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-)

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.

Yes, I think that's true. Ontology is only ever us doing ontology, right? We can't get beyond our own doings to the Real itself, as it is in itself absolutely independent of our doings.

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'.

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.)

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. — apokrisis

I think this is kind of true if you think Hegel, but I think of spirit more as a process of expressing freedom than as any kind of substance. The world is the process of restrictng freedom; and there is an interplay between the freedom and its restriction, that I'm guessing you would think in terms of possibility and constraint. I think the notion of substance, like identity, has provenance only in the realm of pure logic. Process is much more in accordance with the world we experience

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. — apokrisis

A challenge? Please, don't flatter yourself. Your modus operendi consists of waltzing into a thread, declaring a position wrong from the point of view of your already-established orientation, then proceeding to pontificate on how that orientation works itself out. After which you conclude, thanks to this circluar hop on the spot, that the original position is wrong. You wouldn't know how to effectively engage with another position on it's own terms if your life depended on it. So no, your don't offer challenges, you self-aggrandize by using other people's posts as platforms to preach your system-mormonism from.

Conversely I have to spend most of my time explaining how your two-bit categories of thought are generally entirely inadequate to the discussion at hand, and then have to deal with you mounting rearguard actions to fit things into your misshapen boxes. The blunt hammer of your 'systemetizing' treats everything it encounters as a nail, and you lack the very ability to imagine that not everything amenable to it's bluntness. This is nicely dramatized in your request for a 'generality that does not come trailing the other for context': as I've told you time and time again, this isn't what it's meant by a singular, but because you literally lack the capacity to think outside of your pre-fab categories, you take your own failure of imagination for a failing on my part.

So it's cute that you think you're trying to help me, but until you develop some sense of just how inadequate your categories of thought are, I'm afraid that all you're doing is consistently charging me with not living up to an extraneous position, which, as far as I'm concerned, gets everything entirely bottom-up to begin with. Your 'help' is of the same kind offered by Mormons at the door - mostly irrelevant and preaching for the sake of conversion.

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.

You must have a dim view of 'everyone' if you think 'everyone' is as rigidly dogmatic in their approach to conversation as you. But as we've established, you can't think singularity, so even your view of 'everyone' is tainted by that self-same monotony. Thankfully, almost no one I know approaches discussion in the way you tend to do, so you're wrong about that too.

As I tried to show above the dichotomy proceeds from our reasoning, which I think is fairly obvious. One side of it comes from logical reasoning and the other from ontological reasoning. These two incommensurable kinds of reasoning cannot be grounded in ontology simply because one of them is firmly grounded in logic. — John

You've forgotten one important step. Prior to reasoning, whether it be "logical reasoning" or "ontological reasoning" (whatever difference there's supposed to be here), we need to identify and describe the identified thing. The description of a thing is not derived from logical reasoning, logical reasoning follows the description as an attempt to understand the described thing.

It seems that we have a name for the thing, "becoming", but without a description of the thing referred to by the name, that name could signify anything. And if we proceed with reasoning alone, when we just have a name, then "becoming" could refer to anything which is logically possible. So unless we have a description of what it is which is referred to by "becoming", then all your forms of reasoning and your various dichotomies are completely meaningless in this inquiry.

I think the thread has progressed to the point where we can recognize that "relation" is not an acceptable descriptive term for "becoming". There was some talk of "functions", but a function is a particular type of relation, so this appears like a step in the wrong direction. Until we can get some acceptable terms, there is no call for any sort of logical reasoning.

You've forgotten one important step. Prior to reasoning, whether it be "logical reasoning" or "ontological reasoning" (whatever difference there's supposed to be here), we need to identify and describe the identified thing. The description of a thing is not derived from logical reasoning, logical reasoning follows the description as an attempt to understand the described thing. — Metaphysician Undercover

'Becoming' or 'flux' are words used to denote what is as it presents itself to us. What is presents itself as a vast field of more or less changing similarities and differences. Some things remain so similar through time that the differences may be indistinguishable to us; they are for us so much the same across time that they are logical identities. But we believe that they are not ontological identities, at least insofar as their physicality is concerned, because we know that they must be changing, however subtly, as time passes. So becoming is not a determinably identifiable 'thing', but a general attribute of phenomenal reality.

