formulate the conditions for a methodological critique of the transcendental, perhaps Bachelard’s claims will not seem particularly revelatory with respect to the epistemology of science. Yes, of course, science relies upon the empirical testing of mathematically formulated theories, and it relies upon the mathematical formalization of experimental results. But the philosophical consequences of Bachelard’s methodological dialectic are more curious. For example, following his remarks about the epistemological polarity of rationalism and empiricism, and about the epistemological field mediating between theory and practice, mathematics and experience, he tells us that “to know a natural law scientifically is to know it at once as phenomenon and as noumenon.”13 What is interesting here is that Bachelard retains the distribution of Kant’s categories—wherein phenomena are objects of experience while noumena can only be thought by reason—while rejecting the firm epistemological divide Kant had imposed between them. Natural laws, for Kant, are laws of phenomena, which can in no way be known as noumena themselves, nor applied to knowledge of noumena. Yet Bachelard claims that the methodological dialectic of scientific thought gives us knowledge, “at once” (à la fois), of the same thing (a natural law) as both phenomenon and noumenon. How can we make sense of this thesis?
What is at issue here is the status of knowledge per se. What is it to know something? In particular, how does the constitution of knowledge bear upon the distinction between objects of experience and objects of reason? To know a natural law, according to Bachelard, is to know it as both of these at once. In my view, it is the ground of knowledge that is at stake in such a claim. According to Kant, objects of experience can be known because they are grounded by transcendental conditions that determine their presentation as phenomena, as part of “nature” considered as the realm of transcendental laws. Objects of reason cannot be known precisely because they are not grounded by categorial conditions; the categories of the understanding cannot properly be applied to them, and thus they can only be thought. The distribution of objects between experience and reason (phenomena and noumena) and the distribution of mental activity between knowing and thinking are thus correlated to a distinction between the grounded and the ungrounded. According to transcendental philosophy, only that which can be grounded can be known. Bachelard’s epistemology of science depends upon surrendering this distinction: upon a radical acceptance that knowledge is without ground. To surrender the transcendental is to surrender the grounding of knowledge by transcendental conditions; the ground of the transcendental is replaced by the ungrounded dialectic of rationalism and empiricism.
This dialectic is ungrounded because it relies upon an alternation between epistemological poles that do not share criteria, yet which counter and inform one another through a transmutation of epistemological values across differential criteria. Because this transmutation is “ceaseless,” it never settles upon a ground; its epistemology is genetic, in the sense that what Bachelard calls the “rectification” of knowledge is continuous and recursively transformative. What we know undergoes revision through the differential imbrication of reason and experience, their exposure to one another’s discrepantly constituted fields of coherence, entailment, and legibility. What is at issue in such an epistemology is not so much a distribution of faculties within a subject of knowledge as the distribution of methodological coherence across a historical process open to the perpetual reconstitution of what can only seem to be its grounds. This is why Bachelard says that “the philosophy of physics is perhaps the only philosophy which is applicable even when it decides to overstep its own principles. In short it is the only open-ended philosophy. All other philosophies posit their principles as intangible, their primary truths as total and complete.”14 Scientific thought has to be able to overstep its principles because its principles must remain subject to correction by future developments, and such openness is itself the principle of a method ungrounded by either reason or experience but rather constituted by the perpetual transmutation of their values.
How can knowledge of noumena be subject to correction? Or, to put the question the other way around, how can revisable knowledge be knowledge of noumena? This is the epistemological problem with which Bachelard’s formulation confronts us, and we can approach it through the problem of ground if we begin not with noumena but with phenomena. If it is the basis of transcendental grounding that distinguishes objects of experience from objects of reason, and thus knowledge from thinking, then this distinction does not hold; so far as modern science is concerned, objects of experience are not grounded by the transcendental conditions of a cognizing subject. On the contrary, they are accessed through scientific apparatuses, by the technological constitution of givenness, not by that of transcendental categories. And even this technological constitution of givenness itself is not necessarily relayed to or by subjects through the synthesis of intuitions and concepts; scientifically, it is made legible through mathematical formalizations, into whose orders of coherence it is translated. Of course, the categorial structure of cognition is relevant to the interpretation of results (e.g., what sort of causality is at issue in the double-slit experiment of quantum mechanics). But the integration of technological givenness into mathematical formulae, their chains of entailment and their recursive modification, are indifferent to competing interpretations of the formalisms, and they need not obey the formal regularities by which objects of human perception are constituted. This discrepancy between scientific results and perceptual regularities is the source of modern science’s formidable evasions of the synthesis of receptive intuition with the categories of the understanding.
Technological conditions for the constitution of givenness are not transcendentally grounded insofar as they are themselves historically transformed and transformative. There is a historical technogenesis of “experience” itself, of the conditions of all possible experience, insofar as the field of what becomes technologically available to experimental inquiry undergoes ceaseless alteration, and it does so in concert with transformations of scientific knowledge. We could say that the availability of phenomena to experience is grounded in technological capacities, but the historical transformation of these capacities is itself ungrounded. It is itself subject to the dialectic of reason and experience, experiment and formalization, which generates transformations of scientific knowledge and concretizes the latter in devices, apparatuses, mathematically configured and accountable experimental setups. Since the reconstitution of technological capacities is a historical process that is itself constantly involved in the transmutation of epistemological values theorized by Bachelard, its condition of possibility is precisely that it be shorn of transcendental guarantee. What Kant said of noumena—that knowledge of noumena cannot be grounded, and thus is not knowledge—can be both accepted and transformed with respect to experimental phenomena: the technological conditions by which phenomena are constituted are ungrounded, and scientific knowledge changes on this condition. Since knowledge of phenomena is not only knowledge of what can be observed through regularities of perception but also observation and formalization of what cannot be made accessible through regularities of perception, to know a natural law scientifically is to know it at once as phenomenon and noumenon. The condition of possibility of this “at once” is the surrendering of transcendental ground as the fundamental criterion of knowledge, and the opening of knowledge to the ungroundedness of its historical transformation. This historical transformation works through the non-synthetic, relational disjunction of rationalism and empiricism, mathematics and experiment, formalization and technogenesis.
To know something as both phenomenon and noumenon is to know it as both empirically and rationally constructed, as neither given nor refractory to determination. A natural law is known as phenomenon insofar as it is determined, as least partly, through experimental observation. It is known as noumenon insofar as it is inaccessible to experimental observation. It must be determined as an object of reason, but this determination is also mediated by the experimental constitution of objects of experience. The rationally determined setup of the experiment, the multiplication of modes of technical perception, the filtration of indexical traces through formalization, the routing of mathematical formalizations back through new technological concretions, and so on—these produce and “stratify” regularities of experimental perception in such a way that they cannot simply be understood as given. Such stratification constructs an object of knowledge that is neither given to experience nor separated from its determinations: an object of reason that is not purely thought, but rather constrained