According to Husserl, “the teleological beginning, the true birth of the European spirit as such” (Crisis, § 15), lies in the Greek primal establishment of the idea of a universal science whose foundation in intersubjectively reconstructable truths makes it a science that in absolute self-responsibility accounts for all of its claims. Although the European spirit is born in Greece, it manifests itself properly only with another primal establishment that occurs in the Renaissance, and “which is at once a reestablishment [Nachstiftung] and a modification of the Greek primal establishment” (Crisis, § 15). But the reestablishment of the idea of an all-encompassing rational science at the beginning of modernity is not a wholesale underwriting of the Greek heritage. It is a modification that transforms the idea in question. This reestablishment is responsible not only for the modern sciences’ indisputable accomplishments but also for the current crisis of the sciences, that is, for what Husserl diagnoses as the sciences’ inability to account for the meaning of their own activity, and, hence, their loss of any relation to humanity’s basic concerns. Perhaps more importantly, the success and simultaneous crisis of the European sciences is also an indication of the problematic nature (if not the narrowness) of the concept of universality that informs the modern sciences. Indeed, as Husserl remarks, “a definite [bestimmtes] ideal of a universal philosophy and its method forms the beginning; this is, so to speak, the primal establishment of the philosophical modern age and all its lines of development” (Crisis, § 5). Hereafter, I will discuss in some detail the founding event of the modern sciences in the Renaissance, primarily in order to elicit what, precisely, this specific concept of universality amounts to and what its intrinsic limitations are in comparison to the Greek idea of universality. The aim of this elucidation is to show that, for Husserl, the concept of universality that dominates the modern sciences fails to make good on the promise of a universal horizon, which emerged as a task with Greek philosophy. Furthermore, since Husserl links the European spirit to this promise, one must conclude that, essentially, the modern sciences have also failed that spirit.
The project of an all-encompassing science, or metaphysics, which originates in ancient Greece, is not only a science of the one world—the world that encompasses all the relative worlds. It is one that, in order to secure access to this one world and to establish for it terms that are in principle intelligible to all, independently of their race, gender, customs, culture, religion, nationality, and so forth, presupposes an attitude that is critical of everything that is of the order of such particulars. This universal science embodies the ideal of a community freeing itself precisely from all traditions, and traditionalisms, and shaping itself freely according to insights of reason that are recognizable for their universality. However, the primal establishment of the new philosophy that characterizes the Renaissance, and which, according to Husserl, coincides with “the primal establishment of modern European humanity itself—humanity which seeks to renew itself radically, as against the foregoing medieval and ancient age, precisely and only through its new philosophy” (Crisis, § 5), lacked this critical attitude with respect to the Greek heritage. The Renaissance takes it over as “an unquestioned tradition” (Crisis, § 9g), and it thus essentially misses what is so essential about the Greek project. Indeed, by its very nature the project and the task of a humanity that understands itself from the one world cannot be taken over slavishly. As the Crisis suggests, the ancient model of a universal rational science, which implies the critical rejection of tradition, precludes being appropriated in a traditionalist spirit. Husserl writes that the ancient model “was not to be taken over blindly from the tradition but must grow out of independent inquiry and criticism” (Crisis, § 3). The very spirit of the Greek conception of reason demanded a critical attitude toward the model in question as a heritage bequeathed upon Europe as well as a free and independent reactivation of this heritage.1 But if the very idea of a universal and rational science radically excludes all uncritical acceptance of any received heritage (including that of itself), then it is also the case, as Husserl notes, that the way in which ancient philosophy, in its first, original establishment seeks to realize the universal task of philosophy is not without its own naiveties and inherent limits.2 In fact, although this task is, as we have seen before, a remarkably strange one, Greek philosophy soon lost sight of its strangeness in the very attempt to develop an all-encompassing science. Furthermore, by conceiving of this task as self-evident, “the naive obviousness of this task [became] increasingly transformed ... into unintelligibility,” with the result that “reason itself and its [object], ‘that which is,’ became more and more enigmatic” (Crisis, § 5). If reason has become enigmatic, it is, Husserl suggests, because the wonders that mathematics and physics have accomplished, in particular, “the wonderful symbolic arts of the ‘logical’ construction of their truths and theories,” have become “incomprehensible” to the extent that the reason or meaning for their existence is no longer evident.3 As Husserl suggests, the Renaissance philosophers did not question what had been handed down from antiquity, and therefore, “the first invention of the new idea [of a universal science in the Renaissance] and its method allowed elements of obscurity to flow into its meaning” (Crisis, § 9g). These elements prevented the exact sciences from achieving “knowledge about the world,” that is, about and for the world shared by all. Foregoing any reflective inquiry into the original meaning of the received conceptions, the new sciences adopted the universal insights of Greek geometry and mathematics without questioning their origin and proceeded to develop a kind of disengaged universality on the basis of the mathematization of nature and the formalization of mathematics. The abstraction and emptiness of the latter—although not altogether illegitimate, and above all, highly successful—not only became increasingly severed from the concerns of humanity as such, but also remained tied to one particular world, one particular mankind, and one particular horizon—to Europe as a particular ethnia. The reestablishment and modification of the Greek idea of a universal rational science by the modern sciences thus obfuscates the true spirit of the primal establishment of the idea of a universal science in Greece. It follows from this that “the spectacle of the Europeanization of all other civilizations” that begins with the Renaissance, rather than bearing witness “to the rule of an absolute meaning, one which is proper to the sense ... of the world,” may be, in Husserl’s own words, for the time being at least, “a historical non-sense” (Crisis, § 6). Indeed, what is exported under the guise of the techno-sciences is a kind of universality that no longer has any relation to the one world, the one in which we all live.
