Category Archives: Philosophy

Temporality and arche-temporality

There was a moment during my reading of Peter Wolfendale’s OOP: TNNC where I demurred somewhat, and it was at his reading of Harman on time/space.

Harman claims that real change is spatial, not temporal; in this he seems to me to be in agreement with Badiou, amongst others. Time for Harman, as for Badiou, is the temporality of permutation, during which an object’s properties cycle through various actualisations; real change is change to the disposition of the elements over which the temporal “cursor” ranges, and is experienced as temporal discontinuity, a break between epochs. (cf Foucault and the episteme, etc). Pete complains that this doesn’t enable us to account for the “deep” cosmological time of the arche-fossil, since all we have is local temporalities, cursors over objects – cosmological time must encompass the history of all possible objects, and cannot be local in that sense. On the other hand, the notion of a global temporality is tricksy to say the least, for good scientific (relativistic) reasons. In space-time, the everything that happens is intertwined with the temporality of its happening – when we say “such-and-such happened twenty billion years ago”, we typically omit a number of qualifications that it would be troublesome to spell out in detail.

This afternoon I read, in Chatelet:

“Time is born along with the Heavens, Plato assures us in the Timaeus, and was created on the model of eternal nature. It is the image of that eternal progression whose rhythm is number. The perfect year, the conjunction of the revolutions of the eight planets, has elapsed precisely once the Same has completed its revolution. Closed up in the gilded cage of Eternity, Time is certainly not responsible for the flux of becoming. So what is it that permits change? It is Space, the condition of dispersion, and thus also the condition of the meaningless scandals and provocations of the Other.”

So, I think it’s safe to say that this isn’t a deviant position, philosophically speaking. It’s arguably a very orthodox position within continental thought – you can see an echo of it in Bergson’s distinction between temps and durée, for example. It therefore seems a bit unfair to pick on Harman for playing his own variation on this theme – it’s reasonable within his system for him to localise temporality to objects, since objects are the foci of what-there-is. If we want to say that the temporality of scientific cosmology is different (non-cyclic, for one thing), we should certainly be able to say so, but the problem here is a problem for all philosophy within this tradition of thinking about temporality, not just Harman’s.

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.

Flat Ontology = One God Universe

Reza on flat ontology as a One God Universe:

In procedurality, we should understand that faraway global behaviors are not simply the similar or homothetic variations of local behaviors. Procedurality or the shift of the perspective according to the shift of landscape of rules is a response to this asymmetry between the global and the local. For example, contingency differs at different levels. We cannot overextend the concept of contingency at the level of the individual gambler to the contingency at the level of a collection of games to the contingency at the level of casino. These have different levels of probability which cannot be over-stretched to one another. By calling this hierarchy of gambles within gambles ‘contingency’ without any regard to the specifications of each distinct level, we are making a flat universe.

A flat universe is a trivial environment in which the content of a local domain is uniformly distributed across the entire horizon. It’s another variation of what Mark Wilson calls “the classical picture of concepts”.5 According to the classical picture, a concept fully and in one-to- one relationship covers the object. The speculative implications of such a universe are indeed appealing because everything can be applied all the way down, concepts can be overextended from one domain to another at will. But as Mark Wilson points out, this conceptual universe is precariously overloaded. It is akin to a house where the basement is leaking, in trying to fix the basement, the kitchen floor sinks in, in repairing the floor, some of the pipes burst. Everything always needs to be patched up because ultimately in this universe nothing works, the entire edifice is a house of cards.

It wouldn’t be too hard to detect this pattern in certain speculative philosophies [lol] where either the object or contingency is the crazy glue – the big idea – that holds everything at the levels of local and global together. Flatness is another name for the condition of triviality where the global structure has the same properties and/or behaviors of its local fields. But when there is an asymmetry between the global and the local – a non-triviality – we cannot solely resort to analysis (locally oriented) to produce or examine a global structure. Conceptual mapping for a non-trivial universe requires various conceptual maps or navigational atlases distributed at different elevations according to their different a priori statuses.

(That’s “One God Universe” as in Burroughs: “Consider the impasse of a one God universe. He is all-knowing and all-powerful. He can’t go anywhere since He is already everywhere. He can’t do anything since the act of doing presupposes opposition. His universe is irrevocably thermodynamic having no friction by definition. So, He has to create friction: War, Fear, Sickness, Death….to keep his dying show on the road…”)

The guiding (mathematical) metaphor here is that of the manifold, which patches together an “atlas” of local spaces, or the sheaf, which ensures the availability of “gluings” for consistent local data. Both entities have the property that local qualities are not globally preserved: a manifold is “locally Euclidean”, but globally may be very weirdly-shaped indeed; sheaves construct a sort of protocol of descent/ascent which determines how local consistency is globally represented and how global data is locally enriched or deformed. To put it another way: they schematise situations in which, to adapt a phrase of Geoffrey Bennington’s, you need more than one idea to think with.

