Adjacency of the Possible: Teleology of Autocatalysis. Thought of the Day 140.0


Given a network of catalyzed chemical reactions, a (sub)set R of such reactions is called:

  1. Reflexively autocatalytic (RA) if every reaction in R is catalyzed by at least one molecule involved in any of the reactions in R;
  2. F-generated (F) if every reactant in R can be constructed from a small “food set” F by successive applications of reactions from R;
  3. Reflexively autocatalytic and F-generated (RAF) if it is both RA and F.

The food set F contains molecules that are assumed to be freely available in the environment. Thus, an RAF set formally captures the notion of “catalytic closure”, i.e., a self-sustaining set supported by a steady supply of (simple) molecules from some food set….

Stuart Kauffman begins with the Darwinian idea of the origin of life in a biological ‘primordial soup’ of organic chemicals and investigates the possibility of one chemical substance to catalyze the reaction of two others, forming new reagents in the soup. Such catalyses may, of course, form chains, so that one reagent catalyzes the formation of another catalyzing another, etc., and self-sustaining loops of reaction chains is an evident possibility in the appropriate chemical environment. A statistical analysis would reveal that such catalytic reactions may form interdependent networks when the rate of catalyzed reactions per molecule approaches one, creating a self-organizing chemical cycle which he calls an ‘autocatalytic set’. When the rate of catalyses per reagent is low, only small local reaction chains form, but as the rate approaches one, the reaction chains in the soup suddenly ‘freeze’ so that what was a group of chains or islands in the soup now connects into one large interdependent network, constituting an ‘autocatalytic set’. Such an interdependent reaction network constitutes the core of the body definition unfolding in Kauffman, and its cyclic character forms the basic precondition for self-sustainment. ‘Autonomous agent’ is an autocatalytic set able to reproduce and to undertake at least one thermodynamic work cycle.

This definition implies two things: reproduction possibility, and the appearance of completely new, interdependent goals in work cycles. The latter idea requires the ability of the autocatalytic set to save energy in order to spend it in its own self-organization, in its search for reagents necessary to uphold the network. These goals evidently introduce a – restricted, to be sure – teleology defined simply by the survival of the autocatalytic set itself: actions supporting this have a local teleological character. Thus, the autocatalytic set may, as it evolves, enlarge its cyclic network by recruiting new subcycles supporting and enhancing it in a developing structure of subcycles and sub-sub-cycles. 

Kauffman proposes that the concept of ‘autonomous agent’ implies a whole new cluster of interdependent concepts. Thus, the autonomy of the agent is defined by ‘catalytic closure’ (any reaction in the network demanding catalysis will get it) which is a genuine Gestalt property in the molecular system as a whole – and thus not in any way derivable from the chemistry of single chemical reactions alone.

Kauffman’s definitions on the basis of speculative chemistry thus entail not only the Kantian cyclic structure, but also the primitive perception and action phases of Uexküll’s functional circle. Thus, Kauffman’s definition of the organism in terms of an ‘autonomous agent’ basically builds on an Uexküllian intuition, namely the idea that the most basic property in a body is metabolism: the constrained, organizing processing of high-energy chemical material and the correlated perception and action performed to localize and utilize it – all of this constituting a metabolic cycle coordinating the organism’s in- and outside, defining teleological action. Perception and action phases are so to speak the extension of the cyclical structure of the closed catalytical set to encompass parts of its surroundings, so that the circle of metabolism may only be completed by means of successful perception and action parts.

The evolution of autonomous agents is taken as the empirical basis for the hypothesis of a general thermodynamic regularity based on non-ergodicity: the Big Bang universe (and, consequently, the biosphere) is not at equilibrium and will not reach equilibrium during the life-time of the universe. This gives rise to Kauffman’s idea of the ‘adjacent possible’. At a given point in evolution, one can define the set of chemical substances which do not exist in the universe – but which is at a distance of one chemical reaction only from a substance already existing in the universe. Biological evolution has, evidently, led to an enormous growth of types of organic macromolecules, and new such substances come into being every day. Maybe there is a sort of chemical potential leading from the actually realized substances and into the adjacent possible which is in some sense driving the evolution? In any case, Kauffman claims the hypothesis that the biosphere as such is supercritical in the sense that there is, in general, more than one action catalyzed by each reagent. Cells, in order not to be destroyed by this chemical storm, must be internally subcritical (even if close to the critical boundary). But if the biosphere as such is, in fact, supercritical, then this distinction seemingly a priori necessitates the existence of a boundary of the agent, protecting it against the environment.

Bacteria’s Perception-Action Circle: Materiality of the Ontological. Thought of the Day 136.0


The unicellular organism has thin filaments protruding from its cell membrane, and in the absence of any stimuli, it simply wanders randomly around by changing between two characteristical movement patterns. One is performed by rotating the flagella counterclockwise. In that case, they form a bundle which pushes the cell forward along a curved path, a ‘run’ of random duration with these runs interchanging with ‘tumbles’ where the flagella shifts to clockwise rotation, making them work independently and hence moving the cell erratically around with small net displacement. The biased random walk now consists in the fact than in the presence of a chemical attractant, the runs happening to carry the cell closer to the attractant are extended, while runs in other directions are not. The sensation of the chemical attractant is performed temporally rather than spatially, because the cell moves too rapidly for concentration comparisons between its two ends to be possible. A chemical repellant in the environment gives rise to an analogous behavioral structure – now the biased random walk takes the cell away from the repellant. The bias saturates very quickly – which is what prevents the cell from continuing in a ‘false’ direction, because a higher concentration of attractant will now be needed to repeat the bias. The reception system has three parts, one detecting repellants such as leucin, the other detecting sugars, the third oxygen and oxygen-like substances.