So I didn't say that the idea of becoming derives from logic. It is the idea of identity which is derived form logic, it is a formulation of the idea of similarities that are perceived to be so lacking in difference to the naked eye, so to speak, that some things at least may count as being the same across time.

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.

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' or 'flux' are words used to denote what is as it presents itself to us. What is presents itself as a vast field of more or less changing similarities and differences. Some things remain so similar through time that the differences may be indistinguishable to us; they are for us so much the same across time that they are logical identities. But we believe that they are not ontological identities, at least insofar as their physicality is concerned, because we know that they must be changing, however subtly, as time passes. So becoming is not a determinably identifiable 'thing', but a general attribute of phenomenal reality. — John

If something presents itself to us, as to "remain so similar through time that the differences may be indistinguishable to us", yet we "know" that it must be changing, then how is it that we know this, other than by the means of logic?

So I didn't say that the idea of becoming derives from logic. — John

You haven't described how you can derive a concept of becoming without the means of logic. You say "'Becoming' or 'flux' are words used to denote what is as it presents itself to us." But I see static things present to me, far more than I see activity present to me. And if things which present themselves to me are not the same now as they were before, I conclude that there has been change, and therefore becoming. How is this not a use of logic? What presents itself to me is many different static things which are not necessarily changing, but could change, and do change. I also observe some activity, such as a fire, and I conclude that this is something which is in the process of changing. These changes are so rapid that I cannot identify the static things.

The question for you, is why do you use your logic to conclude that all the static things I observe are really in a process of becoming, instead of concluding that all the processes of becoming are a change between static things. If you are going to use logic to make the claim to "know" that what appears as "beings" are really "becomings", what are your premises to support this? How are you describing "becoming" such that it is not just a relation between static things?

It is the idea of identity which is derived form logic... — John

This is not true. Logic proceeds from identity, so identity is necessarily prior to logic. It is quite clear that we must have a good grasp of identity before we can proceed with any logic, as logic operates on identified things, so the very opposite of what you say is the truth, logic is derived from identity.

That is why we must accurately identify "becoming" prior to applying any logic. The conclusions of the logic will represent the identity given, in the relation of premise/conclusion. The accuracy of the conclusion will reflect the accuracy off the identity. If we cannot identify "becoming" as something other than a relation between definable states, then all of our conclusions will be representations of this.

I'm a little lost here, but the claim that you can generate a polynomial function from its differential is wrong.

For example, f(x) = 3x + 1 and f(x) = 3x + 2 are different functions, but their derivative is the same: f(x) = 3. You cannot go 'backwards' from 3 to either of these lines, not even around a single point (they're parallel and share no points in common). The lines can be specified without reference to the differential, as I just did.

Also, the claim that the differential is not a number is confusing: if by 'differential' you mean the result of performing the differential operation on some function, then of course it's not a number, it's another function. The result of differentiating is of the same sort as the thing differentiated, it's just of a lower power.

If by differential you mean the infinitesimal, I don't know what people think about it generally, but certainly you don't need to treat it as a number. You seem to be saying you don't want to treat it as an ideal limit, either, but then, I'm not sure what you're proposing instead. — The Great Whatever

Okay, I wanna backtrack here a little because a) we've both misread the passage on generation, because of my out-of-context quote, and b) I wanna deal more precisely with the Deleuzian treatment of the differential, which I wasn't clear enough about. First, the passage on the creation of the polynomial refers not to (re)creating the entire function, but the function around the point in question: "You are given one point on a function and a sequence of numbers representing the values of the derivatives of the function at that point, and from these numbers, you can reconstruct an approximation of the whole function not just at that one point, but also in an area around that point." So the reconstruction referred to is pretty local rather than global, but the thrust and stake of the passage is that this locality is nonetheless not correlative to a single, particular point: the successive derivatives express the overall behaviour of points around any one particular point.*

