You have a "____" there. Are you saying that the "____" is nothing, in an absolute sense? I don't think it is. Clearly it signifies something, just like if you had a word there. The only difference is that the ___ provides a higher degree of vagueness than the word.


It is due to the nature of time, that relations are always becomings. Relations are changing in time, that is fundamental to relativity theory. A static, and therefore eternal relation, would belong to the category of being. But such a relation would be outside of time, so we can dismiss that relation as unreal.

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

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

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

Are you saying that the "____" is nothing, in an absolute sense? — Metaphysician Undercover

It is not anything in particular; i.e., it need not be something that actually exists. The relation is real apart from any individual relata.

The only difference is that the ___ provides a higher degree of vagueness than the word. — Metaphysician Undercover

Hmm, maybe you are finally starting to catch on. The relations as I formulated them are general, rather than singular.

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

&

But it is confusing to now talk to individuation (or particularisation, or contingent being) as "singularity" when singularity was instead some kind of claim about monism over dualism or triadicism (who knows what SX really thought he meant).

I'm even more confused now. I can understand your thinking that I'd shifted the goalposts, if, earlier, we had both been speaking of singularity qua monism (rather than the singularity of any particular thing.)

But then what was this:

Think again about the reciprocal argument. Note the 1 that gets employed. We are saying in effect, whatever is the thing we have in mind, let's start by calling it a singular one, a pure standalone whole.

Now this singularity is ill-defined. And yet we can give it complete definition by saying whatever it is, it is the y that is the 1/x.

&

We call whatever the hell this is, this thing we call the singular X, now a mathematical 1. A unity or whole ... despite the fact that it is only the vaguest 1. It is the oneness of whatever the hell might be the case.

So that is where singularity enters the picture. And we can define X now as 1/Y ... Y being a second singular that feels most like the pure antithesis of X.

Weren't you talking, literally, about any thing at all? And wouldn't that include complex negentropic objects? & The problem with my discussion of singular objects is it that's not general enough [for what]? And the method-of-generating-complete-definitions of any thing at all we may have in mind - that doesn't work with complex negentropic objects?

Again, I get what the whole 1/x thing for Being/Becoming etc, but I still haven't the foggiest how it's being applied to singular things (which is especially troubling if, as you say, this is precisely how all natural scientists progress. I'd still love if you could sketch a quick example of how this plays out. Since, as you say, this kind of thing is ubiquitous, wouldn't it be easy to do this?)

(I'll respond to the second half of your post in another post)

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

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

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

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

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

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

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

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

So time has an outside! — apokrisis

No, that's why I said that we can dismiss this idea as unreal. I said, such a relation would be outside of time, therefore we can dismiss it as unreal. We have not established any premise whereby we can assume the existence of anything outside of time. Doing such, with the premises and conclusions that we have, is completely unjustified and unwarranted, it's nothing more than an excursion into fantasy.

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

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

Becoming seems more like that which changes, lives or is present, than a movement from here to there.

Indeed, becoming is sort absent in reflective discourse; it only picks out two states which have no more change to undergo. If we point out X had changed to Y, we aren't referring to something which becomes, but two moments captured in suspension. The X we talk about goes nowhere else. The same is true of the Y.

Becoming is necessarily a relation because it involves a distinction. To become means something is in realationship to other things-- a boundary of object, change and presence-- even when it's not made explicit or sorted into specific catergory. The moment anything is, becoming is so. It's not a thing of existence, but an expression given by anything that exists.

Ok, but even if you were speaking about metaphysical generality, I still don't understand what you're doing here:

We call whatever the hell this is, this thing we call the singular X, now a mathematical 1. A unity or whole ... despite the fact that it is only the vaguest 1. It is the oneness of whatever the hell might be the case.

So that is where singularity enters the picture. And we can define X now as 1/Y ... Y being a second singular that feels most like the pure antithesis of X.

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

That doesn't make any more sense to me than the pure antithesis of Ollie.

But what prevents more general notions of relation that exist outside such contraints? — apokrisis

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

How can we speak of time with any counterfactal definiteness and particularity if we can offer no story on how it stands "other" to some suitable context? — apokrisis

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

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

Becoming is necessarily a relation because it involves a distinction. To become means something is in realationship to other things-- a boundary of object, change and presence-- even when it's not made explicit or sorted into specific catergory. The moment anything is, becoming is so. It's not a thing of existence, but an expression given by anything that exists. — TheWillowOfDarkness

But the op asks us to consider the primacy of becoming. This means that we must reject this idea that "becoming is necessarily a relation", because "becoming" expressed in this way logically excludes the primacy of becoming. So "becoming" as "necessarily a relation" is not the same "becoming" which is referred to by the op.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

On the contary, the OP is arguing becoming is necessarily a relation. The point is how we think about relation is frequently flawed. Rather than a secondary feature, formed out specific judgement, relations are actually primary. For anything, from the moment it is, it is of becoming and in relation. Becoming is necessary a relation and also primary.