The cell’s behavior forms a primitive, if full-fledged example of von Uexküll’s functional circle connecting specific perception signs and action signs. Functional circle behavior is thus no privilege for animals equipped with central nervous systems (CNS). Both types of signs involve categorization. First, the sensory receptors of the bacterium evidently are organized after categorization of certain biologically significant chemicals, while most chemicals that remain insignificant for the cell’s metabolism and survival are ignored. The self-preservation of metabolism and cell structure is hence the ultimate regulator which is supported by the perception-action cycles described. The categorization inherent in the very structure of the sensors is mirrored in the categorization of act types. Three act types are outlined: a null-action, composed of random running and tumbling, and two mirroring biased variants triggered by attractants and repellants, respectively. Moreover, a negative feed-back loop governed by quick satiation grants that the window of concentration shifts to which the cell is able to react appropriately is large – it so to speak calibrates the sensory system so that it does not remain blinded by one perception and does not keep moving the cell forward on in one selected direction. This adaptation of the system grants that it works in a large scale of different attractor/repellor concentrations. These simple signals at stake in the cell’s functional circle display an important property: at simple biological levels, the distinction between signs and perception vanish – that distinction is supposedly only relevant for higher CNS-based animals. Here, the signals are based on categorical perception – a perception which immediately categorizes the entity perceived and thus remains blind to internal differences within the category.

Pandemic e coli

The mechanism by which the cell identifies sugar, is partly identical to what goes on in human taste buds. Sensation of sugar gradients must, of course, differ from the consumption of it – while the latter, of course, destroys the sugar molecule, the former merely reads an ‘active site’ on the outside of the macromolecule. E . Coli – exactly like us – may be fooled by artificial sweeteners bearing the same ‘active site’ on their outer perimeter, even if being completely different chemicals (this is, of course, the secret behind such sweeteners, they are not sugars and hence do not enter the digestion process carrying the energy of carbohydrates). This implies that E . coli may be fooled. Bacteria may not lie, but a simpler process than lying (which presupposes two agents and the ability of being fooled) is, in fact, being fooled (presupposing, in turn, only one agent and an ambiguous environment). E . coli has the ability to categorize a series of sugars – but, by the same token, the ability to categorize a series of irrelevant substances along with them. On the one hand, the ability to recognize and categorize an object by a surface property only (due to the weak van der Waal-bonds and hydrogen bonds to the ‘active site’, in contrast to the strong covalent bonds holding the molecule together) facilitates perception economy and quick action adaptability. On the other hand, the economy involved in judging objects from their surface only has an unavoidable flip side: it involves the possibility of mistake, of being fooled by allowing impostors in your categorization. So in the perception-action circle of a bacterium, some of the self-regulatory stability of a metabolism involving categorized signal and action involvement with the surroundings form intercellular communication in multicellular organisms to reach out to complicated perception and communication in higher animals.

Revisiting Catastrophes. Thought of the Day 134.0

The most explicit influence from mathematics in semiotics is probably René Thom’s controversial theory of catastrophes (here and here), with philosophical and semiotic support from Jean Petitot. Catastrophe theory is but one of several formalisms in the broad field of qualitative dynamics (comprising also chaos theory, complexity theory, self-organized criticality, etc.). In all these cases, the theories in question are in a certain sense phenomenological because the focus is different types of qualitative behavior of dynamic systems grasped on a purely formal level bracketing their causal determination on the deeper level. A widespread tool in these disciplines is phase space – a space defined by the variables governing the development of the system so that this development may be mapped as a trajectory through phase space, each point on the trajectory mapping one global state of the system. This space may be inhabited by different types of attractors (attracting trajectories), repellors (repelling them), attractor basins around attractors, and borders between such basins characterized by different types of topological saddles which may have a complicated topology.

Catastrophe theory has its basis in differential topology, that is, the branch of topology keeping various differential properties in a function invariant under transformation. It is, more specifically, the so-called Whitney topology whose invariants are points where the nth derivative of a function takes the value 0, graphically corresponding to minima, maxima, turning tangents, and, in higher dimensions, different complicated saddles. Catastrophe theory takes its point of departure in singularity theory whose object is the shift between types of such functions. It thus erects a distinction between an inner space – where the function varies – and an outer space of control variables charting the variation of that function including where it changes type – where, e.g. it goes from having one minimum to having two minima, via a singular case with turning tangent. The continuous variation of control parameters thus corresponds to a continuous variation within one subtype of the function, until it reaches a singular point where it discontinuously, ‘catastrophically’, changes subtype. The philosophy-of-science interpretation of this formalism now conceives the stable subtype of function as representing the stable state of a system, and the passage of the critical point as the sudden shift to a new stable state. The configuration of control parameters thus provides a sort of map of the shift between continuous development and discontinuous ‘jump’. Thom’s semiotic interpretation of this formalism entails that typical catastrophic trajectories of this kind may be interpreted as stable process types phenomenologically salient for perception and giving rise to basic verbal categories.


