, as well as of world and thing. However, the idea of a continuum of appearances profoundly transforms the basic structure of transcendentalism in phenomenology: it deprives it of its exclusive finitism. In opposition to Kant, Husserl interprets both the world and the single thing as infinite wholes.

One should not think that this turn to infinity marks a relapse into an objectivism which had already been overcome by transcendentalism. It is not in their objective givenness that phenomenology considers world and thing as respective infinite wholes.40 On the contrary, the infinite totalities Husserl has in mind are totalities of appearances (in the sense of aspects or profiles) which, as such, remain dependent upon subjective standpoints and perspectives. This is tantamount to saying that it is only the phenomenological reduction which opens the way for interpreting world and thing as infinite totalities. From this it already fol-

39 Cf. R. Bernet, Conscience et existence. Perspectives phénoménologiques, Paris, PUF, 2004, p. 161: "[...] l'Idée au sens kantien est [...] l'idée d'une réalité particulière."

40 Cf. E. HUSSERL, Entwürfe, Husserliana, vol. XX/1, p. 195: "Die aktuelle Erfahrungswelt bietet natürlich keine Dinge mit unendlich vielen Eigenschaften. Faktisch lässt der Fortgang der Erfahrungen immer wieder neue Eigenschaften hervortreten. Dass das aber immer wieder möglich sein müsse, ist kein bloßes Faktum, sondern eine im Wesen der Dingerfassung liegende, also apriorische Notwendigkeit."




lows that, as opposed to Kant's Copernican revolution, Husserl's phenomenological reduction cannot be considered as a turn to human finitude.

2.

On the basis of the identification of each single thing with the continuum of its partial aspects, Husserl undertakes to overcome the Kantian distinction between 'thing in itself and 'appearance'. Of course, no refutation of this venerable doctrine is intended by him. He does not attempt to reconstruct Kant's own motives to draw this distinction. Nor does he consider the manifold functions which the concept of a thing in itself fulfills in the critical philosophy. The task Husserl sets himself is quite different. What he is seeking for is a philosophical possibility to eschew what he takes to be a pitfall for his own thinking.

In order to understand this task, we have to take into account how, in Kant, 'appearance' and 'thing in itself are related to each other. It is important to see that these two terms do not refer to two distinct en- tities. In saying this, I am relying upon a whole tradition of the interpretation of Kant's Critique of Pure Reason, marked mainly by the names of Gerold Prauss in Germany and of Henry Allison in the English- speaking world.41 This conception of the relationship between appearance and thing in itself is clearly confirmed by some passages in the Critique of Pure Reason. It may be sufficient here to quote the most important of them: "[...] the word appearance must be recognised as already indicating a relation to something, the immediate representation of which is, indeed, sensible, but which, even apart from our constitution (upon which the form of our intuition is grounded), must be something in itself, that is an object independent of sensibility."42 It is also in this sense that certain claims in Kant's Opus postumum are to be understood.

41 I hasten to add that, in my opinion, the original view of Prauss was rightly modified by Allison. 42 1. Kant, Kr.d.r.V, A 252.




Here we are told once more that a thing in itself is not a different en-

tity from appearance; it is, on the contrary, "just the same, but considered from a different point of view".43 Appearance' - even if this term is now taken in the sense of a phenomenal object, and not in that of a partial aspect - designates indeed only the way in which a thing is

necessarily grasped "from [a] human standpoint".44 Kant adds, however, that this is not the only possible way in which a thing can be seized. It is at least not contradictory45 to assume that a divine being, equipped with intellectual intuition, could comprehend the same thing in a different manner. Consequently, appearance (even in the sense of a phenomenal object) has to be distinguished from what the thing may be in itself.46 If this distinction is once drawn, it may be added that such a divine being can perhaps relate also to things which do not even

appear to us. From these reflections it is clear why the proper task of Kant s fol-

lowers, who try to liberate themselves from the conceptual burden of a

thing in itself, consists in showing that the distinction between a human and a divine comprehension of a thing is not pertinent.47 In German idealism this endeavor leads up to an assimilation of human mind to divine intellect or spirit. That is why here the boundary between the finite and the infinite gets more and more blurred. Husserl