We can bring out the importance of this seemingly trivial point however if we turn again to Deleuze's reading of the calculus. I said originally that "the differential must differ in kind from the numbers that make up the primitive curve" - this was ambiguous and you were right to call me out on this. It's indeed far more precise to say that the derivative of f(x) yields another function f'(x): 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: at the point at which dy/dx = 0/0, the value of the derivative is itself neither zero nor an infinitesimal. As Sean Bowden puts it, "dx represents only the cancellation of quantity in general"; instead, Deleuze's argument is that while it cannot be determined in the form of quantity, it can (only) instead be determined in "qualitative form".

And what does it mean that the differential can be determined only in qualitative form? Simply that, as we've said, the derivative is never simply a value that correlates to a single, particular point on a primitive function, but instead defines the qualitative character of the function around a particular point. In Simon Duffy's words, "the differential relation characterises or qualifies not only the distinctive points which it determines, but also the nature of the regular points in the immediate neighbourhood of these points" (Duffy, "The Mathematics of Deleuze's Differential Logic and Metaphysics"). This is the import of the Aden quote above. 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. 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).

Why is this reciprocal determinability of the differential important to Deleuze? For two reasons: first, not only does it provide a model for pure relationality, but second and even more importantly, 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. What's at stake here? It's this: while Deleuze agrees that one must begin any approach to individuation from the perspective of the undifferentiated (at the point at which there are not yet 'crisply defined individuals', to use Apo's parlance), it is nonetheless a complete mistake to think that this undifferentiated realm is indeterminate. 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.

To bring it all together then, the determination of the pre-individual realm means that it is characterized buy the distribution of singular and ordinary points. And what does this mean? Again, back to the differential: if we accept that the differential characterizes the qualitative behaviour of a primitive function, then one can argue for the 'existence' of two kinds of behaviours: singular and ordinary. Points with 'singular behaviours' are, as we've said before, things like inflexion points and stationary points (where the value of a gradient changes or equals to zero or infinity); points with 'ordinary behaviours' are those that remain relatively continuous to their neighbouring points. So with the calculus as his model, Deleuze will refer individuation to the manner in which singular and ordinary points are distributed among a series, and from which, taken together, a primitive function can be generated. Hence Deleuze's affirmation that "the reality of the virtual [the pre-individual] consists of the differential elements and relations along with the singular points which correspond to them […] Far from being undetermined, the virtual is completely determined.”*

--

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. The terminological disputes over the general and the particular, the singular and the universal, and pretty much the rest of it, all turn upon this difference. The idea that the pre-individual is a vague generality is the 'null hypothesis' which Deleuzian metaphysics tests itself against, even as it responds to a similar motivation - which accounts for the closeness and the distance between our respective position. Anyway, sorry for the long reply, but I'm working on two fronts at once - if you haven't noticed already not all of this post is for you TGW - so I don't have to post multiple times.

*See also Gil Morejon's paper, "Differentiation and Distinction: On the Problem of Individuation from Scotus to Deleuze" (on academia.edu), which helped me clarify alot of these issues to myself (sneak peak: "What we will suggest is that the positive notion of common nature or virtuality, as something both completely determined and undifferentiated, far exceeds in its explanatory capacities a negative notion of possibility as purely indifferent... This is an important insight because it forces a re-evaluation of the idea of possibility, which was classically understood as the negation of actuality. Hegel’s famous critique, that Schelling’s philosophy of Indifferenz amounted to ‘the night where all cows are black’, exposes the paucity of such a conception, through which we ultimately are left incapable of accounting for the reality of actual individuals or distinguishing between empirical instances"

(^ i.e. accounting for the singular - this explains why so many of Apo's posts end up being a simplistic 'taxonomy' of being: things and processes only have 'value' in his system to the degree that they correspond to one or another of his pre-established categories - in themselves, they are meaningless, devoid of significance. I wasn't just being snide when I said earlier that the whole edifice is self-referential - it really is).