One of the simpler catastrophes is the so-called cusp (a). It constitutes a meta-diagram, namely a diagram of the possible type-shifts of a simpler diagram (b), that of the equation ax4 + bx2 + cx = 0. The upper part of (a) shows the so-called fold, charting the manifold of solutions to the equation in the three dimensions a, b and c. By the projection of the fold on the a, b-plane, the pointed figure of the cusp (lower a) is obtained. The cusp now charts the type-shift of the function: Inside the cusp, the function has two minima, outside it only one minimum. Different paths through the cusp thus corresponds to different variations of the equation by the variation of the external variables a and b. One such typical path is the path indicated by the left-right arrow on all four diagrams which crosses the cusp from inside out, giving rise to a diagram of the further level (c) – depending on the interpretation of the minima as simultaneous states. Here, thus, we find diagram transformations on three different, nested levels.

The concept of transformation plays several roles in this formalism. The most spectacular one refers, of course, to the change in external control variables, determining a trajectory through phase space where the function controlled changes type. This transformation thus searches the possibility for a change of the subtypes of the function in question, that is, it plays the role of eidetic variation mapping how the function is ‘unfolded’ (the basic theorem of catastrophe theory refers to such unfolding of simple functions). Another transformation finds stable classes of such local trajectory pieces including such shifts – making possible the recognition of such types of shifts in different empirical phenomena. On the most empirical level, finally, one running of such a trajectory piece provides, in itself, a transformation of one state into another, whereby the two states are rationally interconnected. Generally, it is possible to make a given transformation the object of a higher order transformation which by abstraction may investigate aspects of the lower one’s type and conditions. Thus, the central unfolding of a function germ in Catastrophe Theory constitutes a transformation having the character of an eidetic variation making clear which possibilities lie in the function germ in question. As an abstract formalism, the higher of these transformations may determine the lower one as invariant in a series of empirical cases.

Complexity theory is a broader and more inclusive term covering the general study of the macro-behavior of composite systems, also using phase space representation. The theoretical biologist Stuart Kauffman (intro) argues that in a phase space of all possible genotypes, biological evolution must unfold in a rather small and specifically qualified sub-space characterized by many, closely located and stable states (corresponding to the possibility of a species to ‘jump’ to another and better genotype in the face of environmental change) – as opposed to phase space areas with few, very stable states (which will only be optimal in certain, very stable environments and thus fragile when exposed to change), and also opposed, on the other hand, to sub-spaces with a high plurality of only metastable states (here, the species will tend to merge into neighboring species and hence never stabilize). On the base of this argument, only a small subset of the set of virtual genotypes possesses ‘evolvability’ as this special combination between plasticity and stability. The overall argument thus goes that order in biology is not a pure product of evolution; the possibility of order must be present in certain types of organized matter before selection begins – conversely, selection requires already organized material on which to work. The identification of a species with a co-localized group of stable states in genome space thus provides a (local) invariance for the transformation taking a trajectory through space, and larger groups of neighboring stabilities – lineages – again provide invariants defined by various more or less general transformations. Species, in this view, are in a certain limited sense ‘natural kinds’ and thus naturally signifying entities. Kauffman’s speculations over genotypical phase space have a crucial bearing on a transformation concept central to biology, namely mutation. On this basis far from all virtual mutations are really possible – even apart from their degree of environmental relevance. A mutation into a stable but remotely placed species in phase space will be impossible (evolution cannot cross the distance in phase space), just like a mutation in an area with many, unstable proto-species will not allow for any stabilization of species at all and will thus fall prey to arbitrary small environment variations. Kauffman takes a spontaneous and non-formalized transformation concept (mutation) and attempts a formalization by investigating its condition of possibility as movement between stable genomes in genotype phase space. A series of constraints turn out to determine type formation on a higher level (the three different types of local geography in phase space). If the trajectory of mutations must obey the possibility of walking between stable species, then the space of possibility of trajectories is highly limited. Self-organized criticality as developed by Per Bak (How Nature Works the science of self-organized criticality) belongs to the same type of theories. Criticality is here defined as that state of a complicated system where sudden developments in all sizes spontaneously occur.

Mathematical Reductionism: As Case Via C. S. Peirce’s Hypothetical Realism.


During the 20th century, the following epistemology of mathematics was predominant: a sufficient condition for the possibility of the cognition of objects is that these objects can be reduced to set theory. The conditions for the possibility of the cognition of the objects of set theory (the sets), in turn, can be given in various manners; in any event, the objects reduced to sets do not need an additional epistemological discussion – they “are” sets. Hence, such an epistemology relies ultimately on ontology. Frege conceived the axioms as descriptions of how we actually manipulate extensions of concepts in our thinking (and in this sense as inevitable and intuitive “laws of thought”). Hilbert admitted the use of intuition exclusively in metamathematics where the consistency proof is to be done (by which the appropriateness of the axioms would be established); Bourbaki takes the axioms as mere hypotheses. Hence, Bourbaki’s concept of justification is the weakest of the three: “it works as long as we encounter no contradiction”; nevertheless, it is still epistemology, because from this hypothetical-deductive point of view, one insists that at least a proof of relative consistency (i.e., a proof that the hypotheses are consistent with the frequently tested and approved framework of set theory) should be available.

Doing mathematics, one tries to give proofs for propositions, i.e., to deduce the propositions logically from other propositions (premisses). Now, in the reductionist perspective, a proof of a mathematical proposition yields an insight into the truth of the proposition, if the premisses are already established (if one has already an insight into their truth); this can be done by giving in turn proofs for them (in which new premisses will occur which ask again for an insight into their truth), or by agreeing to put them at the beginning (to consider them as axioms or postulates). The philosopher tries to understand how the decision about what propositions to take as axioms is arrived at, because he or she is dissatisfied with the reductionist claim that it is on these axioms that the insight into the truth of the deduced propositions rests. Actually, this epistemology might contain a short-coming since Poincaré (and Wittgenstein) stressed that to have a proof of a proposition is by no means the same as to have an insight into its truth.

