Still, it seems hard to deny that the "raw materials" are there in nature prior to the emergence of life. 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

What you write here seems to me to risk blurring a very good binary distinction between the digital and the analogue, or between the dichotomous and the analogical. Are you just wanting to say that the potential for the digital is inherent in the analogical continuum and that the apparently binary nature of the distinction between digital and analogue is itself a hypostatization?

The 'fully blown' digital seems to emerge with symbolic language. For example, all numbers in ordinary arithmetic are made up of just ten kinds of digits.

This raises the question of 'where' the boundary is set, given that by your own stipulation there is no preexistent 'place' for it to go (a boundary can only act as such at a place if it is put there), which would require the very identity you're denying exists to begin with before the placement of the boundary.

A boundary is only put precisely there by digitization.

But, the digitization was supposed to be effected by the introduction of the boundary?

Digitization just is the introduction of precise boundaries. Problem?

...and where does the boundary get introduced?

I.m not sure I understand the question. Digitization is the introduction of crisply discrete values, One discrete value cannot be another discrete value so there is a crisp distinction (boundary if you like) between them

Suppose you introduce a boundary by separating one piece of a continuum from another. By hypothesis, we are now at least treating the continuum as digital, which means the border must be somewhere. That is, there must be some piece of the continuum that is on one side of the border, and another piece on the other side (or at least, we treat things this way). And there must be no distance between these two points, or else the border itself will have distance, and the question of the digitalization of how long the border is then just repeats the problem whole again. But then, the only way for this to happen is if we can identify two discrete pieces of the continuum, and say that one is on one side, the other on the other. So for any piece of the continuum, once the boundary is there, we can say definitively which side it's on, and as a result there now is, or at least we take there to be, an absolutely discrete cutoff between one side of the boundary or the other.

But where is that boundary? How can we tell, in virtue of placing the boundary? How can we tell where we've put the boundary at all? One way is to say, we just look at which things fall on either side of it: but this begs the question, since if we could determine precisely to begin with, before knowing where the boundary is set, which side each was on, then there will have ipso facto been digitalized distinctions between those two things that lie on opposite sides of the border all along, since we need to make this digitalization in order to place the border. But if we do not assume this, then we have no reason to say that the border was placed at once place rather than another, and we literally cannot figure out exactly where it is, or which things digitally fall on either side of it, hence the border itself becomes analog, and contrary to hypothesis we have done no digitalizing in placing the border.

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.

I'm inclined to say that's the point being refuted: the boundary is not placed anywhere upon the world. It's entirely on it's own-- when I speak a catergory, I do not do it through the world in front of me. I am the one speaking. The saying of the catergoy a particular state of me, not any object I'm pointing at.

Boundaries are without being within the outside world. The drawn line is its own, not whatever is underneath it.

You seem to be running together two different processes in your thinking; you seem to be conflating perceptualization and symbolic conceptualization. Crisp boundaries are established only by symbol-based conceptualization, but more or less distinct boundaries are always already a condition of perception itself (of which pre-symbolic conceptualization is also a necessary condition). These pre-symbolic boundaries are not absolutely precise, though. I see the apple on the table and I can see the outer skin (boundary) of the apple. I can say that the apple ends precisely where the air begins, and that establishes a conceptually precise boundary. Of course the imagined precision of that boundary may be blurred by thinking in terms of the fundamental particles that constitute the apple and the air, for example; so it is not a case of believing that there is an absolutely precise boundary in actuality. I think that is rather the whole point of SX's OP.

But we can conceive of a precise boundary just as we can conceive of a perfect geometrical figure; and we would be, for example, establishing a conceptually precise boundary by specifying a geometrical figure using plane coordinates. Same goes for entities. We can conceive a precise identity (boundary) in terms of entity/ non-entity; but of course I cannot say where the actual boundary between some object and its environment is precisely located. I think the question about the location of conceptual (digital) boundaries is based on a category mistake.

I may be being flippant about this, but I just don't see how this addresses my post.