If something presents itself to us, as to "remain so similar through time that the differences may be indistinguishable to us", yet we "know" that it must be changing, then how is it that we know this, other than by the means of logic? — Metaphysician Undercover

I haven't said that, I have said that 'what is' presents itself as a vast field which displays a whole range of rates of change in its different parts. The world as a whole is never the same from one moment to the next, and we observe this constantly. It is scientific investigation, not logic, that has revealed that everything physical is constantly changing.

This is not true. Logic proceeds from identity, so identity is necessarily prior to logic. It is quite clear that we must have a good grasp of identity before we can proceed with any logic, as logic operates on identified things, so the very opposite of what you say is the truth, logic is derived from identity. — Metaphysician Undercover

I haven't denied that identity is the basis of logic. We arrive at the notion of identity by thinking about the logic of our ways of communicating about our experience. Certainly the idea of identity was implicit in human discourse long before it was identified as an explicit concept. But its realization as an explicit concept came about via logical thought, by seeing how, for example identity is implicit in the the Law of Non-Contradiction and the Excluded Middle.

So, the idea of being is the idea of identity, and the idea of becoming is the idea of change. To state it again, my contention is that identity is not observed. Change is observed, difference and similarity are observed, And thinking about difference and similarity leads to the formal idea of sameness. Sameness or identity is never actually instantiated in the temporal world of constant physical change, only difference and similarity are. So being is a more purely logical idea than becoming. We actually witness becoming, we do not witness being.

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.

We can bring out the importance of this seemingly trivial point however if we turn again to Deleuze's reading of the calculus. I said originally that "the differential must differ in kind from the numbers that make up the primitive curve" - this was ambiguous and you were right to call me out on this. It's indeed far more precise to say that the derivative of f(x) yields another function f'(x): 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: at the point at which dy/dx = 0/0, the value of the derivative is itself neither zero nor an infinitesimal. As Sean Bowden puts it, "dx represents only the cancellation of quantity in general"; instead, Deleuze's argument is that while it cannot be determined in the form of quantity, it can (only) instead be determined in "qualitative form". — StreetlightX

The existence of the difference, or relation, which cannot be expressed quantitatively can be demonstrated by the difference between spatial dimensions. The relation between spatial dimensions is incommensurable. The relation between the circle (2d) and the diameter (1d), is pi, which is an irrational ratio. If one takes two equal length line segments at a right angle to each other (representing two distinct dimensions), the diagonal (which crosses both dimensions), is again irrational.

Consider the difference between a straight line and a curved line. We could assume points on those lines to mark off segments. No matter how small the segment of line is that one marks off with the points, the segment of curved line will always be fundamentally different from the segment of straight line, and the relation between them is incommensurable. I believe there are two approaches to this problem. First, we could consider giving dimensionality to the point. Then a point on the curved line would be fundamentally different from a point on a straight line. But this would make "points" complicated, requiring different types of points for different applications, a 1d point, a 2d point, etc.. Furthermore, the non-dimensional point has been proven to be very useful, so there is very good reason to consider that it has some basis in reality. The second possibility then, is to maintain the non-dimensional point but to allow that the space between the points on the curved line is fundamentally different from the space between the points on the straight line. This requires that we reify space itself. We must allow that the space between points is something real, if we desire to maintain the use of non-dimensional points, and also allow for the reality of the non-quantifiable relation between different spatial dimensions. Space exists and it has real qualities which we do not know how to measure. We measure objects, but since objects are merely the way that space is represented to us, the unintelligible aspects of space render absolute accuracy impossible.