Attempts to disclose the ontology of mathematical objects reveal the following tendency in epistemology of mathematics: Mathematics is seen as suffering from a lack of ontological “determinateness”, namely that this science (contrarily to many others) does not concern material data such that the concept of material truth is not available (especially in the case of the infinite). This tendency is embarrassing since on the other hand mathematical cognition is very often presented as cognition of the “greatest possible certainty” just because it seems not to be bound to material evidence, let alone experimental check.

The technical apparatus developed by the reductionist and set-theoretical approach nowadays serves other purposes, partly for the reason that tacit beliefs about sets were challenged; the explanations of the science which it provides are considered as irrelevant by the practitioners of this science. There is doubt that the above mentioned sufficient condition is also necessary; it is not even accepted throughout as a sufficient one. But what happens if some objects, as in the case of category theory, do not fulfill the condition? It seems that the reductionist approach, so to say, has been undocked from the historical development of the discipline in several respects; an alternative is required.

Anterior to Peirce, epistemology was dominated by the idea of a grasp of objects; since Descartes, intuition was considered throughout as a particular, innate capacity of cognition (even if idealists thought that it concerns the general, and empiricists that it concerns the particular). The task of this particular capacity was the foundation of epistemology; already from Aristotle’s first premisses of syllogism, what was aimed at was to go back to something first. In this traditional approach, it is by the ontology of the objects that one hopes to answer the fundamental question concerning the conditions for the possibility of the cognition of these objects. One hopes that there are simple “basic objects” to which the more complex objects can be reduced and whose cognition is possible by common sense – be this an innate or otherwise distinguished capacity of cognition common to all human beings. Here, epistemology is “wrapped up” in (or rests on) ontology; to do epistemology one has to do ontology first.

Peirce shares Kant’s opinion according to which the object depends on the subject; however, he does not agree that reason is the crucial means of cognition to be criticised. In his paper “Questions concerning certain faculties claimed for man”, he points out the basic assumption of pragmatist philosophy: every cognition is semiotically mediated. He says that there is no immediate cognition (a cognition which “refers immediately to its object”), but that every cognition “has been determined by a previous cognition” of the same object. Correspondingly, Peirce replaces critique of reason by critique of signs. He thinks that Kant’s distinction between the world of things per se (Dinge an sich) and the world of apparition (Erscheinungswelt) is not fruitful; he rather distinguishes the world of the subject and the world of the object, connected by signs; his position consequently is a “hypothetical realism” in which all cognitions are only valid with reservations. This position does not negate (nor assert) that the object per se (with the semiotical mediation stripped off) exists, since such assertions of “pure” existence are seen as necessarily hypothetical (that means, not withstanding philosophical criticism).

By his basic assumption, Peirce was led to reveal a problem concerning the subject matter of epistemology, since this assumption means in particular that there is no intuitive cognition in the classical sense (which is synonymous to “immediate”). Hence, one could no longer consider cognitions as objects; there is no intuitive cognition of an intuitive cognition. Intuition can be no more than a relation. “All the cognitive faculties we know of are relative, and consequently their products are relations”. According to this new point of view, intuition cannot any longer serve to found epistemology, in departure from the former reductionist attitude. A central argument of Peirce against reductionism or, as he puts it,

the reply to the argument that there must be a first is as follows: In retracing our way from our conclusions to premisses, or from determined cognitions to those which determine them, we finally reach, in all cases, a point beyond which the consciousness in the determined cognition is more lively than in the cognition which determines it.

Peirce gives some examples derived from physiological observations about perception, like the fact that the third dimension of space is inferred, and the blind spot of the retina. In this situation, the process of reduction loses its legitimacy since it no longer fulfills the function of cognition justification. At such a place, something happens which I would like to call an “exchange of levels”: the process of reduction is interrupted in that the things exchange the roles performed in the determination of a cognition: what was originally considered as determining is now determined by what was originally considered as asking for determination.

The idea that contents of cognition are necessarily provisional has an effect on the very concept of conditions for the possibility of cognitions. It seems that one can infer from Peirce’s words that what vouches for a cognition is not necessarily the cognition which determines it but the livelyness of our consciousness in the cognition. Here, “to vouch for a cognition” means no longer what it meant before (which was much the same as “to determine a cognition”), but it still means that the cognition is (provisionally) reliable. This conception of the livelyness of our consciousness roughly might be seen as a substitute for the capacity of intuition in Peirce’s epistemology – but only roughly, since it has a different coverage.