If the modern age, an age characterized by its rediscovery of philosophy as a universal task, is “not merely a fragment of the greater historical phenomenon” constituted by the inaugural establishment of philosophy in Greece (Crisis, § 5), it is because this rediscovery is not a simple repetition of that event. Husserl writes that
as the reestablishment [Neustiftung] of philosophy with a new universal task and at the same time with the sense of a renaissance of ancient philosophy—it is at once a repetition and a universal transformation of meaning. In this it feels called to initiate a new age, completely sure of its idea of philosophy and its true method, and also certain of having overcome all previous naiveties, and thus all skepticism, through the radicalism of its new beginning. (Crisis, § 5)
Indeed, the reestablishment of philosophy as universal rational science during the Renaissance marks a radically new beginning, in that the modern age reshapes the universal task at the heart of philosophy, and thus also reshapes the very meaning of universality. But this reformulation of the universal task comes with its own naiveties, which are a function of the way the Renaissance relates to the Greek heritage.
Philosophy as “universal science, science of the universe, of the all-encompassing unity of all that is,” which, according to The Vienna Lecture , arises in Greece as a result of the “new sort of attitude of individuals toward their surrounding world” (The Vienna Lecture, p. 276)—that is, a radically critical attitude—is the science of the one world, the world for everybody, that is, of humanity itself. The discovery of this one world enables the conception of a universal science in Greece—a science concerned with what is universal, and which seeks to proceed according to principles and rules that are reconstructable by everyone. Now the science that sustained this idea of universality in Greece, and that served to flesh out the conception of the one intersubjectively shared world, is first and foremost geometry. Its pure forms, its ideal shapes of space-time, which are constructed according to rules that are verifiable at all times, and which permit everyone to reproduce them identically, have absolute and universal value with regard to the one and same world shared by everyone. Husserl writes:
Out of the undetermined universal form of the life-world, space and time, and the manifold of empirical intuitable shapes that can be imagined into it, [geometry] made for the first time an objective world in the true sense—i.e., an infinite totality of ideal objects which are determinable univocally, methodically, and quite universally for everyone. Thus mathematics showed for the first time that an infinity of objects that are subjectively relative and are thought only in a vague, general representation is, through an a priori all-encompassing method, objectively determinable and can actually be thought as determined in itself or, more exactly, as an infinity which is determined, decided in advance, in itself, in respect to all its objects and their properties and relations.” (Crisis, § 9b)
As Husserl observes, “scientific acquisitions, ... after their method of assured successful production has been attained ... are imperishable; repeated production ... produces in any number of persons something identically the same, identical in sense and validity” (The Vienna Lecture, pp. 277–78). What is thus found to be identical, and to obtain for all relative worlds—the pure forms of space and time—are imperishable idealities. Indeed, “what is acquired through scientific activity is not something real but something ideal,” which itself, moreover, becomes “material for the production of idealities on a higher level, and so on again and again” (ibid.). This discovery of pure geometric shapes is not that of “mere spatiotemporal shapes” abstracted from bodies experienced in the intuitively given surrounding world. Nor are they arbitrarily imagined shapes, or shapes transformed by fantasy (Crisis, § 9a). In distinction to the imaginary (hence, still sensible) idealities of pure morphological types, such as roundness, for example, which have never the perfection that allows for their absolute identical repetition, the pure forms of geometry—such as the circle—are, as Husserl writes, “limit-shapes,” that is, identical and invariant idealities obtained by way of a passage to the limit (Crisis, § 9b).4 These idealities arise from “a peculiar sort of mental accomplishment” (Crisis, Appendix V, p. 348), which Husserl terms an “idealizing accomplishment,” and thus possess “a rigorous identity” (Crisis, Appendix II, p. 313), which submits to “the conception of the ‘again and again’ ... in infinitum,” a repetition that in nature differs from the open endlessness characteristic of abstract figures.5 “The great invention of idealization” (Crisis, § 9h) by geometry and mathematics, which provides “the pure shapes it can construct idealiter [in the form of an idea]” (Crisis, § 9), and in such a manner that anyone can reconstruct them, is what permits an insight of universal scope into the one objective world shared independently of all particularities.6
The universal science recast in the Renaissance, along with its distinctly new conception of universality, thus rests on a rediscovery of ancient geometry. It is a discovery, however, that dispenses with the task of reconstructing what had given birth to it in ancient Greece. The latter’s accomplishments are taken for granted. As Husserl submits, geometrical methodology, which permits overcoming “the relativity of subjective interpretation” and attaining “something that truly is”—“an identical, nonrelative truth of which everyone who can understand and use this method can convince himself ”—is a given for Galileo, and he takes it over “with the sort of naiveté of a priori self-evidence that keeps every normal geometrical project in motion” (Crisis, § 9b). Furthermore, this identical truth revealed by geometry is understood as the truth of nature. In fact, for him, “everything which pure geometry, and in general the mathematics of the pure form of space-time, teaches us, with the self-evidence of absolute, universal validity, about the pure shapes it can construct idealiter,” belongs to “true nature” (Crisis, § 9). It must also be said that the geometry that Galileo inherited was “a relatively advanced geometry,” one that had already become “a means for technology, a guide in conceiving and carrying out the task of systematically constructing a methodology of measurement for objectively determining shapes in constantly increasing ‘approximation’ to geometrical ideals, the limit-shapes” (Crisis, § 