Becoming is necessary a relation and also primary. — TheWillowOfDarkness

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

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

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

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

There's nothing intrinsically 'taller than' about Peter, but there is something intrinsically 'taller than' about the dyad <Peter, Paul>. Increasing the number of substances by one doesn't seem to change anything. — The Great Whatever

This is a valid move I think, but I also think that it comes with a trade off, which is precisely to give up thinking about relations. That is, it's possible to translate: "Peter is taller than Paul" to: "Peter being taller than Paul is a property of the dyad <Peter, Paul>", but at this point, you've lost the specificity of relationality. I mean, if you expand this 'translation strategy' to include the whole universe (that is, if you take any relation that <Pr,Pl> might enter into and then make that a property of a larger dyad and so on ad infinitum), you'd end up with something like a set U with elements (x,y,z) where each element is a relation-turned-into-a-property like (<P,P>(P>p)). Not unlike - or pretty much exactly like - a Leibnizian monad.

But the whole point is to think relation outside or beyond the subject-predicate model such that - to use the Deleuzian phrasing - 'relations are external to their terms'. I think that terms can always 'co-opt' relations in precisely the way you've proposed, but in order to secure the autonomy of relation, one ought to resist that kind of move. Of course at this point I'm not trying to adjudicate between the 'two paths', as it were, but just exploring where this particular one might take me.

Sorry it's taken a while to reply, yours was a great reply which I had to think about a bit and I've been a tad busy recently.

Weren't you talking, literally, about any thing at all? And wouldn't that include complex negentropic objects? & The problem with my discussion of singular objects is it that's not general enough [for what]? — csalisbury

General enough to fit into the artificial coordinates of his 'system' of course. The whole thing is a kind of watered-down Hegelianism: if the singularities don't fit the system, simply throw away the singularities. There is simply no 'place' in Apo's 'system' to accommodate the singular: it - and consequently he - cannot think in terms of the specificties of a given, concrete situation because the whole thing is designed to 'level' singularities and subject them to a (general) order of equivalence in order to render them into particulars. That's why you never actually learn anything from Apo's posts except how the system itself works - it's a self-referential mess that basically ends up talking about itself more than the phenomena it supposedly accounts for. Hence also their mind-numbing monotony.

It's what Deleuze speaks of in the opening pages of D&R, where he specifically points out how such conceptions render themselves blind to both the singular and the universal:

"There is no reason to question the application of mathematics to physics: physics is already mathematical, since the closed environments or chosen factors also constitute systems of geometrical co-ordinates. In these conditions, phenomena necessarily appear as equal to a certain quantitative relation between the chosen factors. Experimentation is thus a matter of substituting one order of generality for another: an order of equality for an order of resemblance. Resemblances are unpacked in order to discover an equality which allows the identification of a phenomenon under the particular conditions of the experiment. Repetition appears here only in the passage from one order of generality to another, emerging with the help of - or on the occasion of - this passage.

... However, If repetition exists, it expresses at once a singularity opposed to the general, a universality opposed to the particular... It puts law into question, it denounces its nominal or general ... In its essence, repetition refers to a singular power which differs in kind from generality, even when, in order to appear, it takes advantage of the artificial passage from one order of generality to another."

In first-order logics, properties are in fact just treated as relations: they're just relations of a specific arity (1). What I am trying to see is how the change from an arity of 1 to 2 changes anything, or removes dependence on the 'terms' or 'individuals' that take part in properties and relations.

Peter being taller than Paul isn't, I would say, a property of the dyad <Peter, Paul>. Perhaps I would say that the dyad takes part in the relation 'taller than,' or that this relation is true of, or holds of, <Peter, Paul>. 'Taller than Paul' is a (one-place, intrinsic) property of Peter, of course.

What does it mean for a relation to be external to its terms, in a way a property isn't? If I think of a property as a set of individuals, those individuals of which the property is true, and think of a relation as a set of ordered pairs of individuals, then it seems they depend in the same way upon the relevant individuals, it's just that one involves one individual, while the other involves two.

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

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

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

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

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

Oh there's the paradoxing. So predictable.

On the contary, the OP is arguing becoming is necessarily a relation. — TheWillowOfDarkness

No I don't think that's the case. Look closely at how the relation between becoming and relation is described in the op. Relations are said to "belong" to becoming. It also puts relation in "the domain of becoming". And says that relation "implies" becoming. This means that relations are becomings, but there is nothing to indicate that becomings are necessarily relations.

So I think this is the way that we are supposed to be looking at "becoming" here, such that it is the broader category than "relation", therefore a becoming is not necessarily a relation. This is the only logical way that we can give primacy to "becoming", because relation is necessarily a relation between things. So if becoming is necessarily relation, then we would give primacy to the things being related.

Peter being taller than Paul isn't, I would say, a property of the dyad <Peter, Paul>. Perhaps I would say that the dyad takes part in the relation 'taller than,'... — The Great Whatever

Interestingly, this was almost exactly Plato's solution: to posit the (supersensible) Idea of the Small and the Idea of the Large which things could 'participate' in - as in, to say Peter is taller than Paul is to say Peter participates in the Idea of the Large in relation to Paul and that Paul participates in Idea of the Small in relation to Peter: but of course this just kicks the problem down a level because this 'taking part' or 'participating in' is itself a relation - and it's no good to account for a relation in terms of a relation.