The Concern for Historical Materialism. Thought of the Day 53.0


The concern for historical materialism, in spite of Marx’s differentiation between history and pre-history, is that totalisation might not be historically groundable after all, and must instead be constituted in other ways: whether logically, transcendentally or naturally. The ‘Consciousness’ chapter of the Phenomenology, a blend of all three, becomes a transcendent(al) logic of phenomena – individual, universal, particular – and ceases to provide any genuine phenomenology of ‘the experience of consciousness’. Natural consciousness is not strictly speaking a standpoint (no real opposition), so it can offer no critical grounds of itself to confer synthetic unity upon the universal, that which is taken to a higher level in ‘Self-Consciousness’ (only to be retrospectively confirmed). Yet Hegel does just this from the outset. In ‘Perception’, we read that, ‘[o]n account of the universality [Allgemeinheit] of the property, I must … take the objective essence to be on the whole a community [Gemeinschaft]’. Universality always sides with community, the Allgemeine with the Gemeinschaft, as if the synthetic operation had taken place prior to its very operability. Unfortunately for Hegel, the ‘free matters’ of all possible properties paves the way for the ‘interchange of forces’ in ‘Force and the Understanding’, and hence infinity, life and – spirit. In the midst of the master-slave dialectic, Hegel admits that, ‘[i]n this movement we see repeated the process which represented itself as the play of forces, but repeated now in consciousness [sic].

Biogrammatic Vir(Ac)tuality. Note Quote.

In Foucault’s most famous example, the prison acts as the confluence of content (prisoners) and expression (law, penal code) (Gilles Deleuze, Sean Hand-Foucault). Informal Diagrams are proliferate. As abstract machines they contain the transversal vectors that cut across a panoply of features (such as institutions, classes, persons, economic formation, etc), mapping from point to relational point, the generalized features of power economies. The disciplinary diagram explored by Foucault, imposes “a particular conduct upon a particular human multiplicity”. The imposition of force upon force affects and effectuates the felt experience of a life, a living. Deleuze has called the abstract machine “pure matter/function” in which relations between forces are nonetheless very real.

[…] the diagram acts as a non-unifying immanent cause that is co-extensive with the whole social field: the abstract machine is like the cause of the concrete assemblages that execute its relations; and these relations between forces take place ‘not above’ but within the very tissue of the assemblages they produce.

The processual conjunction of content and expression; the cutting edge of deterritorialization:

The relations of power and resistance between theory and practice resonate – becoming-form; diagrammatics as praxis, integrates and differentiates the immanent cause and quasi-cause of the actualized occasions of research/creation. What do we mean by immanent cause? It is a cause which is realized, integrated and distinguished in its effect. Or rather, the immanent cause is realized, integrated and distinguished by its effect. In this way there is a correlation or mutual presupposition between cause and effect, between abstract machine and concrete assemblages

Memory is the real name of the relation to oneself, or the affect of self by self […] Time becomes a subject because it is the folding of the outside…forces every present into forgetting but preserves the whole of the past within memory: forgetting is the impossibiltiy of return and memory is the necessity of renewal.


The figure on the left is Henri Bergson’s diagram of an infinitely contracted past that directly intersects with the body at point S – a mobile, sensorimotor present where memory is closest to action. Plane P represents the actual present; plane of contact with objects. The AB segments represent repetitive compressions of memory. As memory contracts it gets closer to action. In it’s more expanded forms it is closer to dreams. The figure on the right extrapolates from Bergson’s memory model to describe the Biogrammatic ontological vector of the Diagram as it moves from abstract (informal) machine in the most expanded form “A” through the cone “tissue” to the phase-shifting (formal), arriving at the Strata of the P plane to become artefact. The ontological vector passes through the stratified, through the interval of difference created in the phase shift (the same phase shift that separates and folds content and expression to move vertically, transversally, back through to the abstract diagram.)

A spatio-temporal-material contracting-expanding of the abstract machine is the processual thinking-feeling-articulating of the diagram becoming-cartographic; synaesthetic conceptual mapping. A play of forces, a series of relays, affecting a tendency toward an inflection of the informal diagram becoming-form. The inflected diagram/biogram folds and unfolds perception, appearances; rides in the gap of becoming between content and expression; intuitively transduces the actualizing (thinking, drawing, marking, erasing) of matter-movement, of expressivity-movement. “To follow the flow of matter… is intuition in action.” A processual stage that prehends the process of the virtual actualizing;

the creative construction of a new reality. The biogrammatic stage of the diagrammatic is paradoxically double in that it is both the actualizing of the abstract machine (contraction) and the recursive counter-actualization of the formal diagram (détournement); virtual and actual.

It is the event-dimension of potential – that is the effective dimension of the interrelating of elements, of their belonging to each other. That belonging is a dynamic corporeal “abstraction” – the “drawing off” (transductive conversion) of the corporeal into its dynamism (yielding the event) […] In direct channeling. That is, in a directional channeling: ontological vector. The transductive conversion is an ontological vector that in-gathers a heterogeneity of substantial elements along with the already-constituted abstractions of language (“meaning”) and delivers them together to change. (Brian Massumi Parables for the Virtual Movement, Affect, Sensation)

Skin is the space of the body the BwO that is interior and exterior. Interstitial matter of the space of the body.


The material markings and traces of a diagrammatic process, a ‘capturing’ becoming-form. A diagrammatic capturing involves a transductive process between a biogrammatic form of content and a form of expression. The formal diagram is thus an individuating phase-shift as Simondon would have it, always out-of-phase with itself. A becoming-form that inhabits the gap, the difference, between the wave phase of the biogrammatic that synaesthetically draws off the intermix of substance and language in the event-dimension and the drawing of wave phase in which partial capture is formalized. The phase shift difference never acquires a vectorial intention. A pre-decisive, pre-emptive drawing of phase-shifting with a “drawing off” the biogram.


