Triadomania. Thought of the Day 117.0

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Peirce’s famous ‘triadomania’ lets most of his decisive distinctions appear in threes, following the tripartition of his list of categories, the famous triad of First, Second, and Third, or Quality, Reaction, Representation, or Possibility, Actuality, Reality.

Firstness is the mode of being of that which is such as it is, positively and without reference to anything else.

Secondness is the mode of being of that which is such as it is, with respect to a second but regardless of any third.

Thirdness is the mode of being of that which is such as it is, in bringing a second and third into relation to each other.

Firstness constitutes the quality of experience: in order for something to appear at all, it must do so due to a certain constellation of qualitative properties. Peirce often uses sensory qualities as examples, but it is important for the understanding of his thought that the examples may refer to phenomena very far from our standard conception of ‘sensory data’, e.g. forms or the ‘feeling’ of a whole melody or of a whole mathematical proof, not to be taken in a subjective sense but as a concept for the continuity of melody or proof as a whole, apart from the analytical steps and sequences in which it may be, subsequently, subdivided. In short, all sorts of simple and complex Gestalt qualities also qualify as Firstnesses. Firstness tend to form continua of possibilities such as the continua of shape, color, tone, etc. These qualities, however, are, taken in themselves, pure possibilities and must necessarily be incarnated in phenomena in order to appear. Secondness is the phenomenological category of ‘incarnation’ which makes this possible: it is the insistency, then, with which the individuated, actualized, existent phenomenon appears. Thus, Secondness necessarily forms discontinuous breaks in Firstness, allowing for particular qualities to enter into existence. The mind may imagine anything whatever in all sorts of quality combinations, but something appears with an irrefutable insisting power, reacting, actively, yielding resistance. Peirce’s favorite example is the resistance of the closed door – which might be imagined reduced to the quality of resistance feeling and thus degenerate to pure Firstness so that his theory imploded into a Hume-like solipsism – but to Peirce this resistance, surprise, event, this thisness, ‘haecceity’ as he calls it with a Scotist term, remains irreducible in the description of the phenomenon (a Kantian idea, at bottom: existence is no predicate). About Thirdness, Peirce may directly state that continuity represents it perfectly: ‘continuity and generality are two names of the same absence of distinction of individuals’. As against Secondness, Thirdness is general; it mediates between First and Second. The events of Secondness are never completely unique, such an event would be inexperiencable, but relates (3) to other events (2) due to certain features (1) in them; Thirdness is thus what facilitates understanding as well as pragmatic action, due to its continuous generality. With a famous example: if you dream about an apple pie, then the very qualities of that dream (taste, smell, warmth, crustiness, etc.) are pure Firstnesses, while the act of baking is composed of a series of actual Secondnesses. But their coordination is governed by a Thirdness: the recipe, being general, can never specify all properties in the individual apple pie, it has a schematic frame-character and subsumes an indefinite series – a whole continuum – of possible apple pies. Thirdness is thus necessarily general and vague. Of course, the recipe may be more or less precise, but no recipe exists which is able to determine each and every property in the cake, including date, hour, place, which tree the apples stem from, etc. – any recipe is necessarily general. In this case, the recipe (3) mediates between dream (1) and fulfilment (2) – its generality, symbolicity, relationality and future orientation are all characteristic for Thirdness. An important aspect of Peirce’s realism is that continuous generality may be experienced directly in perceptual judgments: ‘Generality, Thirdness, pours in upon us in our very perceptual judgments’.

All these determinations remain purely phenomenological, even if the later semiotic and metaphysical interpretations clearly shine through. In a more general, non-Peircean terminology, his phenomenology can be seen as the description of minimum aspects inherent in any imaginable possible world – for this reason it is imaginability which is the main argument, and this might point in the direction that Peirce could be open to critique for subjectivism, so often aimed at Husserl’s project, in some respects analogous. The concept of consciousness is invoked as the basis of imaginability: phenomenology is the study of invariant properties in any phenomenon appearing for a mind. Peirce’s answer would here be, on the one hand, the research community which according to him defines reality – an argument which structurally corresponds to Husserl’s reference to intersubjectivity as a necessary ingredient in objectivity (an object is a phenomenon which is intersubjectively accessible). Peirce, however, has a further argument here, namely his consequent refusal to delimit his concept of mind exclusively to human subjects (a category the use of which he obviously tries to minimize), mind-like processes may take place in nature without any subject being responsible. Peirce will, for continuity reasons, never accept any hard distinction between subject and object and remains extremely parsimonious in the employment of such terms.

