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.