43 1. Kant, Opus postumum, in: Gesammelte Schrifien, Academy Edition, vol. XXII, p. 45. 44 Cf. I. Kant, Kr.d.r. V, A 26. 45 Cf. I. KANT, Kr.d.r. Vf, B 310: "The concept of a noumenon - that is, of a thing which is not to

be thought as an object of the senses but as a thing in itself, solely through a pure understanding - is not in any way contradictory. For we cannot assert of sensibility that it is the sole possible kind of intuition." Kant adds, however, that we are by no means justified in "presupposing the possibility of another kind of intuition than sensible". (I. KANT, Kr.dr.V, B 309.) Therefore, "the [sort of] understanding to which [a thing in itself] might belong is itself a problem". (I. KANT, Kr.d.r. V, A 256.)

46 Cf. I. KANT, Kr.dr. V.> A 249: "[...] if I postulate things which are mere objects of understanding and which, nevertheless can be given as such to an intuition, although not to one that is sensible -

given therefore coram intuitu intellectuali - such things would be entitled noumena (intelligibilia)." 47 Cf. M. HEIDEGGER, Die metaphysischen Anfangsgründe der Logik im Ausgang von Leibniz^ in: Gesamtausgabe ' vol. 26, ed. by K. Held, Frankfurt am Main, Kohlhammer, 1978, p. 210: "Der Begriff des Dinges an sich [. . .] (als Korrelat eines absoluten Verstandes) fällt nur dann, wenn man zeigen kann, daß die Voraussetzung eines absoluten Verstandes philosophisch nicht notwendig ist."




takes a different course. What he aims at demonstrating is almost the opposite: it is, as he claims, only in the form of appearances that a thing can be intuited, not only by ourselves, human beings, but also by God (as the ideal representative of absolute knowledge)}*

This statement is somewhat surprising, because, at a first glance, the interpretation of a thing as the omnilaterally infinite continuum of its partial aspects seems to allow, or even to require, a distinction between human mind and divine intellect. Undoubtedly, it is always only a partial aspect of a thing which we, human beings, can grasp in a perceptual situation. It seems, however, as if the very difference between aspect and thing could be overcome at least in an infinite synthesis of all aspects of one and the same thing. To be sure, the result of an infinite synthesis remains unattainable for finite beings like ourselves. But is it equally unattainable for an infinite being? Is it not quite natural to assume that the thing itself in the totality of its partial aspects may be the adequate object of absolute knowledge?

Even if this thought is natural, it is, alas, only a natural illusion. As a matter of fact, it is an entirely unwarranted assumption to think that the totality of all partial aspects of a thing is something like a total aspect of it, which may be grasped at once, if not by a human mind, then at least by a divine intellect. It is worth indicating that, according to a retrospective remark to be found in the 1907 lecture on Thing and Space, Husserl himself had fallen victim to this illusion,49 before he came, precisely in the just mentioned lecture, to the insight that no total aspect of a thing can ever be regarded as given. In Ideas I he considers the confusion between the totality of partial aspects with a total aspect as equivalent to the absurd idea of "a finite infinity".50

48 E. Husserl, Ideen /, § 150, p. 351. 49 E. HUSSERL, Ding und Raum, Husserliana, vol. XVI, p. 123: "Ich selbst bin der hier so nahelie- genden Täuschung früher unterlegen und habe darüber noch in meinen Vorlesungen vor zweieinhalb Jahren Falsches vorgetragen." 50 E. Husserl, Ideen /, § 143, p. 331.