From Peirce’s New Elements of Mathematics (The New Elements of Mathematics Vol. 4),

But just as the qualities, which as they are for themselves, are equally unrelated to one other, each being mere nothing for any other, yet form a continuum in which and because of their situation in which they acquire more or less resemblance and contrast with one another; and then this continuum is amplified in the continuum of possible feelings of quality, so the accidents of reaction, which are waking consciousnesses of pairs of qualities, may be expected to join themselves into a continuum. 

Since, then an accidental reaction is a combination or bringing into special connection of two qualities, and since further it is accidental and antigeneral or discontinuous, such an accidental reaction ought to be regarded as an adventitious singularity of the continuum of possible quality, just as two points of a sheet of paper might come into contact.

But although singularities are discontinuous, they may be continuous to a certain extent. Thus the sheet instead of touching itself in the union of two points may cut itself all along a line. Here there is a continuous line of singularity. In like manner, accidental reactions though they are breaches of generality may come to be generalized to a certain extent.

Secondness is now taken to actualize these quality possibilities based on an idea that any actual event involves a clash of qualities – in the ensuing argumentation Peirce underlines that the qualities involved in actualization need not be restrained to two but may be many, if they may only be ‘dissolved’ into pairs and hence do not break into the domain of Thirdness. This appearance of actuality, hence, has the property of singularities, spontaneously popping up in the space of possibilities and actualizing pairs of points in it. This transition from First to Second is conceived of along Aristotelian lines: as an actualization of a possibility – and this is expressed in the picture of a discontinuous singularity in the quality continuum. The topological fact that singularities must in general be defined with respect to the neighborhood of the manifold in which they appear, now becomes the argument for the fact that Secondness can never be completely discontinuous but still ‘inherits’ a certain small measure of continuity from the continuum of Firstness. Singularities, being discontinuous along certain dimensions, may be continuous in others, which provides the condition of possibility for Thirdness to exist as a tendency for Secondness to conform to a general law or regularity. As is evident, a completely pure Secondness is impossible in this continuous metaphysics – it remains a conceivable but unrealizable limit case, because a completely discon- tinuous event would amount to nothing. Thirdness already lies as a germ in the non-discontinuous aspects of the singularity. The occurrences of Secondness seem to be infinitesimal, then, rather than completely extensionless points.

Quantifier – Ontological Commitment: The Case for an Agnostic. Note Quote.

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What about the mathematical objects that, according to the platonist, exist independently of any description one may offer of them in terms of comprehension principles? Do these objects exist on the fictionalist view? Now, the fictionalist is not committed to the existence of such mathematical objects, although this doesn’t mean that the fictionalist is committed to the non-existence of these objects. The fictionalist is ultimately agnostic about the issue. Here is why.

There are two types of commitment: quantifier commitment and ontological commitment. We incur quantifier commitment to the objects that are in the range of our quantifiers. We incur ontological commitment when we are committed to the existence of certain objects. However, despite Quine’s view, quantifier commitment doesn’t entail ontological commitment. Fictional discourse (e.g. in literature) and mathematical discourse illustrate that. Suppose that there’s no way of making sense of our practice with fiction but to quantify over fictional objects. Still, people would strongly resist the claim that they are therefore committed to the existence of these objects. The same point applies to mathematical objects.

This move can also be made by invoking a distinction between partial quantifiers and the existence predicate. The idea here is to resist reading the existential quantifier as carrying any ontological commitment. Rather, the existential quantifier only indicates that the objects that fall under a concept (or have certain properties) are less than the whole domain of discourse. To indicate that the whole domain is invoked (e.g. that every object in the domain have a certain property), we use a universal quantifier. So, two different functions are clumped together in the traditional, Quinean reading of the existential quantifier: (i) to assert the existence of something, on the one hand, and (ii) to indicate that not the whole domain of quantification is considered, on the other. These functions are best kept apart. We should use a partial quantifier (that is, an existential quantifier free of ontological commitment) to convey that only some of the objects in the domain are referred to, and introduce an existence predicate in the language in order to express existence claims.

By distinguishing these two roles of the quantifier, we also gain expressive resources. Consider, for instance, the sentence:

(∗) Some fictional detectives don’t exist.

