I can agree with Wilden. It is when you start pulling in Deleuze and "aesthetics" and other such baggage that it loses analytic clarity and becomes a romantic melange of allusions. — apokrisis

Yes, yes, if it doesn't come from the one of five of six philosophers you've bothered schooling yourself in it's all allusion and romantic melange.

So contra your position, existence has to start with the digitisation of the analog - a primal symmetry-breaking. Or as I say, to make proper sense of this, we have to introduce the further foundational distinction of the vague~crisp. We have to reframe your LEM-based description in fully generic dichotomy-based logic. — apokrisis

But your 're-framing' does nothing but dilute a perfectly rigorous distinction with a fuzzy, unprincipled one. As I've said quite a few times now, the distinction between the digital and the analog is quite precisely defined by the presence of negation and self-reflexivity. At stake is a difference in kind, not a difference of degree. Wilden himself is unequivocal about this: "'Not' itself is a metacommunicative boundary essential to the 'rule about identity' which is the sole sufficient and necessary condition of any digital logic"; elsewhere: "A digital system is of a higher level of organization and therefore of a lower logical type than an analog system. The digital system has greater 'semiotic freedom', but it is ultimately governed by the rules of the analog relationship between systems, subsystems, and supersystems in nature. The analog (continuum) is a set which includes the digital (discontinuum) as a subset". Insofar as your whole line of reasoning does not respect this fact, it is less a refinement than it is a watering down.

No it isn't, and yes you can. If you want elaboration, see what I've previously written about the analog as the knowing of relations.

Been through this multiple times now, Meta, to know is not to identify. Won't go through it again.

Hey, I'm just relaying the theory here. Actually, now that you mention it, I relayed it wrong. It's the monopoly on the legitimate use of force, generally within a bounded geographic area.

Also taxes can be collected by feudal lords as well as local gangsters; they aren't specific to the state as such.

It's perhaps the most well known definition of the state - first given by Max Weber - that it possesses a 'monopoly on violence'. That is, the state possesses the legitimacy to exercise violence - for the sake of warmaking, law enforcement, etc - while depriving other entities (ordinary citizens, gangs, corporations, etc) from such power. This is said to define a state's sovereignty. Thus the violation of sovereignty happens when there exists the capacity for violence which is not state sanctioned. This is why, for example, no foreign police force can act on another country's soil without express permission from the state. Doing otherwise would be a violation of sovereignty. This conception itself has it's grounding in social contract theory like that of Hobbes, Locke, and rousseau, which is a cornerstone of political philosophy in itself.

Agamben's own work aims at refining this notion of sovereignty to deal with the particular form it has taken on in modern times. Following Foucault, sovereignty for Agamben isn't just about a monopoloy on violence so much as it producing certain forms of life. This is referred to as 'biopolitics'. But that's Agamben's own particular project. If you're more interested in the very notion of the political with it's connotations of inclusion and exclusion, maybe check out something like Bonnie Honig's Politics Theory and the Displacement of Politics, or even Hannah Arendt's The Human Condition.

But as I said, I don't think you are working with a well defined dichotomy in talking about analog vs digital. They are not a reciprocal pairing in the way a proper dichotomy like discrete and continuous are. — apokrisis

Au contraire mon ami, the reference to the discrete and the continuous mean nothing without the index of negation and reflexivity which quite precisely define the distinction between the analog and the digital.

Forgive me for thinking you were using it in the more usual sense.... — apokrisis

Consider yourself forgiven; we all begin somewhere, even if that somewhere is Wikipedia. But of course aesthetics in the broader sense has to do with the shaping of space and time; rhythm, form, and everything that belongs to the realm of the sensibility in general. From the Greek Aisthēsis, that which relates to the sensible; the vulgar sense of the aesthetic as relating to the art and the beautiful being a particularly modern, restricted and derivative sense of the term.

I can see how you/Deleuze might be driving at a substantialist ontology - one that takes existence to be rooted in the definiteness of material being. And so the inherent properties of substance would seem more fundamental than the relational ones. — apokrisis

Except you're wrong; the whole point is that 'substances' are differentially engendered. It's process all the way down; though perhaps not all the way up. But your misreading is not worth entertaining too far.

I understand what intensive and extensive properties mean in the standard physics context. I completely don't get your attempts to argue that they somehow reflect an analog~digital distinction. — apokrisis

By intensive I simply mean sub-representative/digital (i.e. analog) differences. A bit of history of philosophy helps here too: Aristotle's understanding of difference is premised on his metaphysics of the categories. A thing can only be said to differ from something else if they belong to the same genera: "Difference is said of things which, while being other, have some identity, not according to number, but according to the species, or the genus, or the proportion" (Aristotle, Metaphysics, book Gamma). In every case for Aristotle difference is derivative or parasitic upon a more primal identity; that is, difference can only ever be digital. But if it agreed that the digital is itself a product of boundary setting, then, in Deleuze's terms, there ought to be a concept of difference not subordinated to differences in the concept (read: genera). That is, there are differences which are not digital differences; in the context of the thread, these are referred to as intensive differences.