9b). Its proven effectiveness was one more reason to exempt it from the need for questioning. According to the Crisis, Galileo received this heritage in such a way that “he, quite understandably, did not feel the need to go into the manner in which the accomplishment of idealization originally arose (i.e., how it grew on the underlying basis of the pre-geometrical, sensible world and its practical arts) or to occupy himself with questions about the origins of apodictic, mathematical self-evidence” (Crisis, § 9b).7 For Galileo, the original strangeness of geometrical idealization, that is, the discovery of pure shapes and their universally reconstructable evidence, is gone. Geometry is for him an unquestioned cultural acquisition. Without having to reflect back on its genesis, the selfenclosed world of its pure forms can be manipulated like any other cultural tool. Geometry’s evidences have become self-evident; in other words, rather than reflecting on the origin of geometry—a reflection that would have permitted Galileo to link it to the universal and transcendental eidetic structures of the pre-geometrical life-world—he takes it over uncritically, as an abstract truth. It did not dawn on Galileo to make geometry, “as a branch of universal knowledge of what is (philosophy), [and] geometrical self-evidence—the ‘how’ of its origin—into a problem” (ibid.). However, Galileo in turn develops a conception of universal science that, even though it has become obvious for us today, was definitely merkwürdig , strange, or odd at the time. The notion of universality characteristic of the modern sciences that comes into being with Galileo is a strange notion as well. But its oddity is distinct from that which characterizes the universal in the primal establishment of the European spirit in Greece. The strangeness of the universality peculiar to the modern sciences derives, as we will see, from its alienation from the life-world. The strangeness of this new conception of universality is that of the merely abstract. 8 At any rate, since the Renaissance slavishly takes the truths of geometry as abstract givens, the radically novel conception of universality of the emerging natural sciences (that marks the inception of modernity), notwithstanding the fact that it will have been a clear advance over the Greek notion of a universal science, is tinged with naïveté. As Husserl holds, this naïveté is responsible for the current crisis of the sciences.
Of what, then, does the new idea of the universality of the sciences consist? According to Husserl, the sciences inherited from the ancients—“Euclidean geometry, and the rest of Greek mathematics, and then Greek natural science”—undergo “an immense change of meaning” during the Renaissance. This change, which primarily affects mathematics, namely geometry and the formal-abstract theory of numbers and magnitudes, sets new tasks for its disciplines, “tasks of a style which was new in principle , unknown to the ancients,” in being not only “universal tasks,” but infinite tasks (Crisis, § 8). Indeed, in spite of the Greeks’ idealization of empirical numbers, units of measurement, and empirical figures in space; in spite of their transformation in geometry of propositions and proofs into ideal-geometrical propositions and proofs; and, finally, in spite of their understanding of Euclidian geometry as “a totality of pure rationality, a totality whose unconditioned truth is available to insight and which consists exclusively of unconditioned truths recognized through immediate and mediate insights,” Husserl nonetheless holds that “Euclidian geometry, and ancient mathematics in general, knows only finite tasks, a finitely closed a priori” (ibid.). The Greek world is a finite world—a cosmos within natural limits whose unexceedable horizon encloses all the pragmata of mortal beings. The discovery of infinite ideals, and hence infinite tasks, is, for Husserl, a positive achievement of modernity, and represents a clear advantage that the modern sciences have over the ancient ones. Antiquity, Husserl notes in the Crisis, does not grasp “the possibility of the infinite task which, for us, is linked as a matter of course with the concept of geometrical space and with the concept of geometry as science belonging to it” (ibid.). As Jacques Derrida has argued, as a passage to the limit, geometric idealization is by definition the infinite transgression of the sensibly ideal morphological shapes of the life-world. Hence, the inaugural idealization that opened Greek geometry endows it from the outset with infinite fecundity. Yet this infinitization “no less first limits the a priori system of the productivity. The very content of an infinite production will be confined within an a priori system which, for the Greeks, will always be closed ” (Derrida, 1978, 127).9 In distinction from the Greeks, for whom the ideal and universal knowledge of geometry was limited to a finite number of forms or shapes for which it furnished a rational foundation, the moderns take geometry as a science capable of accounting for all possible forms. Husserl writes: “To ideal space belongs, for us, a universal, systematically coherent a priori, an infinite, and yet—in spite of its infinity—self-enclosed, coherent, systematic theory which, proceeding from axiomatic concepts and propositions, permits the deductively univocal construction of any conceivable shape which can be drawn in space” (Crisis, § 8). The very notion of ideal space to which the Greeks arrived by idealizing empirical figures contains, for us, in ideal form, all possible spatial shapes. For us, as opposed to the Greek finite understanding, ideal space is “a rational infinite totality of being,” “an infinite world” of idealities whose ideal objects “become accessible to our knowledge [not] singly, imperfectly, and as it were accidentally, but as one which is attained by a rational, systematically coherent method. In the infinite progression of this method, every object is ultimately attained according to its full being-in-itself ” (ibid.). With “the actual discovery and conquest of the infinite mathematical horizon,” one that is not only limited to ideal space but is soon extended to numbers as well, the task of the sciences becomes infinite, one of infinite universal tasks. However, the radicality of this reconfiguration of the concept of universality does not come to a close with mathematics. Indeed, as Husserl remarks, the latter’s rationalism “soon overtakes natural science and creates for it the completely new idea of mathematical natural science—Galilean science” (ibid.). Posing “the radical problem of the historical possibility of ‘objective’ science, objectively scientific philosophy,” it is not merely a matter, for Husserl, “of establishing science’s historical, factual point of origin in terms of place, time, and actual circumstances, of tracing philosophy back to its founders, to the ancient physicists, to Ionia, etc.; rather, it must be understood through its original spiritual motives, i.e., in its most original meaningfulness [Sinnhaftigkeit] and in the original forward development of its meaningfulness” (Crisis, Appendix V, p. 347). Only by following Husserl through his discussion of Galileo’s mathematization of nature, and the genesis of modern natural sciences, will we be able to evaluate the full extent of the reformulation of the concept of universality in the Renaissance and its underlying unquestioned self-evidences.10