Can this expression be translated in the usual formalism of classical first-order logic with the Quinean interpretation of the existential quantifier? Prima facie, that doesn’t seem to be possible. The sentence would be contradictory! It would state that ∃ fictional detectives who don’t exist. The obvious consistent translation here would be: ¬∃x Fx, where F is the predicate is a fictional detective. But this states that fictional detectives don’t exist. Clearly, this is a different claim from the one expressed in (∗). By declaring that some fictional detectives don’t exist, (∗) is still compatible with the existence of some fictional detectives. The regimented sentence denies this possibility.

However, it’s perfectly straightforward to express (∗) using the resources of partial quantification and the existence predicate. Suppose that “∃” stands for the partial quantifier and “E” stands for the existence predicate. In this case, we have: ∃x (Fx ∧¬Ex), which expresses precisely what we need to state.

Now, under what conditions is the fictionalist entitled to conclude that certain objects exist? In order to avoid begging the question against the platonist, the fictionalist cannot insist that only objects that we can causally interact with exist. So, the fictionalist only offers sufficient conditions for us to be entitled to conclude that certain objects exist. Conditions such as the following seem to be uncontroversial. Suppose we have access to certain objects that is such that (i) it’s robust (e.g. we blink, we move away, and the objects are still there); (ii) the access to these objects can be refined (e.g. we can get closer for a better look); (iii) the access allows us to track the objects in space and time; and (iv) the access is such that if the objects weren’t there, we wouldn’t believe that they were. In this case, having this form of access to these objects gives us good grounds to claim that these objects exist. In fact, it’s in virtue of conditions of this sort that we believe that tables, chairs, and so many observable entities exist.

But recall that these are only sufficient, and not necessary, conditions. Thus, the resulting view turns out to be agnostic about the existence of the mathematical entities the platonist takes to exist – independently of any description. The fact that mathematical objects fail to satisfy some of these conditions doesn’t entail that these objects don’t exist. Perhaps these entities do exist after all; perhaps they don’t. What matters for the fictionalist is that it’s possible to make sense of significant features of mathematics without settling this issue.

Now what would happen if the agnostic fictionalist used the partial quantifier in the context of comprehension principles? Suppose that a vector space is introduced via suitable principles, and that we establish that there are vectors satisfying certain conditions. Would this entail that we are now committed to the existence of these vectors? It would if the vectors in question satisfied the existence predicate. Otherwise, the issue would remain open, given that the existence predicate only provides sufficient, but not necessary, conditions for us to believe that the vectors in question exist. As a result, the fictionalist would then remain agnostic about the existence of even the objects introduced via comprehension principles!

My Appresentations Rest in Protention.

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The ego often originally feels the pull of an object in the case of great contrast, where a unified object stands out from its background and from other objects. While contrast is not a necessary contributor to affectivity in an object, it does often accompany an object’s affective pull. An object that is not the focus of my attention cannot pull me toward it, however, unless I am able to perceive beyond what is in focus at this moment. Apperception is my ability to extend beyond my currently intended object to other objects and meanings and beyond what is now. Only if an object which has pulled me to it were at least partially constituted in the background, attracting my attention, could there have been any pull at all. Thus we discover a link between affectivity and apperception, because an object can only call me to it if my consciousness is able to extend beyond that which is in my focus now. And, because apperception must rest in a protentional temporality in order to allow for my ability to extend beyond the zone of actualization, we also find an indirect link between affectivity and protention. Therefore, affectivity requires a temporal structure that extends my consciousness beyond the immediate present and what is currently fulfilled so that an object in the periphery can attract my attention. In other words, affectivity is related to apperception, and both function through the protentional aspect of my temporality.

This relation also reminds us of the relation between protention and appresentation, where appresentation, the concept that any presentation of an object necessarily goes beyond itself to presentations of the object not currently in view – like the back side or the inside of the building across the street – clearly requires protention. As we explained earlier, protention is the condition of possibility of my going beyond the presentation at hand to other presentations or experiences. Thus the possibility of my viewing an object as having other sides, even though I am only perceiving one side at any moment, rests in a protentional temporality; my appresentations rest in protention. The transformed affectivity that draws me to learn more about an object after it has attracted my attention, then, also resides in protention; it always calls me to experience more, to move beyond what is currently presented.

The New Husserl A Critical Reader 

Gnostic Semiotics. Thought of the Day 63.0

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The question here is what is being composed? For the deferment and difference that is always already of the Sign, suggests that perhaps the composition is one that lies not within but without, a creation that lies on the outside but which then determines – perhaps through the reader more than anything else, for after all the meaning of a particular sign, be it a word or anything else, requires a form of impregnation by the receiver – a particular meaning.