Now we approach the basis of the non-quantifiable relation. This is the relation between space (being now described as something real), and the non-dimensional point. In order to understand this relation we must give the non-dimensional point a position with respect to space. Without a position, it cannot be related to space. I believe its position is in time. The non-dimensional point is a point in time. Now we must reverse the relationship between space and time, which makes time the 4th dimension, such that time can have its proper relation to space, as the 0th dimension.

And what does it mean that the differential can be determined only in qualitative form? Simply that, as we've said, the derivative is never simply a value that correlates to a single, particular point on a primitive function, but instead defines the qualitative character of the function around a particular point. In Simon Duffy's words, "the differential relation characterises or qualifies not only the distinctive points which it determines, but also the nature of the regular points in the immediate neighbourhood of these points" (Duffy, "The Mathematics of Deleuze's Differential Logic and Metaphysics"). This is the import of the Aden quote above. — StreetlightX

This is very good, because if we consider the point in time, as the non-dimensional point, we can start to see the vague relationship between points in time, and the surrounding space. Recognize that we have reified space, such that it is something "real", in the sense that physical objects are real, but what we are actually looking for now is the real reality, the reality which is the "becoming" that lies beneath the object which has been identified as space, and is associated with the 0th dimension, time. Since the incommensurability has been identified as existing within the dimensions of space, the vagaries which exist around the non-dimensional points are proper to that object, space itself. So we must go deeper, into the non-dimensional points to find real quantity, or quantifiability.

Why is this reciprocal determinability of the differential important to Deleuze? For two reasons: first, not only does it provide a model for pure relationality, but second and even more importantly, 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). — StreetlightX

With respect to this then, my position is that the whole appearance of indeterminateness is due to the somewhat unintelligible nature of space. Because space has unintelligible aspects, we can conclude that space does not necessarily behave in the way that it should. The "way that it should", is the way that is determined by this underlying reality, the sphere which Deleuze is saying is completely determined. This is the realm of what Bohm calls "hidden variables". In his "Wholeness and The Implicate Order", he posits an underlying realm of activity, becoming, of which we see only a reflection of, in the spatial existence of objects, just like Plato's cave people only see a reflection of reality.

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.

Yes - it's a limit precisely from the perspective of the already-individuated, which in this case would be the primitive function. But the whole point is to reverse the order of priority in order to think the construction of the primitive out of the virtual, which, although not actual, is in every regard real: "The virtual is fully real in so far as it is virtual [it is] real without being actual, ideal without being abstract [...] The reality of the virtual consists of the differential elements and relations along with the singular points which correspond to them". 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 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.

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 ?

They is why Evens - inspired entirely by Deleuze from whom these terms are borrowed - speaks of individuation as a matter of 'problem solving'. Not 'symmetry-breaking' but problem-solving is the model for the process of individuation: the differential qua genetic element of quality defines an open-ended problem (like the coupled rates of change in an economy) that can be 'solved' in multiple ways (two different companies might attempt to 'solve' an inequality of supply and demand in two different ways, even though the 'problem' itself is entirely determined); a distribution of singularities can give rise to varied curves, so long as the points of that curve behave in roughly the right ways around those singularities themselves.

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. A problem forms like a soap bubble stretched across the wire outline of an abstract geometric figure. How to connect the vertices most efficiently, how to find the correct degree of curvature, how to distribute density so as to bend without breaking? And when a weakness is stretched beyond its breaking point, the bubble snaps into a new shape, determining new criteria, new boundary conditions, posing and solving a new problem in a flash, so that one would never suspect the whole network of differential calculations that take place in this instant. Problems determine themselves incrementally and always in relation..."

