The Peircean or systems view is that possible difference becomes actual difference as it is regularised by constraining habit. The further category of repetition makes sense once there is sufficient similiarity (in terms of the freedoms that have been suppressed) to talk of the the freedoms that concretely remain in play. What incompossibility weeds out becomes the definite variety that compossibility enforces.

And (tricky ain't it?) this compossible variety is itself dualised into the purposeful and the accidental. There are the acts that are desired by telos - even if it is the dilutest possible form of constraint in the being the second law's desire to entropify. And then there is - by mutual definition - all the other compossibilities that are beneath the notice of any such active law or constraint. I can buy a blue car or a red car. It makes no real difference to anything really.

Anyway, can we make any sense of the Deleuzean project to reduce existence to bare difference? Clearly - as a self-proclaimed inversion of Plato - it as least foregrounds the "other" to constraining sameness. And so it is going to sound Peircean in at least also taking difference or development as fundamental.

SX is hopeless at explaining the actual machinery that might link virtual differencing (this frozen sounding multiplicity) to actual "almost repeating" difference. It is dangerous for him to even to attempt an explanation of course as the whole metaphysic project will immediately unravel. He will start to have to talk about the dichotomous othering that is used to achieve a reductionist monism. And once you start talking openly about dichotomies, well that leads to the inevitable triadicity of a hierarchically organised relation. Holism has arrived and your dreams of monistic finality have just gone up in smoke.

So how do others handle this. I'll look at Todd May's "Gilles Deleuze, Difference, and Science" - www3.nd.edu/~hps/May=Deleuze.doc

We start - as is PoMo convention - with wisdom as paradox. We know we are really being deep when our very words contradict themselves.

...seeking to understand what Deleuze means when he says that “difference is behind everything, but behind difference there is nothing.”

Then fair enough, the issue is to get away from tales of transcendent perfect order to talk about the "imperfect" immanent order that can arise via self-differentiation (and self-integration of course). For Deleuze, this is achieved in Spinozian univocity (noting Peirce was also a big fan of Duns Scotus for the same reason).

What is the significance of embracing the concept of a single substance and thus the univocity of Being? It lies in the abandonment of transcendence. Here we might recall Nietzsche’s critique of transcendence, a critique with which Deleuze is in sympathy. The effect of positing any form of transcendence (of which the transcendence of the Judeo-Christian God would be the prime example) is to set up a tribunal, a judge that is not of this world but that nevertheless evaluates it and always finds it wanting. The transcendent is always the more nearly perfect (or the Perfect itself). It is always pictured as higher, above this world. It is the ideal toward which this world must strive through self-denial but which, because of some inherent flaw—be it the existence of the flesh or the finiteness of its creatures—it can never fully achieve.

Now note two bum notes in this reading of univocity. Already we are lapsing back into substance talk - the ontology of form materially actualised. And we are setting up an illegitimate grounds for rejecting the eternal "other".

Dichotomies are being read as always having to generate a good guy and a bad guy as thesis and antithesis. But it is a bad dichotomy that does that rather than producing two generalities that are of equal (because necessarily complementary) status. Instead of focusing on what makes a good dichotomy (as I do), this is clearing the ground to reject dichotomies in toto.

Then the sensible question...

With the embrace of the univocity of Being, however, two questions arise. First, how is it that the perceived world exists as a manifold of differences in continuous evolution when there is only a single substance that comprises them? How can the univocity of Being be reconciled with the manifoldness of existence? This, of course, is the traditional philosophical question of the One and the Many. The second question, bound to the first one, is,What is the relation between the single substance and the manifold of existence? As Heidegger might put the question, what is the relation between Being and beings?

Yes indeedy. Where is the mechanism that connects? (In Peirceanism, it is semiosis.)

And here the beginnings of a bad answer.

The first question presents no insurmountable conceptual barrier if we jettison the idea that a single substance implies some kind of identity. For Deleuze, the single substance of Spinoza must be conceived not in terms of identity but in terms of difference. Substance, Being in its univocity, is difference itself. “Being is said in a single and same sense of everything of which it is said, but that of which it is said differs: it is said of difference itself.” Difference is behind everything, but behind difference there is nothing. If substance in some sense contains or comprises the differences that manifest themselves in the world, then there is no difficulty reconciling the One and the Many. The One is many; it is difference, difference itself, or, in the later term used in the collaborative works with Guattari, it is multiplicity.

So now we are talking from the point of view of actuality - already formed materiality, or substance.

Yes, it does make sense in the usual Aristotelean fashion in that substance is actuality with attributes and properties. A dog has the characteristics of its species. It has that family resemblance than means it is quite liable to chew your shoes, piss on your fencepost, slobber on your carpet.

But this is metaphyics and the question is how does substantial being itself become? How does it develop as informed or constrained materiality? And therefore, how do we account for the sameness that is form, the difference which is material haecceity?

Peirceanism explains them by putting them at opposite ends of the spectrum. Materiality is brute firstness or potential. Form is the regularity imposed by the seiving necessity of compossibility. Each is placed at sufficient distance from the other for them to have a formally inverse or reciprocal relation. (Remember, form = 1/material, and material = 1/form.)

Anyway, this indicates why SX wants to treat the virtual as itself a species of substance. Which is also then why he cannot in fact explain anything in terms of some actual developmental relation. Difference becomes just a property of a higher level notion of substantial being. Repetition is as repetition does.

Luckily May is alert to these issue. An urgent paradox arises....

For if Being is difference, doesn’t it collapse into beings themselves? If Being is as manifold as the beings that it comprises, doesn’t Being just reduce itself to nothing more than the manifoldness of our particular world?

The day is saved by capitalisation - or dichotomisation that conceals its "othering" by using the same term, just discretely denoting generality by using a big B (while continuing blithely to undermine generality's ontic connection to formal cause by treating Being as already formed Univocal Substance!).

Deleuze denies this reduction, claiming instead that the kind of difference associated with substance or Being is distinct (different) from the kind of differences associated with beings.

Then follows a Bergsonian analysis of time vs space which we can skip as I sort of agree. Let's get on to where there is some attempt to account for an interaction between virtuality of differencing and actual substantial differences. ;)

The relation between the virtual and the actual is, however, very different from that between the possible and the real. As Deleuze uses these terms, the real is the mirror of the possible; it has the same structure as the possible, with the sole but ontologically crucial exception that it is real and not merely possible. So there are two ontological realms, a realm of the possible and a realm of the real. By contrast, the virtual does not lack the reality; it is part of the real. There is only one reality, comprising aspects that are at once virtual and actual. The virtual actualizes itself in order to become actual, but in actualizing itself it does not gain in any reality it had lacked before, nor does it stand outside or behind the actuality that is actualized. It is not part of the actual, but it remains real within the actual.

OK. So does this work, anyone?

The virtual contains the structure that produces difference. Then material difference is what gets actualised.

So far, so Platonic.

But then the virtual is a substance. It "actualises itself". So not only is the virtual the general form or the general structure of difference-generation, it seems to possess its own material means too.

Where I would have a more traditional conception of the virtual as a principle of formal necessity - expressing the telos of the least action principle in interaction with the material restriction that is the complementary principle of generalised compossibility - Deleuze wants simply a tale of a "ground difference" that substantially exists as a generating mechanism (a hopper complete with the materiality to fulfil its desires) and only needs to be turned on so that it starts spitting out actual instances bearing a family resemblance to the originating seed (or - snort - rhizome).

So we see why SX strains so hard to find a generating seed difference in calculus. Materiality is the obvious issue for this Deleuzean scheme (as it is for all metaphysical schemes I agree - even Peirceanism). If you duck into maths - the science of patterns, the conjuring with pure immaterial forms - then you can simply sideline the very issue that your metaphysics must address. You can appear to be speaking about substantial actuality when really - in shifting into the register of the model - you most definitely ain't.

(How does Peirceanism answer the foundational question of materiality or primal action - the question of "why anything?". Well as I say, it doesn't in the final analysis. But it does make it explicit that it is a different kind of question and does not try to subsume in into a substance ontology like SX/Deleuze. Instead, it set it out apophatically - it approaches it via a model of vagueness or firstness.)

OK, so having emphasised some differences, let's look for some reconciliations....

In his discussion of Spinoza, Deleuze utilizes the term “expression” to indicate the relationship between the virtual (substance) and the actual (attributes and modes). In contrast to medieval creationist or emanative theories of causality, in which God is said to cause the beings of this world either by explicit authorship or by emanation, Spinoza holds an expressive view of causality, in which that which is expressed is not ontologically distinct from its expression. Attributes and modes may explicate, involve, and complicate substance, but they do not emerge from it on a distinct ontological plane.

Again, this is utterly wrong ( :) ) from a fully holistic point of view - the synchronic view of a development of regularity out of vagueness. But it is - in Aristotelean hylomorphic fashion - quite reasonable once understood diachronically as a slice across temporal development (so as a slice not across a moment in time, as such, but across the transition from vague to crisp "coming into being").

Once substantial being arises, it can of course host further development in the usual hierarchically complex fashion. Physics - in closing off one set of possibilities or differences, as it does with describing some universal telos like entropification - then itself creates the further possibility of its own counter-action. In the case of life and mind - or even just dissipative structure in general - that reaction is of course negentropy as a counter-telos.

But anyway, this hierarchical logic holds as a generality. It is precisely the system's take of constraints and the further freedoms they can't help but create. In - via compossibility - imposing a limit on free variety, that produces the now far more definitely defined freedoms which can start to do their next level of interacting and habit formation.

So yes. Examine reality at any particular level (look at it either side of some "singularity" or symmetry breaking critical point) and you will find that substantial being is "intrinsically" dual. An object is both a species of a genus (it has attributes due to a context), and it itself possesses further properties or freedoms of actions (as that is why we would indeed distinguish it as a concrete object - it has been transformed into the context for new happenings, or novelties.)

