Science in Deleuze and Guattari's "What is Philosophy?"

Thanks to Streetli for comments on an early draft

The account of science given in Gilles Deleuze's and Felix Guattari's What is Philosophy intriguingly enough begins with chaos. We should be careful not to identify "chaos" too directly with what the scientists talk about when it comes to chaos theory, chaos science (and we must be careful not to over-excitedly over-extrapolate from the popular literature on chaos, as its often done), and yet there are certain resonances between the two.

Deleuze and Guattari define chaos as having to do with a particular "infinite speed" (again, not to be confused with the empirical speeds of particles and objects. It might be better to think of "speed" as not a quantitative measurement of distance over time, but rather a particular grasping.) Chaos is associated with the virtual, which contains all possible forms. This should remind us that chaos doesn't exactly to have to do with individuated objects, entities and subjects but is in some sense prior to them, and it is the actualization of this virtual that produces all sorts of individuated entities (differentiation and differenciation.)

For Deleuze and Guattari, what science does with chaos is not to select an infinite movement as philosophy does, but rather to slow down this infinite speed, to give it a reference that could actualise the virtual. This is quite congenial to the pragmatic and constructivist theories of science that can be found, especially in Whitehead. Science does not directly impinge on the real, because of the near-infinite (or infinite) complexity involved, and therefore has to work off a pragmatic foundation, a series of idealisations or limitations. Therefore, Galileo decides to treat the problem of the free-fall of bodies by taking the idealised free-fall of the body with no air resistance, as Deleuze and Guattari point out. What this does is give scientists a way to confront the blooming confusion of the world. Operational definitions are used in such a way as not to multiply confusion and possible interactions to infinity, to make the object of science something that can be dealt with easily. This corresponds to what Deleuze and Guattari mean when discussing providing reference. We can see Cantor trying to tame infinity in mathematics—being unable to deal with the complexities involved therein, his strategy is to neutralise these by giving infinity a particular specific reference. "A set X is infinite if there is some one-to-one function from X to some subset of X." This is an operation that vastly simplifies the matter at hand—no longer having to deal with the boundless, to scale the apeiron.

The reference only has its meaning in relation to a particular slowing-down. Even something as non-problematic as a telescope only can be interpreted in a meaningful manner only with reference to a stabilized state of affairs (the distance is not wildly outside the range of the telescope, and there aren't too many vibrations...) The slowing-down that the scientist does is co-extensive with these phenomena that she is investigating, which allows the scientist to extract a particular measurement from it.

Science is concerned with the function, the parts of which are functives. The first functives that are offered to us are the limit and the variable. Reference is not found in the variable and the limit in themselves, but rather in relations between them, without which they wouldn't mean anything (the variable and the limit, the variable and the variable). Limits—like absolute zero, the speed of light, the Big Bang, and the various cosmological constants that are scattered around physics. It is these limits that determine the unfolding of the various variables that they are associated with, like the speed of light and velocity, or absolute zero and temperature.

This limit sometimes reappears on a "higher" level, in a relationship with the whole of the universe taken as a determinate entity. Here we come across the various conservation laws—the conservation of energy, mass, momentum, of charge, all appear here. But for us to be able to talk about the whole of the universe, we should be able to grid the universe with a particular frame of reference. This is the exoreference, the second type of limit. It is from these limits that you can start to generate variables, coordinates. (I suppose one way you can do so is, if you take a collision as a closed system, you can take the conservation of momentum from the centre-of-mass frame and then end up having a set of coordinates to grid the system.) A particle, or any sort of entity can only be spoken of as being actual and individuated when it can be comprehended by a system of coordinates.

These limits do not work because of the particular values that they hold. It does not matter that the total energy of the universe or some closed system is this or this, or that the value of the speed of light is approximately 3e8 (indeed, we can work with systems of coordinates where the speed of light is unity). What does matter is that the individuation of the variations of energy in a system, or the speed of a particle, have as conditions the limits associated with them. These limits end up as functioning as a horizon or as a reference point around which variables are oriented around.

The diversity of limits precludes a unity of science because each limit ends up creating a heterogenous system of coordinates, each of which is not reducible to the other. The plane of reference can almost be taken as the set of all these systems of coordinates. The plane does a preselection of forms such that they are all matched to limits. The limit in the end becomes the origin of a system of coordinates with more than one independent variable.