Miguel de Beistegui sums things up nicely: "[in Aristotle's schema], differences... make sense only in relation to the species and genus under which they are subsumed. And so, were we to rehabilitate differences in philosophical discourse, we would need to overcome the primacy of ontology as ousiology or, more specically, overcome the punctual character of substance, and the conception of discourse as propositional. We would need to begin with differences, and with matter, and to show how they themselves are generative of identities and substances. We would need to consider them no longer as accidents ... since accidents always presuppose a substance to which they occur, but as events, and as events constitutive of our world. In so doing we would begin to move from an ontology of substance and essence to an ontology of events" (de Beistegui, Truth and Genesis). This is not to mention also Kant's original use of the distinction between intensive and extensive magnitudes from whom Deleuze draws the terms from in modified form.

Wilden too puts the whole issue in terms of difference, although he doesn't employ the vocabulary of intensive/extensive: "There are thus two kinds of difference involved, and the distinction between them is essential. Analog differences are differences of magnitude, frequency, distribution, pattern, organization, and the like. Digital differ­ences are those such as can be coded into distinctions and oppositions, and for this, there must be discrete elements with well-defined boundaries. In this sense, the sounds of speech are analog; phonology and the alphabet are digital. In the same way, the continuous spectrum of qualitative, analog differences ranging from black to white in the visible color spectrum may be digitalized by the boundaries of a color wheel or coded around the opposi­tion of black and white (which, for another system of explanation, as the absence of color, are identical)". (System and Structure).

I think it's worth noting that the continuum, just as much as digital logic, exists only by virtue of thought. Thought enables the coming-to-be of parts, and that coming-to-be consists in the self-distinguishing of the part from the whole, as much as it does the self-distinguishing of the whole from the part. — John

I don't think this is quite right. As a matter of principle, it trades too heavily on some kind of thought/world duality which I think is unsustainable, if not mystical. As far as the facts go, however, digitality is present at the level of things like gene expression and axon function in nerve cells, and require no 'thought' in order to function. What matters in both cases is not thought but behaviour, or better, semiotic function. At this level - the level of life - behaviour is regulated by feedback which means that casual processes operate as sign-relations: whether or not an axon will propagate a signal, for example, depends on the (chemical) feedback it receives from it's environment; as such, signals operate not as efficient causes but as signs.

To use another example, consider a tree-line that doubles as a national border. The tree-line does not 'cause' you to avoiding crossing it without the proper documentation, but it stands as a sign which regulates your behaviour nonetheless. If everyone were to ignore national borders, the tree-line would no longer stand as a sign. But again, what is crucial here is not thought but behaviour: you can't 'think away' the fact that the tree-line is a border, and even if you do, you will (possibly) suffer the real-life consequences of being caught if you cross it illegally. The institution of the digital is a result of a decision, but the status of this decision is not 'in thought' so much as it is 'in practice' (which is why you can't 'find it' anywhere in particular). One must remain a materialist about these things.

Certainly there can be analog and digital measurements, but ultimately what exists at the present is what I believe apokrisis calls "crispness" - the vague becomes the discrete, or the digital. Digital corresponds to certainty, analog to uncertainty or vagueness. — darthbarracuda

See my reply above to Apo - the analog is not just uncertainty and vagueness. It has specific properties of it's own defined primarily by relationality.

Furthermore, analog systems inherently have digital parts anyway, they just aren't computational. Additionally, the way I understand it, analog systems are not so much a separate kind of thing than they are a less discrete digitalization.

As I emphasized previously, the difference between continuity and discontinuity is indexed by negation, and by implication, self-reflexivity. No amount of fine-graining of the digital will allow it to lapse over into the analog. The difference is a difference in kind, and in principle, not just one of degree.

There is a relation of exclusion involved here, but (as others have alluded to) it's the exclusion of contrariety rather than contradiction. So for example, red and green are contraries whereas red and not-red are contradictories. The former is associated with "material" negation, the latter with "formal" negation. Interestingly, formal negation can be defined in terms of material negation: not-red is the just the set of all of red's contraries, etc.

Similarly, the sense in which the magnitude at point A is not the magnitude at point B (within the context of a gradient) also appears to be that of material negation. Having a psi of 40 at point A is materially incompatible with simultaneously having a psi of 50 at point A, and in that sense the former excludes the latter (and vice versa). Crucially, the magnitude at A is not the magnitude at B quite regardless of the activities or even the existence of ens vitae. — Aaron R

But the measure of psi is still not 'intrinsic' to the notion of pressure gradient; it still a digital model of the analog; this has nothing to do with the measure of psi per se, but simply because it is a numerical measure to begin with. Recall that the whole number line is generated by utilizing 'zero' as a rule (that is, a boundary) to distinguish between integers; as per Frege, one begins by defining zero as the 'object under which the concept 'not equal to itself' falls', and then from there, generates the whole of the number line:

"Zero is implicitly defined as a meta-integer, and indeed its definition is what provides the rule for the series of integers which follow it ... [Number] depends upon the distinction between 0 as an object falling under a concept, and 0 as the number belonging to a concept. All that needs to be established is that zero is not simply a number as such, but a rule for a relation between integers. The number which belongs to the concept 'identical with 0' is also the interval or gap between the integers (the number one). Thus a⁰ (but not 0°, which equals 0) is arbitrarily defined as 1, because it is the boundary between a¹ and a⁻¹." (System and Structure)

So the measure of psi - as a measure - is not intrinsic to the analog gradient that is a pressure gradient. While I appreciate that the two measures of psi at different points of a pressure gradient may stand in a relation of contrariety rather than contradiction, not even contrariety is, strictly speaking, an analog value. Hence Deleuze: "It is difference in intensity, not contrariety in quality, which constitutes the being 'of' the sensible. Qualitative contrariety is only the reflection of the intense, a reflection which betrays it by explicating it in extensive. It is intensity or difference in intensity which constitutes the peculiar limit of sensibility" (Difference and Repeition).