But what do you do when faced with the need to make substantial Being univocally fundamental still....

First, the virtual is not a mirror of the actual, as the real is of the possible. In Difference and Repetition, Deleuze marks this by saying: “We call the determination of the virtual content of an Idea differentiation; we call the actualization of that virtuality into species and distinguished parts differenciation.”

...you quietly change the spelling of the word just a little bit to hide how big an explanatory gap you want your fanboys to vault.

A proper dichotomy is one that openly proclaims the absoluteness of its reciprocal transformations.

If you invert the continuous, you bloodly well get the discrete. You don't just get the discontinuous, let alone the continious, or some other rat-swallowing circumlocution. You get an upfront assertion of a proper categorical difference.

In contrast to the possible/real distinction, the virtual/actual distinction involves three kinds of difference. First, there is the difference in itself of the virtual; second, there are the specific differences of the actualization of the virtual; finally, there is the difference between virtual and actual difference, between differentiation and differenciation.

Oh hold up! Not triadicism to the rescue?

Does this sound like 1) vague difference - the raw possibility, 2) reactive difference - actual particulars now having actual reactions, and 3) habitual difference - the stably broken asymmetry of a hierarchically developed organisation between globalised or general differencing vs localised or particular differences to you?

Well yes indeedy. Got there backwards, but that is now where this line of thought has arrived.

I think we can leave it there for the moment. SX - being the tough samurai kid he is - is probably doing the honorable thing of self-evisceration right about now.

But time is not "a sequence of change or development", it is a means by which we measure such. — Metaphysician Undercover

Well we can count the changes, can't we? Or is "sequence" a notion alien to you?

And the reason we can count changes is because they are locked into as history. When changes stops (when it is equilibrated and looks to change no more) then we can count the change as "being over" and "part of history, not part of the future".

A metre is not the same as a thing which is a metre long. — Metaphysician Undercover

Merde! The French bureau of standards have a problem with that strip of metal they've got locked up in temperature controlled vault then.

It is the fact that the vast masses of humanity accept this relation as ontologically sound, without referencing ontologically sound principles, which horrifies me. — Metaphysician Undercover

Yep. MU right. Humanity wrong. Sounds legit.

But you don't seem to get that spacetime relativity is God's way of preventing everything happening all at once. It creates the separation between events that is ontically essential for there to be anything interesting in the form of a "world". If forces acted instantaneously and without dilution across any span of time and distance, where would we all be, hey?

So if you want to talk about sound principles, begin with the fact that physical action needs to have an interesting structure. Things must divide and connect, differentiate and integrate. There must be separation, but only relatively speaking.

Plato was a dualist. Deleuze wanted to collapse his dialectical distinctions to be a univocal monist. Peirce was a triadicist who argued instead for an irreducibly complex or hierarchical relation as the basis of being.

So for Peirce, actuality is a process, an eternal coming-to-be. It can be talked about as being monistically "one relation". And it also "starts" with a monism in the grounding notion of Firstness, or Vagueness. But through a principle of incompossibilty - not everything that might want to be, can be, because it clashes and contradicts in a way that suppresses its actualisation - it describes how regulation or constraint emerges to organise a world bound by habits.

So similarity or generality emerges to organise difference itself. Vagueness is not nothingness, but chaotic everythingness - unbounded fluctuation without structure. In Deleuzean fashion (it seems), vagueness is multiplicity - but more than multiplicity as it includes even the actions that coming-to-be must suppress (through incompossibility).

Vagueness is thus an ultimate kind of difference - the difference of an infinity of disconnected impulses that sum to nothing.

And then from that chaos you have developing the regularity of actuality. The raw energy falls into dissipative patterns as the wildness of possibility falls away and the sum over possibility - the least action path - emerges. Difference changes character so that now it is regulated and well behaved - repetitive in the way that properties and attributes are the developed habits of concrete beings. Development ends up producing a classical world of atomistic material objects at play within a blank void - the spacetime backdrop that is all those other now well-suppressed fluctuations or opportunities for action.

So that is the triad. Vagueness is every possible difference (and thus a state of utter indifference and lack of constraint). But as soon as differences start to react against each other (the Secondness that follows Firstness), you get a collective or emergent effect. Some differences cancel each other away, other differences reinforce each other by feedback. (This is all standard non-linear physics or chaos theory.) And so in short time you have the beginnings of self-organising global regularity or generality.

As with the water draining out of your bath, a vortex begins as a slight suggestion of a symmetry breaking. In the beginning, the twist could be to the left of the right. Both are going to be happening - it doesn't make any difference which way the symmetry breaks. But the breaking of the symmetry - spin left or spin right - then makes a big actual difference. It quickly locks itself in, completely suppressing its "other" as an accidental fact of history.

In Peircean terms, the world (or the draining bathwater) is now ruled by the Thirdness of persistent habit. But Thirdness itself is a monism in that it incorporates Secondness and Firstness. We are talking about the wholeness of a relation. So just because there is one symmetry breaking that gets things started doesn't mean that the new state (this singularity, as SX terms it after the notion of a phase transition) can't break again.

Vague potential will still remain within the system. Reaction could set in. A higher level of organisation could break out that regularises this grounding action, gives it shape, turns it into a repetitively generated action that constructs a more complex state of habit or law.

Biophysics shows how life and mind arise as that kind of further semiosis. The "vortexes" of chemico-physical gradients can be harnessed and turned into the complex hierarchies that are bodies with cells and organs.

Anyway, it is foolish to talk of doing away with similarity to found metaphysics on "pure difference". Instead we must recover difference from difference by way of similarity. Vague difference (that is of course not even a difference, being a differencing lacking any relations) must be turned into crisp difference by a general relation (a habit of constraint, a principle of least action) that sorts difference into its various forms of dichotomous actuality. So for instance, we can speak with definiteness of differences that are purposeful versus those that are accidental.

So Deleuze gets some things right. If we are going to make something fundamental, it has got to be process, change or development. Plato needs to be inverted to make sense.

But then just to invert is only half the story. It is the invertibility of all things that is the foundational relation. So really, Being is still founded on stasis. It is just that it is equally founded in flux. While your metaphysics has to explicitly include an axis of development (as in the vague~crisp), it also has to have within itself a matching axis of "equilibrium balance" (as in the stable local~global, or part~whole, hierarchical structure that Thirdness describes).

So Deleuze makes the mistake of simply "othering" to arrive at a reductionist monism. And the error can be seen in that he ends up - like Plato - lacking the resources to account for how differencing actually happens. Plato could only say rather weakly that matter ends up "participating" in the ideal forms to achieve an imperfect repetition of similarity. Deleuze - as channeled by SX - is burbling something about virtuality as the (Platonic sounding) multiplicity which generates difference as its eternally different actuality.

The Peircean view places differencing - or dichotomisation, or the secondness of reaction - in the middle of a hierarchical sandwich. It is the individuated or particularised actuality that arises from vagueness - possibility in its rawest sense - in interaction with generality or habit, the emergent order which provides the other "eternal" thing of a system of constraints or "transcendent" necessitation.

But emerging is an activity which necessarily requires time. — Metaphysician Undercover

Or instead, emergence IS time, time being what we call a sequence of change or development.

Apo wants time to emerge from space-time. — Metaphysician Undercover

Well I would want a model of thermal or thick time that is consistent with the theory of relativity. And spacetime really is a thing in physics, despite your horror of all metaphysics that is post Newtonian.

And Apo isn't exactly some innocent wide eyed lamb whom I've been eviscerating; — StreetlightX

Biggest laugh of the day. But whatever keeps your spirits up sunshine. :)

If everything's the necessary and the accidental, then to say ollie, this cat (hey this cat) is the intersection of the two, is to say nothing, at all, about ollie. You could be talking about a star or a cell or a neutron. That's self-evident. Isn't it? — csalisbury

I think you've stop trying.

Talk of similarity and difference could be extended to the level of the genus "Cosmos". But here we are talking just of the already highly constrained genus of "Feline".

It can thus be taken for granted that "my dead cat Ollie" is not a gas cloud undergoing explosive fusion, or something you would need a microscope or particle accelerator to interrogate.

Indeed the reason you can only think in terms of mutually-constraining limits is precisely because you are unable to countenance exactly this reality of the virtual.

Which is just another way of saying that you are unable to properly consider the process of individuation because you can only ever look at it from the perspective of the already-individuated. And from that POV, all you will ever see is limits and a process of othering.

As usual, you are trying to shoehorn my Peircean approach into some more familiar (to you) metaphysics to which you have a prefab template answer.

If everything begins in vagueness, that is hardly beginning with the already-individuated, Perhaps you are confused because the argument to define vagueness (firstness, apeiron, the indeterminate) is apophatic.

We do have to start with the highly differentiated and highly organised world in which we find ourselves in. Whatever was the "source" of this developed state of being, we at least know what it has to be able to produce. So if differentiation and integration, or material difference and formal organisation, are what are produced, the image of the vague is formed apophatically as that which must "contain" both as its prime possibility.
— StreetlightX

As Deleuze puts it, "Negation is difference, but difference seen from its underside, seen from below. Seen the right way up, from top to bottom, difference is affirmation." In other words, if we reverse the picture and look upon individuation from the perspective of individuation, what you see instead are differential relations - coupled rates of change - and distributions of singularities which define thresholds of mutation. — StreetlightX

OK. So Deleuze's key party trick is to invert Plato - replace identity as sameness with identity as difference. How trivial.

My constraints-based approach instead makes the generating seed of Being a story of integration and differentiation. And how this is achieved - unlike Plato's "participation" or Deluze's hand-waving - is explained in transparent fashion. But you might have to read some books on hierarchy theory to get it.

