So which is it - do vague and crisp map on to analog and digital or do they not? If they do, in what sense can you claim that the analog/digital distinction is derivative from vagueness (circularity). If they don't, you're back to mythology. — StreetlightX
The answer is the same as before. When we are talking about the ontology of a modelling system, we have two realms in play - the material and the symbolic. And the vague~crisp can apply as a developmental distinction in either. And indeed to the modelling relation as a whole. The vague~crisp is about a hierarchy of symmetry-breakings, a succession of increasingly specified dichotomies.
So in the symbolic realm, a vague state of symbolism is indexical. A still vaguer state is iconic.
If you say "look, a cat", that 's pretty definite. If you point at a cat, I might be a little uncertain as to exactly what your finger indicates. If you make mewing and purring noises, I would have to make an even greater guess about the meaning you might intend.
So as I argued using the example of the wax cylinder, informational symmetry breaking can be weak because it is easily reversible - still strongly entangled in the physics of the situation - or it can be strongly broken in being at the digital end of the spectrum and thus as physics-free as possible.
If I were to say "look, the universe", then physically the words involve no more effort that talking about a cat. But pointing gets harder, and pantomiming might really work up a sweat.
But then any form of communication or representation has already crossed the epistemic cut Rubicon in creating a memory trace of the world and so made the step to being physics-free. So even vague iconicity is already crisp in that sense. And thus there is another whole discussion about how the matter~symbol dichotomy arose in nature. And a further whole discussion about whether the abiotic world - with its dissipative organisation - has pansemiotic structure, and so this notion of "digitality" as negatively-self reflexive demarcation (or the constraint of freedom) has general metaphysical import there.
We can see that discrete~continuous is just such a general metaphysical dichotomy - the two crisp counter-matched possibilities that would do the most to divide our uncertainty about the nature of existence. And I would remind you of your opening statement where you said this was all about a generic metaphysical dichotomy that applied to all "systems"....
Broadly speaking, one can speak of two types of systems in nature: analog and digital. — StreetlightX
So that sweeping claim is what I have been addressing. And my argument is that when it comes to reality as a system, it is just the one system - formed by dividing against itself perhaps.
This is why I find your exposition confused - although also on the right track. So I tried to show that to resolve the dualism implicit in your framing here, we have to ascend to Peircean triadic semiosis to recover the holism of a systems' monism. We have to add a dimension of development - the vague~crisp - so as to be able to explain how the crisply divided could arise from some common source.
Your opening statement would be accurate if it made it clear that you are talking about symbolic systems or representational systems - systems that are already the other side of the epistemic cut in being sufficiently physics-free to form their own memory traces and so transcendently can have something to say about the material state of the world.
But instead you just made a direct analogy between analog~digital signal encoding in epistemic systems and continuous~discrete phenomena in ontic systems.
Now again, there is something important in this move. It has to be done in a sense because the very idea of a physical world - as normally understood in its materialistic sense - just cannot see the further possibility of semiotic regulation, the new thing that is physics-free memory or syntax-based constraints. So you can't extract symbols from matter just by having a full knowledge of physical law. As you/Wilden say, the digital, the logical, the syntactical, appears to reach into the material world from another place to draw its lines, make its demarcations, point to the sharp divisions that make for a biinary "this and a that".
So saying in a general metaphysical way that the material world is analog, and the digital is sprung on this material world from "outside itself" as a further crisply negating/open-endedly recursive surprise, is a really important ontological distinction.
But then confusion ensues if one only talks about the source of crispness and the fact of its imposition, and neglects to fit in its "other", the vagueness which somehow is the "material ground" that takes the "formal mark" of the binary bit. Or even the analog trace.
So to talk generically about reality as a system - which indeed is a step up from process philosophy in talking about symbol as well as matter, hierarchy as well as flow - is where we probably agree in a basic way. Structuralism was all about that. Deconstructionism was also about that - in the negative sense of trying to unravel all symbolic distinctions. Deleuze was about that I accept.
But again, the metaphysics of systems is always going to be muddy without being able to speak about the ontically vague - Peircean Firstness, Anaximander's Apeiron, the modern quantum roil. Sure we can talk about grades of crispness - iconic vs indexical vs symbolic. But to achieve metaphysical generality, we have to be able to define crispness (computational digitality, or material substantiality/particularity/actuality) in terms of what crispness itself is not.
And to return to your OP.....
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. — StreetlightX
...this is where your keenness to just dichotomise, and not ground your dichotomy as itself a developmental act, starts to become a real blinkering issue.
Analog signals are still signals (as Mongrel points out). They are differences to "us" as systems of interpretance. An analog computer outputs an answer which may be inherently vaguer than a digital device, but did use to have the advantage of being quicker. And also even more accurate in that early digital devices were 8 bit rather than 16 bit or 64 bit - or however many decimal places one needs to encode a continuous world in floating point arithmetic and actually draw a digitally sharp line close enough to the materially correct place (if such a correct place even exists in a non-linear and quantumly uncertain world).
So whether variation or difference is encoded analogically or digitally, it already is an encoding of a signal (and involves thus a negation, a bounding, of noise). Then while the digital seems inherently crisp in being a physics-free way to draw lines to mark boundaries - digital lines having no physical width - in practice there still remains a physical trade-off.
The fat fuzzy lines of analog computing can be more accurate at least in the early stages of technical development. The digital lines are always perfectly crisply defined whether they use 8-bit precision or 64-bit precision - this is so because a continuous value is just arbitrarily truncated (negated) at that number of decimal places. But that opens up the new issue of whether the lines are actually being dropped in the right precise place when it comes to representing nature. Being digital also magnifies the measurement problem - raises it now to the level of an "epistemic crisis". Ie: the fallacy of misplaced concreteness.
So it just isn't good enough to say analog signals can be signals without the need for negative demarcation and the open-ended recursion that allows. A bell rings a note - produces a sine wave - because vibrations are bounded by a metal dome and so are forced to conform to a harmonic whole number. Identity or individuation does arise in analog processes - in virtue of them being proto-digital in their vaguer way.
Yes, this is a complication of the simpler starting point you made. It is several steps further down the chain of argument when it comes to a systems ontology. And as I say, you/Wilden are starting with a correct essential distinction. We have to pull apart the realms of matter and symbol to start to understand reality in general as a semiotic modelling relation with the power to self-organise its regular habits.
But for some reason you always get snarky when I move on to the complexities that then ensue - the complexities that systems ontologists find fruitful to discuss. The vague~crisp axis of development being a primary one.