There Are No Identities In Nature

Streetlight

Broadly speaking, one can speak of two types of systems in nature: analog and digital. Analog systems are defined by continuous variables, like the distance between points or changes in velocity; rulers, thermometers, or accelerator pedals are all examples of analog systems. Digital systems, by contrast, are defined by discontinuous or discrete variables: as with the ten 'digits' of the fingers, digital systems, unlike analog systems, involve discontinutous 'jumps' between measurement values. Thus the transistor based computer, with it's on/off electrical gates, is an example of a digital system.

Now, one particular feature of analog systems that they admit of no negation. Because analog systems employ continuous variables, there cannot be any 'gaps' in the variables of the system: all the quantities involved are always positive; there are no minus quantities (consider the movement of mercury in a thermometer - it is a smooth, continuous variation). Anthony Wilden, speaking in terms of the difference between analog and digital computation, puts it like this:

"It is impossible to represent the truth functions of symbolic logic in an analog computer, because the analog computer cannot say 'not-A'. Negation in any language or simulated language depends upon syntax, which is a special form of combination, and the analog computer has no syntax beyond the level of pure sequence (and that only in a positive direction). There is no 'either/or' for the analog computer because everything in it is only 'more or less', that is to say: everything in it is 'both-and' ... Because the analog does not have the syntax necessary to say 'No' or to say anything involving 'not', one can refuse or reject in the analog, but one cannot deny or negate.' (Wilden, System and Structure).

How then, do we turn an analog system into a digital one? By doing nothing other than introducing negation into the analog continuum: that is, by placing a 'cut' into the continuum which would prase the continuum into A and not-A. Doing this creates a boundary in the continuum. Here is Wilden again: "Boundaries are the condition of distinguishing the 'elements' of a continuum from the continuum itself. 'Not' is such a boundary. ... the differential boundary of the figure and ground is a primitive digitalization generating a distinction, and the distinction may then become an opposition. [Thus], figure and ground form a binary relation, one and two form a binary distinction, [and] A and non-A in analytical logic form a binary opposition (an identity). 'Not' is a rule about how to make either/or distinctions themselves."

A few quite important things follow from this, but I want to focus on one: it is clear that if the above is the case, the very notion of identity is a digital notion which is parasitic on the introduction of negation into an analog continuum. To the degree that analog systems do not admit negation, it follows that nothing in an analog system has an identity as such. Although analog systems are composed of differences, these differences are not yet differences between identities; they are simply differences of the 'more or less', or relative degrees, rather than 'either/or' differences. The same follows for the principle of the excluded middle, which, to the degree that it is defined by the disjunction between an identity and it's negation ("either p or not-p" [⊢pv¬p]), is rendered inoperative at the level of the analog.

A way to summarise all of the above is this: to the degree that nature is a continuum, there are no brute identities in nature. Or less provocatively, to the degree that there are identities in nature, they are constructed and derivative of analogic differences. 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. As Wilden acknowledges, 'boundaries in fact are the conditions of all communication'; but it will not do to confuse those conditions which those of nature. The all-too-quick takeaway I want to draw from this - the thread is getting too long now - is that any kind of ontology or metaphysics which would rely on the machinery of formal logic to do it's heavy lifting would be severely crippled one (here's to looking at you, analytic metaphysics!).

Streetlight

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!

Mongrel

A way to summarise all of the above is this: to the degree that nature is a continuum, there are no brute identities in nature. — StreetlightX

But the difference between analog and digital has a digital character. It's an opposition in which the poles are interdependent.

Movies seem analog because we aren't fast enough to see that it's discrete frames passing by. Maybe time and space are like that at a fundamental level.... atomic... blinking. If you claim that it's not... how do you know?

Streetlight

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.

Mongrel

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. — StreetlightX

Yea. I used to work in telecommunications hardware engineering.. all up in the A to D and vice versa.

It's true you could say that digital exists because of boundaries we cast. Transistors were originally used only for analog applications. Using it as a switch means picking a threshold. Since the threshold is artificial, digital is fundamentally artificial. I think that's what the author you mentioned was trying to say?