If effects realize something this is because the relations between forces or power relations, are merely virtual, potential, unstable vanishing and molecular, and define only possibilities of interaction so long as they do not enter a macroscopic whole capable of giving form to their fluid manner and diffuse function. But realization is equally an integration, a collection of progressive integrations that are initially local and then become or tend to become global, aligning, homogenizing and summarizing relations between forces: here law is the integration of illegalisms.


Husserl’s Melodies of the Absolute Flux. Note Quote.


Husserl elaborates the basic problem of time-consciousness by taking the simple example of a melody. Observing that what we perceive endures – i.e., a melody is experienced as a unity of discrete tones, with each tone and the melody as a whole grasped as unified enduring objects – he sets out to examine how this can occur. Clearly, more than one tone must be retained in consciousness, since if each disappeared entirely after it had sounded then their succession, and therefore the melody as a whole, could never be grasped: “in each moment we would have a tone, or perhaps an empty pause in the interval between the sounding of two tones, but never the representation of a melody.” And each tone must also undergo some form of modification in consciousness, enabling it to appear “as more or less past, as pushed back in time, as it were,” since otherwise “instead of a melody we would have a chord of simultaneous tones, or rather a disharmonious tangle of sound, as if we had struck simultaneously all the notes that had previously sounded“. It is in order to account for our ability to experience such temporally extended objects as temporally extended that Husserl takes an immanent tone as his phenomenological datum.

In the characteristic phenomenological move Husserl proposes, at the outset of his lectures, “the complete exclusion of every assumption, stipulation and conviction with respect to objective time”. This suspension of the “natural attitude” towards time leaves – as the phenomenological residue – the indisputable immanent time (succession and duration) of lived experience (erlebnis). And immanent temporal objects within the immanent time of the flow of consciousness will enable reflection of the phenomenon of temporal experience free of all transcendent presuppositions. Husserl can therefore declare his task as being to “exclude all transcendent apprehension and positing and take the tone purely as a hyletic datum”.

Posing the question of “How, in addition to ‘temporal objects,’ immanent and transcendent, does time itself – the duration and succession of objects – become constituted?” Husserl points out that these are “different lines of description….” For example: “When a tone sounds … [we] can make the tone itself, which endures and fades away, into an object and yet not make the duration of the tone or the tone in its duration into an object”. Focusing on the latter, we can observe that the tone appears in “a continuity of ‘modes’ in a ‘continual flow'” – that is, appears in the mode of (as) ‘now’ or as ‘immediately past’ – even though “‘Throughout’ this whole flow of consciousness, one and the same tone is intended as enduring, as now enduring”. Because the tone itself is the same but the manner in which it appears is continually different, then description of the tone itself must be distinguished from description of “the way in which we are ‘conscious’ of … the ‘appearing’ of the immanent tone”. It is this latter that the phenomenology of time-consciousness will analyze.

Husserl accounts for our experience of the duration of the tone by distinguishing the intended temporal determinations of ‘now,’ ‘just-past,’ and ‘about-to-be’ from the consciousness that intends them: the impressional, retentional and protentional consciousness which constitute present, past, and future, respectively. As he describes it, the “source-point” (Quellpunkt) of the enduring object in the flowing stream of consciousness is the “primal impression” – consciousness of the (constantly changing) “tone-now” (Tonjetzt). And as this ‘tone-now’ is modified into ‘something that has been,’ so the primal impression passes over into retention: “the tone-now changes into a tone-having-been; the impressional consciousness, constantly flowing, passes over into an ever new retentional consciousness”. Retention not only “holds in consciousness what has been produced and stamps on it the character of the ‘just-past'” – ensuring that consciousness is always “consciousness of what has just been and not merely consciousness of the now-point of the object that appears as enduring” – but each retention is also retention of the elapsed tone retention, including in itself “the entire series of elapsed intentions in the form of a chain of mediate intentions”. In this way, retention “extends the now-consciousness” such that the “now-apprehension is, as it were, the head attached to the comet’s tail of retentions”.

This description of the extended moment is completed with the addition of protention as the symmetrical futural counterpart of retention. Protention, the intuition of the immediate future, is “just as original and unique as the intuition of the past,” Husserl writes. “Every process that constitutes its object originally is animated by protentions that emptily constitute what is coming as coming”. Retention and protention together combine to form “the living horizon of the now,” for every primal impression “has its retentional and protentional halo” ensuring that “The now point … [always] has for consciousness a temporal fringe”. The punctual now is therefore only an ideal limit, which cannot be phenomenologically given or encountered. And this description of the now as an ideal abstraction therefore applies equally to the primal impression of which it is the correlate: “In the ideal sense … perception (impression) would be the phase of consciousness that constitutes the pure now…. But the now is precisely only an ideal limit, something abstract, which can be nothing by itself”.

The temporal phases of the immanent object are, then, on a different stratum of analysis than the consciousness of those phases; the impressional, retentional, and protentional consciousness which, in intending the object as ‘now,’ ‘just-past,’ or ‘about-to-be’ “constitute the very differences belonging to time”. Husserl reaches the heart of his phenomenological account of time-consciousness with his description of how these “acts that create time” – primal impression, retention, and protention – “can be understood as time-constituting consciousness, as moments of the flow”. The ‘flow’ is made up of these partial intentions which are not fully fledged acts as such because their correlates are not objects but the temporal phases of objects. Retention, for example, “is an intentionality” but it “is not an ‘act’ (that is, an immanent duration-unity constituted in a series of retentional phases)”. The intentionality of these elements of the primal flux differs from that of apprehending or perceptual acts – they in fact constitute as a unity the apprehending act: “In perception a complex of sensation-contents, which are themselves unities constituted in the original temporal flow, undergo unity of apprehension. And this unitary apprehension is again a constituted unity”.

