Category Archives: Philosophy

He Knew He Was Right

The crucial point in my conception of non-empirical theory confirmation is that all three arguments of non-empirical theory confirmation that I’ve described before rely on assessments of limitations to underdetermination. In effect, scientists infer the strength of limitations to underdetermination from observing a lack of known alternatives, the surprising explanatory extra value of their theory or a tendency of predictive success in the research field. Eventually, these observations amount to theory confirmation because strong limitations to underdetermination increase the probability that the known theory is viable. The connection between the number of possible alternatives and the chances of predictive success is intuitively most plausible when looking at the extreme cases: if there are infinitely many alternatives to choose from and just one of them is empirically viable, the chances to pick the correct one are zero. If there is just one possible consistent theory – and if I assume that there is a viable scientific theory at all -, the chance that the consistent theory I found will be predictively successful is 100 percent.

Richard Dawid, on String Theory and Post-Empiricism

This type of reasoning – from bounded probability, given an infinite search space – throws up all kinds of surprises. But there’s another theme here, slightly submerged: it turns out that theory choice, or axiom selection, isn’t really arbitrary (even if it is necessarily “ungrounded”). There are background reasons why a particular theory proposes itself, or a particular collection of axioms seems initially plausible.

The argument I’m familiar with is that such a choice “proves” itself through its own performativity: it’s retroactively validated (in the weak sense of “shown to be useful”, rather than a strong sense of “proven to be true”) by the results it makes available. But this may be a kind of rationalisation – see, we were right to start here after all! – of a choice that was already guided by criteria that aren’t formally specifiable (i.e. you couldn’t generate the “good” starting-points by following a computational procedure). We start out with a sense of the affordances and constructive capacities of particular forms and combinatorial operations, and pick out likely candidates based on practical intuitions.

This is certainly how it goes in programming – to the extent that I’m a “good” programmer, it’s because experience enables me to be consistently “lucky” in picking out a pragmatically viable approach to a problem. There’s usually an “experimental” stage where one sets up a toy version of a problem just to see how different approaches play out – but what one is experimenting with there is theoretical viability, not empirical confirmation.

Often the initial intuition is something like “this is likely either to turn out to be right, or to fall down quickly so we can discard it early and move on to something else”: what we dread, and become practised in avoiding, is floundering about with something which is wrong in subtle ways that only reveal themselves much later on.

Lather, Rinse, Repeat

The (possibly alarmist) claim recently surfaced on social media that it was only a matter of time before some enterprising hacker managed to connect the records held by porn sites of their users’ browsing histories to the individual identities of those users, creating considerable opportunities for individual blackmail or general mischief. My personal reaction to this scenario –oh god please no – was balanced by a tranquil sense that a great many people would be in the same boat, and that the likely social impact of mass disclosure was difficult to anticipate. It might be horrific and hilarious in about equal measure. However, sites such as Pornhub already occasionally release their own statistical analyses, showing which US states evince the greatest interest in teenagers, spanking, interracial couples and so on. Public access to their – suitably anonymised – access logs might yield much of sociological interest.

My review of Tim Jordan’s Information Politics: Liberation and Exploitation in the Digital Society is now up at Review 31.

Psychedelic Investigations (conversation with Trent Knebel)

Leonora Carrington: El Mundo Mágico de los Mayas
Leonora Carrington: El Mundo Mágico de los Mayas

DF: The psychedelic (or phenoumenodelic) is a mode of investigation into perception, periodically renewed by new technical means – drugs, synthesizers, fractals, neural nets. We are now entering into a new phase of psychedelic investigation; that is, investigation into how we perceive what we perceive, what perception is “made out of” or “drawn from”, and what extensions or modifications it is susceptible to.

Psychedelic investigation is sometimes taken to be investigation into the ultimate nature of reality, which it is but not directly. In psychedelia, perception is relieved of its sufficiency and submitted once again to the real. That doesn’t mean that we see what’s “really always there”, but that what we see is other than what our standard frame of perception acknowledges as capable of “being there”. Givens appear outside of the established regime of givenness. The stranger enters into manifestation.


(Give the neural net a picture of some sky, and ask it to extrapolate images of Lucy with diamonds…)

Computer-generated psychedelia
What androids actually dream of

TK: Re: neural networks: I’ll be impressed when a computer can uncover a new correspondence between apparently unconnected domains of reality, progressively deforming things is fairly trivial and I don’t think stretches much past ideas of what computers are capable of (even if it does generate some interesting visuals).


DF: I agree, what we’ve seen so far with this is pattern recognition over-egged into hallucination, rather than pattern recognition uncovering previously undiscovered real structures. But I think that has always been true of psychedelia: it doesn’t bring insight into the real directly, but insight into the construction of illusions.

