Tag Archives: laruelle

Immanence and Objectivity

In her 1979 paper “Cognitive Repression in Contemporary Physics”, Evelyn Fox Keller describes the scientific viewpoint associated with classical (i.e. Newtonian) mechanics as based on a pair of conjoined assumptions. Firstly, that the subject of scientific knowledge is strictly separable from the possible objects of such knowledge; and secondly, that it is possible to establish a direct correspondence between what is known of each such object and its actuality. According to this viewpoint, “nature” is both objectifiable and ideally knowable by a scientific subject which stands apart from that nature in order to observe it.

We have here an operation of dividing-and-regluing very like that described by Laruelle as characteristic of philosophy (and, indeed, Laruelle would likely describe Fox Keller’s account as true of a certain philosophy-of-science, or philosophical epistemology, rather than of science itself as a practical stance). The immanent Real is split into an objectifiable domain of distinct entities, and a transcendental order of knowledge which proposes to organise those entities into a world (“the scientific worldview”, let’s say). Rather than thinking “according to the Real”, or from the premise that both “knower” and “known” are immanent to the same reality (and thus share a fundamental identity), the stance Fox Keller describes is “decisional” in Laruelle’s sense: it begins by making a cut, and by giving itself the authority to repair that cut.

Fox Keller observes that the principles of objectifiability and knowability break down in the face of quantum mechanical phenomena: they cannot be maintained simultaneously, and every attempt to do so produces metaphysical monsters in the guise of “interpretations” of quantum mechanics (as Derrida once put it: coherence in contradiction indicates the force of a desire). Her Piagettian reading of the resistance to non-classical epistemology in terms of affective positions is suggestive (in that smug “clever men in white coats are really just big babies” sort of way that has never quite seemed to go out of vogue, for reasons I could probably venture some pseudo-psychological explanations for myself), but doesn’t particularly help us resolve the problem of how to develop such an epistemology.

Susskind describes the situation as follows: in a classical system, we are confident of always being able to make a “gentle enough” measurement that the system being measured is not perturbed: the apparatus is able to determine how the system would behave if the apparatus itself were not present. This is, in fact, perfectly possible a lot of the time. Within a quantum system, however, measurement is carried out by means of operations* which participate in the total behaviour of the system itself, such that we are always observing the outcome of what I will call an effectuation. Any such effectuation is the effectuation both of a measurement and of a new state of the system. Both (classical) objectifiability and (classical) knowability are untenable under these conditions; the former because the apparatus of measurement is not strictly separable from the system being measured, and the latter because the process of obtaining information about one aspect of the system may render information about another aspect inaccessible.

This is helpful, but doesn’t go quite far enough. If we had not measured the particle’s position, we should have been able to measure its momentum (and vice versa); but this does not mean that, at some moment prior to measurement, the particle necessarily had both position and momentum (i.e. possessed some complete, if hidden, state in which both position and momentum were simultaneously inscribed). Rather, measurement-of-position and measurement-of-momentum are distinct operations that effectuate one value at the expense of being able to effectuate the other.

A thoroughgoingly immanent account of how science proceeds will be one which sees scientific theory-building, measurement and knowledge-formation as effectuations of the same Real, rather than the work of one kind of agent – the detached scientific knower – upon one kind of patient – “Nature”, etherised upon a table. That is one way of looking at the problematic with which Laruelle is engaged, and of understanding why the “quantum” has taken on such a totemic significance for him in his later work.

  • As Susskind also reminds the reader, an operator is a mathematical entity, which acts on state vectors to produce new state vectors. It does not, however, change physical reality – rather, it describes how a real-valued measurement is derived from a state vector in a quantum system. How the state of that system changes in the process of carrying out the measurement is a quite different matter. Accordingly, I have corrected “operator”, where it appears above, to “operation”. Caveat lector, as always when I’m trying out new stuff.

Solace of Quantum

Early on in Leonard Susskind and Art Friedman’s Quantum Mechanics: The Theoretical Minimum, the authors illustrate a difference between the logic of predicates and sets, and the logic of observations at quantum scale. One way to look at it is in terms of modelling.