Husserl can therefore distinguish and outline the three levels of his analysis of time and consciousness as follows: Firstly, “the things of empirical experience in objective time”; secondly, “the constituting multiplicities of appearance … the immanent unities in pre-empirical time”; and lastly, “the absolute time-constituting flow of consciousness” which, as that which “lies before all constitution,” is the ultimate stratum of the constitutive process. This absolute consciousness “is not itself content or object in phenomenological time”. It is a ‘flow’ of “continuous ‘change'” which cannot be described as having constancy or duration, nor even as a ‘process,’ since the concept of process presupposes persistence and a ‘something’ that persists and endures through change. However, the flow does possess, in a sense, something abiding: “What abides, above all, is the formal structure of the flow, the form of the flow”. This unchanging form of the absolute flux is the retentional/impressional/protentional structure by which “a now becomes constituted by means of an impression and … a trail of retentions and a horizon of protentions are attached to the impression”. The question remains, of course, of how we can know this flow which is neither content nor object:

Every temporal appearance, after phenomenological reduction, dissolves into … a flow. But I cannot perceive in turn this consciousness itself into which all of this is dissolved. For this new percept would again be something temporal that points back to a constituting consciousness of a similar sort, and so in infinitum. Hence the question arises: How do I come to know the constituting flow?

To deal with this question Husserl recalls the ‘double intentionality’ of retention. One of these is the “‘primary memory’ of the (just sensed) tone” which “serves for the constitution of the immanent object”. But there is also the other, the second retentional intentionality which “is constitutive of the unity of this primary memory in the flow”. This “retention of retention” ensures that “each past now retentionally shelters within itself all earlier stages” and also therefore that “there extends throughout the flow a horizontal intentionality [Längsintentionalität] that, in the course of the flow, continuously coincides with itself”. By means of this, the unity of the flow becomes itself “constituted in the flow of consciousness as a one-dimensional quasi-temporal order”. The absolute flux is, therefore, self-constituting. It constitutes the unity of immanent objects in a unitary immanent time and thereby, “as shocking (when not initially even absurd) as it may seem,” also its own unity:

two inseparably united intentionalities, requiring one another like two sides of one and the same thing, are interwoven with one another in the one, unique flow of consciousness. By virtue of on limits of language of the intentionalities, immanent time becomes constituted…. In the other intentionality, it is the quasi-temporal arrangement of the phases of the flow that becomes constituted…. This prephenomenal, preimmanent temporality becomes constituted intentionally as the form of the time-constituting consciousness and in itself.

And it is this second retentional intentionality that gives us our oblique self-awareness of the flux, removing the problem of infinite regress whilst simultaneously resolving the difficulty of knowing the flow. “The self-appearance of the flow does not require a second flow: on the contrary, it constitutes itself as a phenomenon in itself”. It requires no second flow because this is a non-objectivating awareness – experienced in the same way as we experience acts, in a perceptual objectivation, without thematizing them. Unlike such acts, however, it cannot itself be made an object of reflection. Because there is no object or substance that endures, and no ‘time’ here as such, our ability to speak of the absolute flux runs up against the limits of language and conceptual thought. “We can say nothing other than the following: This flow is something we speak of in conformity with what is constituted, but it is not ‘something in objective time.’ It is absolute subjectivity and has the absolute properties of something to be designated metaphorically as ‘flow’.” Husserl is blunt about the inescapable inadequacy of his vocabulary here: “For all of this, we lack names”.

In a sense Husserl’s project in the lectures on time-consciousness can be understood as an inquiry into the constitution of constitution; into the way in which intentional acts of consciousness are constituted as temporal unities able to have as their correlate the transcendent temporally extended object. As he observes: “It is certainly evident that the perception of a temporal object itself has temporality, that the perception of duration itself presupposes duration of perception, that the perception of any temporal form itself has temporal form”. Yet Ricoeur writes that “The fact that the perception of duration never ceases to presuppose the duration of perception did not seem to trouble Husserl“, implying that Husserl was blind to the significance of his own observation. This rather offhand remark plays little role in Ricoeur’s argument for the conflict between Kant and Husserl’s respective treatments of time, but given that Husserl was clearly sorely troubled by this ‘fact’ – that it is arguably the very observation that led him beyond Kant’s standpoint to explore the temporality of the constitutive act itself.

