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.