Individuation as symmetry-breaking in comparison is an incredibly basic and rather naive approach to the whole issue. Indeed, the entire model is a back-formation, a retroactive posit that takes the actual and, through a fantasy or a daydream that operates by means of an hallucinatory extrapolation, imagines that there must be some vague, indeterminate potentiality out of which individual, 'crisp' things are coalesced. But just as the 'limits' which apparently drive this process are fictional, so too is the entire edifice a just-so story that weaves itself in order to justify itself. As a good King Lear might have said to you: only fantasy comes of fantasy - speak again. This is why what you bring to the table is not philosophy but taxonomy: you have a sterile descriptive framework under which various entities and processes can be slotted into as so many indifferent elements, but which itself does nothing to account for their ontogenesis except by means of an ineffectual handwave. The Apeiron, like the Anaximandian myth that spawned it, is exactly that: a fable told in the place of any concretely engaged analysis.

And what does it mean that the differential can be determined only in qualitative form? Simply that, as we've said, the derivative is never simply a value that correlates to a single, particular point on a primitive function, but instead defines the qualitative character of the function around a particular point. In Simon Duffy's words, "the differential relation characterises or qualifies not only the distinctive points which it determines, but also the nature of the regular points in the immediate neighbourhood of these points" (Duffy, "The Mathematics of Deleuze's Differential Logic and Metaphysics"). This is the import of the Aden quote above. 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. 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

I want to return to this point (pardon the pun) because I like it so much. If we assume a particular point (a non-dimensional point of location), then there is a surrounding area, "the neighbourhood", which may have a number of positions in the neighbourhood related to this point by the same function. These points are exactly the same, functionally. In a simple spatial relation we could say that these functionally identical points make a sphere around that original point. The points equidistant from the original point.

Now from this point of view, of functionality, each of these related points has the exact same relation to the original point. They are the very same point, functionally, but my description has described them as a number of different points in a neighbourhood. So we need a principle whereby we can individuate the parts of the neighbourhood, as different from each other. They must be different because they are being described as different, and we can visualize the points on the surface of a sphere as different from each other. We need to introduce dimensions. Dimensions will provide the basis for this difference. To do this, we must return to the original point, and give that original point context, a position. We cannot appeal to the functional points for context because this would constitute circular reasoning, and there is nothing to distinguish one from the other, so such a determination would be completely arbitrary. So the context, and therefore dimensionality, must be derived from the underlying flux which relates one non-dimensional point to another, and this presents a problem due to the nature of "flux". Bohm's proposal is a local clock, an inner time for each neighbourhood. The clock takes the place of the non-dimensional point of location. But since he hasn't assumed a non-dimensional point, just a neighbourhood with a clock, he gets an infinite regress of a clock within a clock within a clock. If we assume a non-dimensional point, then dimensionality can only be determined from within that point.

LOL This seems to be gibberish and reminds me of Nietzsche: "They muddy the water to make it seem deep".

Eh, your random opinion doesn't really matter tho. It's true that the notions discussed here are pretty abstract, but they are so of necessity, given how widely they can be cashed out. I already gave the example of an economy, here's a few more, courtesy of John Protevi from his Deleuze and the Sciences, regarding other fields:

Neural functioning: "We can see the embodied and embedded nervous system as a preindividual virtual field: (1) a set of differential elements (reciprocally determined functions —in other words, neural function is networked: there is no such thing as the function of “a” neuron; some argue the same for higher-level cognitive processes, i.e., that they emerge from global brain activity and hence cannot be understood in isolation) (2) with differential relations (linked rates of change of firing patterns) (3) marked by singularities (critical points determining turning points between firing patterns). The dynamics of the system as it unrolls in time are intensive processes or impersonal individuations, as attractor layouts coalesce and disappear as singular thresholds are passed (Varela 1995)"

A football game: "Let's take the Idea of football games. ... What are the [virtuals] that conditioned the genesis of American football? Well, it would be a multiplicity of differential elements, differential relations, and singularities. The differential elements would be the players, the field, and the ball. They are differential elements because they are defined only in relation to each other. A prolate spherical of pigskin leather is only a football in relation to the players, who are only players when the entertain a certain relation to each other and to the ball, and of course, to the field, which in turn. The differential relations are what the players are able to do with the ball and with each other. They are differential in that they are relations of change in the elements: how they are able to move, to advance and retreat. And these relations are strewn with singularities, or sensitive points: when the ball moves between players across a certain threshold of the field, a touchdown or field goal is scored."