And in Kantian fashion, we never of course grasp the thing-in-itself. That remains formally vague. But the epistemic cut now renders the thing-in-itself as a digitised system of signs. We know it via the measurements that come to stand for it within a framework of theory. And in some sense this system of signs works and so endures. — apokrisis

As usual, we stand imperceptibly close on some issues, and unbridgeably far on others. While I agree with the thrust of your post, you continue to hold a very narrow view of knowledge as digital, when your own comments ought to disabuse you of this notion. As I commented on elsewhere in reply to Pierre, the analog is not some kind of unknowable 'thing-in-itself' which is simply 'vague'; the analog has qualities which are knowable, but simply in a different mode than that of the digital. If the digital is composed by (stark/crisp/extensive) differences defined by negation, the analog is composed by (non-denotative) relational differences of intensity: "differences in magnitude, frequency, distribution, pattern and organization" (Wilden).

Bateson himself speaks of how analog communication works "by means of kinesthetic and paralinguistic signals, such as bodily movements, involuntary tensions of voluntary muscles, changes of facial expression, hesitations, shifts in tempo of speech or movement, overtones of the voice, and irregularities of respiration. If you want to know what the bark of a dog "means," you look at his lips, the hair on the back of his neck, his tail, and so on. These "expressive" parts of his body tell you at what object of the environment he is barking, and what patterns of relationship to that object he is likely to follow in the next few seconds. Above all, you look at his sense organs: his eyes, his ears, and his nose" (Steps To An Ecology of Mind)

None of these things are noumenal 'things-in-themselves' which stand on the other side of knowledge. They are simply of a different order of knowledge, one relating to sensual movements of and in space and time: aesthetic knowledge. At it's base, this is what 'aesthetic' means: relating to space and time, as with Kant's 'transcendental aesthetic'.

Gilles Deleuze is the philosopher who has perhaps attended to the specificity of analog differences with the most care, referring to them as differences of 'intensity' as opposed to digital differences of 'extensity', noting how the former necessarily underlie the latter: "Every diversity [read: identity - SX] and every change refers to a[n analog] difference which is its sufficient reason. Everything which happens and everything which appears is correlated with orders of differences: differences of level, temperature, pressure, tension, potential, difference of intensity ... The expression 'difference of intensity' is a tautology. .. Every intensity is differential, by itself a difference. ... Each intensity is already a coupling (in which each element of the couple refers in turn to couples of elements of another order), thereby revealing the properly qualitative content of quantity. ... Difference or intensity (difference of intensity) is the sufficient reason of all phenomena, the condition of that which appears." (Difference and Repetition).

So again, to turn back to our eternal debate, any metaphysics based on modeling relations - itself premised on discrete, digital knowledge - is derivative of a more primal aesthetic ground out of which it is born. Elsewhere Deleuze will note that all representation - as with models - depend on 'sub-representitive dynamisms' which are nothing other than intensive (non-conceptual) differences: "No concept would receive a logical division in representation, if this division was not determined by sub-representative dynamisms ... These dynamisms always presuppose a field in which they are produced, outside of which they would not be produced. This field is intensive, which is to say it implies a distribution in depth of differences in intensity ... the concept would never divide or specify itself in the world of representation without the dramatic dynamisms which determine it in this way in a material system beneath all possible representation." (The Method of Dramatization).

Actually, the issues around the question of boundary setting are quite important and worth pursuing in some detail. Recall that to institute any digital logic, a continuum must distinguish a part of itself, from itself. In other words, the 'flatness' of the analog must become self-reflexive and thus stratified into 'levels': the object level of the continuum itself, and the meta-level at which the continuum can 'refer' to itself. Negation is the operator which allows this stratification to occur. This is why it is vital to define 'continuity' and 'discontinuity' in terms of negation: negation provides the unassailable index for what counts as continuous (analog) and what counts as discontinuous (digital): if a system includes negation, it is digital, if it does not, it is analog.

If negation is not used as an index, it becomes all too easy to paper over the in principle difference between the analog and the digital by appealing to limit-procedues which simply granulize the digital, like the ones suggested by TGW previously. But no limit procedure, no amount of granulation can account for the irreflexivity of the analog which is without negation. A corollary of this is that digital languages, thanks to their reflexivity, can represent things, while analog languages cannot. Analog communication is at best iconic or indexical, but never symbolic, which belongs by right to the digital alone.

Now, the interesting question that has been raised a few times - and that I've avoided talking about - has to do with the status of the boundary itself. Does it belong to the continuum itself, or does it belong to the instituted digital system? The answer can only be that the boundary belongs to neither. It cannot belong to the continuum, because if it did, the continuum would be already-digitized; on the other hand, it cannot belong to the digital system because it is the very condition by which the digital is instituted. Like Russell's barber who both shaves and does not shave himself, the boundary's status is constitutively undecidable.