Of course hierarchy theory does explicitly model individuation in terms of a cascade of phase transitions. Which is kinda what you are saying. But a phase transition or symmetry breaking involves both differentiation and integration.

It begins because a difference makes a difference. Water turns to ice because the balance between thermal dissociation and atomic bond forces pass the singularity of a critical point. But then the freezing stops once a new state of global integration has been achieved. The broken symmetry runs its course until ... a new state of symmetry terminates the change. Keep cooling ice and it doesn't get more crystalline. The atomic bonds have arrived at a state of constraint where the remaining differences of molecular orientation no longer make a difference. The ice state has lowered the general entropy to the degree that it is equipped to "care".

So my Peircean approach is different because it doesn't rely on Plato's pure sameness, or Deleuze's pure difference. Instead it argues for the irreducible complexity of the dynamic duo of constraining sameness (to the degree the sameness matters) coupled to the freely different (to the degree it doesn't matter).

And if you could only realise it, this is how to arrive at a Husserlian notion of thick time. The past becomes the current constraint on future free action. History, having happened, locks in all the accidents of the past and so place crisp limits on what can happen next. But the future is then free to disposed of those degrees of freedom as it wishes. The present is then the "epistemic cut" that relates the two. It defines when the past has stopped - as an event horizon on "prior" interaction - and so when the "to be created" future begins its process of becoming.

One can think of an economic system this way: flows of labour and capital, rates of birth and death, employment and wage (all of which reciprocally determine each other as coupled rates of change), together with thresholds of mutation (environmental carrying capacity, minimum survival income, etc): these are the parameters out of which 'economic individuals' are crystallized from - companies, trade agreements, tax rates, etc. The 'virtuals' here are not 'possibilities' which are then culled by a process of mutual limitation to give rise to actualities: the virtualities are fully real and they engender creativity at the level of the actual. Given these rates of change, given these singularities which define thresholds of tolerance, in what way should 'economic individuals' go about achieving whatever it is they do - in what manner do they become the individuals that they are ? — StreetlightX

But this is what my approach says. The individual is shaped by general dichotomies or coupled relations. These are the constraining boundary conditions on individual possibility.

The difference again is you then want to shoehorn the complexity of a dynamical hierarchical system into your prefab monisms.

To avoid talking about generalities that are Platonic ideas, Deleuze talks about them as virtual differences. But generality makes no sense except as complementary limits on being. And so - as you just did - generalities are identified using dialectical reasoning.

Then what is missing is the further category that is complementary to the general - vagueness. Which is where the power of the virtual to "be" pure difference (in the symmetry breaking form of differentiation~integration) would have to develop out of.

So virtuality fails on two scores from what I can understand of your definition. Its reality is already crisply developed in your telling. And it is pure difference (of some hand-waving brute kind) rather than the dynamical relation of differentiation~integration (with its bootstrapping logic).

Not 'symmetry-breaking' but problem-solving is the model for the process of individuation: — StreetlightX

That's fine for talking about complex being - especially life and mind which indeed is negentropically problem solving.

But if we are talking at the simplest possible level of physical existence, then as I described, symmetry-breaking is a self-limiting process (otherwise existence would disappear gurgling down its own fundament). Symmetry-breaking ends with the arrival of some new state of symmetry - some persistent equilibrium state where all further fluctuations are a matter of general indifference.

Evens: "The function thus takes shape gradually, progressively, as the singular points shift and glide relative to each other, tense and relax to alter their configuration. — StreetlightX

Yep. I noted Evens very shaky grasp of physics. His descriptions of chaotic atttactors is especially off-track.

But the least action principle is fundamental to the ontology of physics. If you want to call that "problem-solving", I bet you think that your brain does maths to work out how to catch a ball.

Individuation as symmetry-breaking in comparison is an incredibly basic and rather naive approach to the whole issue. — StreetlightX

I think you blew your credibility by quoting Evens describing conformational change as:

one would never suspect the whole network of differential calculations that take place in this instant.

what I wanted to convey is that on Deleuze's reading, the difference between these two functions is not simply quantitative but rather qualitative. What does this mean? Negatively, that the differential cannot be a magnitude or a quantity — StreetlightX

It means that the derived function is less constrained in adding a further dimension. And yes, it would be fair to dichotomise that in terms of quality~quantity. The quality is the "twist away" that this extra dimension of change represents. And that is quantified by some value which is a measurement of the degree of "twist".

Negatively, that the differential cannot be a magnitude or a quantity: at the point at which dy/dx = 0/0, — StreetlightX

But 0/0 is the limit. So the point never exists - except as an idea, a goal, a virtual object (in the way that singularities, event horizons, virtual particles, renormalised fields, etc, are all virtual objects in physics).

So all we can do is imagine the point as the virtual locus - a bare property-less location - to which we can then start artificially gluing dimensionality (the general or global quality that is constraint!) back on to.

0/0 of course refers to a 2D realm - the complementary extrema of the x and y axis. In a 3D realm, we would have to specify "the point" as 0/0/0. So yes, the idea of a point already - dichotomistically - invokes its own local neighbourhood. In a flat Euclidean space or Newtonian inertial frame, the lack of curvature indeed means the idea of the point in fact defines the global space out to infinity. And advantage of simplicity or linearity.

So 0/0 deals fully with one quality - location - if we are safe to presume that the point lives in a flat plane as its quantities (zero x change, zero y change) implies. And then that point can start being granted further qualities - like the energy of a velocity. It can be seen to be speaking about, in fact, a trajectory or line.

So 0/0 specifies a point that can stand for a line - if you add a velocity term. 0/0 certainly does not contain that "difference" itself in speaking only for some definite lack of change (qua a flat plane). All it does - for the sake of easy reductionist representation - is erase the world (the plane with its lines and locations) of all possible change so that change can now be added in, degree by definite degree, by hand.

Now, the point of this giant mathematical detour is that insofar as the differential is understood as this element of pure quality ('the cancellation of quantity in general'), it serves as the model for Deleuze's notion of pure relationality. — StreetlightX

But plainly the located 0/0 point has the quality of being located on an x/y plane. So change as an actual quality has been cancelled - it now measures zero in both directions on the change scale. But in reciprocal fashion, the quality of locatedness is at its maximum. It measures infinity (or reciprocally, any deviation from absolute and ideal locatedness is infinitesimal - too small to make a difference).

So this mathematical detour exposes some really sloppy thinking.

Again in Bowden's words: "even though dx is totally undetermined with respect to x, as is dy to y [[dy/dx can only be determined in relation to each other, without each each value is nothing], since the relation subsists, they are in principle determinable with respect to each other" (my emphasis). — StreetlightX

Again this is bogus as x/y specifies a relation - the quantifiable quality of being a fixed location on a plane. The generality is that the plane has infinite locations as an attribute. And that global attribute can be picked out as a point with arbitrary precision. The transcendent modelling machinery of x/y - the idea imposed on the plane in a sign relation - can be used to quantify the quality being claimed.

So even at the zeroeth derivative, there is a complementary dyad of quality and quantity - general concept and particular fact. The x/y definition of a quality waits to be cashed out as (3,7), or some other pair of actual co-ordinate values.

Then first, second, and further derivatives are the tacking on of further qualities, further degrees of freedom. And it takes tangents - new global co-ordinate frames - to give these further qualities (the many varieties of possible change) some definitely measurable character.

One point turns out to participate of a hierarchy of worlds of measurement, each with its own general quality of change (when measured against the point as a reciprocal absolute lack of change). We can tell they are qualities because we give them substantial sounding names (or terms) like "velocity", "acceleration", "jerk", "snap"....

What we can measure is always then "a thing". ;)

this model itself has a distinctive trait that allows Deleuze to set himself against a position that his entire oeuvre pitches itself against: the idea that what exists prior to individuation is an indeterminate generality which is then progressively differentiated though limitation or negation (which itself calls for a correlative abandonment of any hylomorphic model of individuation). In other words, Apo's entire metaphysical picture. — StreetlightX

It's great that Deleuze may offer a different view. That's why I am interested. But in the past, I've found it to be half-baked. And so far you have done a great job confirming that view.

But as to my own position - the Peircean one - you misrepresent it. Indeterminism is explicitly distinguished from generality. Again to remind you, one does not participate in the principle of non-contradiction, the other does not participate in the law of the excluded middle. So the distinction is clear just in terms of the way they "other" the standard laws of thought.

So the indeterminate is the vague and undivided. The general is instead the crisply dichotomised, the crisply symmetry-broken. So generalities are the emergent habits - the triadic relation that is what it is to be the actuality, the substantial, hylomorphically formed by there being complementary bounds to that existence (as in globally structuring constraints vs local material degrees of freedom).

I agree this is a sophisticated and subtle metaphysics. It tends to go over heads. But you need to understand it right if you don't want to look such an idiot when going off on your epic whinges against me.

On the contrary, he will argue that this pre-individual, undifferentiated sphere of being is entirely determined - and determined precisely in the qualitative form as outlined above: this is it's 'distinctive trait' that I mentioned. — StreetlightX

But there is a deep and obvious metaphysical argument against any such scheme that wants to found itself on stasis rather than flux. The primary fact of nature is that it has this direction - this irreducible broken symmetry - that we call time.

So space and matter are locally symmetric qualities. You can erase a spatial change by going back and forth, or erase a material change by introducing any particle to its anti-partner other. But time stands apart in being a globally broken symmetry. It has only the one direction - entropically downhill forever.

So that makes change a fact that exists "before" stasis. Metaphysics has to be done in terms of process or development.

That can be cashed out itself in terms of differentiation. But we would have to be talking globally general differention - as in the Big Bang story of a cooling/expanding. Deleuze is making the classical error of taking the humanly local scale of being - the Universe as it is for us right at this small moment in its history - as the metaphysically typical scale of description.