Edge detection
Edge detection

TK: I’ve never tried psychedelic drugs so can’t comment in that area, however, I do think Catren style psychedelia uncovers real structures that are only glimpsed distortedly when seen from any particular perspective, and Zalamea’s oeuvre is filled with example realizations of synaesthetic glimpses of structural kernels.


DF: I think I have to modify my previous statement: psychedelia is essentially undecided between reality and illusion, it’s an investigation of areas for which there is as yet no decision procedure. The question of whether or not there’s any “there” there is temporarily suspended. Later on it may be possible to discern some “structural kernel”, but the psychedelic moment is about developing the intuition that there is a “there” where something might conceivably be.

60s Psychedelia
60s Psychedelia

TK: Perhaps psychedelia is perceiving a correspondence in a synaesthetic manner without conscious grasp of the higher order principles governing the correspondence- eg synaestheticaly perceiving homotopy and type theory together without formally understanding homotopy type theory.

Bridget Riley
Bridget Riley

DF: Yes, it’s a kind of unchained synaesthesia, a synaesthesia that might always come to nothing.

Diagram from Zalamea
Diagram from Zalamea

TK: Might, but I’d also say that ascension to higher order structures (coupled with rich fleshing out of those structures, which is obviously there in psychedelia. this is opposed to hollow knowledge of higher order structures without understanding the lower level things they control) is one of the most fundamental types of progress, if not the most fundamental.

Transits: Notes on the Xenofeminist Manifesto

It’s a bold gesture, to be sure: to insist on the conjugation of lived experience with stringent formal abstraction, on the compatibility and even identity in the last instance of intersectionality and “the right to speak as no-one”, on the possibility and necessity of a transfeminism that is also a rationalism. As if one wanted to have all the enemies in the world at once. “We must draw a line between ourselves and the enemy”, but here are many lines crossing each other at many points, a mesh of antagonisms. If nothing else, the XFM presents an imposingly compact yet comprehensive mapping of the contemporary terrain of struggle within feminism, or amongst feminisms.

The underlying wager is that a connection can be drawn between the theoretical and experiential resources of contemporary transfeminism and those of an earlier feminist transhumanism, in such a way that the white-male-supremacism that is always seeking to inhabit and possess the mutating body of the transhuman can be checked, subverted and put to rout. This is both the resumption of a feminist political project that was active in 1990s cyberculture — notably in the symbolic and theoretical subversions of VNS Matrix — and the mutation of that project in the light of new experience, and by new theoretical means. What has to be repelled, continually, is “the facile tendency of conflation [of the universal] with bloated, unmarked particulars — namely Eurocentric universalism — whereby the male is mistaken for the sexless, the white for raceless, the cis for the real, and so on”. It is a question of discriminating the true universal from the false, and mobilising the former against the latter.

As the postmodern, in Lyotard’s formulation, precedes the modern, so the postmodernism of 90s cyberfeminism precedes and conditions the modernism of the XFM. Modernism extracts new formal techniques from the “paralogisms” of postmodern experimentation, and uses them to extend its logical apparatus. It forms a new canon from diverse materials. Thus: “From the postmoderns, we have learnt to burn the facades of the false universal and dispel such confusions; from the moderns, we have learnt to sift new universals from the ashes of the false”. In the symbolic register, a process of alchemical transmutation; in the logical register, a diagonalisation or transversal procedure.

In playing with the various different valances of “trans-” here, I’m both exploiting an affordance and signalling a danger. The danger is that trans* politics, the politics of trans existence within and against a patriarchal-capitalist and transphobic/transmisogynist social order, will end up being strip-mined for its conceptual and metaphorical resources and put into use by, well, people like me: cis people without all that much skin in the game, for whom those resources can be safely diverted into a more or less “academic” interest in gender and sexuality and so on. So there’s a question of how to affirm what the XFM affirms, which is that any contemporary feminism must be a trans-feminism and that feminism-modulo-”trans” is vitally necessary for the development of a genuinely emancipatory technoculture, without ending up making a rather instrumental and exploitative use of trans* politics, which has some pressing concerns of its own to attend to. If you’re chiefly in it, as I am, for the emancipatory technoculture, then you need to take care that the proposed adjunction between transfeminism and feminist transhumanism provides benefits in both directions.

Here there is a particular tension between the “right to speak as no-one” — access to the scientific-theoretical register, to which belong statements such as “there exists no largest prime number”, or “Earth’s climate is changing due to human release of carbon into the atmosphere” — and the right to be acknowledged as a “someone” who can speak for themselves in a radical democracy of identity positions. The former belongs to what Lyotard called “rights of the infinite”, the latter to what we might call “rights of the finite”. The XFM repudiates the assumption that the former must be subordinated to the latter — that we should seek, for example, a more “democratic” science. It is important here not to confuse science with technoculture: the argument is that in order to have an emancipatory technoculture, we need a science that acts as far as possible as a vector for the inhumanisation of knowledge, since it is this inhumanisation that renders it uniquely capable of overturning socially-entrenched positions and attachments.