These independent variables interact in such a way that a third variable depends on them. The third variable, the dependent variable, is the state of affairs. What a state of affairs does is to depotentialise a chaotic virtual, and actualises it into something extensive. We can move from states of affairs to things when we deal with not one but with several axes, according to variables that are functions of each other. We might have a state of affairs of mechanics, and a state of affairs of thermodynamics, but a thing has both momentum and temperature. This is the individuation of the thing in science.

The next level of abstraction is the body, when we discover that particular properties are invariant under changes in coordinates. We move on from measurement to the discovery of invariants, originally formalised in mathematics under the work of group theory. This is the foundation of the Erlangen program in geometry, as Euclidean geometry can be seen as generated by a particular group of transformations (the rigid transformations). Topology can also be seen under this frame, dropping most, but not all invariants when it comes to "changing of coordinates" (continuous homeomorphisms). The body introduces a new relationship between the independent variables, introducing a new potential to renew individuation (especially when it comes to biological bodies. The individuation of the body “proceeds by a cascade of actualizations”). The biological body self-differentiates, determining functions in relation to internal and external milieus.

What is interesting about their account of science is what it fails to include, what is conspicuous by its absence. Most philosophical treatments of science discuss its epistemology and its ontology, and a lot of work has been done on this by Anglo-American philosophers of science. Deleuze and Guattari fail to discuss the problem of the demarcation between science and non-science, between good and bad science. They discuss functions but fail to analyse the ontological commitments implied (eg the existence of mathematical objects and the Quine-Putnam indispensability argument). They are uninterested in the ontological status of scientific objects, from electrons to dark matter, and certainly do not come down to the question and anti-realism in the traditional way. Not the problem of induction, not theory-laden data.

On one hand, this could be explained because of the fact that Deleuze and Guattari do not inherit the analytic tradition of the philosophy of science, which finds itself as a neutral universal background to science—the problems and concepts in the line of Russell, Carnap, Reichenbach, Quine, Kuhn, Lakatos et al. Only Kuhn is mentioned, and in a context that would perhaps be perplexing to most readers who come from the Structure. "...which amounts to saying with Kuhn that science is paradigmatic, while philosophy is syntagmatic.” It is anyway an offhand reference that owes much more to French structuralism and semiotics than to Kuhn himself, anyway.

“Rationality”, that old bugbear of discourse on and about science is uninteresting to them, perhaps given that it stays only on the level of mere opinion, doxa (look at the dreary mediocrities that are bet on in the name of rationality), that creates no function or concept or affect (science, philosophy, art), but rather is a mere abstraction assimilable to the Universals of contemplation, reflection and communication. What Deleuze and Guattari offer is not to adjudicate the issues of science, to teach the scientists how to be scientific, how to ensure progress—they are appropriately coy when it comes to the need the scientist has for philosophical concepts. “This amounts to asking whether science is, as we believe, equally and intensely in need of philosophy. But only scientists can answer that question.” This is rather a delineation of the mode of existence of science, which is irreducible to philosophy and art. To map, not to make a tracing of science, to use the terminology of A Thousand Plateaus.

The analysis of science is not an analysis of the epistemic or ontological nature of the functions involved in science, but rather to give an account of science not from the point of view of the scientist or the rational Subject (that exemplar of the State and the Market) but an account of the internal dynamics of science from the point of view of the functions themselves.

The functions are not taken as summaries of experience or acts of consciousness, nor are they taken as beliefs held by a scientist, or the Scientist, who uses them in some manner x, y, z. In fact, the scientist is not a figure that appears prominently, the generic scientist as a rational subject, but rather the “signed” partial observer, which is not identical to the scientist with whom it shares a name but still has an intimate connection with, who is not taken with the empirical situation of the scientist but is internal to the affairs of the function itself. (The difference in emphasis might have to do with the differing focus of French epistemology vis-à-vis analytic philosophy.) Their references, therefore, do not stand outside of science but are immanent to it—in that they zero onto the problematics opened up by science itself—Cantor, Gödel, Mendeleyev, Riemann, Euclid, Newton, Einstein, Laplace, Maxwell, Heisenberg.

It is almost that Deleuze and Guattari are saying, “Scientists! We are not going to lord it over your work—science is science, philosophy is philosophy, art is art (even if there may be zones of exchange and indistinction when there are secret becomings between one and another).”