Phantom Originary Intentionality: Thought of the Day 16.0


Phantom limbs and anosognosias – cases of abnormal impressions of the presence or absence of parts of our body – seem like handy illustrations of an irreducible, first-person dimension of experience, of the sort that will delight the phenomenologist, who will say: aha! there is an empirical case of self-reference which externalist, third-person explanations of the type favoured by deflationary materialists, cannot explain away, cannot do away with. As Merleau-Ponty would say, and Varela after him, there is something about my body which makes it irreducibly my own (le corps propre). Whether illusory or not, such images (phantoms) have something about them such that we perceive them as our own, not someone else’s (well, some agnosias are different: thinking our paralyzed limb is precisely someone else’s, often a relative’s). One might then want to insist that phantom limbs testify to the transcendence of mental life! Indeed, in one of the more celebrated historical cases of phantom limb syndrome, Lord Horatio Nelson, having lost his right arm in a sea battle off of Tenerife, suffered from pains in his phantom hand. Most importantly, he apparently declared that this phantom experience was a “direct proof of the existence of the soul”. Although the materialist might agree with the (reformed) phenomenologist to reject dualism and accept that we are not in our bodies like a sailor in a ship, she might not want to go and declare, as Merleau-Ponty does, that “the mind does not use the body, but fulfills itself through it while at the same time transferring the body outside of physical space.” This way of talking goes back to the Husserlian distinction between Korper, ‘body’ in the sense of one body among others in a vast mechanistic universe of bodies, and Leib, ‘flesh’ in the sense of a subjectivity which is the locus of experience. Now, granted, in cognitivist terms one would want to say that a representation is always my representation, it is not ‘transferable’ like a neutral piece of information, since the way an object appear to me is always a function of my needs and interests. What my senses tell me at any given time relies on my interests as an agent and is determined by them, as described by Andy Clark, who appeals to the combined research traditions of the psychology of perception, new robotics, and Artificial Life. But the phenomenologist will take off from there and build a full-blown defense of intentionality, now recast as ‘motor intentionality’, a notion which goes back to Husserl’s claim in Ideas II that the way the body relates to the external world is crucially through “kinestheses”: all external motions which we perceive are first of all related to kinesthetic sensations, out of which we constitute a sense of space. On this view, our body thus already displays ‘originary intentionality’ in how it relates to the world.

Deleuze on Right versus Left. Thought of the Day 12.0


Deleuze says to be on the Right is to perceive the world starting with identity, with self and family, and to move outward in concentric circles, to friends, city, nation, continent, world with diminishing affective investment in each circle, and with an abiding sense that the centre needs defending against the periphery. On the contrary to be on the Left is to start one’s perception on the periphery and to move inwards. It requires not the bolstering of the centre, but an appreciation that the centre is interlaced with the periphery, a process that undoes the distance between the two. 

Carnap’s Topological Properties and Choice of Metric. Note Quote.

Husserl’s system is ontologically, a traditional double hierarchy. There are regions or spheres of being, and perfectly traditional ones, except that (due to Kant’s “Copernican revolution”) the traditional order is reversed: after the new Urregion of pure consciousness come the region of nature, the psychological region, and finally a region (or perhaps many regions) of Geist. Each such region is based upon a single highest genus of concrete objects (“individua”), corresponding to the traditional highest genera of substances: in pure consciousness, for example, Erlebnisse; in nature, “things” (Dinge). But each region also contains a hierarchy of abstract genera – genera of singular abstracta and of what Husserl calls “categorial” or “syntactic” objects (classes and relations). This structure of “logical modifications,” found analogously in each region, is the concern of logic. In addition, however, to the “formal essence” which each object has by virtue of its position in the logical hierarchy, there are also truths of “material” (sachliche) essence, which apply to objects as members of some species or genus – ultimately, some region of being. Thus the special sciences, which are individuated (as in Aristotle) by the regions they study, are each broadly divided into two parts: a science of essence and a science of “matters of fact.” Finally, there are what might be called matters of metaphysical essence: necessary truths about objects which apply in virtue of their dependence on objects in prior regions, and ultimately within the Urregion of pure consciousness.

This ontological structure translates directly into an epistemological one, because all being in the posterior regions rests on positing Erlebnisse in the realm of pure consciousness, and in particular on originary (immediate) rational theoretical positings, i.e. “intuitions.” The various sciences are therefore based on various types of intuition. Sciences of matters of fact, on the one hand, correspond to the kinds of ordinary intuition, analogous to perception. Sciences of essence, on the other hand, and formal logic, correspond to (formal or material) “essential insight” (Wesensschau). Husserl equates formal- and material-essential insight, respectively, as sources of knowledge, to Kant’s analytic and synthetic a priori, whereas ordinary perceptual intuition, the source of knowledge about matters of fact, corresponds to the Kantian synthetic a posteriori. Phenomenology, finally, as the science of essence in the region of pure consciousness, has knowledge of the way beings in one region are dependent on those in another.

In Carnap’s doctoral thesis, Der Raum, he applies the above Husserlian apparatus to the problem of determining our sources of knowledge about space. Is our knowledge of space analytic, synthetic a priori, or empirical? Carnap answers, in effect: it depends on what you mean by “space.” His answer foreshadows much of his future thought, but is also based directly on Husserl’s remark about this question in Ideen I: that, whereas Euclidean manifold is a formal category (logical modification), our knowledge of geometry as it applies to physical objects is a knowledge of material essence within the region of nature. Der Raum is largely an expansion and explication of that one remark. Our knowledge of “formal space,” Carnap says, is analytic, i.e. derives from “formal ontology in Husserl’s sense,” but our knowledge of the “intuitive space” in which sensible objects are necessarily found is synthetic a priori, i.e. material-essential. There is one important innovation: Carnap claims that essential (a priori) knowledge of intuitive space extends only to its topological properties, whereas the full structure of physical space requires also a choice of metric. This latter choice is informed by the actual behavior of objects (e.g. measuring rods), and knowledge of physical space is thus in part a posteriori – as Carnap also says, a knowledge of “matters of fact.” But such considerations never force the choice of one metric or another: our knowledge of physical space also depends on “free positing”. This last point, which has no equivalent in Husserl, is important. Still more telling is that Carnap compares the choice involved here to a choice of language, although at this stage he sees this as a mere analogy. On the whole, however, the treatment of Der Raum is more or less orthodoxly Husserlian.