You could look at it that way.... the other way is this: reality is all about consequences.

I think it's actually just different ways of looking at the world (ways that are interdependent)... although I have zero will to argue for my own intuition. Maybe somebody else will.

Streetlight

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.

Mongrel

Do you mean something along the lines of the Sorites Paradox?

The Great Whatever

So then let's try this:

-There is negation in language. This looks indisputable.
-By your argument, language must therefore be a digital system.
-So there is no problem with there being identity of a thing to itself in language.
-Therefore, language must be profoundly metaphysically mistaken, and can't be used as a guide to metaphysics. The problem is that logic is derivative of intuitions based on natural language.

Cavacava

MIT is working on synthetic biology that might be of assistance to people with diabetes as well as other ailments.

http://news.mit.edu/2016/gene-circuits-live-cells-complex-computations-0603

The team has already built an analogue-to-digital converter circuit that implements ternary logic, a device that will only switch on in response to either a high or low concentration range of an input, and which is capable of producing two different outputs.

Bypassing the law of the excluded middle.

Metaphysician Undercover

In any discussion of identity, it should be noted that there are two very distinct types of identity, sometimes referred to as qualitative and numerical identity. I do not believe that these terms actually do justice to the real nature of the difference, as the two types of identity may be understood as completely incompatible.

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. This principle allows that a changing thing continues to be the same thing, through the course of time, despite having a changing form. For instance, I am the same person today, as I was as a child, and my car is the same car after the accident as it was before the accident, despite the fact that a new formula is required to describe what the thing is, with each such change..

The point here, is that what I've called "material identity" is based in an assumed temporal continuity. It is this assumed temporal continuity of matter which allows us to say that the object is the same object from one moment to the next, despite the changes which are going on with that thing. With reference to the op then, the digital perspective describes the world, and identity of things, by referring to formal identity, and this may be a sequence of states through time. Each state is logically different from the preceding state. However, we assume a continuity between states, such that something connects them, a temporal order, and this allows us to say that we are observing a thing which is changing, rather than a succession of different individual things. This assumed continuity is the analogue perspective.

What Aristotle demonstrated is that the two forms of identity are actually incompatible, formal identity involves itself with being and not being, what is and is not, while material identity is involved with becoming, what lies between when a thing is of one description, and when it is not of that desciption. He showed how becoming, and therefore the associated material identity, cannot be described in terms of is and is not. Leibniz, attempted to establish compatibility between the two with his identity of indiscernibles. If the formula of what the thing is, could capture everything about the thing, even its spatial-temporal positionings, the material identity could be captured by the formal identity. This would require that the formal identity of the thing would describe its form, or what it is, at every moment of time, and this would allow for temporal extension and the associated changes. But Hegel had already laid the groundwork for dialectical materialism with his dialectics of being, which allows that the formal categories of being and not being are subsumed within the material identity of becoming. This assigns reality to the continuous, analogue identity of becoming, leaving reality, as becoming, exempt from the formal laws of logic. Furthermore, Einstein's special theory of relativity renders it impossible to produce a description or formula of what is, at any moment in time, because this concept, a moment in time, is itself incoherent.

In conclusion, there are two distinct forms of identity, the formal, or logical, which lends itself to a digital, discrete world, and the material identity of becoming, which allows for the continuity of an analogue world. The two are incompatible, but a complete understanding of reality requires that one provide a position for both within the world..

Janus

↪Metaphysician Undercover

Yes, the two kinds of identity: formal and material, you are referring to do seem to be in accordance with the two ideas of identity as digital and analogue implicit in SX's OP. They also seem to be in accordance with the distinction between identification and identity I have argued for in a couple of other threads recently.

So, the material identity of anything consists in its unique existence; in its being a unique entity, where the formal identity of anything consists in what it is called, or what it is identified as; which as SX points out always entails the idea of negation; the idea that what something is identified as being, is conceptually determined by what it is identified as not being.

Streetlight

↪The Great Whatever

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.

Streetlight

↪Mongrel

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.

Mongrel

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. — StreetlightX

True. Logically, there can't be a 1:1 correspondence because there are no 1's in a continuum. Maybe infinitesimals, but I think that's a hybrid digital/analog concept.