Is there any choice but to assume a meaning in a sign? Only through the simulation, or ‘belief’ if you prefer (there is really no difference in the two concepts), of an inherent meaning in the sign can any transference continue. For even if we acknowledge that all communication is merely the circulation of empty signifiers, the impregnation of the signified (no matter how unconnected it may be to the other person’s signified) still ensures that the sign carries with it a meaning. Only through this simulation of a meaning is circulation possible – even if one posits that the sign circulates itself, this would not be possible if it were completely empty.

Since it is from without (even if meaning is from the reader, (s)he is external to the signification), this suggests that the meaning is a result, a consequence of forces – its signification is a result of the significance of various forces (convention, context, etc) which then means that inherently, the sign remains empty; a pure signifier leading to yet another signifier.

The interesting element though lies in the fact that the empty signifier then sucks the Other (in the form of the signified, which takes the form of the Absolute Other here) into it, in order to define an existence, but essentially remains an empty signifier, awaiting impregnation with meaning from the reader. A void: always full and empty or perhaps (n)either full (n)or empty. For true potentiality must always already contain the possibility of non-potentiality. Otherwise there would be absolutely no difference between potentiality and actualization – they would merely be different ends of the same spectrum.

Post-Foundationalism Versus Anti-Foundationalism. Thought of the Day 58.0

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In the words of Judith Butler,

the point is not to do away with foundations, or even to champion a position which goes under the name of antifoundationalism: Both of these positions belong together as different versions of foundationalism and the sceptical problematic it engenders. Rather, the task is to interrogate what the theoretical move that establishes foundations authorizes, and what precisely it excludes or forecloses.

The notion of contingent foundations, proposed by Butler as an alternative framing, could best be described as an ontological weakening of the status of foundation without doing away with foundations entirely. It is on its account, that what came to be called post-foundationalism should not be confused with anti-foundationalism. What distinguishes the former from the latter is that it does not assume the absence of any ground; what it assumes is the absence of an ultimate ground, since it is only on the basis of such absence that grounds, in the plural, are possible. The problem is therefore posed not in terms of no foundations (the logic of all- or -nothing), but in terms of contingent foundations. Hence, post-foundationalism does not stop after having assumed the absence of a final ground and so it does not turn into anti-foundationalist nihilism, existentialism or pluralism, all of which would assume the absence of any ground and would result in complete meaninglessness, absolute freedom or total autonomy. Nor does it turn into a sort of post-modern pluralism for which all meta-narratives have equally melted into air, for what is still accepted by post-foundationalism is the necessity for some grounds.

What becomes problematic as a result is not the existence of foundations (in the plural) but their ontological status – which is seen now as necessarily contingent. This shift in the analysis from the ‘actually existing’ foundations to their status – that is to say, to their conditions of possibility – can be described as a quasi-transcendental move. Although implicitly present in Spivak’s notion of a ‘perpetually rehearsed critique’ as well as in Butler’s notion of ‘interrogation’, this quasi-transcendental turn is made explicit by Ernesto Laclau who, starting from the post-foundational premise that ‘the crisis of essentialist universalism as a self-asserted ground has led our attention to the contingent grounds (in the plural) of its emergence and to the complex process of construction’, comes to the conclusion that ‘[t]his operation is, sensu stricto, transcendental: it involves a retreat from an object to its conditions of possibility’.