Even though the idea of the mathematization of nature is something that today is taken for granted, it was initially a rather strange idea, as Husserl contends. In my analysis of the underpinnings of this idea, I will highlight this strangeness, not only because it is, as I have argued elsewhere, a constitutive aspect of universality (one that has drawn little attention as far as I am able to judge), but also because the kind of strangeness that Husserl associates with the universality of the modern sciences differs in kind from the one associated with the Greek idea of universality. 11 It is perhaps not insignificant that while speaking of the Greek project of a universal rational science, Husserl uses the German term merkwürdig, remarkable, but also strange, or odd, whereas the modern sciences are described as a befremdliche Konzeption, that is, as a conception that appears strange, if not displeasing or disconcerting (Crisis, § 9c). Husserl begins his discussion of Galilean science by noting that for the Greeks, ideality, identity, and universality are primarily characteristics of the realm of the pure forms. For them “the real has [only] a more or less perfect methexis in the ideal” (Crisis, § 9). Husserl therefore concludes that all application of the pure forms of geometry to nature was only “a primitive application” (ibid.). Now with Galileo, nature no longer participates in a realm of idealities distinct from it; it itself is idealized and is shown to possess its own ideal substratum. Husserl writes that “through Galileo’s mathematization of nature, nature itself is idealized under the guidance of the new mathematics; nature itself becomes—to express it in a modern way—a mathematical manifold” (ibid.). Needless to say, with this idealization of a domain initially foreign to the ideality of pure forms, nature becomes the object of universal insights. But what is it that allows pure mathematics and geometry to become the guide to the formation of exact physics in the first place? What is, Husserl asks, the “hidden, presupposed meaning” of Galileo’s guiding model of mathematics, which “had to enter into his physics along with everything else,” that is, with everything that “consciously motivated him” (Crisis, § 9a). If I am interested in Husserl’s answer to this question, it is precisely because it will tell us something significant about the idealities and the universality peculiar to the modern sciences.
Even though the abstraction of mere spatio-temporal shapes from things intuited in the world of everyday life never on its own leads to the formation of geometrically ideal, that is, absolutely identical shapes, the perfection of technical capabilities in the practical world allows for the experience of the progressive precision of these shapes, and hence of “an open horizon of conceivable improvement” regarding these shapes (ibid.). As Husserl remarks, “out of [this] praxis of perfecting, of freely pressing toward the horizons of conceivable perfecting ‘again’ and ‘again,’ limit-shapes [Limes-Gestalten] emerge toward which the particular series of perfecting tend, as toward invariant and never attainable poles” (ibid.). From the repetitive attempts aimed at perfecting, say, the measurements of shapes, the ideal limit-shapes, or pure shapes, which subsequently become the object of geometry, arise by way of acts of idealization, that is, by way of acts that Husserl characterizes as distinctly different from acts of abstraction. Unlike the shapes abstracted from spatio-temporal bodies, these limit-shapes are pure idealities, that is identically repeatable forms that are “intersubjectively determinable, and communicable in [their] determinations, for everyone” (ibid.). Husserl writes: “If we are interested in these ideal shapes [for their sake] and are consistently engaged in determining them and in constructing new ones out of those already determined, we are ‘geometers.’ The same is true of the broader sphere which includes the dimension of time; we are mathematicians of the ‘pure’ shapes whose universal form is the co-idealized form of space-time” (ibid.). Next to real practice, geometry and mathematics (whose objects are the pure limit-shapes, or spatio-temporal forms, that emerge in real praxis where they can only be infinitely approximated) thus give rise to “an ideal praxis of ‘pure thinking’ which remains exclusively within the realm of pure limit-shapes” (ibid.). However, what also sets this ideal praxis radically apart from empirical praxis is the fact that in pure mathematics and geometry, these shapes are no longer the object of graduation and approximation. In mathematical praxis exactness is attained “for there is the possibility of determining the ideal shapes in absolute identity, of recognizing them as substrates of absolutely identical and methodologically, univocally determinable qualities” (ibid.). But besides the idealizations of all sensibly intuitable shapes (such as straight lines, triangles, and circles) that mathematics and geometry can carry out according “to an everywhere similar method,” it also becomes possible to use “these elementary shapes, singled out in advance as universally available, and according to universal operations which can be carried out with them, to construct not only more and more shapes which, because of the method which produces them, are intersubjectively and univocally determined” (ibid.). Indeed, the discovery that characterizes modern geometry was that of the possibility of “producing constructively and univocally, through an a priori, all-encompassing systematic method, all possible conceivable ideal shapes,” (ibid.) whether or not there are sensibly intuitable models for them in reality. With this, the ideal space has become infinite as has the task, “which for us, is linked as a matter of course with the concept of geometrical space” (Crisis, § 8).