So right now, we humans clearly live in a world that is a big, dark, cold space, and yet also filled with this mess of concrete objects (like stars, planets, mountains, bacteria, iPhones).

The proper long run view of the Universe is that it is simply a cooling and spreading featureless bath of radiation to close approximation. At no point in its history does the small scum of "complex material objects" amount to anything significant or fundamental. We can literally quantify that level of insignificance. If all the objects in the visible universe were vaporised to radiation immediately rather than waiting for another 100 billion years, it would add only a percent or two to the sum total of its radiative being.

Anyway, we can see why Deleuze may again return metaphysics to a focus on "differentiation" in terms of highly negentropic local structure. It is of course what we humans must care about most for pragmatic reasons.

But in terms of metaphysics, its just dumb to take the negentropic exception as foundational. We already know from cosmology that entropy rules - it provides the arrow of time that is the primary fact of nature.

It's ultimately over the question of the determination of the pre-individual that the debate between me and Apo turns. Apo is unable to recognize - perhaps because he's never encountered it before - the idea of a determinate but undifferentiated realm of the pre-individual. — StreetlightX

It's more the case it is so transparently confused that I give the benefit of the doubt that it could be truly meant.

if you haven't noticed already not all of this post is for you TGW — StreetlightX

I'm sure he noticed that you only kept mentioning me. LOL.

I wasn't just being snide when I said earlier that the whole edifice is self-referential - it really is — StreetlightX

So you were being snide as well. Cool.

But the charge of being self-referential is hardly going to bother me when a bootstrapping self-organising
relation is what I seek from a sophisticated metaphysics.

Although reading Smith's essay and seeing your OP is basically a crib of that, Smith also relies on dichotomies to define the singular. Traditionally it might be opposed to the universal, but he is drawing on geometry to talk of ordinary vs singular points. And also phase transitions with their critical points.

So Smith is absolutely relying on dichotomies to define terms epistemically and also making the ontic connection to physical symmetry breaking with its critical point behaviour.

This makes your replies still more inexplicable.

To get back to the question you failed to address, your accusation to me was that I am unable to think the singular. What you meant by that has not been made clear.

I'm guessing you mean monism in some sense. And in the OP's case, the suggested monism is that of relations being all you need to account for becoming. You don't need "terms" (relata?). Dan Smith says terms are just "packets of variable relations" - whatever that might mean.

Anyway, I suggested how the Peircean would view this (surely one is alllowed to try to make sense of a strange and disjointed OP by seeing how it is similar or different to an established and respected metaphysics?).

So yep, triadic semiosis is a monism in the sense it is an irreducible whole. And even better, it is a developmental ontology - based on a becoming which is radical by most lights. And better yet, it is "pure relations". It doesn't begin with the usual existence of things like material substances or even necessary ideas. These regularities themselves must arise, or become, from the pure possibility of vagueness.

So Peircean metaphysics seems to fit the bill you describe. It is different just in being a highly structured or systematised view of becoming/relating. And so, as said, it achieves monistic holism only via an irreducibly complex sign relation.

But for some reason, rather that responding to my argument, you just immediately launched into a personal attack.

Perhaps now you will reconsider and actually explain what the difference might be if it exists. What am I not understanding about your notion of singularity?

Is it more that some thought that such a singularity would have to be ultimately simple and structureless? Yet then I would have to wonder about how a relation could be structureless. What could that even mean?

Even Smith seems to think terms or relata cash out as packets of variable relations. So in some way, they certainly can't be simples, let alone the same simple as the "singular" relation of which they appear to compose a part.

So your OP does spark a set of questions as it seems on the face of it to be patently self-contradicting. It would be nice if you could focus on legitimate questions and not go into further tirades of abuse.

Getting it off your chest yet? :D

Of course I would employ the same analytic tools on every question. It is what everyone does - they just call it being logical. I simply make the added distinction between the kind of logic that is good for thinking in terms of atomistic particulars and the kind of holistic or dialectical logic that is traditional at a metaphysical level of thought.

For some reason you take it terribly personally. And that will limit you professionally.

My point, though, was that being (identity) since it is grounded in the human eternalistic doing called 'logic' cannot be grounded in the human temporalistic doing called 'ontology', because in the latter there is no being that is not becoming, when we examine and think about 'what is'. — John

I'm not exactly sure but this certainly sounds the same as what I'm saying. :)

You may focus more on Geist or spirit - which I say is treating mindfulness as a substance rather than a process. I take the Peircean route that mind is the process of semiotic reasoning - it is an enactive relation with the world based on sign.

But in some sense, "eternal" reasoning or intelligibility is what results in the "doing" that is a materially actual world.

However when it comes to being and becoming, I take a (no surprise) tradic approach in which becoming seems to take two forms - vague potential and crisp degrees of freedom. And most talk about becoming - ever since Aristotle - has focused firmly on the modal and atomistic later, the definite possibilities that are the result of having become largely well-organised.

So vagueness is what begets being and becoming dichotomistically. That is a deep state of unformed and unlimited possibility that is pretty impossible to imagine (it seems).

But the world as we find it is grown up and set in its ways. It has a history that tightly constrains its raw possibilities. True vagueness has largely been dissipated.

Yet in becoming constrained to become Being, that also makes definite some remaining set of generic properties or freedoms that material objects can possess. So now from definite Being arises the kind of equally substantial becoming which is what Aristotle was talking about. It is actually possible that a horse is white because we are in a world where there are these definite states of being that can be thus combined with (relative) freedom.

So dichotomies simply serve to dispel vagueness. They get the party started by separating existence in complementary fashion. Then as crisp states of being, the separated can now be mixed and combined in free fashion. That sets up the secondary play of Becoming which is the evolution of complex Being.

And complex Being is an ascent that is unbounded. We can imagine minds even more powerful and marvellous than a mere humans. We can imagine subjectivities unlimitedly more ... intense.

Or is that too a bounded fact? Are their material constraints on such complex being? (Answer: yes. Too much computation concentrated in the one place is going to melt with its own heat, or exhaust all resources, or - failing that - eventually find its ontic limit in gravity. It will curl up and become a Black Hole when its massiveness can no longer be sustained.)

These two incommensurable kinds of reasoning cannot be grounded in ontology simply because one of them is firmly grounded in logic. — John

Personally I am much more on the idealist side than that. We can't ground belief in ontology at all. We can only truly know our own "ontic commitments".

I mean at least we know what our own (rationally expressed) ideas are, right? But beyond that, we have to leave it to the world to suggest we might be getting it wrong somehow.

This is just circular reasoning. What I'm asking is to ground the dichotomy in ontology, rather than to base your ontology in dichotomy, simply because dichotomy is logical. Why would you think that existence has to adhere to logic? And if not, then why assume dichotomy as a fundamental ontological principle? — Metaphysician Undercover

If you think that a modelling relation is circular - and that active cybernetic relation is a problem - then fine. I'm not explaining it yet again.

Whether or not it "works", is relative. — Metaphysician Undercover

Great. Relativity is all there is in the final analysis.

I don't understand how you can claim a dichotomous holism. — Metaphysician Undercover

Yep. True that.

And I don't understand what you mean by "crisp existence". — Metaphysician Undercover

Again something I've explained to you ad nauseam. Things are crisp when they are sharp, definite, fixed, energy degenerate, etc. All the different ways of saying fully and unambigously individuated. (Which as I also keep saying, is a state that nature can only approach with arbitrary closeness, never in fact completely achieve - as bloody quantum theory makes bloody convincingly clear by now.) 8-)

This "need" you refer to must be justified, or else it's not a need at all, just an assertion. — Metaphysician Undercover

But dichotomies are justified logically. They are crisply defined as an operator or symmetry-breaking relation in being mutually exclusive and jointly exhaustive.

So yes, one still needs to argue the case that something about the real world can indeed be best explained using this standard dialectic template. I have no problem with that.

But the validity at the level of logic is another matter.

As usual, the worst case scenario is that it might be an arbitrary scheme to impose on nature in being axiomatic. Maybe because there is such a vast gulf between phenomenon and noumenon, even our best tools may still be inadequate for approaching the thing in itself. And yet, if it works, it works.

You may claim that there can be no knowledge or understanding without dichotomy, and this may be justifiable, — Metaphysician Undercover

You are not listening because I frequently say that there is nothing wrong with reductionism, mechanicalism, atomism, predicate/modal logic, and other such tools of thought, from a pragmatic point of view. Where human purpose is limited to the "close at hand" - our own classical scale of existence - then this kind of general framework is indeed the most materially efficient way of thinking about nature. It shortcuts things by cutting out the very question of formal and final cause that a holistic view of nature is concerned with.

So sure, reductionism works to build laptops and cities. But by definition, it is not holism.

And my argument is that the two are in fact related by the reciprocity of a dichotomous relation. If we understand reductionism vs holism properly, each is "true" as the inverse of the other.

So one does not have to reject the other. Instead each represents a different natural limit on our modelling of nature. We have the choice of thinking either in terms of the particular or the general. And both are right - so long as we respect their appropriate scales of description.

I'm the only one around here who doesn't in fact get stuck in some monistic rut of thought. I can switch between reductionism and holism with ease as I have two complementary logics with which to do the work.

The problem of course is that the whole of human education is organised around a reductionist mentality because that is what is materially efficient. Virtually no one can get a interdisciplinary training in holism. You have to be at least post-grad to find your way into some obscure university institute that might pursue that explicitly.

And once you allow for the possibility of non-dichotomous existence it gives you a completely different perspective on the relationship between existing and knowing. — Metaphysician Undercover

Well if you can explain what kind of crisp existence is not the result of a symmetry breaking dichotomy, go for it.

I've already asked SX to name a single generality that does not come trailing the "other" that is its context. He failed to come up with any term that could possibly stand alone.

