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

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

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

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

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

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

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

Perhaps - and this just struck me - the best way to get a handle on this is to speak in terms of coupled rates of change. A rate of change, we can recall, is already a 'derivative': it is a change of a second order, a change that measures a change. Now, rates of change are interesting because they are not simply measurements of on-going processes so much as they define those processes themselves. For example, a population (of cells, of animals in an ecosystem, of a nation-state) can be defined not simply in terms of it's numbers - in fact a rather poor definition - but in terms of it's rates of change with respect to parameters like births, deaths, migration flow and resource availability.

Even more importantly, these rates of change can be said to be coupled, which is just to say that rates of change very in relation to each other. The higher the birth rate, the higher the change in resource consumption, for example. What we're dealing with here, in other words, is relations between relations; moreover, it's these relations which define the very 'objects' of which they are said to be relations 'of'. In embryogenesis for example, it's the differing rates of change between cell birth and death, along with the synthesis and degradation of so called 'adhesion molecules' (which bring cells together), that define what kind of cell (brain cell, skin cell, etc) will be formed. These coupled relations - which are productive and not merely derivative of their relata - have the 'form' of the relation prescribed in the differential calculus: dy/dx (the ratio between the change in one series and the change in another).

Note that one can of course, artificially reverse this whole enterprise so that rates of change are mere 'properties' of self-identical substances. But everything that is in any way important is thereby missed: the entire process of individuation whereby a thing 'takes on' an identity is missed. Any attempt to treat these relations as properties - which is entirely possible - simply misses the becoming of the entity or process at hand. Recall too that in the OP, I marked a distinction between becoming and change. In a process such as embryogenesis, becoming is taking place 'all the time': change, however, only occurs when coupled rates of change cross certain thresholds, when enough cells accumulate in a certain point at a certain speed in order to trigger certain reactions which in turn engender cell mutation, etc. Predicate logic basically operates entirely at the level of 'change': it literally cannot see, by design, the intensive becomings which operate at the level of relations.

I should also note that none of this is particularly 'out of the box': the sciences have been operating in this domain for decades, and continental philosophy has never taken predicate logic seriously. I would suggest instead that the whole institution of formal logic has on the contrary 'boxed itself in', playing formal-logical games without actually attending to the world about it.

Except I have no problems with reciprocal relations on the condition that what is reciprocally related are themselves relations. What's at stake here are not reciprocal relations between terms - and especially oppositional or dichotomous terms - but a reciprocal relation operating already at the level of relation. Every time you cash out reciprocity at the level of generalities, you go wrong. Which is basically all the time.

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. On such a compromised view, "difference can no longer be anything but the negative determined by the concept: either the limitation imposed by possibles upon each other in order to be realised, or the opposition of the possible to the reality of the real.... It is contradictory to speak of 'potential' ... and to define differenciation by the simple limitation of a global power, as though this potential were indistinguishable from a logical possibility."

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.

Doesn't matter: The very fact that you're speaking of limits at all is to go awry.

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.

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.

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

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

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

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

Note that one can of course, artificially reverse this whole enterprise so that rates of change are mere 'properties' of self-identical substances. But everything that is in any way important is thereby missed: the entire process of individuation whereby a thing 'takes on' an identity is missed. Any attempt to treat these relations as properties - which is entirely possible - simply misses the becoming of the entity or process at hand. Recall too that in the OP, I marked a distinction between becoming and change. — StreetlightX

This is the deep, and most fundamental problem of acceleration. If we assume that an object is at rest, and it is, due to some force, induced to move, then there is a moment in time when it moves from zero velocity to some determinable velocity. That initial movement cannot be expressed as a "rate of change", because it is fundamentally, therefore conceptually, different from a rate of change.

Of course physicists have no heed for this issue because relativity theory disallows the possibility of rest, so ultimately there is no such thing as a zero velocity, rest is relative. Then the change from rest to acceleration is just an expression which doesn't represent anything real. Consequently, acceleration is understood as a change in direction, so we have curves, and the ever present pi, in relativity formulations of acceleration.

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. — apokrisis

This must be why they say ignorance is bliss. It saves you from this kind of embarrassment. As usual, the terms in play aren't so easily coopted into your pre-fab categories: 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: “The only danger in all this is that the virtual could be confused with the possible. The possible is opposed to the real; the process undergone by the possible is therefore a 'realisation'. By contrast, the virtual is not opposed to the real; it possesses a full reality by itself…. Any hesitation between the virtual and the possible, the order of the Idea and the order of the concept, is disastrous, since it abolishes the reality of the virtual.” 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.

