“With A Single Bound, He Was Free”

A trio of questions from Z:

It is not immediately clear that the rationalism you describe is conscious of its historicity, of the way particular ‘rational’ subjects and knowledge practices are historically constituted — and therefore it appears to be unconscious of its limitations. The “rhetoric of transcendence” further suggests this inattention. Again, the question here is not one of intellectual imperialism, but about how, whether, and with what limitations you can know. Is a rationality that transcends the standpoints of particular rational subjects possible? Can it be practiced by these subjects? Are the tools being relied upon, whether maths or something else, capable or sufficient of producing knowledge that transcends given subjects’ limitations?

Yes, yes and yes, otherwise we might as well pack up and go home. But the trap’s in the word “transcendence”, which implies a magic trick that one could always remain unpersuaded had actually been performed. Actually, the notion that “the standpoints of particular…subjects” constrain rationality in such a way that it must somehow escape them in order to function as the rationality it thinks it is, is fatally question-begging. Such “transcendence” is in fact an everyday occurrence, banal and unmagical: it takes place every time you or I take up an argumentative form and commit ourselves to reasoning consequentially according to its rubric.

There is no fact of the matter about my standpoint that can have any bearing whatsoever on the validity of a mathematical proof: if I am able to know that the proof has been performed successfully, it is because I am able to follow it through. If I am able to detect an error, it is because in the process of following the proof through I have stumbled upon an invalidating condition (usually a contradiction of some kind). Formalisms enable us to get to places that are not prescribed or localised by our immediate situations as users-of-form. That is, in fact, precisely what we use them for.

Most of the things we know, we don’t know in quite that kind of way of course. Much of the time, what we know or think we know is stabilised as knowledge against a backdrop of assumptions and heuristics supplied by our “standpoints”, which is one of the reasons why we misunderstand each other so often and so deeply. So I’m not suggesting that we take proof-following reasoning as a model for reasoning in general, or that knowers in general are not situated and not simultaneously enabled and constrained by situational constraints and affordances. What I do want to argue is that our image of a knower’s “situation” as wholly-localised and wholly-limiting is false: we are in fact situated within view, and within reach, of a rich variety of navigational affordances which enable us to reason from context to context. Reason is not an instantaneous ascent into the empyrean heights, from whence the whole terrain is visible at once: it involves traversals, translations, the construction of linkages from context to context, and whereabouts you start on the map is often significant. The crux I think is that it’s significant but not wholly determining: we don’t have to have perfect, godlike freedom in order to have some degrees of freedom.

Rationalism in the present

The label “rationalism” has already a somewhat anachronistic aura about it, as if it named something that had no proper place in the present. We have been (or, plausibly, “have never been“) rationalists; but who could be such a thing now? Both the rationalism of the past and the rationalism of the future have a phantasmal quality; it doesn’t seem unreasonable to many people to treat them purely as objects of fantasy, and to focus their critique, such as it is, at the level of libidinal investment. What do these strange people want from rationality? How do these wants relate to the usual generators of desire – anxiety about social position, for example? Why the embattled posture, the rhetoric of transcendence?

Answers to these questions are not difficult to produce – in a sense they’re encoded into the questions themselves – and so the desire-named-rationalism can without much effort be rendered transparent and intelligible. What the would-be rationalist really wants – we are immediately sure of it – is to recover a (fantasised-as-) lost position of mastery, no doubt imbricated with the self-image of the colonial slaveowner; they feel threatened by women and queers and people of colour, whose political demands they wish to subordinate to their own privileged sense of what would be “reasonable”; and so on. Inasmuch as all of this registers only at the level of unconscious fantasy, they are (for now) at least one step away from the out-and-out racists and sexists and reactionaries. If only they could be brought to acknowledge the unsavory unconscious content of all their high-minded talk, they might yet be saved.

Now, this hermeneutic has its own self-sufficient logic: it supplies to itself guarantees of its own correctness. It does not have to reckon with rationalism as a concrete position, taken in the here-and-now, because its founding gesture is one of incredulity that such a position could be held in earnest, that it might have any ramifications beyond the fugitive gratification it offers to a handful of hapless nerds. You cannot be serious. It will not, for example, distinguish between the doing of mathematics, an activity which has real ramifications inasmuch as one thing really does lead to another, and the performance of mathiness, the brandishing of the matheme as a totem of sophistication (or abstract fedora). In short, the source of its power (as a derailer of argument) lies in its capacity for inattention: since I already “know” that the object of your attention is a fantasy with no real purchase on the present, I am authorised to focus my attention on your attention, rather than upon the thing attended-to.