Maybe you can do better?

the virtual - which refers here to the register of coupled rates of change - is precisely opposed to the possible, and in fact is more or less defined directly in distinction to it: — StreetlightX

Yep. So as I said. A limit is defined "directly in distinction" - dichotomously - with the immanently realisable or actually possible. Becoming ends in being. Or rather, more subtly, being is our conception of an absolute state, a limit, that can be approached arbitrarily closely without ever being perfectly grasped. That is why it might be called virtual in some metaphysical jargons.

Your conception of limits - as having ‘negative reality’ that constrains a general ‘vagueness’ could not be better described as exactly what Deleuze considers to be the entirely wrong approach to things. — StreetlightX

Well maybe Deleuze does say it is exactly wrong. But in my view it seems Deleuze who muddles things up now.

As far as I can tell - it is hard to make sense of what doesn't actually make sense - Deleuze wants to reduce existence to differencing or individuation. Which is fine. That is a constraints kind of thinking.

But then he doesn't get the need to remain dichotomous. The systems view is that a world forms by a reciprocal action of differentiation and integration. What is separated must also mix. Divisions must be globally coherent to persist in a general long-run fashion.

So at the top, constraints define sameness rather than (directly) difference. They encode an idea or purpose (ie: traditional formal/final cause) that thus - negatively - encodes also a matching idea of indifference. Constraints are semiotic relations which "know" what differences make a difference ... and so also define and ignore all the differences that don't make a difference.

They are a sieve that acts on reality. A sieve that separates the causes of actuality into the necessary and the accidental. So if "anything is possible" in an initial state of vagueness or symmetry, constraints emerge to organise this brute potential into a space of the lawfully possible. And laws have the character I just described. They define the regularity that is a necessity - the generality that is the form a local symmetry breaking must take. And then they leave to informal measurement the other part of existence which has been now rendered the contingent or accidental - the degrees of freedom which are the values we measure as some physical state of affairs and plug into our symmetry breaking equations.

So this is what seems missing if one seeks simply to invert the traditional formula where identity is defined in terms of "being similar (to an ideal)", to one of identity being "difference all the way down".

Both ways of looking at it leave out the actual reciprocal relation involved by trying to describe reality in monistic terms - as bounded by one kind of action, either cohering or differencing.

My way of looking at it - or the systems way, ably represented by Peirce and modern hierarchy theorists - instead explains how constraint carries within itself a limit on caring, in being actually (or virtually really) caring. In being a definite limitation on possibility - and yet vague potential being still unlimitedly fecund - constraint only exerts its influence so far on existence. There is point at which constraint doesn't care because it can't care. Its purpose has been met and the rest becomes just a sea of differencing that doesn't make a difference.

As for the Evens paper, the irony of complaining that I have a comprehension problem is kinda hilarious considering that the whole paper is geared towards treating the differential not as a question of limits, but as a question of generative production that is everywhere opposed to understanding the differential in terms of limits. — StreetlightX

But that is just your misunderstanding of calculus as others note.

This "differential" is indeed a mathematical singularity - that is a violence against nature. A singularity of that kind is "a bad thing" in that it becomes a Pandora's box of (vague) possibility. Physics knows it has a problem when it arrives at a singularity.

So what is really going on here is that the dynamics of geometry are encountering this useful fiction of the zero dimensional point - the point that does not exist. It is a limit on existence in being the ultimate possible constraint on dimensionality, and so - as I say - the very thing that cannot itself be real except negatively as pure idea. (We can certainly talk about zero dimensional points.)

So what you call the differential - the seed relation - is simply the unlimited possibilities of a zero dimensional fiction. A point could be tracing out any kind of trajectory. So it embodies infinite freedoms - once we imagine its zero dimensionality now inhabiting some actually dimensional space.

This mathematical device alllows us to start to cloak the point in derivatives of motion. Even though the point has no extent, we can place it within a hierarchy of motions. We can "add back" the constraints we have just abstracted away. We can grant the point a first degree of freedom - a velocity or constant motion. Then a second degree of freedom - an acceleration. A third degree - a jerk. A fourth degree - a snap.

So the "differential", as you call it, is just the ability to strip down dynamical geometry of "everything" that is an actual state of change to a bare potential - strip away all possible constraints to produce the radically vague, infinite possibility of a zero dimensional point - in a way that allows us to build reality back up in terms of localised degrees of freedom.

So reality, as we know, tends to energy degeneracy. Constraints over time remove meaningful degrees of freedom. The calculus then is a way for humans to imagine reality as a negentropic inverse of that. We can pretend reality is constructed bottom up by gluing together degrees of freedom. So - by adding energy - we can set balls rolling inertially, accelerate them with a constant force, accelerate that acceleration with a steadily increasing force, and so on.

But the mechanical nature of that way of creating real states of affairs is the reason why you wouldn't want to start taking it as the metaphysically basic picture of reality. So that is where you conception of the singular differential seems wildly astray. You are falling straight into the usual trap of understanding the point as a definite thing and not actually a singularity - a radical vagueness that can take on any crisp identity (or set of bounding constraints) because it has none itself.

And speaking of preaching - dude, if it were up to me I wouldn't engage with you ever, except you can't help but spew your babble in every thread I post in. Trust me, I have never once initiated a conversation with you except when you barge in telling me how I got it all wrong from the perspective of your ready-made monotone pseudo-system. The only one who incessantly rocks up time and time again to spread the gospel of symmetry-breaking and general-particular bullshit here is you. So if you feel hard done by feel free to fuck off any time - you won't exactly be missed. — StreetlightX

You have a hard life ahead if you can't tell the difference between a challenge to your arguments and an attack on your person. I've really tried to help you out in the past because I could see you were following a similar trajectory to me, so I thought it useful to point out folk like Peirce, Rosen, Salthe and Pattee who I found to be at the end of the trail (in my opinion of course).

Instead you seem to be so wedded to PoMo and its own realist counter-reactions that any mention that others have got there long ago sends you into a fit of anger.

But, ah well. At least its entertaining. ;)

it is incredibly apparent that I can imagine an inexistent object right now - namely a 2 x 2cm box. — Rawrren

So we can imagine what is not. We can be ready to act in every way that is "realistic" to something that could physically exist.

The reason we can do this is because of symbols. A symbol is a physical thing - some mark, a vocal noise, a gesture, a DNA sequence, a brain state. It takes up time, space and energy. But it also has a meaning that exists outside the physical world.

And so symbols give the power to think about what is not. We can think about the world as any kind of other. We can indeed think about the world from the generalised idea of being a self in a purposeful or pragmatic relation with the world.

So intentionality arises because we can act on the wish of the world being physically other than it actually is. Symbols, or a modelling relation, create a space for ideas that exist outside the physics of the world even though the means of being outside that world are always still unmysteriously physical.

Deleuze warns exactly against this conflation - of which you engage in every time - of what he calls the virtual with the actual, wherein the terms of the reciprocal relation are taken to be themselves terms rather than relations — StreetlightX

So you added this further idiocy. Explicit in my description of limits is that they don't "actually exist". Limits are what actuality can approach - with asymptotic closeness. But by the same token, actuality can never arrive at the limit. The limit is where existence ceases to be an intelligible possiblity.

Thus a limit is virtual - in having this kind of negative reality. The reality of a general constraint on actualisation or individuation.

But I guess you are just desperate to misrepresent my position. It can't be that your comprehension skills are that weak.

Its like the way you rail against my talk about constraints-based causality and top-down hierarchical order and yet preach to me about Bateson's cybernetic restraints and differences that are signs to a system.

It is boggling that you can't see they are the same thing using slightly different jargon.

But Evens was your cite. You brought up the maths of limit functions. So maybe you don't understand math, maybe you don't read your cites, or maybe you are just the perpetual Mr Angry. Probs all three.

Did I say that generals were terms or complementary limits on being?

Terms are a term you introduced. You might be thinking epistemically of concept formation or "names for things". I am thinking of an actual ontic process - symmetry breaking.

check out Aden Evens's paper on this: — StreetlightX

What a surprise. It makes the very case you so strenuously want to deny!

It points out that dy/dx is a reciprocal relation. It is entire to itself because it is a dichotomy. The x axis and y axis are orthogonal - mutually exclusive and jointly exhaustive as dimensionality. Change is then mapped to points by allowing for a hierarchically organised cascade of constraints - the derivatives that internalise actual change by measuring it against the imagined tangent.

So the first derivative is just linear y/x. The velocity change in both axes is symmetric and so we start with each velocity a perfect image, the simplest possible reflection, of each other. We have a general symmetry waiting to be broken in some particular way. We await ... the swerve.

Now we see the line created by a moving point is curving or accelerating. And we need some means to measure this new kind of change. It looks like y is growing faster than x, or vice versa. The symmetry is being broken in one of its reciprocally defined directions.

So a new "lack of change" has to be imagined locally to give a secondary symmetry which the curvature breaks. Hence the tangent. The tangent is a line which is flat to the change. You can see the symmetry it re-imposes on the scene because the tangent has equal angles either side of where it brushes the curve. It is the new flatness from which there can be a definite degree of change.

And so it goes on. You can keep repeating the trick for ever higher derivatives. The differential is always tracking the same notion - the dichotomy of a change as revealed against a flatness. If you can hold one end of existence absolutely still, you can measure exactly how much the other end is definitely changing within a reciprocally exact reference frame.

We can say as apo does, that the property is related to the object in some way, such as habituation, or we can say that the property is related to the subject by predication, depending on how you categorize "property" — Metaphysician Undercover

But what I actually say is the predicate relation - as the "thing" that exists between "two other things" - is, as holism recognises, a relation between particulars and generals. Or particular things and general things - if one must continue to use a metaphysics that relies on entification.