Elsewhere again: "The notion of 'generality' here suffers the disadvantage of suggesting a confusion between the virtual, in so far as it is actualised by a process of creation, and the possible, in so far as it is realised by limitation.” And I’ve already quoted it, but since you seem to have a selective reading problem, here it is again: on your view, "difference can no longer be anything but the negative determined by the concept: either the limitation imposed by possibles upon each other in order to be realised, or the opposition of the possible to the reality of the real.... It is contradictory to speak of 'potential' ... and to define differenciation by the simple limitation of a global power, as though this potential were indistinguishable from a logical possibility.”

So no, the only idiocy here is yours, thanks to your ever-reliable inability to think beyond the six or seven words you have at your disposal to talk about anything whatsoever. Thanks too for affirming beyond doubt that you take the entirely wrong view of how to understand the problem of relationally here. 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 please, don’t let that stop you from trying to continually jam your misshapen pegs in to spaces where they don’t fit.

As for me occasionally adopting the parlance of Bateson and the cyberneticists - yeah, I do actually recognize the usefulness and importance of such concepts, when taken in certain contexts. However I'm not so fool as to pretend that they constitute anything close to a reasonable metaphysics, and I'll be the first to tell you that they are only useful within a very limited and circumscribed domain of application. And besides, if we're simply 'talking about the same thing with different jargon', then one wonders about the pathetic arrogance of your introduction to thread by declaring that the OP is 'a dangerous pipe dream' which is 'particularly wrong headed'. Perhaps the vacillation is function of your literal inability to understand most anything of what's going on here coupled with the need to preach your gospel despite it's utter intellectual poverty.

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.

I don't recall my calculus well, but so far as I know, the derivative still uses the function-argument schema, and I'm not sure what you were trying to say about it: the dx/dy are essentially notations for explicitly binding variables. The rate of change with one value w.r.t. another still just means, if the argument were to change 'infinitesimally,' how the value would change, and then extrapolating from that.

I should also note that none of this is particularly 'out of the box': the sciences have been operating in this domain for decades, and continental philosophy has never taken predicate logic seriously. I would suggest instead that the whole institution of formal logic has on the contrary 'boxed itself in', playing formal-logical games without actually attending to the world about it. — StreetlightX

I think the general continental illiteracy with modern technical advances in logic is unfortunate. Even if there are metaphysical qualms, it's a useful skill to have, and has lots of applications in computer science and linguistics and so on.

I don't recall my calculus well, but so far as I know, the derivative still uses the function-argument schema, and I'm not sure what you were trying to say about it: the dx/dy are essentially notations for explicitly binding variables. The rate of change with one value w.r.t. another still just means, if the argument were to change 'infinitesimally,' how the value would change, and then extrapolating from that. — The Great Whatever

The issue is that much like the quantum formalism, there are differing interpretations of the differential, and the general attitude in math is mostly 'shut up and calculate'. While Newton and Leibniz - who 'discovered calculus' - appealed to infinitesimals to explain the efficacy of the calculus, modern interpretations like the epsilon-delta method get rid of any such notion and appeal to the idea of limits instead. Basically the e-d method gets rid of any reference to geometry. There is also non-standard analysis, which formalizes the notion of the infinitesimal, but there's lots of people who're are pretty sus about it.

Deleuze sits somewhere in the middle here. He refuses the turn to either infinitesimals and limits to explain the differential, and instead argues that the differential must differ in kind from the numbers that make up the primitive curve; negatively, the differential is not another number. Positively and specifically, the differential must be productive and generative of the primitive curve, and indeed, of number more generally. So while infinitesimals posit the existence of 'really little numbers', and limits do away with any reference to such numbers, Deleuze - whose reading is indebted to Jean-Baptise Bordas-Demoulin and Hoene-Wroński - instead reads the differential as determining the behaviour of the curve around a singularity. Singularities are points at which the curve changes it's overall behaviour: generally a change in the value of the slope of the curve (from positive to negative, or from either one to zero and back again, for example)

What's important about this is that the differential no longer simply corresponds in a one-to-one manner with a value on the primitive curve. Rather, what's important is that the differential determines the overall character or quality of the curve. Here's Evens: "This is the sense in which the differential is a universal: the differential packs into each point the nature of the entire function, for the differential relation generates not the value of the function, but its behavior, its character, what the function is doing at each point. It’s not that the differential relation represents the slope of the function at each point; it’s that by representing the slope of the function at each point, the differential relation presents or characterizes the whole function in each of its points... The differential relation captures... how many times [the primitive function] changes direction, how many bumps it has and how regularly they occur, how often it becomes infinite, and how often it crosses the x-axis." (my emphasis).

The point - after this long digression - is this: the differential - interpreted thusly - is not a matter of binding variables. On this reading, it is explicitly the opposite of that. Evens again: "In other words, the differential relation is not a formula that relates x to y over some range of values for x, though this is how we are taught to interpret it: in school, the differential relation, or derivative, is just another formula, another function akin to the primitive function. Rather, the differential relation relates x to y not in breadth, over a range of values, but in depth; it operates in each point on the function, condensing the quality, the character of the entire function into every point... In fact, if you know the values of all the derivatives of a function at a given point, you can construct a polynomial, another function, that is equivalent to the primitive function near that point."