(edit: I have as usual misremembered the phrase, which is from Bennington’s review of books by Gillian Rose and Peter Dews: “the ‘anarchy’ whose spectre is reported to be looming whenever Left or Right finds it needs more than three ideas to think with”)

Universality and Heresy

Heretics of Dune book cover
Sexy heretics!

Now the violent exclusion inherent in the institution or realization of the universal can take many different forms, which are not equivalent and do not call for the same politics. A sociological and anthropological point of view will insist on the fact that setting up civic universality against discrimination and modes of subjection in legal, educational, moral forms involves the definition of models of the human, or norms of the social. Foucault and others have drawn our attention to the fact that the Human excludes the “non-Human”, the Social excludes the “a-social”. [cf the Afropessimist version of this critique, which identifies this exclusion with its specific, racialising form in anti-blackness]

These are forms of internal exclusion, which affect what I would call “intensive universalism” even more than “extensive universalism”. They are not linked with the territory, the imperium; they are linked with the fact that the universality of the citizen, or the human citizen, is referred to a community. But a political and ethical point of view, which we can associate with the idea or formula of a “community without a community”, or without an already existing community, has to face yet another form of violence intrinsically linked with universality. This is the violence waged by its bearers and activists against its adversaries, and above all against its internal adversaries, i.e. potentially any “heretic” within the revolutionary movement.

Many philosophers – whether they themselves adversaries or fervent advocates of universalistic programs and discourses, such as Hegel in his chapter on “Terror” in the Phenomenology or Sartre in the Critique of Dialectical Reason – have insisted on this relationship, which is clearly linked to the fact that certain forms of universalism embody the logical characteristic of “truth”, i.e. they suffer no exception. If we had time, or perhaps in the discussion, our task now should be to examine the political consequences that we draw from this fact. I spoke of a quasi-Weberian notion of “responsibility”. Responsibility here would not be opposed simply to “conviction” (Gesinnung), but more generally to the ideals themselves, or the ideologies that involve a universalistic principle and goal.

A politics of Human Rights in this respect is typically a politics that concerns the institutionalization of a universalistic ideology, and before that a becoming ideological of the very principle that disturbs and challenges existing ideologies. Universalistic ideologies are not the only ideologies that can become absolutes, but they certainly are those whose realization involves a possibility of radical intolerance or internal violence. This is not the risk that one should avoid running, because in fact it is inevitable, but it is the risk that has to be known, and that imposes unlimited responsibility upon the bearers, speakers and agents of universalism.

Etienne Balibar, On Universalism

If I had to give a name to the present moment in philosophy, I would call it the time of the heretics – this is the moment in which heresy is elevated into a value, almost a (negative-)universal value, the value of the exception, of that which is not tolerated by any politics which “[embodies] the logical characteristic of ‘truth'”. Can one distinguish the figure of the heretic from that of the renegade? Certainly the renegades like to think of themselves as heretics; but the true heretic is always something more and other than simply a renegade.

Notes on “the digital”

It is mathematically demonstrable that the ontology of set theory and the ontology of the digital are not equivalent.

The realm of the digital is that of the denumerable: to every finite stream of digits corresponds a single natural number, a finite ordinal. If we set an upper bound on the length of a stream of digits – let’s say, it has to fit into the available physical universe, using the most physically compact encoding available – then we can imagine a “library of Boole”, finite but Vast, that would encompass the entirety of what can be digitally inscribed and processed. Even larger than the library of Boole is the “digital universe” of sequences of digits, D, which is what we get if we don’t impose this upper bound. Although infinite, D is a single set, and is isomorphic to the set of natural numbers, N. It contains all possible digital encodings of data and all possible digital encodings of programs which can operate on this data (although a digital sequence is not intrinsically either program or data).

The von Neumann universe of sets, V, is generated out of a fundamental operation – taking the powerset – applied recursively to the empty set. It has its genesis in the operation which takes 0, or the empty set {}, to 1, or the singleton set containing the empty set, {{}}, but what flourishes out of this genesis cannot in general be reduced to the universe of sequences of 0s and 1s. The von Neumann universe of sets is not coextensive with D but immeasurably exceeds it, containing sets that cannot be named or generated by any digital procedure whatsoever. V is in fact too large to be a set, being rather a proper class of sets.