That's the problem with a continuum. There's nothing to get a hold of... no units. The golf ball can never make it to the hole.

TheWillowOfDarkness

A way to summarise all of the above is this: to the degree that nature is a continuum, there are no brute identities in nature. Or less provocatively, to the degree that there are identities in nature, they are constructed and derivative of analogic differences. Nothing is 'equal to' or 'identical to itself', 'in-itself'. — StreetlightX

The telling feature of the "in-itself" is relational. As a concept, it marking the difference between things, between where something belongs and where it does not. It's logic marking how one thing relates to everything else-- it's itself, not any other thing which is its absence. Not even identity itself is of nature.

Nothing is "identical itself" not because the logic is incoherent (i.e. "identical to itself" means nothing or is a contradiction), but rather because "identical to itself" doesn't escape posting a relation.

I think you've more or less said this, but I think it's highlighting cause some appear to because treating the lack of identity in nature the incoherence to the logic of identity. As if, as the idealist are prone to say, the lack of equivalence between logic and nature were to render nature incoherent.

Metaphysician Undercover

So, the material identity of anything consists in its unique existence; in its being a unique entity... — John

Yes, but the considerable point is that this "unique existence" involves a temporal extension. So the principle which allows us to say that the thing here now, is the same thing as the thing which was here yesterday, or over there yesterday, is the assumption of a temporal continuity. Therefore the existence of the thing, as a thing, a self, is completely dependent on this continuity, which is assumed, with good reason I might add. If there was a moment of time, in that period of time, in which the thing's existence could not be confirmed, the continuity would be broken, and the assumption that it is the same thing would not be justified.

Nothing is "identical itself" not because the logic is incoherent (i.e. "identical to itself" means nothing or is a contradiction), but rather because "identical to itself" doesn't escape posting a relation. — TheWillowOfDarkness

The relation here is a temporal one. The thing is related to itself at a before or after moment in time, and this produces the temporal continuity of existence of a thing. The point though, is that the thing is not identified as being the same as itself, through some formal principle, such that it would have the same description from one moment to the next, because the thing is naturally changing in time. So it is identified as being the same as itself through some principle of temporal continuity, not through some formal principles describing what it is and is not.

Janus

↪Metaphysician Undercover

Yes, of course the unique material entity must have temporal extension. The exact duration of its temporal extension up to any moment prior to its 'completion' (its ceasing to exist) is an ineliminable part of its unique identity; as is its unique path through spacetime, its unique set of relations to and interactions with other unique entities, as well as the unique set of physical changes it undergoes due to its unique set of relations to and interactions with other unique entities.

There are some unique entities, though, such as number, and kinds of forces, about which it is not so clear whether they should be counted as 'material entities' (or if that is clear then it is not clear what alternative kinds of entities they are) and it is not clear as to whether they have spatial existence or temporal duration.

TheWillowOfDarkness

↪Metaphysician Undercover

I'd say you've got it reversed. The "thing itself" is clearly not temporal. It's true of a thing no matter its point in time. I'm still a "thing itself" now as I was twenty years ago. In this respect, unlike in the temporal, I have not changed at all.

The "thing itself" is a formal principle: the logical relation of the presence of a thing compared to its absence.

Wayfarer

According to this, is DNA analog or digital?

Streetlight

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.

The Great Whatever

So my problems are:

-I don't see why an analog system can't deal with or include negation or identity
-I don't see why nature would have to be analog (Leibniz for example effectively proposed it wasn't, and certainly some sections of physics traffic in quanta)
-I don't see what's to be gained from cordoning off what is a transcedental addition versus what is really in nature 'in itself,' and there seems to be no interest in the project if you're not a Kantian (the question of 'is identity in the mind/language/computer, or in the thing itself?' is only of interest to someone with Kantian assumptions)

Streetlight

↪Wayfarer

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."