Wilden: "It is impossible to decide whether [the boundary] belongs to the set A or the set non-A. It belongs to neither, it is both neither and nowhere, and it corresponds to nothing in the real world whatsoever". The reason for this undecidability of course, has to do with the paradoxes generated by self-inclusion: if the digital, in constituting itself as a continuum subject to recursion and reflexivity, is to be consistent, it must forgo completeness (the status of the boundary cannot be decided 'within' the system, on pain of inconsistency). As Paul Livingston puts it in his discussion of Graham Priest's dialetheic logic, this is the 'choice' that every formal system must make, of necessity:

"In facing up to the paradoxes of self-reference, formal thought thus defines a fundamental choice: either consistency with incompleteness (and hence the prohibition of total self-reference, and the regress into an open iterative hierarchy of metalanguages) or completeness with inconsistency (and hence reference to paradoxical totalities). On the level of formal­ languages and systems, taken simply as neutral objects of description, either of these choices is evidently a possibility; we can save the consistency of our systems by ascending up the hierarchy of metalanguages or, as Priest suggests, we can model inconsistency within self-contained formal languages by means of what he calls a dialetheic logic, one that tolerates contradictions in certain cases" (Livingston, The Politics of Logic).

Of course, these are the choices that must be faced 'within' the digital itself. From the perspective of the analog, which is without negation, and to which the laws of identity and the excluded middle do not apply, these forced choices are inapplicable. Wilden himself will refer Godel's results to make the same point: "every consistent deductive system will generate Godelian sentences which we know to be true but which cannot be demonstrated within the system. And a system of meta-axioms will engender a meta-sentence, and so on ad infinitum. This implies that all human communication, including mathematics and logic, is an open system which can be subject to closure only for methodological reasons. The problem of the punctuation of the analog by the digital is irresolvable for humankind." (System and Structure, my emphasis). In other words, the irresolvable paradoxes of the digital are a symptom of it's always being too 'loose' to 'fit' the continuum of the analog.

That's a delicate project, insofar as any such critique must itself take some logical form. While certainly not an impossible task, one must be careful not to cut off the branch upon which one sits (sorry for the overworn cliche). — Aaron R

A delicate project indeed. Part of the motivation for this thread was to wonder if, within formal logic, there are resources by which to deal with these kinds of issues, or if these kinds of issues even can be dealt with within the constraints of formal logic. I'm simply not well versed enough to know where to look or what that would even look like. My point of view is very much from the 'outside in'. However, I'm always on the look out for clues and resources which would help; Deleuze's work has been invaluable (as has the work of Francois Zourabichvili, who provocatively reads Deleuze as a logician, albeit a 'non-rationalist/empiricist logician'), so too Gregory Bateson and his spiritual successor, Anthony Wilden, whose System and Structure has been an indispensably invaluable resource for me for trying to think these things through. There are other resources too, but as far as I know, no one has really drawn them all together in a sustained way.

A pressure gradient between two points in space is still a binary difference in magnitude even when its not being leveraged as such by some living system, isn't it (in the sense that the magnitude at point A is not the magnitude at point B)? — Aaron R

I don't think this works: a pressure gradient still has no negative values: there is more pressure here, and less pressure there, but at no point is there a relation of exclusion between the two 'ends' of the gradient; the magnitude at point A is not that of ¬B and vice versa. Identity and the law of the excluded middle is simply not operative at this level. The key again is that pressure is an entirely relative variable; the pressure at any point in a gradient (read: continuum) is defined by it's 'place' in that gradient. It cannot be 'isolated' without losing it's status as a 'point' of pressure to begin with: that is to say, pressure is a differential variable that cannot be taken 'out of context' without losing it's 'identity'. As with all analog systems, the pressure gradient is a matter of the 'more or less', both/and, and never either/or.

But there's no 'dark art' here: in order to digitize an analog continuum, you simply draw a boundary - and then you treat it as such. The cut is a semiotic one, a matter of significance. The Mississipi River may not physically be a 'real' boundary between Iowa and Illinois, but to the degree that it stands for a boundary - it is treated as a sign - it functions as a boundary. Of course, one need not follow a river, one can place a boundary entirely arbitrarily, and nothing in the continuum that will or will not stop one from doing so. What is needed is not something 'in' the analog or 'in' the digital, some something capable of treating something as digital.

It seems that you're real beef here is not with identity and categorization per se, but with the uncritical or dogmatic application of categories (especially those that imply socio-politoc-economic identities) upon individuals in nature. — Aaron R

Yeah, exactly. I said elsewhere in the thread that got this train of thought going that what I'm kind of after is something like a "critique of pure formal logic" as it were.

That said, I still feel hesitant to deny that there is a legitimate distinction to be made between those identities that essentially depend upon contextual relations to "ens rationis" (e.g. the human lebenswelt) and those that essentially depend solely upon contextual-relations to "ens reale". Again, this seems to come part-and-parcel with the notion that some binary distinctions are naturally sustained (e.g. consider the evolution of "switches" in biological nature, and their fundamental role in processes of homeostasis, reproduction, sensation, etc.). The upshot is that I'm not entirely convinced of the notion that identity is merely transcendental in the sense of being confined merely to "ens rationis", while perhaps acknowledging that it is transcendental in the sense of being essentially context-dependent (I believe that medieval scholars actually referred to the fundamental sensitivity of finite, substantial being to environmental context "transcendental relativity").