Yet, as Husserl notes, although geometry construes the entirety of all conceivable shapes in thought alone—and seemingly, in complete abstraction from the practical world, geometrical methodology “points back to the methodology of determination by surveying and measuring in general, practiced first primitively and then as an art in the prescientific, intuitively given surrounding world” (Crisis, § 9a). Since the shapes that are intuitively experienced, or that are merely conceived in general (through abstraction), blend into one another in the “open infinity” of the space-time continuum of the prescientific surrounding world, they are “without ‘objectivity.’ ” They are not “intersubjectively determinable, and communicable in [their] determinations, for everyone—for every other one who does not at the same time factually see” them (ibid.). Now the role of the art of measuring already consists in securing some intersubjective objectivity for these shapes. It serves to render univocally determinable each single shape that is experienced in the space-time continuum of shapes characteristic of everyday life, and this according to a methodology that is intersubjectively grounded. By “picking out as [standard] measures certain empirical basic shapes, concretely fixed on empirically rigid bodies which are in fact generally available,” and holding these against other bodies, the art of measuring becomes capable of determining the latter “intersubjectively and in practice univocally—at first within narrow spheres (as in the art of surveying land), then in new spheres where shape is involved [Gestaltsphären]” (ibid.). What Husserl seeks to bring into the open here is the ultimate rootedness of pure mathematics in the life-world. The purely geometrical way of thinking, and hence, the striving for philosophical knowledge, that is, “knowledge which determines the ‘true,’ the objective being of the world,” is the idealization of “the empirical art of measuring and its empirically, practically objectivizing function.” As is made clear in the “The Origin of Geometry,” the art of measuring is “pregiven to the philosopher who did not yet know geometry but who should be conceivable as its inventor” (Origin of Geometry, p. 376). Even though the “philosopher proceeding from the practical, finite surrounding world ... to the theoretical world-view and world-knowledge ... has the finitely known and unknown spaces and times as finite elements within the horizon of an open infinity,” still he does not yet have “geometrical space, mathematical time, and whatever else is to become a novel spiritual product out of these finite elements which serve as material; and with his manifold finite shapes in their space-time he does not yet have geometrical shapes” (ibid.). Undoubtedly, the philosopher becomes the proto-geometrician only on the basis of a new sort of praxis, one that arises from pure thinking, but also one that takes its clues from the praxis of the gradual perfection of the art of measuring. For Husserl, then, the art of measuring is clearly “the trailblazer for the ultimately universal geometry and its ‘world’ of pure limit-shapes.” Pure mathematics and geometry have their origin in this method for securing intersubjective truth, and it is this origin that provides them with their true meaning. This is the premise on whose basis Husserl argues that, by taking the achievements of these disciplines for granted, Galileo had become oblivious to geometry’s and mathematics’ origin in that life-world, an origin that alone makes them meaningful for mankind. But something else becomes clear at this juncture as well, namely that the rediscovery of ancient geometry in the Renaissance amounted not only to having recourse to “a tradition empty of meaning” (Origin of Geometry, p. 366) but also that the prime (if not the sole) way of seeking to secure universal intersubjective validity in modern Europe takes place by way of spatio-temporal shapes and forms. Yet Husserl’s prime concern is to demonstrate that the new sciences that have come into being by modeling themselves after ancient geometry are disconnected from the prescientific life in the given world that represents the horizon of all meaningful inductions.12 But by highlighting only Galileo’s obliviousness to geometry’s origin in the life-world and the ensuing consequences for the development of the modern sciences, the fact that universality is primarily ascribed to geometrical idealities, and that this priority of the universality of spatio-temporal shapes affects the very concept of universality itself, may fail to receive in Husserl’s work the attention it merits. Undoubtedly, geometry is the first philosophical science because it permits the establishment of the absolute identity of ideal shapes in such a way that they are the same for everyone at any time. But the possibility of universality thus becomes, first and foremost, a function of the shape of the res extensa, of things of nature, more precisely of their idealized shapes, and this to such a degree that in the absence of such shapes it seems to be impossible to secure anything universal at all. The fate of “psychology,” which in the wake of the Cartesian dualism of nature and mind has never been capable of achieving the status of a science comparable to that of the natural sciences, is a clear indication of the limitation of the modern concept of universality to the universality of the idealized shapes of spatio-temporal bodies.