So this is perilously close to transcendent Platonism in granting existence to abstracta, ideas, universals, etc. But only if one insists on reading my words (or holism generally) from an object-based, non-process, point of view. From the process point of view, there are no crisply singular entities. Everything reduces to vagueness. It takes triadic symmetry breaking - the kind of symmetry breaking that is itself asymmetric, divided by its particulars and generals - to produce persistent regularity, or the usual classical realm of (apparently existent) objects with (apparently inherent) properties.

Again, a property is a relation, just with an arity of 1 rather than 2, and everything said about it here could be said of properties as well. — The Great Whatever

But there is a distinction to be had between simply a reaction between two objects and the relation between an object and its world.

So a property is some propensity or habit of an object. And the relation is one of generality. There is something general about the world (a symmetry) that makes it possible for the property to exist as something the object "has" (as a broken symmetry, or particularity).

Let's say Bill is an obtuse sort of fellow. If that is a property, then it characterises Bill's general reaction to the world. It is a habit or regularity. And one defined by the world being - in some generally matching sense - not obtuse.

In Bill's world, it is at least expected that the majority have the property of being completely with it. A general state of symmetry is defined (in terms of the majority being in a similar state). And Bill can then "have" the property of obtuseness as a breaking of this symmetry that persists in every situation he seems involved in.

But if we just see Bill interacting with Fred, then it might seem that Bill is being frustratingly uncomprehending for some reason. However, is Bill really in possession of the property if we only see the one instance? It could be Fred who is simply a bad explainer. Any relation taken as a one off could be read in either direction. The relation is not yet one in which either Bill or Fred can be said to be owners of the relevant properties - either a general tendency to obtuseness or inarticulacy.

So (just as Peirce argued), a property or propensity has an arity of 3. A property doesn't exist except as a persistent habit, and so as a fact of a hierarchically organised triadic relation. A property is a relation between the particular and the general, which develops after a history of relating between the particular and the particular (the dyadic relation of Secondness). And then it all begins back in Firstness or Vagueness where there is only the monism of some brute quality - the possibility that on first appearance seems a bare particular, not yet in reaction with anything, let alone stablised to have a regular identity due to some generalised world history.

So yes. Frege certainly argued the reductionist version of logic - the one that constructs more complex relations by addition. But Peirce nailed the holist story where persistent particularity is instead the product of contextual constraints.

... However, If repetition exists, it expresses at once a singularity opposed to the general, a universality opposed to the particular... — StreetlightX

Yep. So precisely as I say. Intelligibility is claimed on the basis of establishing a dichotomy.

It puts law into question, it denounces its nominal or general — StreetlightX

I forgot though that Pomo likes to a lot of denouncing as well as paradoxing and its other messed up shit.

. In its essence, repetition refers to a singular power which differs in kind from generality, even when, in order to appear, it takes advantage of the artificial passage from one order of generality to another." — StreetlightX

Oh there's the paradoxing. So predictable.

Becoming is necessary a relation and also primary. — TheWillowOfDarkness

Indeed. It is the necessary relation of becoming (crisply) unrelated and so no longer "singular" (or vague).

Only once possibility is divided into some "this" and "that" can those opposed categories of nature start to mix in more interesting fashion.

So in vagueness, all possibility is of the undifferentiated type. It is all "related" by being "all indistinguishably the same".

And then follow the differentiation and integration (the dichotomy and the hierarchy, the symmetry breaking and its going to mixed equilbrium balance) which is the coming into definite being. Now you indeed have the whole show of actual relations between actual relata.

Also, regarding Ollie. So yes, an intersection of the accidental and the necessary, sure. But, then (s)he isn't just the intersection of the Accidental and the Necessary. (S)he's precisely how the accidental and the necessary intersected in just this way. And, that's the singular. — csalisbury

I'm guessing that capitalisation makes some really big difference that is over my head. You are going all Platonic in response to my un-capitalised pragmatism?

You do understand that a process metaphysics is happy with the modesty of self-organising emergence. It doesn't believe in transcendent being?

You can say whatever you like, "square circle", or whatever, but unless you can support what you say, it's meaningless. So you can mention "notions of relations that exist outside such constraints" all you want, but until you give an example, or describe what you are talking about, you may as well be talking about square circles. — Metaphysician Undercover

So did time exist before there was space or matter? Explain that in a way that seems meaningful.

I don't know why you're obsessed with describing everything by referring to its "other". That's not how we describe things, we describe things by saying what the thing is. So we can say what time is, by describing a relation between past and future, and there is no need to say how it stands "other" to something else. — Metaphysician Undercover

How does the future relate to the past if neither - right now - exists? Are they relating "outside" (spatial/material) existence in relating "within" time?

Is the singular x everything - the totality, the cosmos, what is, the world etc. - or some particular thing? If it's everything, then what is this y which is a second singular which is the pure antithesis of everything taken as a whole? — csalisbury

You are asking me to make sense of the use of terms in an OP that made no particular sense to me. But being charitable, I am trying to make the best sense of SX's foggy mention of "the singularity of becoming" - and presumably, the singularities of metaphysical terminology generally.

If you understand SX as saying something different, please explain what he apparently can't. All he will tell us is that the singularity of becoming is a "strange and specific notion". But unless he can say strange and specific in relation to what, I can find no proper meaning in what he says - just like everyone else who has responded so far.

So in my version of this tale, I never use the term. But I point out how I do have it covered in the "1" that the maths of reciprocals employs as its "anything goes" hinge idea. And I said explicitly that in metaphysical reasoning, it stands as a first abductive guess at "what goes". (If you don't know what abduction means in a Peircean context, you can look it up.)

So in speaking vaguely and abductively about "whatever the hell it is - that we will just call the singular one which is now the target of our inquiry", that is merely to say that I at least feel I have latched on to some kind of difference that makes a difference. I dimly sense something that could be right - as a foundational "direction" or dimension of nature. And having found one way to go, antithetically, I can immediately start thinking deductively of its "other" - what it would be to go in the reverse (or rather, dichotomously, inverse) direction.

So intuitively - like a newborn babe even - one can discover that there is the "thing" that is to turn right. And then that is exactly now matched by its opposite - going left again. Dyadically (Peircean secondness), for every action there is a reaction.

And look, I can go up and down and back and forth. Amazing. Reality seems crisply divided so that it always has three orthogonal spatial dimensions no matter where I go, wherever I stand.

But oh? Why only these three directions. Why not four, five or an infinity? There is now a new problem of living in a reality that is bounded by three dimensionality. And yet higher dimensionality seems mathematically unconstrained. What new dichotomy could account for that?

So "singularity" - as I am attempting to deal with it in the logic of dichotomies - is the process of uncovering the constraints that could (retroductively) account for the particular state of the world. It is leaping into the future based on an inkling of a dialectial structure which can account for "what is" (the first thing to smack me in the face as a "brute fact of existence") in terms of "what is not" (the context of everything else that has in turn been constrained, suppressed, restrained, or in other ways bypassed by historical development).

I can only go left, because going right has been negated in the completest sense possible. (Going right has just been made 1/going left - the thing I can be most sure I'm not doing right now.)

But as you say, singularity is a thoroughly bad term because it is ill-defined in the OP. Everyone is already confusing it with the particular. And so you in turn - being diverted down that wrong path by a misreading of SX - must interpret me as talking only about the maximally general.

To be accurate, I am describing how the machinery of the dichotomy is the way to make it clear what we might in fact being talking about - or whatever the hell it was SX might have vaguely understood himself to be saying.

If there was any meat in the OP, dichotomisation is the only sure way to extract it. The singular must be defined in terms of its "other". And the reciprocal relation is the way to force the issue. If there is anything meaningful to say, it will be obvious once the singular has been placed in some definite relation with its proper "other".

So temporal relations might appear to be constrained to relate inside time. But what prevents more general notions of relation that exist outside such contraints?

Didn't you just accuse me of an unwillingness to question these kinds of kneejerk givens of metaphysics? How can we speak of time with any counterfactual definiteness or particularity if we can offer no story on how it stands "other" to some suitable context?

Weren't you talking, literally, about any thing at all? ... Again, I get what the whole 1/x thing for Being/Becoming etc, but I still haven't the foggiest how it's being applied to singular things. — csalisbury

In the context of the OP, clearly I thought not. I was talking about metaphysical generality - which could of course start abductively from anywhere. So if we are talking of that particular rock over there, or this particular cat at my feet, then while they may stand at the long and complex end of a trail of constraint or symmetry breaking, they are clearly not simple dichotomies.

The "other" of that rock or this cat is not going to be some metaphysical strength generality - given the rock and the cat are not themselves metaphysically general. That would be illogical. :)

Even Platonic ideals suffer from not properly getting that individuation is a hierearchically organised business of increasing degrees of constraint. So there is no ideal cat or boulder up there in Platonia. But geology does conform to fractal erosive principles. Cats are the individuated product of a genetic and developmental history.

I already stressed that when talking about individuation, the key dichotomy is this one of the division between constraints and degrees of freedom - or necessity vs accident.

My cat is my cat according to the necessity of some history that makes it impossible for it to be considered anything else (like - for real - that I got the right black cat back from the pet shelter when Ollie went missing for several months as a roving juvenile). But then there is much that I would consider accidental to Ollie being Ollie. Like that he might have lost or gained weight, broken a leg, got covered in muck, is mostly a completly different set of atoms every few months due to molecular turnover, or sadly, he's been dead a few months now. Even the immaterial Ollie remains resolutely real - at least for me.

So the particular - your word for the singular - is the intersection of two forms of information (as made clear in the semiotic version of thermodynamics that would be, for instance, Pattee's epistemic cut or Salthe's infodynamics). There is the formal information and the material information. That is, the information which describes the constraints that produce some particular x, y or z, and the information that describes the accidents that compose particular x, y or z - the little differences that don't make an essential difference, like Ollie losing a leg, changing all his atoms, or becoming part cat/part tumour.