If the state space of a classical system is the set of all the states the system can be in, then a proposition about the system corresponds to a predicate P that picks out certain states as possible states of the system if that proposition is true. Susskind’s example is a single roll of a six-sided die. Let the “state” of the die be the number that is facing upwards after the roll – the state space S is then the set {1, 2, 3, 4, 5, 6}. To the proposition “the value of the die is even” corresponds the predicate P that picks out the subset of the state space S' = {2, 4, 6}. We have S, the state space, P, the predicate, and S' = {x ε s & P(x)}, the subset of the state space which satisfies the predicate.

The state space is thus a model for propositions about the system, which means that we can translate statements about propositions into statements about predicates and subsets. If two propositions about the system are true at once, then the states the system can be in are those which are picked out by both of their corresponding predicates. For example, take the propositions “the value of the die is even”, and “the value of the die is greater than three”. Considered separately, these correspond to two predicates, P1 and P2, which pick out two different subsets of S, S1 = {2, 4, 6} and S2 = {4, 5, 6}. The state subset corresponding to the proposition “the value of the die is even, AND is greater than three” is the intersection of the subset S1 picked out by P1 and the subset S2 picked out by P2: {4, 6}. The subset corresponding to the proposition “the value of the die is even, AND/OR is greater than three” is the union of S1 and S2: {2, 4, 5, 6}. There is thus a “primitive” or “direct” set-theoretic interpretation of propositions concerning the state of the system, based on Boolean algebra.

An important characteristic of classical systems is that they “hold still” while being observed: the state space is a static image of possible measurement results within a given reference frame, and we can combine measurements freely without that image shifting beneath our feet. You can measure both the position and the velocity of a billiard ball, in whichever order you like, since there exists a state of the billiard-ball-system that captures both of these properties simultaneously.

The way we model the state of a quantum system is necessarily different, because the state of such a system is not independent of observation: to every measurement of the truth of a proposition about a quantum system corresponds a new distribution of possible states of the system. We can lose information by measuring (for example, if we observe the velocity of a particle, we lose information about its position). The order in which observations are made is therefore significant: O1 followed by O2 may well get you a different result to O2 followed by O1, which means that the algebra of quantum observation – unlike the Boolean algebra of classical systems – is noncommutative.

Susskind makes the following eyebrow-raising statement – “the space of states of a quantum system is not a mathematical set; it is a vector space” – and then qualifies it in a footnote: “To be a little more precise, we will not focus on the set-theoretic properties of state spaces, even though they may of course be regarded as sets” (italics mine). This is a subtle distinction. A vector space is a set, or at least is not not a set – working in vector spaces doesn’t in any sense take you out of the set-theoretic mathematical universe. But the way states “fit together” in a quantum system – their way of being compossible – is not readily definable in terms of primitive set-theoretic operators like union and intersection: you need the language of linear algebra, of orthonormal bases and inner products, to make sense of it.

In the light of this, it becomes a little clearer why Laruelle mobilises a metaphorics of “quantumness” – of vectors and matrices, superpositions and complex conjugates – as a way of undermining or circumventing the static philosophical architecture of “Being”: the claim he’s trying to establish is that non-standard philosophy is in some sense to standard philosophy as quantum mechanics is to classical mechanics…

Laruelle: from identity to inclusion

I think of Laruelle’s notion of identity as working a bit like the way inclusion functions work (with some caveats, which I’ll raise at the end). Here’s how.

The identity function on a domain is the function which sends every value in that domain to itself: f(x) = x.

Every function has a domain (which identifies the kinds of values it accepts as inputs) and a codomain (which identifies the kinds of values it produces as outputs). We can write this as follows: f : A -> B means “f has the domain A, and the codomain B”, or “f accepts values of type A, and produces values of type B”. The identity function IdA : A -> A is the function f(x) = x for the domain A; that is, it accepts values from the domain A as inputs, and send every value in that domain to itself. Similarly, there is an identity function IdB: B -> B which is the function f(x) = x for the domain B; and so on.

An inclusion function from a domain A to a codomain B, where A is a subset of B, is almost exactly like the identity function on A – it sends every value in A to itself – except that the codomain is B rather than A. So it is the function f : A -> B where f(x) = x.

For example, there is an inclusion function from Z, the set of integers, to R, the set of real numbers, which just is the identity function on Z except that the codomain is R rather than Z. It sends every integer to itself, but to itself “considered as” a real number (since the integers are a subset of the reals). We might say that every integer has a “regional” identity as an integer-among-integers, mapped by the identity function IdZ : Z -> Z, and an “integer-among-the-reals” identity as a real number, mapped by the inclusion function f : Z -> R. Both functions are identical in terms of their inputs and outputs, but they have different meanings.