It’s in the specific polemical context in which proponents of rationalism encounter this hermeneutic – and while that is often a very narrow and specialised context indeed, it is nevertheless legitimately of concern to us – that we find ourselves both at bay, and empowered by concrete demonstrations of the viability of rationalism in the present. The terrain under dispute is not, or not immediately, that of the concrete conditions of everyday life. What we’re trying to do, ultimately, is strengthen the hand of a certain kind of argument, in the hope of bringing closer some of the goods that this kind of argument is – we believe – uniquely able to envisage. It’s all pretty meta. But we do think it’s important – or we wouldn’t bother – and I for one do find it galling when people whose reaction to the accelerationist manifesto was to describe its program as inextricably colonialist, then describe the accelerationists’ sense of being put somewhat on the back foot as histrionic.

A few words are in order about the use made of mathematics. I don’t believe, and don’t believe that anyone else believes, that a sound knowledge of category theory is necessary for salvation. We’re not trying to become Pythagorean sages here. What I think has become apparent during the course of the HKW summer school is that the current rationalist use of “higher” mathematics is partly revisionary and partly metaphorical: it’s about taking apart some old and creaky logico-mathematico-ideological constructions, which had trapped us in a false image of thought, and provoking new images of thought by giving a motivated and metaphorically suggestive account of the technical machinery used to do so. Some of the work involved in doing this is very technical, and requires those performing it to learn and practice some real and quite difficult mathematics. But the ultimate purpose is not to become surpassingly good at maths, but to get away from an inadequate sense of what “rationality” can mean, so that we are not presented with a bogus choice between (for example) first-order predicate logic on the one hand, and everything that isn’t first-order predicate logic on the other. Rationalism in the present moment means using whatever tools are available to reflect on rationality and extend our sense of what it is capable of. It turns out that fancy mathematics is quite indispensable to this endeavour, but we do not hold it to be synonymous with thinking itself. In fact, those of us who are good Badiousians will be well-accustomed to the vertiginous transit between mathematics and poetry:

Someone saw that very clearly, my colleague, the French analytic philosopher Jacques Bouveresse, from the Collège de France. In a recent book in which he paid me the honor of speaking of me, he compared me to a five-footed rabbit and says in substance: “This five-footed rabbit that Alain Badiou is runs at top speed in the direction of mathematic formalism, and then, all of a sudden, taking an incomprehensible turn, he goes back on his steps and runs at the same speed to throw himself into literature.” Well, yes, that’s how with a father and a mother so well distributed, one turns into a rabbit.

The good rationalist, I submit, will be a five-footed rabbit, composing a living present out of the energetic, irreconcilable distribution of antecedents.

An emerging orientation

Why am I so excited about the HKW Summer School? Because it represents an attempt to take some cultural initiative: this is “us” showing what we’ve got and what we can do with it, and showing-by-doing that what can be done in this way is actually worth doing.

I don’t expect everyone to be convinced by such a demonstration – in fact, I expect quite a few people to be dismayed about it, to feel that this is an upstart, renegade movement with distinctly not-for-People-Like-Us values and practices (maths! logics! don’t we know Lawvere* was a worse fascist than Heidegger?). It’s likely that not a few leftish PLUs will be rocking up any moment now to tell us all to curb our enthusiasm. But a glance over the history of Marxist thought will show that there have been plenty of times and places in which the initiative has indeed been held by rationalists – albeit often by warring rationalists, who disagreed ferociously with each other about how a rational politics was to be construed and practised. It’s not at all clear that the present moment, which places such overriding importance on affective tone, is not in fact the anomaly. That’s not to say that we should ditch everything that has declared itself over the past decade – on the contrary, it represents a vast, complex, necessary and unfinished project to which we should aim to contribute meaningfully. But we can only do so by approaching that project from a perspective which it does not encompass, and is hugely unwilling – and perhaps unable – to recognise as valid. To do so requires confidence, of a kind that those who are already confident in their moral standing will find unwarranted and overweening. We are going to be talked down to a lot; we are going to be called names; we are going to have to develop strong memetic defenses against the leftish words-of-power that grant the wielder an instant power of veto over unwelcome ideas. We have a lot to prove. Calculemus!