In The Origin of Geometry, Husserl argues that the persisting truth-meaning of geometry is a function of the possibility of producing invariant and apodictically general contents for the spatio-temporal sphere of shapes, contents that can be idealized and can “be understood for all future time and by all coming generations of men and thus be capable of being handed down and reproduced with the identical intersubjective meaning.” But universality is not equivalent to idealized spatio-temporal shape, as the privilege accorded, from the Greeks via the Renaissance to the present, to what is extended in the world of bodies would seem to suggest. When Husserl adds, “This condition is valid far beyond geometry for all spiritual structures which are to be unconditionally and generally capable of being handed down,” he does not wish to imply that universality is predicated on ideal spatio-temporal shapes alone, but rather that in order to achieve an intersubjectively recognizable universality, “the apodictically general content [alone of other than geometrical forms], invariant throughout all conceivable variation” (Origin of Geometry , p. 377), is to be taken into account in the idealization. Indeed, the possibility of idealization and universality is not exclusively linked to geometrical form; hence the concept of universality itself is not intrinsically limited to shape in the spatio-temporal sense. As The Origin of Geometry points out, “ ‘ideal’ objectivity ... is proper to a whole class of spiritual products of the cultural world, to which not only scientific constructions and the sciences themselves belong but also, for example, the constructions of fine literature” (Origin of Geometry, pp. 356–57). Language (that is, language in general) is particularly a domain from within which “ideal objects” and “ideal cognitive structures” arise (Origin of Geometry, pp. 357, 364). In spite of the preeminence that the ideal shapes of geometry have enjoyed in the sciences, and in a conception of philosophy more geometrico, that is, as Husserl points out, a conception that embraces the “methodological ideal of physicalism,” they constitute only one of the possible formations capable of ideal objectivity and of “intersubjective being” (Crisis, § 34f). Yet the exemplarity of geometrical universal truth is not therefore diminished. Indeed, as Derrida has shown, a distinction made by Husserl in Experience and Judgment bears on these different types of ideality. Compared to the idealities of words or cultural products that are bound idealities—in that they are dependent on an empirically determined temporality or factuality—the geometrical ideal objectivities are free idealities (though free only with respect to empirical subjectivity), and thus the only ones that can claim to be truly universal (Derrida, 1978, 71–72).
Still, the intricate connection between spatio-temporal shapes and rational universal ideality will have to continue to interest us as we now turn to Galileo’s mathematization of nature. In fact, as we will see, the very possibility of the modern exact sciences rests on this connection. Even though pure geometry and mathematics reveal identical and nonrelative truths, these truths pertain only to bodies in the world—to the bodily world. According to the Crisis, Galileo realized that all “pure mathematics has to do [solely] with bodies and the bodily world only through abstraction, i.e., it has to do only with abstract shapes within space-time, and these, furthermore, as purely ‘ideal’ limit-shapes” (Crisis, § 9b). Galileo was thus fully aware of the fact that the universal truth of which pure mathematics is capable concerns exclusively an abstraction of the bodily world, its abstract shapes, and, in the end, only its ideal and fully identifiable limit-shapes. Pure mathematics derives its universal truths from the bodily world alone, more precisely from the idealized shapes of these very bodies. Yet there is much more in the physical world than just bodies. Or, differently put, the spatiality of bodies is only one of the eidetic components of bodies. Hence if there is to be a philosophical or scientific knowledge of the world, the specific qualities, or sensible plena that all actual shapes possess in empirical sense-intuition, as well as “the universal causal style” by which all experienced bodies are bound, must necessarily be accounted for. Needless to say, it is mathematics once again that shows Galileo the way to accomplish this task. The latter had not only shown that through the idealization of subjectively relative objects, one can arrive at objectively determinable entities, but also that by descending again from the world of idealities to the empirically intuited world, as demonstrated by the contact between mathematics and the art of measuring, “one can universally obtain objectively true knowledge of a completely new sort about the things of the intuitively actual world, in respect to that aspect of them (which all things necessarily share) which alone interests the mathematics of shapes, i.e., a [type of ] knowledge related in an approximating fashion to its own idealities” (ibid.). Indeed, by becoming “applied geometry,” ideal geometry made it possible for the art of measuring to calculate, for everything in the world of bodies, “with compelling necessity, on the basis of given and measured events involving shapes, events which are unknown and were never accessible to direct measurement” (ibid.). Galileo thus concluded that it should be possible to do for all the other aspects of nature—the real properties and the realcausal relations of bodies in the intuitable world—what had been done for the sphere of shapes, namely, to extend “the method of measuring through approximations and constructive determinations” (ibid.), that is, a method developed exclusively with respect to shapes, to their altogether different realm. However, a difficulty arises at this point: How can a science or philosophy of the one and same world that binds us all be achieved if “the material plena—the ‘specific’ sense-qualities—which concretely fill out the spatio-temporal shape-aspects of the world of bodies cannot, in their own gradations, be directly treated as are the shapes themselves” (ibid.)? Exactitude is possible only with respect to idealities. Even though sensible qualities are subject to gradation, in their case, as well as in the case of everything that is of the order of the concrete sensibly intuited world, it is, as Husserl writes, “difficult for us to carry out the abstract isolation of the plena ... through a universal abstraction opposed [in universaler Gegenabstraktion] to the one which gives rise to the universal world of shapes” (Crisis, § 9c). As a result, no precise measurement of them is possible nor “any growth of exactness or of the methods of measurements” (ibid.). If no direct mathematization of the plena is possible, it is because there seems to be no world of idealities specifically their own. In short there are no limit-plena, and hence also no “geometry” of such idealities. As Husserl quite unambiguously remarks: “We have not two but only one universal form of the world; not two but only one geometry, i.e., one of shapes, without having a second for plena” (ibid.). What this means is that with respect to the objective world, or nature, we possess, as Jan Patočka formulates it, “only one rational and general form to whose ideal objectivity no parallel in the domain of quality exists” (Patočka, 1988, 233–34). As far as the one and the same world is understood objectively, that is, as a bodily world, there is only one form of universality, and this form of universality is inherently thought from this one aspect that all bodies have in common, namely shape.