Deleuzian Speculative Philosophy. Thought of the Day 44.0

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Deleuze’s version of speculative philosophy is the procedure of counter-effectuation or counter-actualization. In defiance of the causal laws of an actual situation, speculation experiments with the quasi-causal intensities capable of bringing about effects that have their own retro-active power. This is its political import. Leibniz already argued that all things are effects or consequences, even though they do not necessarily have a cause, since the sufficient reason of what exists always lies outside of any actual series and remains virtual. (Leibniz) With the Principle of Sufficient Reason, he thus reinvented the Stoic disjunction between the series of corporeal causes and the series of incorporeal effects. Not because he anticipated the modern bifurcation of given necessary causes (How?) and metaphysically constructed reasons (Why?), but because for him the virtuality of effects is no less real than the interaction of causes. The effect always includes its own cause, since divergent series of events (incompossible worlds) enter into relation with any particular event (in this world), while these interpenetrating series are prior to, and not limited by, actual relations of causality per se. In terms of Deleuze, cause and effect do not share the same temporality. Whereas causes relate to one another in an eternal present (Chronos), effects relate to one another in a past-future purified of the present (Aion). Taken together, these temporalities form the double structure of every event (Logic of Sense). When the night is lit up by a sudden flash of lightning, this is the effect of an intensive, metaphysical becoming that contains its own destiny, integrating a differential potentiality that is irreducible to the physical series of necessary efficient causes that nonetheless participate in it. In order for such a contingent conjugation of events to be actualized (i.e. for effects to influence causes and become individuated in a materially extended state of affairs), however, its impersonal and pre-individual presence must be trusted upon. This takes a speculative investment or amor fati that forms its precursive reason/ground. In Difference and Repetition, Deleuze refers to this will to speculate as the dark precursor which determines the path of a thunderbolt in advance but in reverse, as though intagliated by setting up a communication of difference with difference. It is therefore the differenciator of these differences or in- itself of difference. We find a paradigmatic example of this will to make a difference in William James’ The Will to Believe when he writes: We can and we may, as it were, jump with both feet off the ground into a world of which we trust the other parts to meet our jump and only so can the making of a perfected world of the pluralistic pattern ever take place. Only through our precursive trust in it can it come into being. (James) As Stengers explains, we can and do speculate each time we precursively trust in the possibility of connecting, of entering into a (partial) rapport that cannot be derived from the ground of our current, dominant premises. Or as Deleuze writes: the dark precursor is not the friend (Difference and Repetition) but rather the bad will of a traitor or enemy, since the will does not precede the presubjective cruelty of the event in its involuntariness. At the same time, however, we never jump into a vacuum. We always speculate by the milieu, since a jump in general could never be trusted: If a jump is always situated, it is because its aim is not to escape the ground in order to get access to a higher realm. The jump, connecting this ground, always this ground, with what it was alien to, has the necessity of a response. In other words, the ground must have been given the power to make itself felt as calling for new dimensions. (Stengers) Indeed, if speculative thought cannot be detached from a practical concern, Deleuze at the same time states that [t]here is no other ethic than the amor fati of philosophy. (What is Philosophy?) Speculative reasoning is thus an art of pure expression or efficacy, an art of precipitating events: an art that detects and affirms the possibility of other reasons insisting as so many virtual forces that have not yet had the chance to emerge but whose presence can be trusted upon to make a difference.

In Deleuze’s own terms, there is no such thing as pure reason, only heterogeneous processes of rationalization, of actualizing an irrational potential: There is no metaphysics, but rather a politics of being. (Deleuze) For this reason, the method of speculative philosophy is the method of dramatization. It is a method that distributes events according to a logic that conditions the order of their intelligibility. As such it belongs to what in Difference and Repetition is referred to as the proper order of reasons: differentiation-individuation-dramatisation-differenciation. A book of philosophy, Deleuze famously writes in the preface, should be in part a very particular species of detective novel, in part a kind of science fiction. On the one hand, the creation of concepts cannot be separated from a problematic milieu or stage that matters practically; on the other hand, it seeks to deterritorialize this milieu by speculating on the quasi-causal intensity of its becoming-other.

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Meillassoux’s Principle of Unreason Towards an Intuition of the Absolute In-itself. Note Quote.

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The principle of reason such as it appears in philosophy is a principle of contingent reason: not only how philosophical reason concerns difference instead of identity, we but also why the Principle of Sufficient Reason can no longer be understood in terms of absolute necessity. In other words, Deleuze disconnects the Principle of Sufficient Reason from the ontotheological tradition no less than from its Heideggerian deconstruction. What remains then of Meillassoux’s criticism in After finitude: An Essay on the Necessity of Contigency that Deleuze no less than Hegel hypostatizes or absolutizes the correlation between thinking and being and thus brings back a vitalist version of speculative idealism through the back door?