This idea requires some clarification. Here a recourse to the Cantorian distinction between 'absolute infinity' and 'transfinity proves to be indispensable for understanding HusserPs argument. If things were infinite multiplicities in the first sense, they certainly would offer a total aspect and could, therefore, be seen by an infinite being all at once, just as all parts are at once grasped by a finite being, if a finite whole (e. g. the frontispiece of a house) is given in its totality. Absolute infinity encompasses everything without any internal articulation. The situation is, however, quite different, if things are infinite multiplicities in the second sense. Transfinite multiplicities may differ from each other in composition, order and size. They do not encompass everything, and their internal articulation is by no means negligible. That is why they do not offer any total aspect. The integral continuum of partial aspects never amounts to an absolute totality, which could be grasped at once.51 It remains a relative totality, an open whole, a thing within a horizon. Not even the world itself can be considered as an absolute totality. It is itself only a horizon, even if it is the horizon of all horizons.

It is a natural - and perhaps also necessary, i. e. transcendental - illusion to think that world and thing may be grasped as given wholes, if not by ourselves, then by an infinite being. It is nevertheless an illusion: the mirage of 'a finite infinity'. The exposition of this transcendental illusion leads phenomenology up to a break with a whole tradition of metaphysics, centered around the thesis that an infinite being - as the ideal representative of absolute knowledge - sees all things at once?1 Husserl sets against this thesis the proposition that a thing in its

51 Cf. R. Bernet, Conscience et existence. Perspectives phénoménologiques ; op. cit., p. 160: "[...] l'Idée au sens kantien [...] ne peut jamais faire l'objet d'une intuition adéquate." 52 Cf. Thomas of Aquinas, Summa theologica, p. I, qu. 14, art. 7: "Deus [...] omnia videt in uno [...]. Unde simul, et non successive omnia videt." Heidegger shows in his last Marburg lecture that Leibniz was still profoundly influenced by this tradition, which originated in mediaeval scholasticism. He adds that even Kant and Hegel remain incomprehensible if this tradition is not taken into account. M. HEIDEGGER, Die metaphysischen Anfangsgründe der Logik im Ausgang von Leibniz, in: Gesamtausgabe, vol. 26, op. cit., p. 54: "Die scholastische Gotteslehre ist nicht nur der Schlüssel zur Logik von Leibniz,




particular reality is nothing else but an Idea in a Kantian sense, from which, hereby going beyond Kant, he draws the consequence that not even an infinite being can have access to a thing without a successive synthesis of appearances (in the sense of partial aspects or profiles).

Why is that so? The answer is related to the very nature of partial aspects. Where such an aspect becomes perceptible, others are already pre-delineated, but they still remain imperceptible. Therefore, all aspects of a thing can never be given at once. From this it follows that an Idea in a Kantian sense is not the idea of an absolute infinity. It is rather the idea of an actual but open infinity.53 This infinity is far from being an absolute totality or an unconditional whole. Since it is identified, in each case, with just one thing among others within the world- whole, it does not encompass everything, but remains embedded in larg- er horizons. Moreover, it exhibits an internal articulation. It is an essen- tial characteristic of aspects that, while one of them makes its appearance, all others remain imperceptible.54 Nevertheless, the latter aspects are implied or indicated by the appearance of the former. It is due to this structure of indications or pre-delineations that an Idea in a

auch Kants 'Kritik der reinen Vernunft' und ebenso Hegels 'Logik' werden nur von da her in ihren

eigentlichen Triebkräften faßbar. [. . .] Der philosophische Sinn der Orientierung an der scientia Dei ist der: sie fungiert als Konstruktion einer absoluten Erkenntnis, daran die endliche, menschliche gemes- sen werden soll."

