• Becoming and Relation: Difficult Thoughts
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

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,

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.

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).

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.

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.

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.

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

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

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.
• Becoming and Relation: Difficult Thoughts
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.
• Becoming and Relation: Difficult Thoughts
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.
• Becoming and Relation: Difficult Thoughts
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.
• Becoming and Relation: Difficult Thoughts
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.)
• Becoming and Relation: Difficult Thoughts
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.
• Becoming and Relation: Difficult Thoughts
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?

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.

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

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

Yep. True that.

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

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-)
• Becoming and Relation: Difficult Thoughts
This "need" you refer to must be justified, or else it's not a need at all, just an assertion.

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,

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.

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?
• Becoming and Relation: Difficult Thoughts
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:

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.

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.

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.

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. ;)
• How do physicalists explain 'intentional content'?
it is incredibly apparent that I can imagine an inexistent object right now - namely a 2 x 2cm box.

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.
• Becoming and Relation: Difficult Thoughts
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

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.
• Becoming and Relation: Difficult Thoughts
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.
• Becoming and Relation: Difficult Thoughts
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.
• Becoming and Relation: Difficult Thoughts
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.
• Becoming and Relation: Difficult Thoughts
check out Aden Evens's paper on this:

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.
• Becoming and Relation: Difficult Thoughts
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"

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.
• Becoming and Relation: Difficult Thoughts
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.

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.
• Becoming and Relation: Difficult Thoughts
... However, If repetition exists, it expresses at once a singularity opposed to the general, a universality opposed to the particular...

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

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."

Oh there's the paradoxing. So predictable.
• Becoming and Relation: Difficult Thoughts
Becoming is necessary a relation and also primary.

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.
• Becoming and Relation: Difficult Thoughts
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.

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?

#### apokrisis

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