At stake in Meillassoux’s criticism of the Principle of Sufficient Reason is a double problem: the conditions of possibility of thinking and knowing an absolute and subsequently the conditions of possibility of rational ideology critique. The first problem is primarily epistemological: how can philosophy justify scientific knowledge claims about a reality that is anterior to our relation to it and that is hence not given in the transcendental object of possible experience (the arche-fossil )? This is a problem for all post-Kantian epistemologies that hold that we can only ever know the correlate of being and thought. Instead of confronting this weak correlationist position head on, however, Meillassoux seeks a solution in the even stronger correlationist position that denies not only the knowability of the in itself, but also its very thinkability or imaginability. Simplified: if strong correlationists such as Heidegger or Wittgenstein insist on the historicity or facticity (non-necessity) of the correlation of reason and ground in order to demonstrate the impossibility of thought’s self-absolutization, then the very force of their argument, if it is not to contradict itself, implies more than they are willing to accept: the necessity of the contingency of the transcendental structure of the for itself. As a consequence, correlationism is incapable of demonstrating itself to be necessary. This is what Meillassoux calls the principle of factiality or the principle of unreason. It says that it is possible to think of two things that exist independently of thought’s relation to it: contingency as such and the principle of non-contradiction. The principle of unreason thus enables the intellectual intuition of something that is absolutely in itself, namely the absolute impossibility of a necessary being. And this in turn implies the real possibility of the completely random and unpredictable transformation of all things from one moment to the next. Logically speaking, the absolute is thus a hyperchaos or something akin to Time in which nothing is impossible, except it be necessary beings or necessary temporal experiences such as the laws of physics.

There is, moreover, nothing mysterious about this chaos. Contingency, and Meillassoux consistently refers to this as Hume’s discovery, is a purely logical and rational necessity, since without the principle of non-contradiction not even the principle of factiality would be absolute. It is thus a rational necessity that puts the Principle of Sufficient Reason out of action, since it would be irrational to claim that it is a real necessity as everything that is is devoid of any reason to be as it is. This leads Meillassoux to the surprising conclusion that [t]he Principle of Sufficient Reason is thus another name for the irrational… The refusal of the Principle of Sufficient Reason is not the refusal of reason, but the discovery of the power of chaos harboured by its fundamental principle (non-contradiction). (Meillassoux 2007: 61) The principle of factiality thus legitimates or founds the rationalist requirement that reality be perfectly amenable to conceptual comprehension at the same time that it opens up [a] world emancipated from the Principle of Sufficient Reason (Meillassoux) but founded only on that of non-contradiction.

This emancipation brings us to the practical problem Meillassoux tries to solve, namely the possibility of ideology critique. Correlationism is essentially a discourse on the limits of thought for which the deabsolutization of the Principle of Sufficient Reason marks reason’s discovery of its own essential inability to uncover an absolute. Thus if the Galilean-Copernican revolution of modern science meant the paradoxical unveiling of thought’s capacity to think what there is regardless of whether thought exists or not, then Kant’s correlationist version of the Copernican revolution was in fact a Ptolemaic counterrevolution. Since Kant and even more since Heidegger, philosophy has been adverse precisely to the speculative import of modern science as a formal, mathematical knowledge of nature. Its unintended consequence is therefore that questions of ultimate reasons have been dislocated from the domain of metaphysics into that of non-rational, fideist discourse. Philosophy has thus made the contemporary end of metaphysics complicit with the religious belief in the Principle of Sufficient Reason beyond its very thinkability. Whence Meillassoux’s counter-intuitive conclusion that the refusal of the Principle of Sufficient Reason furnishes the minimal condition for every critique of ideology, insofar as ideology cannot be identified with just any variety of deceptive representation, but is rather any form of pseudo-rationality whose aim is to establish that what exists as a matter of fact exists necessarily. In this way a speculative critique pushes skeptical rationalism’s relinquishment of the Principle of Sufficient Reason to the point where it affirms that there is nothing beneath or beyond the manifest gratuitousness of the given nothing, but the limitless and lawless power of its destruction, emergence, or persistence. Such an absolutizing even though no longer absolutist approach would be the minimal condition for every critique of ideology: to reject dogmatic metaphysics means to reject all real necessity, and a fortiori to reject the Principle of Sufficient Reason, as well as the ontological argument.

On the one hand, Deleuze’s criticism of Heidegger bears many similarities to that of Meillassoux when he redefines the Principle of Sufficient Reason in terms of contingent reason or with Nietzsche and Mallarmé: nothing rather than something such that whatever exists is a fiat in itself. His Principle of Sufficient Reason is the plastic, anarchic and nomadic principle of a superior or transcendental empiricism that teaches us a strange reason, that of the multiple, chaos and difference. On the other hand, however, the fact that Deleuze still speaks of reason should make us wary. For whereas Deleuze seeks to reunite chaotic being with systematic thought, Meillassoux revives the classical opposition between empiricism and rationalism precisely in order to attack the pre-Kantian, absolute validity of the Principle of Sufficient Reason. His argument implies a return to a non-correlationist version of Kantianism insofar as it relies on the gap between being and thought and thus upon a logic of representation that renders Deleuze’s Principle of Sufficient Reason unrecognizable, either through a concept of time, or through materialism.