Well the last did matter for Ollie's existence. The information that held him together was eventually over-run by accidental growth rather than self-sustaining growth. But you get what I mean. All particular are dichotomistic in being some mix of the necessary and the accidental - and there has to be "enough" of the one to balance out the other. That is the nature of a self-organising state of equilibrium.

But such a relation would be outside of time, so we can dismiss that relation as unreal. — Metaphysician Undercover

Aha. So time has an outside! (Or spacetime has an outside! - if you are indeed talking relativistically.) It is itself a definite thing and so is embeded in .... something else.

What are you calling that something in which time (or properly, spacetime) resides (presumably as a more local constraint on its more general degrees of freedom)?

You're saying that proper pragmatism is an ontic inquiry; you can always ask "why," but once you do this past the point of universal invariance, you hit a wall because there's no answer in terms of a more general kind of invariance. — Pneumenon

I mention invariance as Nozick did a good book on that (if you want a more contemporary reference to answer Rorty).

But yes, invariance is the natural limit of skepticism. It defines the point where asking "why" no longer makes a difference. And so you might as well be quiet.

And indeed, Witty was channeling Peirce via the proddings of Ramsey if you check out Cheryl Misak's lastest retelling of the history. So quietism does not simply have to be an epistemic cut-off, it can become the ontic terminus. Invariance is the equilibrium state where further detail cannot disrupt the global whole.

This gets tricky because it is about reaching a metaphysics where both epistemology and ontology are saying the same thing for the same reasons. The grand project is to re-unite what has become philosophically divided.

So Rorty is saying pragmatism means goals are entirely personal. And models of reality are completely socially constructed as a result. The distance between the phenomenal and the noumenal is .... an unbridgeable chasm in the end.

But Peircean pragmatism says, hey look, the universe itself has a "reasoning mind". Our best model of epistemology is thus our best model of ontology. It is the same modelling mechanism (or semiotic sign relation) at work in both cases. It is just that our human or Kantian-level relating is indeed highly specific and personal, while that of the universe is at the other end of the spectrum in being maximally general and "disinterested" in any particulars. That is why the universe can be described in terms of the most generic physical laws, or statements of mathematical symmetry and symmetry breaking.

So sure, this "pansemiosis" of Peirce (he called it objective idealism) sounds pretty mystic ... if you are still a reductionist. But it is a grand unifying project that makes plenty of sense. It accounts for what science has actually found (in itself needing to re-unite observers and observables to achieve any final theory).

Basically, a qualified Principle of Sufficient Reason with a restriction on the kinds of explanations allowed, viz. they must be in terms of more general invariance. — Pneumenon

Well it is more complicated as you have a point of departure - vagueness - as well as one of arrival, in generality. So the genesis of questioning begins with the breaking of one (vague) level of symmetry and ends once continued questioning (or perturbation, or fluctuation) fails to make a general difference.

And Peirce defined that in terms of the Laws of Thought. Vagueness is that to which the principle of non-contradiction does not apply. Generality is that to which the principle of the excluded middle does not apply. So at the heart of logic, these are well defined terms.

Now I want to talk about something else here: why that particular restriction? I would assume that this is motivated by the success of natural science, but that's a guess because you have not yet said so. Does this methodology bootstrap itself out of scientific pragmatism, from "Let's do this because it works" to a more general method, a sort of conceptual ascent? Or is it some other reason? — Pneumenon

The success of natural science does prove that there is an epistemology (of modelling relations) that can lift humans out of their self-interested rut long enough to discover the disinterested invariance of existence "itself".

And historically, the "Let's do this because it works" version of pragmatism came after - if we are talking about the highly utilitarian kind of pragmatism that James made a big hit of, by tapping right into that Enlightenment point of view which then became the familiar Yankee disconnect between the social and economic spheres of life.

So it is crucial to point out that including the very idea of "doing this for a purpose" in pragmaticism is what makes it possible to think that the everyday desires of biologically-evolved and culturally-situated humans are far from an invariant fact of nature. Instead they are highly particular. But then also, by the same token, pragmatism can then model the notion of purpose in general. And thus it starts to make sense that even the universe is formed by its (thermodynamic) desires.

So yes, the whole argument is immanently bootstrapping in any direction you might care to slice it. That is why it is "naturalism". There can be no transcendent get out clauses. It all has to self organise.

Clearly for Peirce, it did arise out of scientific practice. He was - rare for a philosopher - a top scientist. But his metaphysics arose as a holistic and organicist retort to the overly reductionist and mechanical understanding of reality that Enlightenment science - the classical world of Newton - had produced in popular thought.

So Pragmatism proper is about the unity of things. It steers the middle course by being inclusive.

You can see the way philosophy went after the Enlightenment split things apart. You have the analytics who ran with the reductionism. They went for stories of bottom-up material and efficient cause, rejecting top-down formal and final cause as "spooky".

Then you have the Romantic-counter reaction that particular reduction engenders - such as Post Modernism. Now - reacting directly to the popular success of techno-analytic reductionism - you have the alternative camp that says form (or structure) and finality (or meaning) are the true foundation of things. Analytics are just "weird" because they have no soul, don't get poetry, and are generally just uncool and nerdy. Purpose must again be at the metaphysical centre of existence (even if existentialism says that just means purpose as it is to be understood multfariously by "any individual".)

But Peircean pragmatism unites by telling the Aristotelan systems story where existence is the result of a free interaction between bottom up and top down causality. The Universe is holistic in that it really is formed by all four of Aristotle's causes. They are all real and to be taken seriously.

So I get the feeling you want to read a historical direction to this - from science to metaphysics.

But Peirce was rejecting science as it had become (even for analytics and continentals) in order to return it to the more complete thing it once was (and is now becoming again).

So pragmatism is a foretaste of that future science, and a return to the roots of metaphysical understanding we see across many ancient cultures in fact - not just the Greeks with Anaximander or the Hesiod, but Buddhism, Taoism, even Judaism (as in ein sof).

The popular pragmatic answer to this is just to stick with a reference point until it is falsified, which is more or less how science works. — Pneumenon

The problem of goals .... This, I conjecture, is the big problem with trying to analyze the whole history of science, because the people involved may not have even had the same goals. — Pneumenon

Pragmatiism highlights the place goals have in rational inquiry. So that in fact defines "reference points in nature" in explicitly self-interested fashion. Reality is the "view from us". Our goals become an active part of the triangulation.

Vulgar pragmatism says the world-defining goal (the purpose that forms the umwelt of sign, to use the semiotic jargon) is personal utility. The questions about existence are guided by the ultimate anchoring question of "what's in it for me?".

But a scientific pragmatism - that tries to speak as nakedly and disinterestedly of nature as it can - instead might seek the goal of generalised invariance.

If one could imagine the distillation of all possible points of view, then what would emerge is the invariant characterisation of being? Lets look at a rock or a star from the point of view of the "universe". What would we see if we were that kind of "mind".

So in full blown Peircean pragmatism, you get that final ontic shift. The Universe is granted a mind in the sense that it stabilises its being by having a generalised point of view .... that is guided by some central purpose.

Cue the second law, equilibrium dynamics and entropy maximisation.

What you call "a fixed reference point" seems just another way of talking about the invariance of a symmetry. So relativity arises simply from a demand for the symmetry of universal co-variance. The world should look the same at any spatiotemporal scale of observation. So the "special interests of observers" - their particular states of acceleration - have to be factored out as localised, very personal, symmetry breakings.

This extends beyond science, by the way. The history of modern society is the history of us (ostensibly) trying our hardest to be good little children of the Enlightenment. — Pneumenon

Yep. Except the Enlightenment was based on atomism and Newtonian physics. And that reductionism - which presumes material being as brute existence, and spatiotemporal symmetry as transcendently fixed - has long since been revised by more holistic theory.

So society still understands existence in these classical terms. Science - pragmatically - has moved on.

Hypothesis: pragmatic solutions to this problem do not work, because no matter how much time people like Rorty spend asserting that we should just ignore the idea of ultimate goals or transcendence or what have you, there is simply no way to stop humans from constantly asking "Why?" — Pneumenon

Rorty is hardly a pragmatist. But I guess even in his own time Peirce was having to relabel himself a pragmaticist because folk like James could only understand a simplified "Enlightenment" version of his holism. :)

But anyway, again one can always ask "why?". Yet if one's answers achieve the invariance of universality, the questions become merely repetition of differences that don't make a difference. The questions become about chance particulars and not about deep universal laws (or symmetries and the reasons for their breaking).

And note that the goals are emergently immanent. That is the point of pragmatism proper, the ontic kind - to show how the regularity of universal habit could arise.

This is exactly the problem which StreetlightX is trying to bring to your attention. You have transformed "becoming" into a form of "being", and in doing such you leave real "becoming" aside, claiming it's unintelligible so there is no point in guiding the mind toward that direction. — Metaphysician Undercover

And this coming from you who can never deal with the notion of vagueness, or emergent temporality, or finality that is not prior to what it calls to, or prime matter that is not already substantial.

It is you that can't shake the fallacy of misplaced concreteness, not I.

Its just the term that a group of us were using as we were discussing bio- and pan-semiosis a decade or so ago. I think Stan Salthe coined it.

And I think it does admit to degrees of development more easily. But also it just has a pleasing ordinary language match to vagueness.

So we could talk about definiteness and indefiniteness, or determinacy and indeterminacy. But those are explicitly just negative formations - the thing and it's lack.

A dichotomy - as a reciprocal deal - is instead a symmetry breaking so complete that you appear to have two different fully realised things in opposition, So it feels more appropriate to give each its own full name, like vagueness and crispness.

That more than just the continuum issue would be why the pairing sounds right to my ear. So like discrete and continuous, or one and many, it is about making a clear statement that both limits are real and different enough to have their own distinct character. The continuous is not merely the in-discrete. It is the positively completely continuous (as a maximal exclusion of the discrete).