I agree with this actually, although I would even refine it somewhat. I would in fact say that the emergence of the digital goes hand in hand with neither ens rationis nor ens reale but with ens vitae: that is, life. It is no accident or coincidence that all three examples of 'natural' digital systems mentioned so far in this thread are biologial - gene expression, biological switches and synthetic biocircuits, if I recall correctly. Insofar as digital process as self-relating circuits (that operate via negation), it doesn't take a giant leap to recognize that the self-relating 'ens' par excellence is life - that which is autopoietically defines itself by sustaining a boundary been organism and environment. So perhaps it might be fair to say the the transcendental illusions of identity are just those of life itself. It is only by virtue of our biological being that we can engage in digital communication.

Yeah, I was admittedly a little naughty in naming the thread. It was originally something like 'negation and the analog/digital distinction' but that was no fun. But yeah, you're right, it's more the case that what identity there is, is derivative of analogic differences. In a phrase: the digital is the result of an analogic genesis.

It gets complex however, because digital processes, once engendered, can feed-back into their analog 'ground' as it were. So you get something like a self-fulfilling prophecy: treat something as having an identity, and at some point it will have one. There's a dialectic, in other words, between the analog and the digital that takes hold once digital processes have come into being. Manuel DeLanda gives the example of a refugee who, having become aware of the fact of being so classified, changes her behaviour in order to fit better the criteria of refugee in order to gain asylum.

But as he also notes, "to explain the case of the female refugee one has to invoke, in addition to her awareness of the meaning of the term 'female refugee', the objective existence of a whole set of institutional organizations (courts, immigration agencies, airports and seaports, detention centres), institutional norms and objects (laws, binding court decisions, passports) and institutional practices (confining, monitoring, interrogating), forming the context in which the interactions between categories and their referents take place." In any case relational differences (i.e. analogic differences) are constitutive of identity, even if said identity has a real ontological standing, as it were. Identity, as real, is nonetheless context-bound, and constitutively, necessarily so.

As Kant knew, transcendental illusion gave rise to real effects: the entirety of dogmatic, uncritical metaphysics. The claim here is similar: if one uncritically employs categories of identity as metaphysically primitive, this too will this lead to uncritical ontologies. As far as the distinction itself, I'll refer you to the third post I made in this thread, but I'll add this: to the extent that communicative precision depends on digital, rather than analog communication, it is necessary that one employ digital forms of communication to get these - or any fine grained - ideas across. This is what makes the illusions transcendental: recall that for Kant, such illusions were unavoidable and were engendered due to the nature of reason itself. They are illusions intrinsic to reason. Our ability to communicate similarly - unavoidably - tempts us to project the digital into the world in toto.

So you think degrees on a temperature scale are ordinal then?

Oh come on, you were talking about numbers in the context of a metric, numerical scale which is what I was responding to. Talk about shifting goalposts...

If the distinction that matters here is cardinal versus ordinal, one would wonder how you can't have heard of ordinal numbers. — The Great Whatever

And what exactly do you think ordinal numbers indicate? Distinctions between discrete elements in a set? Not at all. What they mark are relationships, which are - guess what - analog, and not digital differences.

The objectionable idea of the thing-in-itself is present in both of those ontologies ... I don't see how an ontology of pure (merely "analogue") processes can account for the possibility of empirical knowledge about anything — Pierre-Normand

As I said above, the analog is not at all anything like a 'thing-in-itself'. It is eminently knowable in the most trivial of ways; it's just that unlike 'digital knowledge' which is denotative and representational, analog knowledge deals with relationships. It's only by confusing knowledge as such with denotative, representational knowledge can one make the kind of objection you have. The most fun example, drawn from Gregory Bateson, comes from thinking about animal communication. No known animal communication is digital, with the exception of our own, human language. This doesn't mean that animals can't know things.

Thus speaking of cats trying to get our attention, Bateson writes, "When your cat is trying to tell you to give her food, how does she do it? She has no word for food or for milk. What she does is to make movements and sounds that are characteristically those that a kitten makes to a mother cat. If we were to translate the cat's message into words, it would not be correct to say that she is crying "Milk! Rather ... we should say that she is asserting "Dependency! Dependency!" [or, following Wilden, who borrows from Bateson here: "will you put yourself in a mother relationship to me?" - SX] The cat talks in terms of patterns and contingencies of relationship, and from this talk it is up to you to take a deductive step, guessing that it is milk that the cat wants." (Bateson, Steps To an Ecology of Mind).

Of communication among bees, Wilden writes: "No bee constructs a message out of or about another message (there is no metacommunication about messages as is possible in digital communication); in other words, no bee can "dance bout dancing". The 'gesture language' of bees involves per­ception (perceptual representations are analogs of what they represent). Moreover, no bee who has not flown the course to find the nectar can send the message 'about' where it is, no bee can tell where the nectar or the pollen will be, no bee can say where the nectar isn't ...The circular dance has the specific function of analog communication: it simply says something about the dancing bee's relationship to the food near the hive, but it cannot say there is no food there. The wagging dance uses a code of signals to point; it is a more complex analog message. In neither case does there seem to be a possibility of a methodological analysis of these forms into discrete elements with a duality of patterning similar to that of morphemes and phonemes, for the indications of distance in the wagging dance are frequencies and times, and relatively imprecise." (System and Strucutre).