Philosophy of Local Time

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Let us hypothesize on the notion of local time.

Existence of temporal order: For each concrete basic thing x ∈ Θ, there exist a single ordering relation between their states ≤.

We now give a name to this ordering relation:

Denotation of temporal order: The set of lawful states of x is temporally ordered by the ≤ relation.

The above is a partial order relation: there are pairs of states that are not ordered by ≤; e.g. given an initial condition (x0,v0) for a moving particle, there are states (x1,v1) that are not visited by the particle.

Proper history: A totally order set of states of x is called a proper history of x.

The axiomatics do not guarantee the existence of a single proper history: they allow many of them, as in “The garden of forking paths”. The following axiom forbids such possibility.

Unicity of proper history: Each thing has one and only one proper history.

Arrow of time: The axiomatics describe a kind of “arrow of time”, although it is not related to irreversibility.

A proper history is also an ontological history. The parameter t ∈ M has not to be continuous. The following axiom, a very strong version of Heraclitus’ hypothesis Panta rhei, states that every thing is changing continuously:

Continuity: If the entire set of states of an ontological history is divided in two subsets hp and hf such that every state in hp temporally precedes any state in hf, then there exists one and only one state s0 such that s1 ≤ s0 ≤ s2, where s1 ∈ hp and s2 ∈ hf.

The axiom of continuity is stated in the Dedekind form.

Continuity in quantum mechanics: Although quantum mechanical “changes of state” are usually considered “instantaneous”, theory shows that probabilities change in a continuous way. The finite width of spectral lines also shows a continuous change in time.

Real representation: Given a unit change (s0, s1) there exists a bijection T : h ↔ R such that

h1 = {s(τ)|τ ∈ R} —– (1)
s0 = s(0) —– (2)
s1 = s(1) —– (3)

Local time: The function T is called local time. The unit change (s0, s1) is arbitary. It defines an arbitrary “unit of local time”.

The above theory of local time has an important philosophical consequence: becoming, which is usually conceived as evolution in time, is here more fundamental than time. The latter is constructed as an emergent property of a changing (i.e. a becoming) thing.

Meillassoux, Deleuze, and the Ordinal Relation Un-Grounding Hyper-Chaos. Thought of the Day 41.0

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As Heidegger demonstrates in Kant and the Problem of Metaphysics, Kant limits the metaphysical hypostatization of the logical possibility of the absolute by subordinating the latter to a domain of real possibility circumscribed by reason’s relation to sensibility. In this way he turns the necessary temporal becoming of sensible intuition into the sufficient reason of the possible. Instead, the anti-Heideggerian thrust of Meillassoux’s intellectual intuition is that it absolutizes the a priori realm of pure logical possibility and disconnects the domain of mathematical intelligibility from sensibility. (Ray Brassier’s The Enigma of Realism: Robin Mackay – Collapse_ Philosophical Research and Development. Speculative Realism.) Hence the chaotic structure of his absolute time: Anything is possible. Whereas real possibility is bound to correlation and temporal becoming, logical possibility is bound only by non-contradiction. It is a pure or absolute possibility that points to a radical diachronicity of thinking and being: we can think of being without thought, but not of thought without being.

Deleuze clearly situates himself in the camp when he argues with Kant and Heidegger that time as pure auto-affection (folding) is the transcendental structure of thought. Whatever exists, in all its contingency, is grounded by the first two syntheses of time and ungrounded by the third, disjunctive synthesis in the implacable difference between past and future. For Deleuze, it is precisely the eternal return of the ordinal relation between what exists and what may exist that destroys necessity and guarantees contingency. As a transcendental empiricist, he thus agrees with the limitation of logical possibility to real possibility. On the one hand, he thus also agrees with Hume and Meillassoux that [r]eality is not the result of the laws which govern it. The law of entropy or degradation in thermodynamics, for example, is unveiled as nihilistic by Nietzsche s eternal return, since it is based on a transcendental illusion in which difference [of temperature] is the sufficient reason of change only to the extent that the change tends to negate difference. On the other hand, Meillassoux’s absolute capacity-to-be-other relative to the given (Quentin Meillassoux, Ray Brassier, Alain Badiou – After finitude: an essay on the necessity of contingency) falls away in the face of what is actual here and now. This is because although Meillassoux s hyper-chaos may be like time, it also contains a tendency to undermine or even reject the significance of time. Thus one may wonder with Jon Roffe (Time_and_Ground_A_Critique_of_Meillassou) how time, as the sheer possibility of any future or different state of affairs, can provide the (non-)ground for the realization of this state of affairs in actuality. The problem is less that Meillassoux’s contingency is highly improbable than that his ontology includes no account of actual processes of transformation or development. As Peter Hallward (Levi Bryant, Nick Srnicek and Graham Harman (editors) – The Speculative Turn: Continental Materialism and Realism) has noted, the abstract logical possibility of change is an empty and indeterminate postulate, completely abstracted from all experience and worldly or material affairs. For this reason, the difference between Deleuze and Meillassoux seems to come down to what is more important (rather than what is more originary): the ordinal sequences of sensible intuition or the logical lack of reason.

