experimental outcomes, the consideration of experimental outcomes within the framework of existing formalisms, or the transformation of those formalisms to accommodate empirical findings.
From a philosophical perspective, which he gleans from Marx’s methodological considerations in the introduction to the Grundrisse, Althusser stipulates that the ideological opposition between the abstract (theory) and the concrete (reality) should be displaced by a relation between two concretes: “the concrete-in-thought, which is a knowledge, and the concrete-reality which is its object.”22 (See Figure 2.) It is not that the rational is abstract and the empirical concrete. What is merely given is abstract and must undergo a process of elaboration to transform it into concrete knowledge. What has to be theorized is not an opposition between the empirical (supposedly concrete) and the theoretical (supposedly abstract), but rather the transformation of ossified facts into the concrete-in-thought (Generality III) which has the concrete-real as its object of knowledge (we will return to this point shortly). Marx describes the transformation of the abstract into the Gedankenkonkretum as “the working-up of observation and conception into concepts” (der Verarbeitung von Anschau ung und Vorstellung in Begriffe).23 Thus, concepts are produced through the dual elaboration of both what is observed (Anschauung) and what is conceived (Vorstellung). The merely given becomes concrete through the integration of observations into conceptual schema and the encounter of rational determinations with empirical facts, their mutual Verarbeitung. In order not to become ideological—not to languish in received ideas or self-evident truisms—knowledge must be continually expelled by and reintegrated into the dialectic of the rational and the empirical, transformed within an operative, never fully unified or totalized theoretico-technical complex.
Figure 2. Abstract, Concrete-in-Thought, Concrete-Real. Althusser displaces the association of theoretical knowledge with the abstract, as opposed to the concrete. What is abstract is inadequate knowledge (ideology, ossified fact, the self-evidence of pure phenomena), while theoretical knowledge is the “concrete-in-thought” (a term borrowed from Marx).
Within the framework of the physical sciences, the recent project to redefine the kilogram unit offers a striking example of this methodological dialectic in action (I treat this example in detail in Chapter 6). The gram was initially defined, in 1795, as the mass of one cubic centimeter of water at the melting point of ice (thus, a kilogram has the mass of one cubic decimeter of water). This definition relies in turn upon the meter unit, which was defined in 1791 as one ten-millionth of the length of a quadrant along the Earth’s meridian through Paris. These quantities were established experimentally—in the case of the meter, through the famous surveying project carried out by Delambre and Méchain from 1792 to 1799.24 Platinum reference objects instantiating the length of the meter and the mass of the kilogram were then fabricated and deposited in a vault in Sèvres. When the metric system was adopted internationally in 1889, new reference objects were fabricated, and definitions of the meter and the kilogram were tied directly to these: the meter was defined as the length of the prototype meter bar; the kilogram as the mass of the kilogramme des archives. The meter has since undergone several redefinitions, most recently as the length of the path traveled by light in a vacuum during a time interval of 1/299,792,458 of a second. In November 2018, the kilogram was redefined in terms of the Planck constant.25 This means that the physical object which previously instantiated the kilogram unit no longer grounds its definition, just as the meter bar was previously eclipsed by reference to a physical constant (c, the speed of light).
The meter bar and the kilogram prototype are concretizations of theoretical knowledge: they instantiated the rational coordination of empirical findings in standards of reference for the ongoing quantitative determinations of scientific practice. Yet the kilogram prototype has been replaced because it had become abstract. No matter how carefully it is preserved, the object gradually accretes irregularities altering its mass, but because its mass is by definition 1 kg, these cannot be accounted for in an operative stipulation of how much its mass has drifted. Redefinition of the kilogram in terms of the Planck constant establishes a fixed quantity (a quantitative determination of the physical constant h), and this required an internationally coordinated effort to measure the Planck value itself with reference to the kilogram as previously defined, through equations correlating electricity to mass. Since 2014, through two fundamentally different experiments, the quantity h has been measured below a particular threshold of uncertainty. The fixing of the Planck number means that this uncertainty migrates to the kilogram unit itself (a far lesser degree of uncertainty than that previously attending the definition of the unit). “The kilogram” (object and unit) thus undergoes what we might think of as a process of reconcretization with respect to scientific knowledge: it is incorporated into a new system of theoretical knowledge coordinated with our best existing technologies, experimental procedures, and formalizations, such that the frame of reference previously grounding the unit is not only displaced but integrated into a new referential context. Meanwhile, what the Planck number designates—the minimal quantum of physical action—is that which is measured in the experimental campaign to redefine the kilogram; it is the concrete-real to which these measurements refer. It cannot be measured with exact accuracy, but it can be measured by experiments with determinate uncertainty and quantified within a margin of 20 parts per billion (2.0 × 10-9). The “real object” (quantum of action) remains exterior to its theoretical determination (it is what is determined by theory). But it has also become a rigorously specifiable object of knowledge, known with a determinate degree of uncertainty within an experimental and theoretical system of reference. The history of measurement recursively refines the very units (kg) upon which it is predicated; it does so through the measurements it makes available (h); and it does so through the integration of measured quantities into interrelated formalizations, such as those relating energy to both the Plank number and to mass (e.g., E = hv; E = mc2), coordinating empirical evidence with rational logic and enabling new programs of theoretico-technical research.
THE OBJECT OF KNOWLEDGE AND THE REAL OBJECT
Having begun to articulate an approach to rationalist empiricism by drawing together Bachelard’s and Althusser’s theories of scientific knowledge, we can now address some of the problems with the relatively thin realist epistemology put forward by Meillassoux in After Finitude. First of all, how can we square Meillassoux’s defense of the Cartesian distinction between primary and secondary qualities with the “non-Cartesian epistemology” formulated by Bachelard?26
We should bear in mind Bachelard’s stipulation that his “non-Cartesian philosophy complements Cartesian philosophy without contradicting it.”27 What he objects to in Cartesian epistemology is its fundamentally analytical method: the grounding of knowledge upon simple ideas according to the principle that “no construction is clear to the mind unless the mind knows how to take it apart.” According to Bachelard, “Descartes never pays heed to the reality of the complex, to the emergence of qualities in the whole not evident in the parts,” whereas “modern science begins with synthesis.”28 Epistemologically, he argues, modern science “relies for clarity on combining ideas rather than on trying to understand individual objects in isolation. In other words, instead of intrinsic clarity it relies on what I shall call operational clarity. Relations do not exemplify objects; objects exemplify relations.”29 Bachelard thus proposes a relational realism according to which
there are no simple phenomena; every phenomenon is a fabric of relations. There is no such thing as a simple nature, a simple substance; a substance is a web of attributes. And there is no such thing as a simple idea, for … no idea can be understood until it has been incorporated into a complex system of thoughts and experiences.30
These formulations emphasize once again that the relational epistemology of “modern science” cannot be grounded by either rationalism or empiricism in isolation;