Ecology: "An example here would be a Deleuzian understanding of niche construction: the activities of organisms change the selection pressures for future generations. The ecological web of relations that we describe as “selection pressures” is not ghostly, it is perfectly real, but for Deleuze, it does not have the same ontological status as a single individuated act (e.g., a predator devouring a prey animal). Rather, the web is virtual, that is, composed of the relations of dynamically interactive processes. The virtual field is not composed of the processes themselves but by the differential elements, relations, and singularities of the processes. These elements, relations, and singularities are progressively determined by intensive individuation processes so that at critical points in the relation of predator and prey activity — at a singular point in the linkage of the rates of change of those processes — we can find the triggering of an event such as a population explosion or, in the opposite direction, an extinction."

Can you give a brief overview of what you mean by this 'singular'?

But the whole point is to reverse the order of priority in order to think the construction of the primitive out of the virtual, which, although not actual, is in every regard real: "The virtual is fully real in so far as it is virtual [it is] real without being actual, ideal without being abstract [...] The reality of the virtual consists of the differential elements and relations along with the singular points which correspond to them". — StreetlightX

I believe that the "virtual" must be actual as well as real. But it cannot be actual in the common sense of physical bodies in motion. The need for two distinct types of "actual", provides the approach to a reconciliation with dualism. Within the virtual exists what you call "the differential elements and relations". But the virtual is what I call the non-dimensional point, which must itself be like a self, with a right and left, up and down, etc., in order to provide for the possibility of dimensionality. The principles which will differentiate the parts of the neighbourhood must inhere within the non-dimensional point. So the principles for dimensionality inhere within the non-dimensional.

Now we must remain true to our premise, the primacy of becoming. This will necessitate that the virtual itself is a world of flux, the relations etc., the principles within the non-dimensional, are active, and changing. It is argued by Lee Smolin in "Time Reborn", that we must allow for the laws of nature themselves, to actively change in time. So, if within the realm of the virtual, there is activity, we must reverse our established relation between space and time (time being presently represented as following from the activities of physical bodies), to allow for becoming within the virtual. This is "the reversal" which gives reason to express time as the 0th dimension, instead of the 4th, allowing for the reality of this activity of the virtual.

The unsubstitutable, the unique, the distinct, the inexchangable; that which has no equal or equivalent. It is what cannot be subsumbed under a regime of generality because it cannot be understood as one particular among an equivalence of particulars (although one can treat singular things as though they are particulars). The singular belongs to the order of novelty: to the degree that it can be thought of in general terms, it brings with it it's own index of generality. It's like what Nietzsche once wrote concerning 'great human beings': "Every great human being exerts a retroactive force: for his sake all of history is put on the scale again".

One of the paradoxes of singularity - and what accounts for it's fragility as a category - is that precisely because it's bears in itself the index of it's own recognition, it can only be recognized as a singularity only retroactively, by means of a repetition. Zizek - whose reference here is Hegel rather than Deleuze - gives the example of both Julius Caesar and Margaret Thatcher, the novelty of whom had to each be affirmed by a repetition: that of Augustus in Caesar's case - who assumed the title of the first 'caesar' - and that of Tony Blair in Thatcher's case, who was said to have institutionalized Thatcherism as a philosophy of government. In both cases it's only in the light of the 'repetition' that the novelty of the 'original' can be recognized. Without Augustus one could not speak of Caesarism, without Blair one could not speak of Thatcherism.