Motivated by the Greek idea of an all-embracing science, Galileo concluded that in order to account for the world of nature as the one and the same objective world that we all share, those aspects of it that (unlike the shapes of bodies) cannot directly be mathematized, and which, because they lack a mathematizable world-form, are heterogeneous to spatio-temporal forms, can nevertheless be mathematized, although in an oblique way. Indeed, since in every application to intuitively given nature, pure mathematics must renounce its abstraction from the intuited plena, without therefore having to give up what is idealized in the shapes, Galileo realized that “in one respect this involved the performance of co-idealization of the sensible plena belonging to shape” (Crisis, § 9d), and that, consequently, the intuited plena are capable of indirect mathematization. In short, the objective world as a whole “becomes attainable for our objective knowledge when those aspects which, like sensible qualities, are abstracted away in the pure mathematics of spatiotemporal form and its possible particular shapes, and are not themselves directly mathematizable, nevertheless become mathematizable indirectly” (Crisis, § 9c). Now the indirect mathematization of that part of the world that has no mathematizable world-form is possible only if one assumes that the plena and the shapes of the bodies to which they belong are intertwined. Husserl notes that indirect mathematization is “thinkable only in the sense that the specifically sensible qualities (‘plena’) that can be experienced in the intuited bodies are closely related [verschwistert, that is, like brother and sister] in a quite peculiar and regulated way with the shapes that belong essentially to them” (ibid.).13 According to this idea, or rather hypothesis, which founds Galileo’s new physics, “every change of the specific qualities of intuited bodies which is experienced or is conceivable in actual or possible experience refers causally to occurrences in the abstract shape-substratum of the world, i.e., that every such change has, so to speak, a counterpart in the realm of shapes in such a way that any total change in the whole plenum has its causal counterpart in the sphere of shapes” (ibid.). Even though this conception has lost “its strangeness [Befremdlichkeit] for us and [has taken] on—thanks to our earlier scientific schooling—the character of something taken for granted,” (ibid.) this was not yet the case for Galileo. We must, Husserl writes, “make clear to ourselves the strangeness of his basic conception in the situation of his time” (ibid.). If this idea with which the groundwork was laid for an all-encompassing science of the objective world is strange, it is not merely because of its novelty. Since it is a conception that in the meantime has become obvious to us, and is universally accepted, we can assume that its strangeness derives, first, from the fact that it permits the establishment of something that is universally valid, and that therefore collides with held beliefs. Undoubtedly, the Renaissance had already opened itself to the general idea (which announces itself in everyday experience) that all occurrences in the intuitive world yield to universal induction. But the assumption that “everything which manifests itself as real through the specific sense-qualities must have its mathematical index in events belonging to the sphere of shapes” (ibid.) and that makes it possible to indirectly mathematize the plena—that is, the construction ex datis (from the facts), and full determination, of all events in the realm of the plena—is also strange in the sense that it is, and always remains, a mere hypothesis. More precisely, this assumption is remarkable and strange because, in spite of its verification in numerous instances, it remains a hypothesis that must endlessly be confirmed. Husserl writes: “The Galilean idea is a hypothesis, and a very remarkable one at that [von einer höchst merkwürdigen Art]; and the actual natural science throughout the centuries of its verification is a correspondingly remarkable sort of verification. It is remarkable because the hypothesis, in spite of the verification, continues to be and is always a hypothesis; its verification (the only kind conceivable for it) is an endless course of verifications” (Crisis, § 9e). The idea that sustains Galileo’s physics—the mathematical approach to nature and the universality that it establishes with respect to the plena and causality—remains forever hypothetical. Indeed, since the mathematization of the plena is based on a substruction in thought of a hypothetic relation between shapes and the qualities of spatio-temporal things, that is, on something that can never be experienced and verified as presenting itself as such, and hence in full self-evidence, the verification of such a relation needs to be repeated again and again. The truth of a connection between bodily shapes and plena cannot be acquired once and for all, and, consequently, is never a given.14 What is strange about Galileo’s founding hypothesis, and what puts it at odds not only with the natural attitude but also with the scientific spirit of Galileo’s time, is that the universality that it establishes with respect to the one and same world of physics presupposes an infinite task. In spite of the repeated verification of this hypothesis in the praxis of the sciences, it must be continuously reasserted. Undoubtedly, this essential instability of the universal laws of the sensible qualities of intuitable things (and of the overall causal style of these things) derives from the indirect mathematization in which the plena are tied to ideal shapes, that is, essentially, to an order foreign to them. In conclusion, we can say that the infinite need to verify the hypothesis that supports the indirect mathematization of nature, by which the one and same physical world is rendered scientifically and universally intelligible, shows that the infinite task-character of the objective universal derives from this universal’s intrinsic foreignness to its object. As Husserl emphasizes, the constant necessity to verify exact physics’ founding hypothesis is not caused by possible error but because “in the total idea of physics as well as the idea of pure mathematics [there] is embedded the in infinitum, [as] the permanent form of that peculiar inductivity which first brought geometry into the historical world” (ibid.). It is rooted in the distinct foreignness of idealities predicated on spatiotemporal shapes—that is, idealities resulting from the objectification of “one abstract aspect of the world”: the pure shapes of “ideal geometry, estranged from the world [weltentfremdete]” (Crisis, § 9b)—to what even within the objective world is not of the order of the bodily. Furthermore, even though in the indirect mathematization of the plena, “one always has to do with what is individual and factual,” the whole method has from the outset, “a general sense.” Husserl writes: “From the very beginning, for example, one is not concerned with the free fall of this body; the individual fact is rather an example” (Crisis, § 9d).