  • a fairly hardcore Maoist, as it happens.

Monday Poem

i)

Charity, you asked for that: tact
never a strong point. Consider yourself snubbed
by moral imbeciles, lesser imaginations,
the scale of valuation going right up
to its asymptote. Nobody knows /
everyone knows. Pivot on the bar.

ii)

You’re going to be living with yourself,
albeit in separate apartments, the makeshift
partition rattling in wartime Morse.
Steptoe is crushing. Covetousness makes
covenant with itself, renews its vows
each episode. There’s comedy in that.

iii)

Tactless but not artless. Some would say
demonic, aggrandizing a minor imp,
mascot of common turpitude. So tell me,
nameless self-accuser, who made you
chief of sinners? Rather a graceless bounder,
hopscotching to perdition across the coals.

iv)

Say you have lost, Perdita, a fat pearl;
lost or dissolved in vinegar. Say we
are the dead, as some of us might well be,
no longer credit-worthy; iris scans
to confirm ongoing probate of remainder.
Remind me: where exactly did we leave things?

Sheaves for n00bs

What itinerary would a gentle introduction to sheaves have to take? I would suggest the following:

  • A basic tour of the category Set, introducing objects, arrows, arrow composition, unique arrows and limits. (OK, that’s actually quite a lot to start with).
  • Introduction to bundles and sections, with a nicely-motivated example.
  • Enough topology to know what open sets are and what a continuous map is, topologically speaking.
  • Now we can talk about product spaces and fiber bundles.
  • Now we can talk about the sheaf of sections on a fiber bundle.
  • Now we back up and talk about order structures – posets, lattices, Heyting algebras, and their relationship to the lattice of open sets in a topological space. We note in passing that a poset can be seen as a kind of category.
  • Functors, covariant and contravariant.
  • That’s probably enough to get us to a categorial description of first presheaves (contravariant functor from a poset category to e.g. Set) and sheaves (presheaves plus gluing axiom, etc). Show how this captures the fundamental characteristics of the sheaf of sections we met earlier.
  • Then to applications outside of the sheaf of sections; sheaf homomorphisms and sheaf categories; applications in logic and so on. This is actually where my understanding of the topic falls of the edge of the cliff, but I think that rehearsing all of the material up to this point might help to make some of it more accessible.

Anything really essential that I’ve missed? Anything I’ve included that’s actually not that important?

Trouser Python

Yes to all of this (Taylor Parkes on Monty Python in The Quietus, continuing a tremendous run of form). I think Python is essentially, and in both the best and worst senses, schoolboy humour – grounded in the libido of subaltern males. It’s anti-authoritarian, but its image of authority is the prefect or chaplain or headmaster. It’s alternately sexistly anti-sexist and anti-sexistly sexist (and only on rare occasions just plain sexistly sexist, but the shell game is a delivery mechanism for sexism either way): certainly the Pythons ridicule the heteronormative game, and the male stance within it, but they also ridicule women for upholding its conventions, and do so without any great sense of deeper solidarity. No Python woman ever indicates that she finds the whole business equally ridiculous and tiresome, or that she might be capable of making some good sharp jokes about it herself.

Neither Miserly Nor Spiteful

Diagram from Zalamea

The reactivation of enlightenment universalism can no longer safely ignore the particular by turning toward the universal, but must aim to trace trajectories that pass from the local to the global. It is on this basis that we must reconceive emancipation in navigational terms, supplementing the parochial cartography of injustice not only with our most abstract resources for analysing space, but with a willingness to treat these resources as constituting their own abstract spaces. This is to say that the resurrection of universalism as an emancipatory vector is oriented by a renewed commitment to rationalism, and that the relationship between local and global is elaborated by means of a movement from abstract to concrete spaces: from the space of reasons to the space of freedoms.

(from the “Event Concept” of the HKW Summer School on “Emancipation as Navigation”)