All I can say is that we're apparently not talking about digital boundaries 'somewhere, wherever they might be, and I don't know or can't know in principle,' but rather digital boundaries that are well-defined in formal systems. The former seems to be more an epistemic matter anyway: to imagine a digital boundary is indeed to imagine it somewhere perfectly precisely, even if one can't say for whatever reason exactly where. We can bypass the epistemic issues by setting them in a thought experiment, and still the problem remains. If this was a conceptual mistake, then we shouldn't be able to say, for any given part of the continuum, whether it fell on one side of the boundary or the other. But this is just to say either that 1) there is no digital boundary, or 2) there is no boundary at all, which are not situations we're interested in ex hypothesi. The issue about perception v. conception also seems to miss the point in that we're not talking about literally perceiving a boundary but rather being able to tell. in the thought experiment, where it is by thinking about it.

But to be honest my interest in this topic isn't proportional to the amount of time I'm spending typing about it, so I'm going to stop replying here.

And in particular:

But to be honest my interest in this topic isn't proportional to the amount of time I'm spending typing about it, so I'm going to stop replying here — The Great Whatever

All I can say is that as I conceive it the discreteness of digitally or symbolically conceptualized entities (the conceptual boundary between them in other words) just consists in the fact that one symbol cannot be thought to be identical to another. It's a matter of logical differences.

When it comes to the continuum, think of something like "Imagine the line of the equator: you obviously know which side of the line Europe is, even though you don't know precisely where the line lies on the planet's surface; but there might be locales in Ecuador, the Congo, Kenya and Indonesia, for example, where the answer is not clear at all. Maybe with GPS you could tell if you were stepping over the equator.

Anyway, I'm not greatly interested in this particular obtuse angle we are trying to explore either, so it suits me well enough to drop it if that's what you want.

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.

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. — StreetlightX

You may be missing the force of the argument SteetlightX. "The analog", continuum, or whatever you wish to call it, is the very same as the "thing-in-itself", in the sense that its existence is simply assumed. We experience the appearance of some sort of continuity within the world, so we assume a continuum to account for this appearance, just like we experience the existence of real substance in the world, and assume the thing in itself..

Accordingly, anything you might say about this analog existence, this continuum, is based only in this assumption. So in order to say anything true about the continuum, your assumption of a real existing continuum must be first validated, justified. Only by validating this assumption does the nature of the continuum become intelligible. To simply assume a continuum, and say that it is of an analog nature, and completely other than the digital, is just an assumption which is completely unjustified, until it is demonstrated why this is assumed to be the case.

Now we must start without the assumption of an analogue continuum, and justify this assumption. We cannot start with the assumption of a continuum, with all the connotations of meaning (identity) which go along with such an assumption, we must demonstrate the need for this assumption, and this demonstration will expose the character of this so-called continuum. In other words, rather than assuming a "continuum", or "analog" existence, with all the features of identity associated with those words, we must bring this thing which we are trying to describe, into focus, such that we can accurately describe it.

Recall that to institute any digital logic, a continuum must distinguish a part of itself, from itself. — StreetlightX

To begin with, this is self-contradictory. If a continuum could distinguish a part of itself from itself, it could not be a continuum. A true continuum would not give any principles for making such a distinction. And if an arbitrary distinction was made, even the points of boundary would consist of something other than the continuum itself, so it is impossible that a continuum itself is distinguishing a part of itself.

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. — StreetlightX

And this approach cannot be satisfactory. The discontinuous is what we can know, the is and is not, so to describe the continuous as that which is opposed to the discontinuous is to employ negation and the tools of logic. But the continuous has already been noted to defy such rules of logic and negation. We cannot use such logical principles to describe the continuous. The existence of the continuous is assumed, based on our experience of living and sensing, so this is what we must refer to in our description of the continuous.

In our living experience, we observe two types of boundaries, spatial boundaries between existing things, and a temporal boundary between the future and past. If one, or both of these boundaries appears to be unreal, then we have reason to assume continuity. Spatial boundaries, between individual entities appear to be real, but the temporal boundary between past and future may not be real, and it is this lack of a real boundary in time, which drives the need to assume continuity.

But there are very real difficulties here. As much as time appears to be a continuum, without any real boundaries, our experience also indicates to us that the boundary between past and future is very real. Time appears to be a continuum, but it also appears to have a real boundary between past and future.