The factual success and inductive productivity of the approach in question is not in doubt. It infinitely surpasses the accomplishments of all everyday forms of prediction. Nevertheless this success, which remains meaningless as long as its method is not tied back to the concerns of the life-world, is also a function of an intrinsic foreignness of a universal derived from one aspect of the world of bodies to other aspects of the latter. Even though such foreignness is an intrinsic feature of universality as such, the particular way in which the idealized bodily shapes are brought to bear on the sensible qualities of the things of nature (those permitting of sensible experience), that is, the need to confirm infinitely the hypothesis of a link between spatio-temporal shape and sensible plena, indicates an intrinsic limit of this very concept of universality in its application to nonphysical, or non-thinglike, aspects of the world. Let us remind ourselves that, for Husserl, the idea of a universal philosophy, or science, that announces itself in Greece, one that is synonymous with what the name Europe stands for, is the idea of an all-embracing philosophy, or science. Such a philosophy cannot limit itself to an intersubjectively binding understanding of the objective world, the world of nature, or to a concept of universality that is only binding for the physical world. Furthermore, given that geometry has been the model for the sciences, the question arises as to the extent to which universality is linked to shape in the first place. In order to achieve an intersubjective consensus about the ideal objectivities of the spiritual products of the cultural world, to which Husserl calls attention in The Origin of Geometry, it thus becomes necessary to uncouple universality from idealized shape and to think the form of other ideal objectivities in terms that are no longer tributary to this feature of bodily things.15
As a result of the absence of a reflection back on the original meaninggiving achievement of the idealization of the spatio-temporal forms that gave rise to the geometrical ideal constructions, it appeared that geometry produced “a self-sufficient, absolute truth which, as such—‘obviously’—could be applied without further ado” (Crisis, § 9h). Rather than being understood as “indices of ‘inductive’ lawfulness of the actual givens of experience,” the mathematical limes-formations arrived at through idealization were taken to correspond to the objectively true being of nature.16 As early as Galileo, a “surreptitious substitution [Unterschiebung ] [took place] of the mathematically substructed world of idealities for the only real world, the one that is actually given through perception, that is ever experienced and experienceable—our everyday life-world” (Crisis, § 9h). Husserl submits that this substitution of idealized nature for the prescientifically intuited nature is of the order of a disguising or covering over and replacement of the life-world. He writes:
In geometrical and natural-scientific mathematization, in the open infinity of possible experiences, we measure the life-world—the world constantly given to us as actual in our concrete world-life—for a well-fitting garb of ideas [Ideenkleid ], that of the so-called objectively scientific truths ... Mathematics and mathematical science, as a garb of ideas, or the garb of symbols of the symbolic mathematical theories, encompasses everything which, for scientists and the educated generally, represents [vertritt] the life-world, dresses it up [verkleidet] as “objectively actual and true” nature. It is through this garb of ideas that we take for true being what is actually a method—a method which is designed for the purpose of progressively improving, in infinitum, through “scientific” predictions, those rough predictions which are the only ones originally possible within the sphere of what is actually experienced and experienceable in the life-world. (Ibid.)
If this is the case, if indeed the pregiven world provides the horizon within which and in relation to which the idealization of nature takes place, then the substitution of the objective world of nature for the life-world amounts to an ethico-philosophical error. By reflecting back on what in the life-world motivated the creation of geometry—and, by extension, the sciences that from the Renaissance modeled themselves after it—the accomplishments of geometry and the sciences are not only tied to purposes “which necessarily [lie] in this pre-scientific life and [are] related to its life-world” (ibid.); but the idealized limit-shapes, in short, the spatio-temporal universals, also reveal themselves to be the products of acts of concrete intentional consciousnesses. In other words, by bringing into relief the life-world from which all idealizations and intersubjective identifications emerge, the geometrical universal exposes its historicity—that is, its production by a constituting consciousness. With this, the intersubjective accomplishments of geometric idealization, which have given rise to the success of the European sciences, are shown to be the product of a transcendental ego whose accomplishments are the very object of the new episteme of phenomenological philosophy sketched out in Part III of the Crisis, and which understands itself as the critical renewal of the Greek idea of an all-embracing science.