Suppose we restrict ourselves to the “constructible universe” of sets, L, in which each level of the hierarchy is restricted so that it contains only those sets which are specifiable using the resources of the hierarchy below it. The axiom of constructibility proposes that V=L – that no set exists which is not nameable. This makes for a less extravagantly huge universe; but L is still a proper class. D appears within L as a single set among an immeasurable (if comparatively well-behaved) proliferation of sets.

A set-theoretic ontology such as Badiou’s, which effectively takes the von Neumann universe as its playground, is thus not a digital ontology. Badiou is a “maximalist” when it comes to mathematical ontology: he’s comfortable with the existence of non-constructible sets (hence, he does not accept the “axiom of constructibility”, which proposes that V=L), and the limitations of physical or theoretical computability are without interest for him. Indeed, it has been Badiou’s argument (in Number and Numbers) that the digital or numerical enframing of society and culture can only be thought from the perspective of a mathematical ontology capacious enough to think “Number” over and above the domain of “numbers”. This is precisely the opposite approach to that which seeks refuge from the swarming immensity of mathematical figures in the impenetrable, indivisible density of the analog.

We Shall Come Rejoicing

Trying to get my head around the interplay between the locality and gluing axioms in a sheaf. In brief, and given a metaphorical association of the “more global” with the “above” and of the “more local” with the “below”:

The locality axiom means that “the below determines the (identity of the) above”: whenever two sections over an open set U are indistinguishable based on their restrictions to the sections over any open cover of U, they are the same. There is no way for data that are more-locally the same to correspond to data that are more-globally different. Our view can be enriched as we move from the global to the local, but not the other way around.

The gluing axiom means that “the above determines the (coherence of the) below”: each compatible-in-pairs way of gluing together the sections over an open cover of U has a representative among the sections over U, of which the sections in the glued assemblage are the restrictions. There is no coherent more-local assemblage that does not have such a more-global representation. The global provides the local with its law, indexing its coherence.

A theme of postmodernism, and particularly of Lyotard’s treatment of the postmodern, was “incommensurability”. Between distinct local practices – language games – there is no common measure, no universal metalanguage into which, and by means of which, every local language can be translated. The image of thought given by sheaves does not contradict this, but it complicates it. The passage from the local to the global draws out transcendental structure; the passage from the global to the local is one of torsion, enrichment, discrimination. The logics of ascent and descent are linked: we cannot “go down” into the local without spinning a web of coherence along the way, and we cannot “come up” into the global without obeying a strict rule of material entailment.

Reasons of Space

Cover of "The Production Of Space", by Henri Lefebvre
It’s mostly made in China these days

“The logical space of reasons” is a figure of speech, and a telling one. C20th philosophy is full of phase spaces and logical spaces, rhetorical spaces and epistemic spaces, from Wittgenstein’s Logische Raum and Heidegger’s Spielraum through to the smooth and striated spaces of Deleuze & Guattari. Spatialisation is one way to “go transcendental”: the movement from point to space is always a virtualising movement, a movement in the direction of overarching (rather than “underlying”) logic, higher-order organisation.

Henri Lefebvre’s argument about spatial metaphors is, more or less, a reworking of Merleau-Ponty’s phenomenological centreing of spatial intuition on the body: for “the body” as that of an individual phenomenal subject, Lefebvre substitutes the social body. For Lefebvre, the contouring of “mental space”, with all its various metaphorical deployments in philosophy and mathematics, is consequent upon the structuring and restructuring of social and geographical space, in particular the space of the city. One could always see Lefebvre’s own project of tracing shifts in the structure of social space as outlining a kind of space of spaces within which such transformations could be plotted; but that would seem somewhat against the spirit of it.

The critical question here concerns the status of the transcendental, relative to the social (and historical, geographical, physical etc) matrix of which it is the transcendental. A “logical space of reasons” might be one sort of thing in a city where argumentative cliques congregated in coffee shops and bars to debate the latest pamphlets and manifestos, and another in a remote village with a primarily oral culture, where collective decision-making and tribal identity were mediated by the same stock of stories and story-tellers. Or – and the use of “space” as metaphor predisposes us towards this alternative – we might be trying to talk about differently-situated instantiations of the same thing, transcendentally speaking.

The key notion that I draw from Zalamea’s metaphorical deployment of sheaf theory is that there is not one “space of reasons”; that the transcendental is only available on condition that one navigates from space to space, constructing “spaces of spaces” through transcendentalising operations. That is why it makes sense to me to argue that the space of reasons is not a “full body”, and is in fact incompletable. There is not an independent space of types, governing a subordinate domain of values: type and value are inextricably entwined.