In taking a stance of “gender abolitionism”, however, the XFM reveals a preference in favour of inhumanisation — in favour of the “scientific” over the “manifest” image. Should the rights of the infinite trump the rights of the finite; or (to put it more concretely) should our knowledge that gender is a social fiction trump the significance of gender identification as a social act? The XFM asserts that intersectionality — the combination, within the finitude of a subject position, of multiple identifications and attachments; or, within the finitude of lived experience, of multiple oppressions and circumscriptions — just is the generic-universal which undoes every particular identity: “Intersectionality is not the morcellation of collectives into a static fuzz of cross-referenced identities, but a political orientation that slices through every particular, refusing the crass pigeonholing of bodies”. I wish — and the manifesto wishes with me. This seems like a hyperstitional move, however: the positing of an accomplished identity that has yet to be achieved in actuality.

“Scientifically”, the conclusion to be drawn from intersectional analysis is that no cross-referencing of identities, no system of pigeonholes, can ever be adequate to the real complexity of embodied social existence. But what is socially “manifest”, at every moment of our lives, is that we are positioned by and within antagonisms that have no particular regard for that complexity. For example: transmisogyny focuses an intense hatred on “feminine” expression, especially when attached to a body sexually coded as male (and therefore as natively entitled to “masculine” expression). The open expression of a “femme” identification, in this context, brings one (whether male or female, trans or cis) into political conflict with a transmisogynist value system. We have to simultaneously know that “femme” cannot be the whole truth of anyone’s embodied existence, and uphold the right to that expression and to the identification “as” femme that supports it.

“Gender-abolitionism” is taken by today’s radfems to mean that “femme” should be eradicated, immediately or as soon as possible (and in the meantime condescended to, with a certain morose delectation, as a regrettable compromise with the malign imperatives of a fallen world); and the practical consequence of this is that the radfems fall politically into line with the transmisogynists, a consequence that the XFM denounces as an “absurd and reckless spectacle”. So the XFM must mean something different: a revision of our understanding of gender in the light of the scientific image, yes, but not simply the violent suppression of gender’s social manifestation. What, then? What emerges from consideration of this point is the extreme delicacy of the universal, the care that must be taken at every point to preserve its genericity, its quality of being “neither this nor that and both somewhat this and somewhat that”. The universal can never come to rest, assume the status of an accomplished fact; hence the XFM’s proposal of an “open platform”, governed by certain orienting principles, rather than a set of prescriptions. Even as bold a manifesto as this has to hedge somewhat — but for the best of reasons.

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.

Matheme and mytheme

I’ve occupied, and still move back and forth between, the world of the figurative and the mythematic, and the world of the thetic and the conceptual. If I have an argument, it is that it is necessary to know both, and to know the difference.

There is a thetic demarcation of the mythematic: the world of myth according to the world of ideas. A pantheon of gods-according-to-the-philosophers, of secularisations that are also elevations, spiritualisations of the concept. There is also, and without any symmetry between them, a mythic re-absorption of the thetic, which does not demarcate and delimit (since that is not the mode of myth), but rather destabilises and re-integrates. The concept appears there in person, or as persona, subject to the trials of storytelling. There is no firm truth there, because there is no firmness anywhere: reversals and transformations are common. The pantheon is brought down to earth, and its gods are set to hustling along with the rest of us.

A mature thinking must set up a transit between these two worlds, and their reflections in each other. That is not the same as constructing a complete model of one inside the other. The domination of the concept leads to a brittle world-image, a server-room infinity. The domination of the mytheme leads to disorientation, apocalypticism or blood-and-soil political poetics. Both are real and present dangers to the future of human thought.

Protocol Duffers

A graph, yesterday
A graph, yesterday

What can we tell by both the order and size of a graph? One of the basic theorems of graph theory states that for any graph G, the sum of the degrees of the nodes equals twice the number of edges of G. That is, if the degree of any node is the number of edges connected to it (for node n1 with two edges connected to it, its degree = 2), the sum of all the degrees of the graph will be double the size of the graph (the number of edges). In other words, a network is not simply made up of a certain number of elements connected to one another, but is constituted by, qualified by, the connectivity of the nodes. How connected are you? What type of connection do you have? For a square, the sum of the degrees is 8 (the nodes [the square’s corners] each have two edges [the square’s lines] connected to them), while the sum of the edges is 4. In the IT industries connectivity is purely a quantitative measure (bandwidth, number of simultaneous connections, download capacity). Yet, in a different vein, Deleuze and Guattari describe network forms such as the rhizome as, in effect, edges that contain nodes (rather than vice versa), or even, paradoxically, as edges without nodes. In graph theory we see that the connectivity of a graph or network is a value different from a mere count of the number of edges. A graph not only has edges between nodes but edges connecting nodes.