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. — StreetlightX

The boundary's status is not specifically undecidable, its appearance is paradoxical, and this is what makes it seem to be undecidable. It is paradoxical because the continuum presents itself to us as essentially indivisible, continuous, but, as constituted with a boundary. The way to avoid the paradox is to understand the continuum as the boundary itself. But this makes the continuum a real identifiable entity, a boundary.

Accordingly, anything you might say about this analog existence, this continuum, is based only in this assumption. So in order to say anything true about the continuum, your assumption of a real existing continuum must be first validated, justified. Only by validating this assumption does the nature of the continuum become intelligible. To simply assume a continuum, and say that it is of an analog nature, and completely other than the digital, is just an assumption which is completely unjustified, until it is demonstrated why this is assumed to be the case. — Metaphysician Undercover

The semiotic relation is triadic. And this insertion of an extra step - an epistemic cut - is what gets you past this kind of problem.

So the analog thing-in-itself is vague. It only comes to be called a continuum in crisp distinction to the digital or the discrete within the realm of symbolisation or signification. It is a logical step to insist the world must be divided into A and not-A in this fashion. And then in forming this strong, metaphysical-strength, dichotomy of possibility, it can be used as a theory by which pragmatically to measure reality. We can form the counterfactually-framed belief that reality must be either discrete or continuous, digital or analog, and then test reality against this self-describing theory.

So the situation is the reverse of the one you paint. We don't need to begin in certainty. Instead - as Peirce and Popper argued with abductive reasoning, as Goedel, Von Neumann and others demonstrated with symbolic reflexivity in general - it can all start with a reasonable guess. We can always divide uncertainty towards two dialectically self-grounding global possibilities. The thing-in-itself must be either (in the limit) discrete or continuous. And then having constructed such a sharply dichotomised state of metaphysical certainty - a logical either/or - we have the solid ground we need to begin to measure reality against that idea of its true nature. Pragmatically, we can go on to discover how true our reasoned guess seems.

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. It is a memory of our past that is certain enough to predict our futures.

So the assumptions here begin in a discussion of existential possibility. If anything exists - in the spatiotemporally-extended sense that we think of as "the world" - then metaphysical logic says there are two options, two extremum principles, when it comes to how that world has definite being. Either it must be continuous or discrete, connected or divided, integrated or differentiated, relational or atomistic, morphism or structure, flux or stasis, etc, etc - all the different ways at getting at essentially the same distinction when it comes to extended being.

And having identified two complementary limits on being - terms that are logically self-grounding because they are seen to be both mutually-exclusive and jointly-exhaustive - we can be as certain of anything we can be that reality, the vague thing-in-itself, must fall somewhere between the two metaphysical-limits thus defined. Exactly where on this now crisply-defined spectrum is what becomes the subject of measurement.

Note that this dichotomy itself encodes both the digital and the continuous in being like a line segment - a continuous line marked by two opposing end-points.

So anyway, the very idea of the analog~discrete is based on the more primal dichotomy of the continuous~discrete - a way of talking about reality in general. But with the analog~digital, we are now drawing attention to the general semiotic matter~symbol dichotomy - the step up in material complexity represented by life and mind.

The analog~digital dichotomy has sprung up in computation and information theory as an ontological basis for a technology - an ontology for constructing machines rather than growing organisms. And yet, in retrospective fashion, it has now become a sharper way of getting at the essence of what life and mind are about - the semiotic modelling relation that organisms have with worlds. The analogy of the code is very useful - not least because it brings so much maths with it.

But in a sense, the analog~digital dichotomy also overshoots its mark. It leads to the idea that modeler and modeled actually are broken apart in dualistic fashion - like hardware and software. And this leads to the breakdown in understanding here - the questions about how a continuous world can be digitally marked unless it is somehow already tacitly marked in that fashion.

So once we start to talk about the Kantian "modeler in the world", the first step is to make this essential break - this epistemic cut - of seeing it as the rise of the digital within the analog. Material events gain the power of being symbolic acts. But then we must go on to arrive at a fully triadic model of the modeling relation. And so attention returns to the middle thing which is the informal acts of measurement that a model must make to connect with its world.

