a relational epistemology renders the philosophical expression “in itself” equivocal, insofar as it is meant to refer to the thing in-itself. On the one hand, the expression designates the independence of the thing from human perception or knowledge, the separability of the object of our knowledge (concrete-real) from our knowledge of the object (the concrete-in-thought). On the other hand, it implies the independence of the thing per se, the separability of objects from relations. In this sense, the “thing in-itself” would designate the simple nature, or simple substance, whose existence Bachelard rejects (on the grounds that it is incompatible with physical theory). It is this second possible sense of the term from which Meillassoux’s terminology in After Finitude needs to be disentangled, while retaining his emphasis on the first. We can reconstruct Meillassoux’s “Cartesian thesis”—“all those aspects of the object that can be formulated in mathematical terms can be meaningfully conceived as properties of the object in itself”31—in such a way that it retains its Althusserian sense (the concrete-in-thought refers to and establishes knowledge of a concrete-real that “survives in its independence, after as before, outside of thought”) without requiring absolute knowledge of simple natures. That is, we can show that Bachelard’s non-Cartesian epistemology complements Meillassoux’s Cartesian thesis without contradicting it—and we can do so by thinking through the inclusion of that Cartesian thesis within the larger framework of rationalist empiricism.
Consider the object of scientific investigation with which Meillassoux is most directly concerned in the first chapter of After Finitude: the earth. The accretion of the earth is an “ancestral” event insofar as its existence pre-dates the emergence of the human species and terrestrial life. From a Cartesian perspective, it is also an event anterior to the existence of those secondary qualities that are specifically modes of relation between a living creature and its environment (e.g. color, heat, scent), such that an ancestral event is only meaningfully described through reference to primary qualities (e.g., wavelength, temperature, chemical reactions).32 Rather than specifically perceptual information, Meillassoux stipulates,
all that can be formulated about such an event is what the “measurements,” that is to say, the mathematical data, allow us to determine: for instance, that it began roughly 4.56 billion years ago, that it did not occur in a single instant but took place over millions of years—more precisely, tens of millions of years—that it occupied a certain volume in space, a volume which varied through time, etc.33
These mathematical data are derived from measurements contemporaneous with us and made available within a particular framework of scientific theory,34 but they specify information about a referent (the accretion of the earth) that preceded our very existence and thus did not itself exist as the correlate of our experimental protocols.
Did not itself exist: What is the “itself” that is referred to here? It is the independence of the physical process under scientific investigation (the accretion of the earth) from our knowledge of that process, the independence of the concrete-real about which we know through the concrete-in-thought. It thus pertains to the “in-itself” in the first sense of the term elaborated earlier: we know that the object of our knowledge is separable from our knowledge of the object. But is it an object that we know about? The earth is an object (a planet), but the accretion of the earth is a process, and studying it offers an excellent object lesson in the processual, relational constitution of “things in-themselves.” We are studying the temporal constitution of the object, its formation as an object, which implies that the alterations it undergoes to become the object it “is” do not simply cease once it has formed—as if there were a specific instant at which its form were established once and for all.35 Mathematizable properties of the object (the datable duration of its formation) make clear that it is not a simple substance or a simple nature, that it is not a “thing in-itself” in the sense that it is thinkable as discrete and self-identical. The thing that the earth is exists as a process that reaches a certain threshold of stability, but that also never freezes into unchanging self-identity. This is true of all objects.
Part of what is at issue here is the passage of a property Kant understood as relevant only to objects of experience (temporal constitution) over to the designation of things in-themselves—which from the perspective of Kantian philosophy could not be subject to transcendental time determinations. This terminological difficulty drives home that the provenance of the term “thing in-itself” (Ding an sich) is Kantian rather than Cartesian. In a sense, this is exactly Meillassoux’s point: the correlational reversal of our thinking about the relation between time and objects is so profoundly embedded in the frameworks of Kantian, Hegelian, and Heideggerian philosophy that our philosophical terminology is “itself” difficult to disentangle from their conceptual schemata. In this respect, however, Meillassoux’s references to the “thing in-itself,” or properties of “objects in-themselves,” are sometimes conceptually equivocal and rhetorically infelicitous. While rejecting Kant’s proscription upon knowledge of the in-itself, Meillassoux does want to retain a Kantian distinction between the “in-itself” and the “for-us” so as to block the post-Kantian collapse of that distinction in German idealism from Fichte through Hegel. But in doing so, he draws the Cartesian distinction between primary and secondary qualities into a sometimes uncomfortable relation to a Kantian terminology difficult to disentangle from the conceptual distributions of transcendental critique.
Meillassoux’s Cartesian thesis is that “all those aspects of the object that can be formulated in mathematical terms can be meaningfully conceived as properties of the object in-itself.” But it is precisely the specifiable uncertainty of quantities determined by measurement that gives the quantitative determination of properties scientific meaning.36 A measurement of the length of my desk (189.2 cm) has scientific value only if I can determine and stipulate the uncertainty of my measurement, which would require a more complex experimental apparatus than my tape measure. Meillassoux acknowledges (of course) that a measurement can be supplanted by one that “exhibits greater empirical accuracy” and that “empirical science is by right revisable.”37 His claim is that the referent of revisable determinations is external to the determinations themselves, and that these determinations constitute revisable knowledge of those referents: “science does not experiment with a view to validating the universality of its experiments; it carries out repeatable experiments with a view to external referents which endow these experiments with meaning.”38 One might ask, however: If it is the specifiable uncertainty of a measurement that makes it scientifically valid, and if the quantitative determination of all measurable properties is attended by uncertainty, can an aspect of the object designated by an uncertain quantity be conceived as a “property of the object in-itself?” After all, it is not the property (or the aspect of the object) that is uncertain “in-itself;” it is the quantity designating it.
What do we know about objects or events, through our quantitative knowledge, that is separable from the uncertainty of our quantitative knowledge? Thanks to radioactive dating techniques, we know that the accretion of the earth occurred billions of years prior to the genesis of the human species (and we did not always know this), though our knowledge of the age of the earth is attended by an uncertainty of some fifty million years.39 I could not quantify, exactly, the length of my desk, and measured at certain scales its length would not be a perfectly stable property. But I know that its length is greater than that of the keyboard it supports. Such examples might seem trivial, but they exemplify an interesting fact: although I cannot assign a perfectly accurate quantitative value to a property of the object “in-itself,” I can know something else about the object, which can be abstracted from my relation to it, on the basis of a determinately uncertain quantitative value that I assign to a metrological model of the object (i.e., the object as determined by measurement).40 What poses a problem for the exact assignment of quantities to objects in-themselves (determinate uncertainty) does not necessarily pose a problem for knowledge of quantitative relations among objects. If I know that the uncertainty of a measurement is within a certain margin, then I can also know something about the relative properties of different objects that is not compromised by that margin of uncertainty (e.g., my watch has more