Now, it seems to me that for Laruelle, the Real is “like” (but see caveats below) a sort of global codomain that absolutely everything has an inclusion function into, since all “regional” domains are just subsets of this codomain. So for absolutely anything you like, it has both a “regional” identity (mapped by the identity function on its regional domain) and a One-in-one identity (mapped by the inclusion function from that domain into the Real).

When we consider everything in the aspect of its One-in-one identity, we can consider juxtapositions that aren’t otherwise possible. For example, let M be the domain of men, and F the domain of women. If we know that there is a common codomain (H, the domain of human beings) of which both M and F are subsets, then we can consider the identities man-among-humans and woman-among-humans as potentially overlapping, able to be combined or mutually transformed in various ways that the identities man-among-men and woman-among-women seemingly are not.

The Laruellian principle of unilateral identity-in-the-last-instance with the Real can be understood as something “like” a global generalisation of this move from identity to inclusion.

Now, there are two caveats to be raised here. The first is that, in set theoretic terms, a global codomain is impossible, because of Russell’s paradox – “the One is not”, as Badiou says. Accordingly, we have to pass from something like a set into something like a “proper class”; and functions are defined between sets, not between sets and proper classes. So at the threshold of the Real, the mathematical analogy breaks down, as we should probably expect it to.

The second is that Laruelle himself is quite emphatic that the kinds of ordering and partitioning operations that sets and functions between sets enable you to perform, belong to the domain of “transcendental” material – language, symbolisation, the material through which the force-of-thought has its material effects. The real, being One, is non-partitionable; and, being foreclosed to thought, is not indexable or schematisable in the ways that the set-theoretic mathematical universe is. (The move to the “quantum” is I think intended as a move outside the set-theoretic mathematical universe; I’ll talk a bit more about that some other time). “Regional” domains may be structured and more-or-less set-like, but that is both their prerogative and their weakness with respect to the Real (or its weakness with respect to them, since it underdetermines them). We must not picture whatever structures we can imagine being stabilised, held fixedly within an underlying global order of structure that is just like them only somehow bigger.

The problem then is that a global generalisation of the move from identity to inclusion takes us beyond what is structurally thinkable, or at least beyond what is thinkable using the tools we use to think about and within regional domains. This prevents us from setting up any particular regional domain (e.g. “physics”) as a master-domain against which all the others can be relativised. We have in Laruelle something like an anti-totalitarian thinking of (or “according to”) totality.

Sufficiency, Adequacy, Fidelity

The “principle-of-sufficient-X” is a principle held by X, stipulating a condition to which it either aspires or already conforms by (its own) definition. Rule 34 is something like a principle of sufficient internet porn: it entails that ∀x: P(x), or equivalently that ¬∃x: ¬P(x), where P(x) means “there is porn of x”. But it is a meta-pornographic principle, a rule “of the internet”, rather than intrinsic to the pornographic stance: porn neither presupposes nor purports to enact its own sufficiency (i.e. the pornifiability of everything). The limit of pornographic inscription is not set by any unrepresentable act, any “last taboo” (there is always one more taboo, and it is always possible to break it – and where else but on the internet?), but by the rubric of explicitness*: porn is emphatically not about anyone’s interiority. (A new rule of the internet is needed, in fact: for every feeling, there is a corresponding “tfw” – “that feeling when” – statement illustrating the circumstances that would give rise to that feeling, ideally paired with a suitable gif. But “tfw” is arguably the gravestone of interiority: its premise is that every feeling is communicable, and linked to an occasion outside the self.)

Here is a trivial model of “sufficiency”: for every set, there is a free monoid whose elements are the finite sequences of elements of that set, whose identity element is the empty sequence, and whose monoid operation is the concatenation of sequences. Every set is convertible with its free monoid, in a precisely definable way (there is a functor from the category of sets to the category of monoids, and what is meant by “free monoid” in this context is that this functor is left-adjoint to the forgetful functor running in the opposite direction. Haskell programmers know the monad arising from this adjunction as the “List monad”; it’s worth studying, as an elementary example of how such things work). The free monoid construction means that there are “sufficient” monoids to cover the entire category of sets (although this shouldn’t be thought of in terms of there being an equal quantity of monoids and sets, since we’re dealing with infinite categories).