But for Deleuze time as the creatio ex nihilo of pure possibility is not just irrelevant in relation to real processes of chaosmosis, which are both chaotic and probabilistic, molecular and molar. Rather, because it puts the Principle of Sufficient Reason as principle of difference out of real action it is either meaningless with respecting to the real or it can only have a negative or limitative function. This is why Deleuze replaces the possible/real opposition with that of virtual/actual. Whereas conditions of possibility always relate asymmetrically and hierarchically to any real situation, the virtual as sufficient reason is no less real than the actual since it is first of all its unconditioned or unformed potential of becoming-other.

Music Territorializes Time: Deleuze. Thought of the Day 19.0

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Deleuze speaks of music expressed through pulsed and non-pulsed time. Pulsed time, or Chronos, is “territorialized time,” the “marking” of time through measure and repetition/return (“ritornello”) that is one expression of musically performative “time because it’s fundamentally the way in which a sonorous form, however simple it may be, marks a territory.” He continues, “Each time that there is a marking of a territoriality, there will be a pulsation of time.” If pulsed time is also musical time, and if both pulsed and musical time is territorial, what can be inferred of proximity?

Territorialization is the assemblage of proximities, in Deleuze and Guattari’s formation, bodies formed through not merely the association but the complicity of parts in their nearness to one another that make up bodies/territories distinct from other bodies/territories. Musical performance territorializes time because the performance of music takes (“appropriates”) embedded times in proximity (the curvature of the rate of change) and creates a body of aesthetic sound and practice distinct from non-territorialized or deterritorialized sound (the noises of traffic and machines or of digestive processes may have musically performative possibilities but are not themselves music or part of a musical territory without coming together through proximities to shared and changing time, to shared and changing space).

Deleuze reminds his listeners that territorialization (and thus pulsed time) may be embedded in measurement but is also contained in “development.” “[A]s soon as you can fix a sonorous form, determinable by its internal coordinates, for example melody-harmony, as soon as you can fix a sonorous form endowed with intrinsic properties, this form is subject to developments, by which it is transformed into other forms or enters into relation or again is connected to other forms, and here, following these transformations and these connections, you can fix pulsations of time.” Pulsations of time, or Chronos, then become even more subject to musical proximities that change in response to one another, an echo of borderswerving’s relationship to borderlinking.

Non-pulsed time, Aion, is defined rather by deterritorialization and the taking apart of “sonorous form.” Deleuze relates non-pulsed time to velocity, recalling the rate of change described by DeLanda and the dromoscopy of Paul Virilio. Aionic time is part of what Deleuze terms the “mixture” of time; Aion and Chronos blend together in a musical territorializing that is also a deterritorializing, and in these opposite yet proximal movements are proximities of becoming and unmaking. The experience of participating in a musical performance as a whole (instruments, performers, audience, composition, context, etc.) and as its component parts (notes, phrases, measures, dynamics, individual characteristics of performers and instruments) is the experience of this mixed time.

And yet, not all mixed time is musical, and not all sounds in proximity are musical. For music to occur, aesthetic proximities must become aware of their possibilities for becoming and unmaking, must perceive the friction and soothing of their near surfaces. As Deleuze questions, “¿Cuando [sic] deviene musical una voz? Yo diría, desde el punto de vista de la expresión, que la voz musical es esencialmente una voz desterrito- rializada. ¿Qué quiere decir eso? Pienso que hay cosas que aún no son música y que, sin embargo, están muy próximas a la música.” (When does a voice become musical? I would say, from the point of view of expression, that the musical voice is essentially a deterritorialized voice. Why does one want to say that? I think that there are things that are not music, and that nevertheless are very close to music.)