Janus

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

I can see how an analog system can deal, albeit somewhat fuzzily, with exclusion and inclusion.

shmik

-I don't see what's to be gained from cordoning off what is a transcedental addition versus what is really in nature 'in itself,' and there seems to be no interest in the project if you're not a Kantian (the question of 'is identity in the mind/language/computer, or in the thing itself?' is only of interest to someone with Kantian assumptions) — The Great Whatever

Yeh I read the analog/digital talk as essentially a restatement of the Kantian view that it's not something out there which "holds objects together" (object = X). Instead concepts are rules in the mind/language - which are therefore always abstractions/simplifications. I'm assuming that the difference here is that there's no transcendental idealism, we do have access to the things themselves 'the analogue system' but it needs to be simplified to be used in language and therefore in logic.

My concern is that if we take this as a limitation, so that identity, negation, formal logic etc. is based on abstraction, what in the end can we say about issues philosophically? Even the split itself of what systems can be considered analogue vs digital is actually a continuum and not a distinct break.

Streetlight

-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).

The Great Whatever

I think there is some sort of confusion here. The point is not that there could be 'negative mercury,' but that an amount of mercury could change in height to model the function of negation in an analog way. Suppose for example the mercury is inside of a thermometer which is marked from degrees 0 to 100 celsius, and negation is an operation that converts any degree so represented into its 'opposite,' given by the absolute value of that number minus 50, if the original number is above 50, and this absolute value plus an additional 50, if the original number is below. Thus applying negation to 1 yields 99, to 45 yields 55, to 80 yields 30, and so on. This is perfectly analog, since we can countenance such a reversal, and even apply the operation precisely, despite the fact that we can count the scale the mercury measures as thick (for any two degrees, there lies a degree between, with no sharp cutoffs). Then if we had an analog way of changing the height of the mercury in accordance with this operation by changing the temperature (with how precisely we can change the temperature corresponding to how precisely we can apply the operation), we have an analog negation. This same procedure could be carried over to the notion of a truth value, or whether an individual has a property, and in fact this is what things like fuzzy logic are designed to do.

Streetlight

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.

The Great Whatever

↪StreetlightX

Not at all. Your example of mercury in a thermometer is precisely an example put to use for the purpose of quantitative measurement. Number in of itself doesn't imply digitization, because in between any two numbers, there is another number. This is, the best I can make of it, exactly what it means to be analog.

Streetlight

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.

andrewk

It seems to me that the analog/digital distinction is not so much about the binary Yes/No nature of digital things, but rather about discrete vs continuous mathematics. Discrete mathematics is about cases where there is a finite or at least countable set of possible states, whereas continuous mathematics - of which calculus is the best-known example - is where there is an uncountable set of states, with a metric over that set to denote distance between states (eg the distance between 2.71 and 3.141 is 0.431).

I've just noticed that it's curious that we tend to (or at least I do) think of digital as 'binary' whereas etymologically it refers to a base-10 system, because 'digital' is in reference to our ten fingers.

Another observation is that, whereas nature may seem continuous, in very many common situations it is actually discrete. For instance QM tells us that there are only a countable number of different energy states of a pendulum. It's just that they are so close together that they seem continuous/uncountable.

Conversely, some processes that seem discrete are actually continuous, or at least have many more states than we think of them as having. For instance we think of a gate on a computer chip as being either Off or On, but actually that is determined by the voltage applied to the gate, which is usually high or low, but it could - in the presence of abnormal environmental factors or a flaw in the chip - be somewhere in between, providing a state in between on and off.

I haven't yet got my head around what that means for DNA, but it seems to me that there may be scope for interpreting the world either as discrete or continuous, digital or analog.

The Great Whatever

↪StreetlightX

What do you think 'analog' means?

Do you think that something analog is incapable of 'making distinctions?' Surely, even if a bucket of water is in some way 'analog,' one can still distinguish between being hit with a little bucket of water and a big one, and measure the size difference between the two. If not, I'm not understanding how that I'm 'effecting a distinction' means that I'm committing to something being digital.

This is a little off topic, but the mercury example is a weird one in that quantities of mercury are in a very real sense digital, in that there is a finite, countable number of mercury atoms in any sample, and broken down beyond this we have not mercury but something else.

There Are No Identities In Nature

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