Again the reason for this is that the singular brings with it it's own index of generalization, the novelty of which is ungraspable without a repetition which brings it to light: "the murder of Caesar - the historical individual - ended up resulting in the establishment of Caesarism; Caesar-the-person is repeated as Caesar-the-title. The crucial point here is the changed symbolic status of [the new]: when it erupts for the first time it is experienced as a contingent trauma, as an intrusion of a certain non­symbolized Real; only through repetition is this event recognized in its symbolic novelty" (Zizek, The Sublime Object of Ideology). Deleuze himself, for exactly these reasons, will link singularity indissolubly with the concept of repetition: "To repeat is to behave in a certain manner, but in relation to something unique or singular which has no equal or equivalent... If repetition exists, it expresses at once a singularity opposed to the general... In its essence, repetition refers to a singular power which differs in kind from generality." (Difference and Repetition)

I mention this because it's easy to see, because of this, how singularity can be so easily mistaken or miscrecognized for particularity. Because repetition retroactively constitutes the singular status of the novel event, it becomes easy to treat both things as particulars, and from there, extract - by means of an imaginary extrapolation - an order of generality to which both might be said to belong. But it's clear that any operation of this kind is simply a kind of epistemological back-formation, an attempt to expel any consideration of novelty by 'levelling' the field of events in order to embed them into an artificial coordinates through which they can be compared, and subsequently particularized. This is why Deleuze warns that "generality, as generality of the particular, thus stands opposed to repetition as universality of the singular."

Eh, your random opinion doesn't really matter tho. — StreetlightX

I can understand and agree with the sentiment that my opinion, per se, doesn't and shouldn't matter to you. On the other hand my opinion is hardly "random". I have invested a fair deal of time into reading and trying to understand the import of the kinds of philosophers you seem to mostly concern yourself with. And I have come to the conclusion that much of their work is of little real philosophical consequence.

If philosophy becomes a specialized activity that is only accessible to those who are prepared to devote their lives to studying a narrow, arcane section, then it becomes of no more import to the common person than bird-watching, butterfly collecting or nuclear physics. At least nuclear physics has practical applications. Philosophy should be primarily concerned with how to live, in my opinion. And since life is short and reading and understanding everything is not possible, then I think a broad, inclusive overview of the whole drift of philosophical, aesthetic and religious ideas is the best foundation for a good philosophical life. Academic specialization is the disease of philosophy, as I see it, it is not the cure.

I try to see the import for life of what you wrote and quoted, and I just can't see anything much but cryptic gobbledygook. If you want to spend your life with that it is fine, though; there may be great art in it for you, but I was just expressing my opinion of it, much like someone might say that they see nothing in the music, poetry or paintings you admire. There is no accounting for taste, after all!
:)

Philosophy should be primarily concerned with how to live, in my opinion. — John

Don't we need to determine what it means "to live", before we can approach the question of how to live?

No. I think that would be backwards. We always already find ourselves living, so we know what it is to live. The important question is what it is to live well.

I don't believe that at all. In order to determine "how" to do something, we must first identify what it is that we want to do. Giving something a name (i.e. "living") does not mean that we have identified what that thing is. Your claim, that we find ourselves living, and therefore we know what living is, is untenable. Ancient human beings found themselves breathing, but they didn't know what this was, as they didn't know what air was.

The opposite to what you say is actually the case. We find ourselves doing things, and then we seek to understand exactly what it is that we are doing. Only when we come to this understanding can we determine a better way of doing it.

So, we are not necessarily living then?

That's unfortunate. Part of the appeal of this approach is precisely that it's allowed me to make sense of fields as far flung as aesthetics, ethics, perception and politics, all the while being in conversation with the great traditions of philosophical history more generally. Indeed, I think most of these are largely unintelligible without an approach grounded in the milieu surrounding questions of relationality, individuation and becoming. So sincerity notwithstanding, I do think that many of your perceived objections are largely off the mark, even if it is, as you say, taste which is the final arbiter here.