Is this really a model of “sufficiency” in the sense intended by Laruelle, when he talks of the “principle of sufficient philosophy”? Not quite, and it’s worth trying to figure out why. The principle of sufficient philosophy doesn’t just entail that for every entity in some domain – the world, or some region of the world – there is a philosophical reflection or representation of that entity and its relations with other entities. It is also implied (in Laruelle’s usage) that this reflection is not “free” (in the sense of being “freely generated”), but rather involves the covert addition of extra structure or information. Philosophy’s “world-system” is then a construction over the world which uses materials taken from philosophy – Laruelle will sometimes describe it as a “hallucination”. Philosophical sufficiency is thus indicted as an imposture: the in-sufficient or over-sufficient specular model poses (itself) as sufficient, and in doing so does a kind of violence to that which it claims to reflect.

We are dealing, in that case, with a kind of failed or defective specularity, which “makes up for” its defects by violently normalising that which it purports to reflect, mutilating the foot to make it fit the glass slipper which supposedly transparently ensheathes it. And there are many such systems abroad in the world today (although I note in passing that this account lines up rather well with Friedrich Hayek’s in The Road to Serfdom: Hayek claims that a centrally-planned economy must compensate for its inability to model the informational complexity of real economic activity through distortion, cover-ups, and ultimately violent political suppression…). But we also have in hand an example of a “mapping”, or transference between categories by means of a functor, which is rigorously, demonstrably, non-violent – which serves, in fact, as a counter-example to the violence of which Laruelle accuses philosophy. For there are “full and faithful” functors as well as “forgetful” ones – and the mathematics of category theory exhibits a panoply of different kinds of specularity, different ways in which one thing can be reflected in, projected on to, extracted from or transformed into another, faithfully or lossily, invertibly or non-invertibly.

The point here is not to say that all we need to do is turn philosophy into mathematics and all will be well. It can’t be done anyway – mathematics can propose images of thought to philosophy, and philosophy can do its best to attend to them carefully, but there is no general-purpose mapping between the two. We have to recognise something like Badiou’s Being and Event as a philosophical construction of ontology with mathematics, which draws on set theory as an organon of ontological stricture.

What I mostly miss in Laruelle is any sense that stricture can be useful: the general drift is towards destriction, letting it all hang out.  In some respects of course Laruelle is very strict – Galloway describes him as having a “prophylactic” ontology, which absolutely forbids the binding together of entities under any representational syntax whatsoever. But this enforced unbinding and excommunication of entities serves the purpose of allowing them to mix promiscuously, to be brought into identity with each other in an ad hoc manner, without regard for regulated channels of communication (or, it must be said, the semantic conventions proper to their discourses of origin). I compare Zalamea’s vision, in Synthetic Philosophy of Contemporary Mathematics, of a universe of “transits” between regions of mathematics, in which extremely delicate constructions make it possible for remote areas of knowledge to be brought into communication with each other, mixed and modulated and amplified in just the manner Laruelle seems to desire, but with complete and unyielding exactitude.

  • But on this, see Helen Hester’s Beyond Explicit, which considers precisely the impasse encountered by porn when it attempts to go beyond the “frenzy of the visible”. The pornographic act may be one of explicit depiction, but it is haunted by the undepictable.

Notebooks Out

You Just Can’t Understand Our Gnostic Sooth-Saying Because You’re Too Occluded

If this book/Voyage could be placed neatly in a “field” it would not be this book. I have considered naming its “field” Un-theology or Un-philosophy. Certainly, in the house of mirrors which is the universe/university of reversals, it can be called Un-ethical. Since Gyn/Ecology is the Un-field/Ourfield/Outfield of Journeyers, rather than a game in an “in” field, the pedantic can be expected to perceive it as “unscholarly”. Since it confronts old moulds/models of question-asking by being itself an Other way of thinking/speaking, it will be invisible to those who fetishize old questions – who drone that it does not “deal with” their questions.