This is what is the focus of modern biosemioticians like Pattee, Rosen, Salthe and many others like Bateson, Wilden, Spencer-Brown, and so on. What is it that properly constitutes a measurement? What is it that defines a difference that makes a difference?

Recall that to institute any digital logic, a continuum must distinguish a part of itself, from itself. — StreetlightX

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.

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. — StreetlightX

Do you understand the question you are indicating here to be asking, when it speaks of "belonging" about the location, in the general sense of its position within ontological space, of the boundary? This is what, it seemed to me, TGW was asking. I think the question is based on a category mistake: I think that boundaries, whether analogue or digital, are logical, not ontological. Imprecise boundaries certainly belong to the continuum, insofar as they are intelligible within its logical space. Think of animal territories, for example. But precise boundaries belong only to the digital as I said before:

Digitization just is the introduction of precise boundaries. — John

[Emphasis added]

Digitization just is the introduction of precise boundaries. — John

That's right. But then there is still the issue of how they can be imposed on the world - the issue of human measurement.

And then - where this gets radically metaphysical - there is the post-quantum issue of measurement in general.

So through semiotics, we come to explain human understanding of the world as a triadic sign relation. And then it now seems as though the world itself is ontically pan-semiotic - a system that self-referentially measures itself into being in some concrete sense. The universe has to observe itself to "collapse the wavefunction" and have a digitally-crisp, atomistic, mechanically-determined, state of being.

Of course we then call that classical world, that realm of continuous Newtonian dynamics, our analog reality in contrast with the digitality of our symbolic representations of that world.

But quantum theory has re-introduced the basic metaphysical dichotomy - is existence continuous or discrete (or indeed, beyond that, indeterministic)? - at base.

So we know how in epistemic fashion we impose intelligible order on the world in a way that makes it pragmatically measurable. But even while arriving at a fully working theory of that - as in biosemiosis - up pops the holographic bound in fundamental physics and other pansemiotic questions about how the Universe solves its own measurement problem. Where does it stand so as to resolve its own indeterminacy in globally-self referential fashion.

Given this seems to be a debate about Analytic metaphysics vs PoMo metaphysics, as usual I would say only Pragmatic metaphysics has the proper resources to answer these kinds of questions properly. :)

But quantum theory has re-introduced the basic metaphysical dichotomy - is existence continuous or discrete (or indeed, beyond that, indeterministic)? - at base. — apokrisis

Yes, I guess that is the big question. But even if the real turned out to be (that is if we could know without question that it definitely was) discrete, is it reasonable to think that discreteness could consist in absolutely precise boundaries between the fundamental units? That would seem to evoke Leibniz' Monadology.

Given this seems to be a debate about Analytic metaphysics vs PoMo metaphysics, as usual I would say only Pragmatic metaphysics has the proper resources to answer these kinds of questions properly. :) — apokrisis

Perhaps all three have their different places and functions if the 'grand scheme'? I''m guessing though, that you see the other two as being subsumed and augmented by pragmatic metaphysics?

;)

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. — StreetlightX

Starting to sound a little mystical here. The snake turns and meets its tail? At the point of meeting, the one becomes the two.

"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". — StreetlightX

The boundary is a line or plane for spacial boundaries. It's an idea. I pondered this a long time ago.. the origin of the concept of negation. Maybe it comes from craving and aversion.

The boundary is a line or plane for spacial boundaries. It's an idea. I pondered this a long time ago.. the origin of the concept of negation. Maybe it comes from craving and aversion. — Mongrel

Or from the possibility of different actions? I think of the fully fledged symbolic logic of negation and opposition as being prefigured in the less distinct analogical conceptions of exclusion and absence. But then these distinctions also seem to be expressed in the language of logic, or the logic of language, as two kinds of not-X: the weaker 'not-X' of exclusion and absence and the stronger 'not-X' of negation and opposition.