This universality of the differential - the fact that it determines behaviour over singular points rather than explicit values in a one-to-one manner - is why Deleuze will explicitly set this understanding against any which would take the differential to be a matter of a general formula generating particular values: "The relation dy/dx is not like a fraction which is established between particular [values], but neither is it a general relation between variable algebraic magnitudes or quantities. Each term exists absolutely only in its relation to the other: it is no longer necessary, or even possible, to indicate an independent variable. ... The zeros involved in dx and dy express the annihilation ... of the general as well as the particular, in favour of the universal..." Anyway, I hope this hasn't gotten too technical, and I'm kind of writing on the edges of my math knowledge as well, but I hope it constitutes something of an answer to your concern here.

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.

So, to illustrate, suppose you had 4x^3 + 3x^2 + 2x + 1 to describe motion, distance v. time. Your derivatives for the velocity, acceleration, and jerk would be as follows:

1) 12x^2 + 6x + 2
2) 24x + 6
3) 24

At each derivative, you lose a piece of information, and clearly there is no way to construct the original function from just 24, or from any intermediate step. For '24' erases the y-intercept of the linear function that comes before it, but this intercept is crucial for determining the character of the original function: that's how you get to the 3x^2. So from each derivative you can reconstruct part of the previous function, and less and less of it at each successive stage. You won't be able to tell how fast something is moving from '24,' nor where it should be located at each moment in time.

The original function, however, can be stated independently of the derivatives.

You can actually use a Taylor series to reconstruct a primitive curve (locally, around a singularity) with a single derivative. I couldn't tell you the details, but that's what the paper is referring to.

As for the derivative, you have to remember that we're speaking about dy/dx under the double condition that dy/dx = 0/0, AND dx > 0. That's what at stake here, not just the derivative of any particular function.

You can actually use a Taylor series to reconstruct a primitive curve (locally, around a singularity) with a single derivative. I couldn't tell you the details, but that's what the paper is referring to. — StreetlightX

Without knowing the original function? In Taylor series the first element f(a) is the most important one in reconstructing the function - has the biggest effect, and then successive terms have lesser effects, the farther down you go with the derivatives. And anyway, Taylor series are useful to approximate and work with functions which have an infinite number of derivatives. Like e^x for example. Or sin(x) or such functions. Definitely not polynomials.

So TGW is right that you can't reconstruct unless you have the original function. The procedure of integrating gives you a range of possible functions and doesn't "zoom-in" to the correct one, you need to know additional information to get that.

I've been dealing with this same problem for a client of mine actually in that some operations cannot be re-constructed backwards. Like my client uses rounding in the calculations of net salaries for his employees. He wants my database to back-calculate for a net salary given by him to give the gross salary, before taxes.

So say I have something like: Gross Salary - Round(Gross Salary*Tax1) - Round(Gross Salary*Tax2) etc. = Net Salary

If I give a Net Salary, I cannot back-calculate a Gross-Salary without error because I cannot take the rounding into account. When you round a value you round an entire set of possible values to a single value. 3.35 and 2.95 all round to 3 for example. It's the same with integration or taking derivatives. Thus it is impossible to get back to the original value that you rounded. There is no "unround" process.

I don't understand Taylor series, but I'd still be curious to know what's to be said about the simple linear example. Doesn't a derivative of '3' determine an infinite class of linear functions, one for each y-intercept?

Edit: no, I get it. You would need to know one point of the line plus its slope for the series to get off the ground, and this uniquely determines a line. But then in this case it's trivial, since knowing this is tantamount to knowing the original function.

Without knowing the original function? — Agustino

I think, for the series, you must know the value of the function at some point, not the function itself. But then you have to know the derivative values at that point, and so on down the line.

I think, for the series, you must know the value of the function at some point, not the function itself. But then you have to know the derivative values at that point, and so on down the line. — The Great Whatever

Yes that would obviously be sufficient if you're only integrating once.

The point is that you only need to know the value at some point for the multiple integrations, not the function itself.

The point is that you only need to know the value at some point for the multiple integrations, not the function itself. — The Great Whatever

Yes, but you'd have to know one value from each derivative. Say I start with f(x) = 3 and the function I'm looking for is 3 integrations up. First integration I need one point on the line 3x+C1, which will enable me to find C1. Second integration I need one point on the curve 3/2 x^2 + C1*x + C2. And so on. Or if not I need as many number of points as the number of integrations I perform to get to the mother function that I'm looking to find.