So the idea that the analog is a kind of noumenal 'in itself' is wrong. To drive the point home: "The analog is pregnant with meaning whereas the digital domain of signification is, relatively speaking, somewhat barren. It is almost impossible to translate the rich semantics of the analog into any digital form for communication to another organism. This is true both of the most trivial sensations (biting your tongue, for example) and the most enviable situations (being in love). It is impossible to precisely describe such events except by recourse to unnameable common experience (a continuum). But this imprecision carries with it a fundamental and probably essential ambiguity: a clenched fist may communicate excitement, fear, anger, impending assault, frustration, 'Good morning', or revolutionary zeal. The digital, on the other hand, because it is concerned with boundaries and because it depends upon arbitrary combination, has all the syntax to be precise and may be entirely unambiguous. Thus what the analog gains in semantics it loses in syntactics, and what the digital gains in syntactics it loses in semantics."

If you can make a distinction between discrete elements in a system, then you're dealing with a digital system. If you can't, you're dealing with an analog system. This isn't to say that one can't talk about differences in analog systems, only that with analog systems, you're dealing with differences of ordinality (position, order, magnitude) rather than cardinality (number of). It maps to the difference between extensive, metric qualities and intensive, topological qualities. The following passage from Manuel DeLanda details things quite nicely:

"Extensive properties include not only such metric properties as length, area and volume, but also quantities such as amount of energy or entropy. They are defined as properties which are
intrinsically divisible: if we divide a volume of matter into two equal halves we end up with two volumes, each half the extent of the original one. Intensive properties, on the other hand, are properties such as temperature or pressure, which cannot be so divided. If we take a volume of water at 90 degrees of temperature, for instance, and break it up into two equal parts, we do not end up with two volumes at 45 degrees each, but with two volumes at the original temperature ... An intensive property is not so much one that is indivisible but one which cannot be divided without involving a change in kind. The temperature of a given volume of liquid water, for example, can indeed be “divided” by heating the container from underneath creating a temperature difference between the top and bottom portions of the water. Yet, while prior to the heating the system is at equilibrium, once the temperature difference is created the system will be away from equilibrium, that is, we can divide its temperature but in so doing we change the system qualitatively." (DeLanda, Intensive Science and Virtual Philosophy)

Um, I don't know what to say other than you're simply wrong. That one can find a number between any two numbers still means you're effecting a distinction between two numbers, which is a digital operation.

But that is not perfectly analog at all. If you've got a numerical scale, you're already operating digitally. The only way to speak of differences in an analog system is with respect to ordinality - orders of magnitude, distribution, pattern and so on. If you're invoking cardinals, you've gone digital.

-I don't see why an analog system can't deal with or include negation or identity — The Great Whatever

How could it? Again, the paradigm is the mercury in the thermometer - what even would negative mercury mean? To speak as such already implies a digitization which is nowhere present in the movement of the mercury. Anyway, one can be more than rhetorical here. The first thing to note is that any digital system, by definition, requires a boundary to be set: in order for an (analog) continuum to distinguish itself from itself, some kind of boundary needs to be set in place in order to digitize the continuum. Digital systems are what happens when a continuum distinguishes an element of itself from itself.

The crux is this: the role of negation ('not') is precisely to enable a continuum to do just that. The ability to distinguish between A and not-A (that is, the setting up of a boundary between one thing and another thing) is the minimal condition which would allow the digitization of a continuum. Now, the reason why negation can play this role is because what negation actually is is a recursive (or 'metacommunicative') operator on an object language. That is, to negate is to take a statement and say something about that statement itself: to enact a negation of A ("not-A") is to say something about "A"; it is communication about communication.

Wilden again: "By introducing at a more complex level the possibility of communicating about communication, metacommunication provides the potentiality of truth, falsity, denotation, negation, and deceit. (The [animal's] nip says "This is play." The next step is to be able to say: "This is not play." And then: "This is/is not play." Only human beings pretend to pretend.) The introduction of the second-level sign into a world of first-level signs and signals detaches communication from existence as such and paves the way for the arbitrary combination of the discrete element in the syntagm. ...'Not' is a rule about how to make either/or distinctions."

So negation - or at least the possibility of negation - is the founding aspect of abstract symbolism, and representation more generally, i.e. the kind employed by formal logic. To represent is to make a distinction. It is the possibility of negation which allows the (analog) continuum to distinguish itself from itself; and insofar as the analog is by definition defined in terms of it's continuity, any negation (a metacommunicative, boundary setting operator) would make it at once a digital system. Thus, as far as analog systems go, they best they can do is to refuse or reject (I can turn away from your request), but not deny or negate. More to say about the charge of Kantianism later (early hint: analog communication is a perfectly valid form of communication; it is just not a representational, denotative, form of communication; the analog is not a unknowable noumenon).

DNA as a brute molecule is neither analog nor digital - it is a not a system or a process - but the process of genetic expression (DNA to protein) is a mixture of both. For instance, although DNA codons (nucleotide tripets) are 'read' in a digital manner, their function is to constrain growth, which is an analog process.

Wilden for detail: "DNA is the molecular coding of a set of instructions for the growth of a certain living system of cells. But these instructions do not cause growth any more than the directions of a cakemix cause the mix to become a cake. They do not cause growth, they control its possibilities. In other words, the instructions of DNA constrain or limit growth... But it is not only the instructions which constrain growth; so does the environment in which they operate. Thus the articulation of the genetic code - which we know to be in some way double, like language, and punctuated, like writing - depends upon processes of combination-in-context (contiguity) and substitution-by-selection (similarity). Like language, also, it is a combined analog and digital process. Like language, it is not ruled by causality, but by goalseeking and constraint."