Philosophers Are Children Scared Of The Dark

Patriarchy is itself the prevailing religion of the entire planet, and its essential message is necrophilia. All of the so-called religions legitimating patriarchy are mere sects subsumed under its vast umbrella/canopy. They are essentially similar, despite the variations. All – from buddhism and hinduism to islam, judaism, christianity, to secular derivatives such as freudianism, jungianism, marxism, and maoism – are infrastructures of the edifice of patriarchy. All are erected as parts of the male’s shelter against anomie.

We Get Ours Straight From The Real

In order to reverse the reversals completely we must deal with the fact that patriarchal myths contain stolen mythic power. They are something like distorting lenses through which we can see into the Background. But it is necessary to break their codes in order to use them as viewers; that is, we must see their lie in order to see their truth. We can correctly perceive patriarchal myths as reversals and as pale derivatives of more ancient, more translucent myth from gynocentric civilization. We can also move our Selves from a merely chronological analysis to a Crone-logical analysis. This frees feminist thought from the compulsion to “prove” at every step that each phallic myth and symbol had a precedent in gynocentric myth, which chronologically antedated it. The point is that while such historical study is extremely useful, we can, whenever necessary, rely upon our Crones’ clarifying logic to see through the distortions into the Background that is always present in our moving Self-centering time/space.

So, Mary Daly is quite the non-philosopher avant la lettre – the same global characterisation of all hitherto-existing thought as a sterile, self-regarding enclosure inextricably linked to a project of domination; the same claim to have discovered a radically different way of seeing (“Crone-logy”, “Spinning” etc) which treats that thought as material for revisionary redeployment; the same belief that one can (iff authentically female) immediately and in-person incarnate and speak “according to” an occluded Real. I was going to say that Laruelle was Mary Daly for dudes, but it would be more true to say that Mary Daly is gnosticism for lesbian separatists.

Immanence and Heresy

Balibar’s definition of heresy is a definition from the point of view of truth, as the “internal adversary” and logically insufferable “exception”. In other words, it is only according to the sense in which “the logical characteristic of truth” creates an enclosure that the adversary can be seen as “internal” to this enclosure, and only according to the sense in which this enclosure must be logically consistent that the heretic can be seen as “exceptional” with respect to this consistency. From this perspective, the heretic and the renegade are indistinguishable: both are identified by the characteristic of being in default of the truth. The renegade completes his renegacy by finally leaving the enclosure; the heretic is the one who remains inside, as an “internal adversary”, in spite of the fact that they truly, if still secretly, belong to the outside, the domain which is not regulated by the truth. For example: the “leftist” renegade continues to identify himself as a “leftist”, hangs out in “leftist circles”, speak in leftist code to leftist friends, whilst secretly harbouring un-leftist attachments, an orientation towards the outside of the leftist enclosure, where the external adversary rules in force. From time to time he will speak his “heresy”, and enjoy for a moment the drama of public contrariness; but it is only a matter of time before he finds the company of non-leftists more congenial, and abandons forever the commitments of his – in piquant retrospect – misguided youth…

Immanence is heretical (says Laruelle), but why? Because according to the point of view of immanence, the logical enclosure which belongs to truth is a kind of hallucination: its consistency is established according to a decision which cannot be justified in terms of immanence. It must find a way to present its self-justification, or justification in terms of its own truth, as underwritten by the Real; this is what Laruelle calls “auto-position” and “sufficiency”. It is as if – in this story, the story told by philosophy to itself – the Real were determined by the truth which it determines, in perfect accord and reciprocity, a relationship of reversibility or exchangeability. What is “heretical” here is to break this symmetry, to insist on the one-way and irreversible priority of the Real before the truth. This is a definition of heresy from the point of view of immanence, as the suspension of the truth’s authority to define its own logical enclosure and determine what is internal to it and consistent with it. The heretic according to immanence is not someone whose secret loyalty is to the “outside”, like the leftist renegade, but someone to whom the distinction between inside and outside, and the logical basis on which that distinction is made, has a limited salience: it no longer has the power to organise all “context” according to its own rubric, but must be seen according to a larger contexture which it does not control. Laruelle leaps directly to the Vision-in-One as a kind of (non)-context-of-all-contexts; he recontextualises philosophical decision within something that cannot be recognised as a context as such. This leap is a leap of gnosis, which relativises everything in a single stroke; but that is not the only way we can go. The imperative of navigation is that one simultaneously refuse to stay put within any given enclosure, and refuse the mystical revelation of the transience of all truths.