This paragraph (from Galloway and Thacker on protocols) is typical of the faults of this kind of writing. Nothing that it says is entirely incorrect; and yet it confuses and misleads where it ought to clarify.

It is certainly true that there is a relationship between the ratio between the order and size of a graph, and the degree of its nodes. This can be stated precisely: given that the sum of all the degrees of the graph will be double the size of the graph, and the average degree of nodes in the graph will be that sum divided by the number of nodes, then the average degree of nodes in the graph will be twice the number of edges divided by the number of nodes. OK, so what? “A network is not simply made up of a certain number of elements connected to one another” – except that it still is. No extra information has been introduced by observing these ratios. There isn’t an additional property of “connectivity” (in the sense meant here, but see below) that is not inferrable from what we already know about size, order and the degree of each node. Saying “a graph not only has edges between nodes but edges connecting nodes” is a little like saying “the sun not only warms sunbathers, but also increases their temperature”.

The reference to “connectivity” as the term is used informally “in the IT industries” is largely a red herring here. The size, order and degrees of a graph are also “purely…quantitative” – what else would they be? As for Deleuze and Guattari, who can say? “Edges that contain nodes (rather than vice versa)” – who says that nodes “contain” edges? What could it possibly mean for either to contain the other? “Edges without nodes” do not exist in standard graph theory – there are no edges-to-nowhere or edges-from-nowhere. A rhizome’s structure is graph-like, in that nodes (in the botanical sense) put out multiple roots and shoots which connect to other nodes, but to map a rhizome as a graph we must introduce abstract “nodes” to represent the ends of shoots; only then can segments of the rhizome be considered “edges” between nodes (in the graph theoretical sense). None of this is particularly helpful in this context.

When we talk about “connectivity” in graph theory, we are typically talking about paths (traceable along one or more edges, e.g. from A to B and then from B to C) between nodes; the question that interests us is whether there are any nodes that are unreachable along any path from any other nodes, whether there are any disconnected subgraphs, how redundant the connections between nodes are, and so on. “Connectivity” in this sense is indeed not a function of the counts of nodes and edges (although if the number of edges is fewer than the number of nodes minus one, your graph cannot be fully connected…). But it is also not a matter of the degrees of nodes. A graph may be separable into multiple disconnected subgraphs, and yet every node may have a high degree, having multiple edges going out to other nodes within the subgraph to which it belongs. In this sense, it is indeed true that “the connectivity of a graph is…different from a mere count of the number of edges” (it is in fact the k-vertex-connectedness of the graph, a precise notion quite separate from that of degree). But the way in which it is really true is quite different from – and much more meaningful than – the way in which the above paragraph tries to suggest it is true.

What has happened here? The authors have clearly done their reading, but they have not synthesized their knowledge at the technical level: they move from learned fact to learned fact without understanding the logical infrastructure that connects them, being content instead to associate at the level of figurative resemblance. If pressed, writers in this style will often claim that they are identifying “homologies” (abusing that word also in the process) between things, and that one thing’s having a similar sort of conceptual shape to another is sufficient reason to associate them. But the available connectives in that case are weak (“it is surely no coincidence that…”, and other rhetorical substitutes for being able to demonstrate a reliably traversable connection), and it is often impossible to move from the resulting abstract quasi-structure back to the level of the explanandum without falling into total incoherence. The required “aboutness” just isn’t there: there is no negotiable passage back from the talk-about-talk to the talk-about-the-things-the-original-talk-was-about.

In the analysis of literary texts (and other cultural artifacts) we often are looking for structures of similar-patterning: for things which “look like” one another, which share a field of associations or a way of relating elements within that field. It is usually quite legitimate to compare two poems and to say that both have a common “logic” in the way they relate temporality and subjective identity-formation, or something like that. But it is foolish to apply the tools of literary analysis to objects whose primary mode of organisation is not figurative. Skimming along the surface of the language used by technicians in the description of their tasks, one may well discover patterns of association that are “telling”, that reveal something at the level of ideology. I am not proposing that cultural studies give up the jouissance of unmasking – without it, the discipline would lose its entire raison d’etre. But I would like to put in a plea for technical focus, of a kind appropriate to the domain, when dealing with technical subjects. You don’t have to ignore the things you’ve been trained to recognise, but you do need to be able to be undistracted by them. Get it right, then be clever. The payoffs may take longer in coming, but they’re so much realer.