The type of identity commonly referred to in logic, is what I would call formal identity. A thing is identified by a form, or formula, such that its identity is based in "what" it is, according to the logical formula. It is impossible that the thing referred to by the word or symbol is anything contrary to what is described by the formula, or else it would not be the thing described. The other type of identity, I would call material identity. This is what Aristotle referred to when he said that a thing is the same as itself. Here, a thing is identified not by a form or formula of what it is, but by itself. The identity of the thing is not to be found in a description or formula, of what the thing is, but within the thing itself. — Metaphysician Undercover

Part of my argument here is that what you refer to as material identity is a kind of hypostatization or transcendental illusion in which 'numerical' (formal) identity is projected (mistakenly) onto nature. I write of course, from the perspective of a kind of philosophy of process where any attempt to think in terms of brute identities ought to be rendered suspect from the beginning. With respect to formal logic, one can see how something as simple as the subject-predicate relation [P(x)] is fraught with metaphysical issues.

LOL Scott Soames senpai noticed us ^_^ — The Great Whatever

I dunno; on first brush I'd say the Sorites Paradox is a kind of symptom of what happens when you try to completely model an analog system in a digital environment - you're simply never going to achieve a 1:1 correspondence, as a matter of principle. It's like when applying a Fourier transform to an analog wave signal, you can in principle only ever get an approximation, and never the signal itself. Most of the famous paradoxes of logic have this issue at their source, I suspect.

Sounds relatively OK to me. I'd definitely affirm that language is a digital system (although not all digital systems are linguistic, and if I were to be precise, language employs both analog and digital modes of communication). As for as formal logic being 'metaphysically mistaken', I'd say it depends on what kind of use you want to put that logic to. I'm sure it has it's uses in some circumstances, but if the above (OPs) considerations are correct, one would be at least limited with the sorts of 'metaphysical moves' one could make using formal logic. I'm not arguing for dismissal so much as for recognizing limits, as it were.

Nah, I wouldn't say that the digital is 'artificial'. Wilden himself will provide a few examples of digital systems in nature (he spends alot of time describing axon firing in nerves for instance). It's more that the digital is derivative of, or parasitic upon, the analog (which doesn't automatically translate to artificial). What I'd like to explore is what consequences this has for formal logic, where things like identity and the principle of the excluded middle are taken as bedrock in many respects. As I put it differently in another thread, in nature, nothing is identical to itself. Similarly, there are no absolute disjunctions between identities and their opposites.

No, the the digital is a subset of the analog, they are not in opposition or in a relation of exclusion. The relation is not a∨d (XOR), rather, d⊆a. Wilden: "The analog (continuum) is a set which includes the digital (discontinuum) as a subset."

Interestingly, the distinction between the analog and the digital is asymmetrical: it's only from the perspective of the digital itself that one can draw the distinction (or can talk of the analog); from the perspective of the analog, digital distinctions are themselves continuous. Consider a thermostat which controls the temperature: although it depends on analog qualities, it turns the heat on or off only once the temperature crosses a certain (digial) boundary. The analog is indifferent to the digital functioning of the thermostat, while the digital, as coarse-grained, can only 'see' a threshold being crossed and is itself indifferent to the continuum of the temperature as such.

Gilles Deleuze and Felix Guattari - What Is Philosophy?
Jeffrey A. Bell - Deleuze and Guattari's What is Philosophy?: A Critical Introduction and Guide
Eric Alliez - The Signature of the World: What is Deleuze and Guattari's Philosophy?

Prep for a course I'm doing on WIP.

This is a spin-off of a discussion I was having in the Dennett thread; there was too much I wanted to pack in a post, so I figured I'd give it a thread of it's own. The conclusion is a little rushed, for brevity's sake (ha!) but I got the meat of it in the post I think. I still need to say something about recursivity, but hopefully they'll be an opportunity to do so in the discussion that follows - if there is any!

Surely this is compatible with the more basic point I'm trying to make, which is that your two earlier assertions:

(1) that people don't say a thing is identical to itself in ordinary speech, and
(2) to say that a thing is identical to itself is nonsensical — The Great Whatever

(1) People don't say a thing is identical to itself in ordinary speech [in isolation from some sort of parameter which would make sense of such an identity claim].
(2) To say that a thing is identical to itself [in the absence of some sort of context] is nonsensical.

I don't think I mean any of those things. That might be implied depending on the situation, sure. But that's not what the sentence means. For example, it's possible for Adam to be Mr. Smith, but not respond to both those names. — The Great Whatever

Ugh, I missed the qualification of 'probably' that I had meant to attach to that (I did the second time I mentioned in it my post!). Not that it matters though: the point remains the same. To assert that Alan is Mr. Smith only makes sense if there is some kind of significance attached to that designation. It may not be that they will respond to the same name, but it will be - of necessity - some (contingent?) fact.

When the same individual is denoted by two names that have two distinct Fregean senses, then, upon learning that they are identical, what is learned by a language user who was acquainted with this individual under those two distinct modes of presentation isn't merely a fact about language. As Kripke has shown, in a clear sense, the fact about language is contingent but the identity statement that has been learned about is necessary. (Kripke, though, thought that he was arguing against a Fregean conception of proper names. Gareth Evans has shown that Kripke's observations are consistent with a Fregean account of singular senses, understood non-descriptively.)