The usual epic whinge....

There's another point to be made: No reason a singularity has to be a 1. It can be a historical situation. Something crazy goes down, rewrites the coordinates, you walk outside, not knowing what's what anymore, then you try to act, in that. — csalisbury

Calling it 1 is again just to say that there is something, abductively, which is just whatever the hell it is. By then going through the further steps to discover the reciprocal relation that can work to clarify what we might have actually been talking about, the 1 is transformed into the scale factor that then specifies the measurement basis.

Does it help to give the equation in more complete form?

1/infinitesimal = infinity/1.

You see that the 1 in fact appears on both sides. But on one side it scales the parts and the other it scales the whole.

On that note - & I'll admit thermodynamics isn't my wheelhouse -but how is the steady march of entropy an increase in crispness? .... Doesn't the possibility of that fade as the world grows cold and dispersed?) — csalisbury

The baseline condition of the Universe is that it was born as a spreading/cooling bath of radiation. So at the heat and smallness of scale near the big bang, by quantum uncertainty, everything is maximally indeterminate. And then roll forward to the heat death, everything is instead so cold and large that it is as classically definite at it can get.

Thus crispness is defined in the sense that the dimensionality of the Universe - its degrees of freedom - are as generally limited at they can get. And this is due to the duality of expansion and cooling. The dichotomy consists of the reciprocal actions of heading towards asymptotic spatial flatness and asymptotic thermal coldness (each being the means by which the other can happen).

Of course the actual universe is a cascade of other symmetry breakings. So it gets complex. At the electroweak symmetry breaking scale, massive particles condense out of the generalised entropic flow. They make the whole universe suddenly somewhat colder than it should be "ahead of time". And those massive particles then have to give back that negentropy at a new rate - one which more complex structure still, like stars and bacteria, can in turn pay for their existence by accelerating the return of the stolen negentropy.

So the early smooth flow breaks up into a hierarchical mess of complexity - but all still entrained to the same final purpose.

It is all essentially or logically exactly the same thing - dissipative structure - but existing parasitically on multiple scales of being (due to there being these further symmetries able to be broken as things cool/expand enough for them to also be revealed).

Deleuze was of course supposedly influenced by Prigogine's ground breaking work on this kind of far from equilbrium dynamics. But I only see a garbled version in any of his writing so far. Not that I've felt the need to dig that deep myself given the science of dissipative structure, and also basic physics, have moved on so much in the past 30 years.

It's still a strange thing, tho, if neither extreme (pure vagueness/pure crispness) can be fully realized, than we're always stretched out between two infinities (infinitely free, infinitely constrained), always have been, always will be. — csalisbury

In what way are we actually ":stretched out" if we are always falling in the one direction (or more accurately, accelerating the world in that direction so as to pay for the right to exist ourselves as passing negentropic organisation)?

And also, remember the subtle difference between how we can think about these things and the thing in itself.

In the end - in Kantian fashion - we can only "know" the world we model. So the dichotomy - with its story of both things having an irreducible degree of its "other" in it - is only our best metaphysical conception. It is the theory we can produce following a dialectical logic. But no theoretical map is ever going to just be the territory it navigates.

Although, again, the evidence is certainly supporting the theory. The "surprise" of quantum physics is the kind of radical confirmation that says classical mechanics - the "physics of predicate logic" - just doesn't predict the world we've actually found. Quantum physics is incomplete, but already it bears out a metaphysics based on vagueness, dichotomies and hierarchies.

It just doesn't look anything like any process I know. — csalisbury

And yet - from my natural science background - it looks exactly like every process I know.

Like what's the pure antithesis of my mother/Beethoven's 5th/this bottle in my room/'Swann's Way'/ ? — csalisbury

Here you are talking of complex negentropic objects and not the metaphysical generality of existence itself.

All particular things are full of accidents - differences that don't make a difference to nature in general. just possibly a difference to some also rather particular observer.

Look. My favourite cup is cracked. The second law doesn't give a stuff (it's entropy in progress my son). And yet for me it feels the end of the world.

So thesis and antithesis don't operate down at the level of the particular or accidental. They speak to what is generally necessary - the only kind of conflicts or symmetry breakings which don't simply cancel themselves away and so can survive to be "things" that exert constraints.

I understand the 1/x thing for big ol headliners like Being/Becoming Determinism/Chance etc. but I'd really need some concrete analysis of some singular thing to understand how it works at the level of singularity. — csalisbury

OK. But it is confusing to now talk to individuation (or particularisation, or contingent being) as "singularity" when singularity was instead some kind of claim about monism over dualism or triadicism (who knows what SX really thought he meant). And I've just defined my acceptable understanding of singularity as the bare abductive "well what ever the hell it is" which of course is the spur needed to get any metaphysics started. And that sense of singularity then explains the third thing of the 1 that has to be introduced to talk about dichotomistics X and Y - becoming the vague possibility that gets divided by the familiar maths of reciprocal or inverse relations.

So if we are talking about individuation, it is absolutely key that not everything in existence is determined. The point about constraints is they encode finality or purposes and so they only limit chance to the degree there is a reason to care. That then leaves abundant scope for accident to play its part in actuality.

Of course we care that the world's highest mountain happens to be in Nepal. But does plate tectonics - as a vicar of the second law - give a fuck? It is a complete accident that that is the particular case. On the other hand, it is completely necessary that hills and valleys form in a way that conforms with fractal statistics. Growth and erosion are the reciprocal actions that must be balanced.

But isn't this just stipulating non-reciprocality (non-dialecticity?) as a fixed absolute in order to hold stable an equally absolute system of reciprocal/dialectal dichotomizing? "Everything has to be defined reciprocally EXCEPT reciprocity which exists in a non-reciprocal asymmetric relationship with non-reciprocity." Can't we use this same template and generate any number of metaphysical systems, depending on our tastes? Essentially what you've done is exempted your own model from the metaphysics of everything else, by carving a special metaphysical niche for it. — csalisbury

But vagueness doesn't need to lack reciprocality. It just has to say there is no order or organisation to it. Any beginnings are just as fast ended as vagueness is a state of perfect symmetry, and thus a perfect condition of constant self erasure.

Again, this just describes the quantum physics of the vacuum. It is exactly how nature is. The vacuum, due to uncertainty, could spit out any kind of possible particle at all. Yet by the same token, there is the same likelihood it will spit out its exact anti-particle - and the two virtual particles will annihilate immediately to leave the vacuum looking still a blank, non-fluctuation, symmetry.

So vagueness can have every possible reciprocal action going on, but none of them have any bite.

Of course, it is also the case that this symmetry breaks - lucky for us. And we thus have to identify - via symmetry maths - how this could be the case.

A big clue for example is that the Universe has just three dimensions. And theorems from network theory tell us that every more complex network can be reduced (constrained) to interactions of three edges. But you can't have a network of lower dimensionality than that.

So it is easy to see that once a self-simplification gets going (of the dichotomous kind, which for networks is the crisp thing of "connections and nodes"), then it will go to its limit. And the limit may have irreducible structure. Hence something is left existing despite all attempts to self-erase. Not everything actually can cancel. (And if you want to be technical about it, now we are talking about the mathematical definition of a singularity!)

So yes, my approach as I've outlined it is metaphysically bootstrapping. And that's its feature, not a bug.

You are basically saying that my metaphysical model doesn't accord with your belief about the thing in itself - the thing in itself not being allowed to bootstrap ... because that then is in conflict with your own metaphysical logic.

But you can see how that is not an acceptable complaint. The "thing in itself" is that for both of us. So all we can do is propose our various models and see which turns out to work best as the map that allows us to navigate reality.

I mean I have no trouble using good old fashioned predicate logic. Classical physics works for everyday engineering. Reductionism makes normal life very simple. So in its domain - roundabout the human scale of physical existence - it works fine, nothing better.

But it should be no surprise that if we are dealing with the extreme scales of existence - the vanishingly small and the incredibly complex - then actually we need a metaphysical logic that deals directly with the very issue of scale extremes. Hence hierarchy theory ... which in turn needs dichotomies that produce separations ... which in turn need vagueness as the foundation on which the rest can get started.

You are just assuming the extensibility that for modal logic - in wanting to include the dichotomy of possibly vs necessary - is what it must establish.

So the general ontic issue here is that the choice (following holism) is either to accept the actuality of vague objects, or (insisting on reductionism) having to suffer the ill fate of having to swallow many worlds in some guise.

If you insist on the absoluteness of the law of identity - no even counterpart fuzziness when it comes to being - then you have to multiply worlds to fit in the infinity of infinitesimally different versions of any object that is the logical result.

This is exactly the problem of quantum physicss. Every fork in the pathway has to bifurcate a new pair of worlds. You can't in fact tell which is the real Algol or Willow whose future had two possibilities to choose from. So both paths were taken and the dog and its master continue in their two worlds.

Yes, it doesn't make any sense at all to duplicate entire world histories at the drop of a hat. So if you want to talk ontology, vague objects dig you out of that hole. You only need an Algol or Willow that fits their description to the degree any differences don't matter.

Willow puts his eye out with a stick. Algol is now a stray not a pet. Yet being objects still of the same world - individuated by its particular history, its particular steady accumulation of constraints - that history alone can still determine whether Willow is still near enough Willow, or Algol is Algol.

On the microscale, they both are certainly vague objects. Most of their molecules are turned over each day, breaking down and getting remade. Functionally (that is, teleologically) it makes no real difference to anything if microtubule a is replaced by microtubule c rather than microtubule b deep in some cell of Willow in the next five minutes. And yet that is a haphazard possibility.

So a "functional actuality" has no logical problem at all with vague objects. Near enough is good enough for a making call on identity. Because that call is made from a higher level of organisation. And semiotically, it is founded on a principle of bounding indifference.