53 E. HUSSERL, Entwürfe, Husseriiana, vol. XX/1, p. 200: "Gegebenheit offener Unendlichkeiten". It is clear from the context that actually infinite multiplicities are meant by this expression. Husserl says: "Sie sind als unendliche Gesamtheit gegeben [...]." {Ibid., p. 199.) He adds: "Es versteht sich leicht, dass

originär gebende Intuition, also auch Evidenz, Unendlichkeiten umspannen kann [...]. Beständig rekurrieren wir, und nicht nur in reiner Logik und Mathematik, auf Unendlichkeiten, deren wahrhaf- tes 'Sein' uns als vollkommen selbstverständlich und wirklich evident gilt: 'offene Mengen' als

Begriffsumfänge, unendliche Reihen, überhaupt unendliche durch formulierbare oder nichformulier- bare Bildungsgesetze geregelte Mannigfaltigkeiten. [...] - Genau so erfassen wir auch sonst geordne- te und konstruierbare Mannigfaltigkeiten, wie übrigens auch ungeordnete 'Mengen', als 'offene' Vielheiten [...], demnach auch in unserem Gebiet die Unendlichkeiten 'möglicher Erfahrungen be- stimmter Progressionsform und korrelativ z. B. unendliche Folgen einstimmig näher bestimmender intuitiver Möglichkeiten eines mit unvollkommenem Bestimmungsgehalt Gegebenen als solchen."

54 Cf. R. Bernet, "Finitude et teleologie de la perception", in: La vie du sujet, Paris, PUF, 1994, p. 133: "[...] ce qui est gagné en intuitivité par une apparence est perdu par une autre [...]."




Kantian sense can serve as a rule regulating a progression in finite steps without prejudice to its infinite character.55

From these considerations we may draw the conclusion that Husserl could not have defined a thing as an Idea in a Kantian sense if he had not relied upon the Cantorian attempt to separate the transfinite from absolute infinity. Cantor himself assigns the notion of absolute infinity to theology, adding that the transfinite is articulated "in the areas of metaphysics and mathematics".56 What the notion of the transfinite signifies for mathematics, is clearly indicated by the set theory he put forward himself. Cantor is, however, firmly convinced that, "to some extent and in certain relations", the transfinite "acquires also reality and existence" in the world.57 That is why he envisages, beyond mathematical set theory, a 'metaphysics of the transfinite' as well. However, what such a philosophical discipline might amount to, remains rather unclar- ified in Cantor's writings. It is in this respect that a particular import- ance can be attributed to Husserl's notion of an Idea in a Kantian sense. It may indeed be claimed that it is the merit of the phenomenological approach to thing and world to give an inkling, or even an outline, of what was designated by Cantor as a 'metaphysics of the transfinite'.

Summary

A reflection upon HusserPs notion of an "Idea in a Kantian sense" calls for an inquiry into the relationship between experience and infinity. This question is first considered in Kant's doctrine of antinomies. It is shown that, in the Critique of Pure Reason, infinity is held to be a mere idea, which, however, has an indispensable regu-

55 Cf. R. Bernet, 'Finitude et teleologie de la perception, in: La vie du sujet, op. cit., p. 136: "[L'Idée au kantien sens] peut se révéler à un sujet fini sans pour autant trahir son caractère infini [...]."

56 G. CANTOR, Gesammelte Abhandlungen, op. cit., , p. 181. 57 G. CANTOR, Gesammelte Abhandlungen, op. cit., , p. 406.




lative function in experience. It is at this point that Kant is compared with Husserl, who, drawing upon the notion of regulative principle elaborated in the Critique of Pure Reason, conceives of a thing in its particular reality as an Idea in a Kantian sense. A major difference between the two thinkers is particularly emphasized: Kant uses his analysis of the antinomies for justifying his distinction between the 'thing in itself and 'appearance'; Husserl, on the contrary, tries to overcome this opposition. It is argued for that this difference between the two philosophers arises from two different notions of infinity: whereas Kant has a potential infinity in view, Husserl, who is familiar with Cantor's mathematical and philosophical thoughts, relies upon a scientifically established form of actual, but nevertheless open infinity.



experience and infinity in kant and husserl

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