For instance Lois Lane may be acquainted both with Superman and with Clark Kent, and know them respectively as "Superman" and as "Clark Kent". When she eventually learns that Clark Kent is Superman she doesn't merely learn a fact about linguistic use -- (although, as TGW hinted, she could learn this fact inferentially through learning another fact about linguistic use). She rather learns the fact that Superman and Clark Kent are the same individual, a fact that no alternative (i.e. counterfactual) conventions of linguistic use could have negated. — Pierre-Normand

Fair point. I should have said something to learn identity is to at least learn a fact about linguistic use, etc. In any case, the point is to resolve identity into a context, to show that identity is never brute, but always relational. To learn that Superman and CK are the same is to learn they both saved that cat from the tree, that they both are excellent at changing clothes very quickly, etc.

Another issue that has been raised in the recent exchanges in this thread is the identity that a material object (i.e. a "substance", or "spatiotemporal continuant") retains with itself through material and/or qualitative change, through time. This issue is related to the first since an object can be encountered at two different times under two different modes of presentation (i.e. while being thought about under the two different Fregean senses of "A" and "B" successively, such that the numerical identity of their denotata may come under question). What settles the question of the identity of A with B are the criteria of persistance and individuation for object of this sort, and the spatiotemporal carrer(s) of the relevant object(s): both things that may be matters of empirical investigation. — Pierre-Normand

But to say all of this is already to subscribe to a very specific kind of metaphysics which is everywhere fraught with problems I think. Part of my line of questioning here is to call into question exactly these sorts of pressuppositions that thinking in terms of formal logic encourage, I think.

After all, when I say that Adam is Mr. Smith, I don't mean that Adam has identical height to Mr. Smith, or something like that -- no, I mean numerically they are the very same guy. — The Great Whatever

But you don't 'just' mean that 'they are the same guy'; you 'also mean' that they will respond to the same name, that Mr. Jones is responsible for the Bad Thing you thought someone else was responsible for, etc, etc. The phrase 'they are the same guy' is a kind of nominal 'condensation' or short hand of these 'existential ramifications' as it were. What I'm trying to do is reverse the order by which we understand what it means to 'be the same guy'. Mr. Jones is Alan not because he is 'the same guy'; he is 'the same guy' because Alan has done everything Mr. Jones has, because he will (probably) respond the same whether he is called Mr. Alan or Jones, etc. That Mr. Jones and Alan 'are the same guy' (=identical) is just a way of saying that. Identity is parasitic, derivative, of these things which have nothing to do with identity 'in themselves'.

But what does it matter whether identity is an imposed category? Have I argued for any specific construal of what numerical identity is? I've only tried to show that your Wittgenstein-inspired comment that to say a thing is identical to itself is nonsensical, is wrong, as is the claim that in ordinary situations we don't do this. — The Great Whatever

(I take) Wittgenstein's comment to apply to statements of identity that do not refer to an identity parameter. And it is the case the those sorts of comments are 'useless propositions'.

So what is it with respect to, in this case? — The Great Whatever

I don't know, give me a context of use. These things can't be talked about in abstraction - which is the point.

Also note that the fact that we can learn something about language use by uttering or assenting to these sentences doesn't detract from the fact that we are asserting the identity of a thing with itself. — The Great Whatever

This simply strikes me as a kind of transcendental illusion, in the Kantian sense. We can say, in a kind of derivative manner, that to assert that Alan = Mr. Jones is to assert the identity of a thing with itself, but the very notion of identity is still a logical category imposed upon an 'existential situation' in which questions of identity or lackthereof are simply absent to begin with. In fact, speaking of Kant, 'A critique of pure formal logic' might adequately title the kind of position that I'm coming from here.

No, no, it's not that people don't assert identity. Of course they do, they do so all the time. But the question isn't about assertion it's about ontology, as it were. As I understand it, to say that 'Mr. Jones is Alan' is to learn a fact about language-use: upon knowing this, I know that Mr. Jones might respond to the call 'Alan!' as he would to the call 'Mr. Jones'. Or that documents which refer to Mr. Jones or Adam actually refer to the same person, and so on. In all cases, there is some kind of parameter by which to make sense of the identity of Mr. Jones and Alan. Or put differently, the identity Mr. Jones = Alan does not 'stand alone', it is always identity 'with respect to.. x,y,z'. And the function of names is ostensibly for identification in social settings, bureaucratic identification, etc.

In any case, the idea is that there is no 'identity as such', identity considered in abstraction from any kind of external parameter, not that 'identity doesn't exist' or whatever. This is made clearer in Wittgenstein's elaborations in the Investigations: "'A thing is identical with itself" - there is no finer example of a useless proposition, which yet is connected with a certain play of the imagination. It is as if in imagination we put a thing into its own shape and saw that it fitted. We might also say: 'every thing fits into itself.' Or again: 'Every thing fits into its own shape.' At the same time we look at a thing and imagine that there was a blank left for it, and that now it fits into it exactly."

Hmm, I don't think that saying Mr. Jones is Adam is the same as saying 'x is identical to itself'. It's the difference between x=x and x=y. One might learn something new upon learning that Adam is Mr. Jones. Not so that Mr. Jones is Mr. Jones.