I don't understand Taylor series, but I'd still be curious to know what's to be said about the simple linear example. Doesn't a derivative of '3' determine an infinite class of linear functions, one for each y-intercept? — The Great Whatever

To understand Taylor just follow the formula. Take an easy second degree order equation:

f(x) = 2x^2+3x+2
f'(x) = 4x+3
f''(x) = 4
f'''...'(x)=0

Say you don't know anything about what the function is. All you know is that f(0) = 2, f'(0) = 3, f''(0) = 4, and f'''(0) and further equal 0. You could also know f at any other point - say you knew f(2), f'(2), etc.

Now, taylor says that the function can be approximated at a certain point by f(a) + f'(a)/1! * (x-a) + f''(a)/2! * (x-a)^2 + f'''(a)/3! * (x-a)^3 + .... and so on where a is any number in the domain of the function

For simplicity pick a = 0;

f(0) + f'(0) * x + f''(0)/2 * x^2 = 2 + 3*x + 4/2*x^2

Is this the original function? Yes. So using the Taylor series, if you have one piece of information at each level you can reconstruct an estimate of the function. For polynomials, because derivatives all become 0 after a certain point, Taylor gives an exact answer. But for a function like sin(x) it doesn't because the derivatives go to infinity.

Yep, I've got it. So the question is the extent to which having a value for one argument for each level is comparable to knowing the original function to begin with, or what conceptually this buys you.

Yep, I've got it. So the question is the extent to which having a value for one argument for each level is comparable to knowing the original function to begin with, or what conceptually this buys you. — The Great Whatever

What do you mean? Are you asking what the use of Taylor series is? Or?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

No, just wondering how SX wants to make use of it.

But then he doesn't get the need to remain dichotomous. — apokrisis

This "need" you refer to must be justified, or else it's not a need at all, just an assertion. Any such dichotomy is artificial, created conceptually, for a purpose. So your "need" only exists in relation to a particular end (necessary for the sake of...). You may claim that there can be no knowledge or understanding without dichotomy, and this may be justifiable, but it does not produce the conclusion that there can be no existence without dichotomy. 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Maybe you can do better?

Becoming is a particularly hard thought to think. So hard, in fact, that at almost every point is it subordinated instead to 'Being'. This is particularly the case when becoming is thought of as simply another word for 'change'. But to think becoming as change is to more or less forget the specificity of becoming altogether. Why? Because to assert the primacy of becoming is precisely to assert what we might call becoming without terms. That is, it's not that one 'thing' becomes another 'thing'. Thinking of Becoming in this way just reverts back to thinking in terms of Being (becoming here is subordinate to 'things', which are primary). If becoming has any cogency at all, it must not be thought of as occurring between two terms, but as a concept self-sufficient unto itself. — StreetlightX

If being is thought in its ontological (temporal) sense, then it simply is becoming. In the temporal sense, being that does not become, does not process or change, is simply unthinkable.

It is when being is considered logically, when the question "What is it that becomes or changes' is asked; that the question of formal (atemporal or absolute) identity is raised; and it is precisely here that there seems to be a dichotomy between being and becoming.

Being is the eternal perspective and becoming is the temporal perspective. They do not contradict one another because they are incommensurable perspectives proper to different contexts. It is when we try to think the two together, try to think of something becoming something else and yet remaining itself that we are faced with paradox. This paradox is a chimera that arises due to a failure to understand the limited contextualities of the ideas of change and identity, of similarity and difference.

So, I agree with you that becoming is a concept "self-sufficient unto itself", but only if the question of identity is kept out of consideration. But, as such it is an eminently vacuous, and even incoherent concept, however self-sufficient it might be. Of course the same might be said about identity (being) considered without becoming. So, I think we must be content to shuttle back and forth from one to the other, and turn a blind eye to the merely apparent aporias, aporias that only arise when we try to unify two wholly incompatible concepts. Why must we demand that all our concepts be compatible? Is good compatible with evil, for example?

But dichotomies are justified logically. — apokrisis

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?

And yet, if it works, it works. — apokrisis

Whether or not it "works", is relative. Walking "works" for getting us places, the horse "works" for getting us places, so does the boat, the train, the car, and the plane. Some of these work better than others, but the others still work. Depending on where you want to go, some of these will not work to get you there at all, though they'll still work to get you places.

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. — apokrisis

I don't understand how you can claim a dichotomous holism. That appears to be self-contradictory.

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

And I don't understand what you mean by "crisp existence". The way that you use "crisp" leads me to believe that crispiness is artificial, produced by the mind which dichotomizes. What leads you to believe that existence itself is crisp?

What I'm asking is to ground the dichotomy in ontology, rather than to base your ontology in dichotomy, simply because dichotomy is logical. — Metaphysician Undercover

What could that possibly mean? If you start from monistic assumptions then you will never accept a dichotomy as being ontologically robust.

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.