It only comes to be called a continuum in crisp distinction to the digital or the discrete within the realm of symbolisation or signification. It is a logical step to insist the world must be divided into A and not-A in this fashion. — apokrisis

Yes, the continuum comes to be called such to distinguish it from the digital or discrete, but this does not imply that these are properly opposed. That's what must be respected, that different from digital does not mean the opposite of, or the negation of digital. So the analog, or continuum, may be different from the digital in the same way that colour is different from red. Therefore this "logical step" is not a valid logical step at all. We cannot assume a proper A and not-A relation between the analog and the digital

So the situation is the reverse of the one you paint. We don't need to begin in certainty — apokrisis

I do not claim that we need to start in certainty, this is more like what you imply. You imply that if a thing is different from A you can establish the logical certainty of not-A of that thing, but this is not the case. If the thing is said to be different from red, we might still be talking about colour, and it would be false to characterize colour as not-red, because colour includes red. What I said, is that we have to get an idea of what this thing, continuum, is, by looking directly at the thing, and describing it. Saying what it is not, will never tell us what it is.

We can always divide uncertainty towards two dialectically self-grounding global possibilities. The thing-in-itself must be either (in the limit) discrete or continuous. — apokrisis

So this is the mistake, these two, discrete and continuous, are not properly opposed and therefore are not mutually exclusive, as you imply. We have discrete colours, red, yellow, green, blue, within a continuous spectrum

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. — Streetlight

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.

But in another sense, I do agree with you. The building of digital systems that depend upon formal negation still involve the "artificial imposition" of boundaries on natural continuums. So a digital computer leverages material differences in voltages as a foundation for binary computation (2V = "true", 5V = "false"). My point was simply (and hopefully uncontroversially) that nature provides the "raw materials" that make the imposition of binary distinctions possible in first place. If it didn't - if there were no materially exclusive differences already within nature to leverage - then the emergence of binary systems could never have occurred.

Are you just wanting to say that the potential for the digital is inherent in the analogical continuum and that the apparently binary nature of the distinction between digital and analogue is itself a hypostatization? — John

Yep, more or less.

it's the exclusion of contrariety rather than contradiction. — Aaron R

Yes, that's a better way of putting it; precisely the expression I was groping for.

So a digital computer leverages material differences in voltages as a foundation for binary computation (2V = "true", 5V = "false"). My point was simply (and hopefully uncontroversially) that nature provides the "raw materials" that make the imposition of binary distinctions possible in first place. If it didn't - if there were no materially exclusive differences already within nature to leverage - then the emergence of binary systems could never have occurred. — Aaron R

The material difference in voltage isn't used to construct that binary distinction though, for the discintion is it own state, not something that necessarily follows from the presence of material voltage.

We might say that the "raw materials" give relevance to binary distinctions, 2V= "true" and 5V= "false" are relevant when talking about voltage. We can use them to achieve something we want in the world. Not true of the 2V/5V distinction if we are talking about the taste of a cake.

The "raw materials" aren't leveraged to form the binary distinction. We don't distinguish 2V/5V by looking at the "raw materials." The distinction itself is a first principle category which we then relate to the "raw materials."

I'm actually taking a digital circuit logic course right now, so this is kind of up my alley a bit. Hopefully philosophizing about all this won't affect my grades X-)

Nothing is 'equal to' or 'identical to itself', 'in-itself'. These notions are heuristics that are imposed upon nature for the sake of communicative ease. — StreetlightX

I'm not so sure about this. 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.

The properties that leech on their objects would be identical to themselves. To be 4.15678 g just is to be 4.15678 g. The fact that the object we are weighing measures at 4.15678 g means it has a discrete amount of mass associated with it. There is a fundamental reason why an object is a certain way - say, 4.15678 g. It's not arbitrary; there are discrete properties of objects.

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. Instead of binary 0's and 1's, you have a much larger range of outputs - but just like in an analog clock, these outputs are restricted. An analog clock can only represent certain intervals. The more we narrow down our constraints, the less able we are to maneuver: there are many different kinds of stars, but there are only two biological and fertile sexes. There are a gazillion species of animals, but there are only three naturally occurring isotopes of carbon.

Isn't the difference between an analog and a digital system a digitalization anyway? Either/or you are analog or digital...

Is a heuristic identical-to-itself?

Or from the possibility of different actions? — John

Sure. The road not taken.

Isn't the difference between an analog and a digital system a digitalization anyway? Either/or you are analog or digital... — darthbarracuda

Ideally, yes. Some effort was being made to show analog as being primal or primary.

If electrons can be either waves or particles, I'm not sure there is a primary.

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).