This is why I think relations are troublesome: either one erases their specificity by treating them as a property, or one ends up recoursing to some Platonic notion of Participation which just makes the whole thing mysterious to begin with. The upshot of treating relations as external to their terms, on the other hand, is to grant relations a kind of autonomy with respect to their terms, or rather, it reverses the relation: rather than the relation being defined by it's terms, terms themselves become defined by their relations. This is the link between relations and becoming: if understood on this model, a change in a relation would imply a change in the relata (rather than the other way around): "If relations are external to their terms, and do not depend on them, then the relations cannot change without one (or both) of the terms changing. A resembles B, Peter resembles Paul: [if] this relation is external to its terms, it is contained neither in the concept of Peter nor in the concept of Paul. If A ceases to resemble B, the relation has changed, but this means that the concept of A (or B) has changed as well. If properties belong to something solid, relations are far more fragile, and are inseparable from a perpetual becoming" (Dan Smith, The New).

One way to cash this out a little more solidly is - as Deleuze does - is to turn to the differential (dy/dx) in differential calculus as a model for a "pure relation" without terms that is at the same time generative of the curve or solution-series which it is the (supposed) 'derivative of'. I won't go too far into this as it's perhaps a bit more math-y than is necessary for a general discussion, but if you have access to Academia.edu, check out Aden Evens's paper on this: https://www.academia.edu/1084825/Math_Anxiety ; long and short of it is that one can look to calculus as model for what it would mean to have a relation without relata, and which also plays the function of generating relata (quick quote for preview's sake: "the differential relation, dy/dx precedes the “primitive” function whose slope it is said to represent. In calculus class we are presented with a function and told to differentiate it, to take the derivative or produce the differential relation. In Deleuze’s rereading of the calculus, the primitive function does not precede the differential relation, but is only the ultimate result or byproduct of the progressive determination of that relation.The differential is a problem, and its solution leads to the primitive function".)

This is why I think relations are troublesome: either one erases their specificity by treating them as a property, or one ends up recoursing to some Platonic notion of Participation which just makes the whole thing mysterious to begin with. The upshot of treating relations as external to their terms, on the other hand, is to grant relations a kind of autonomy with respect to their terms, or rather, it reverses the relation: rather than the relation being defined by it's terms, terms themselves become defined by their relations. This is the link between relations and becoming: if understood on this model, a change in a relation would imply a change in the relata (rather than the other way around): "If relations are external to their terms, and do not depend on them, then the relations cannot change without one (or both) of the terms changing. A resembles B, Peter resembles Paul: [if] this relation is external to its terms, it is contained neither in the concept of Peter nor in the concept of Paul. If A ceases to resemble B, the relation has changed, but this means that the concept of A (or B) has changed as well. If properties belong to something solid, relations are far more fragile, and are inseparable from a perpetual becoming" (Dan Smith, The New). — StreetlightX

This is what relativity theory does, and how physicists come up with "energy". Motion is an expression of relations, and energy is an expression of the motion. Objects are defined by their energy, which is really an expression of their relations. Since the "energy" is seen as the important aspect, we can focus directly on that, and actually lose track of the relata themselves. But I don't think that the suggested logical process in this passage is sufficient to get to the "primacy of becoming". The problem is that this "thing" which is created, the relation itself, or in the case of physics, the energy which is an expression of the relations, is itself artificial. It is a concept derived from relations and therefore there is an inherent reliance on the existence of the relata for the validity of the concept "relation".

To build a concept of "relation" and then remove the relata is inadequate if the desire is to produce a concept of "becoming" which is not dependent on the existence of relata. That is because the concept of "relation" is produced from observation and documentation of the existence of the relata. The concept "relation" is produced with this purpose in mind, it is meant to represent this. It is grounded in this, and it is valid only on this grounding. If we desire to pull out the relata, and have the "relation" stand alone, we no longer have any grounding of the concept.

This is the problem with apokrisis' "symmetry-breaking". This position is an attempt to bring the relation "symmetry-breaking" into a stand alone position, prior to the existence of the relata. But the basic concepts employed here, energy, and relativity, were not meant to be used in such a stand alone position. So when the relata are removed, the concept must be grounded in something else. Now we have the necessity of "symmetry" which is logically prior to symmetry breaking. But this symmetry can be nothing other than an eternal object, like what is found in Parmenidean Being, or Pythagorean idealism. Now the whole exercise, which was to establish the primacy of becoming has failed.

What is evident is that our understanding of "becoming" here, has not even approached the level professed by Aristotle through his cosmological argument. I think that focusing on "relation" is the wrong approach, because "relation" is inherently grounded in the existence of the relata. We have no way to get from the concept "relation" to the other side, which is the non-existence of the relata, and this is what is necessary in order to understand the "primacy of becoming". We must focus on the nature of "becoming" itself, free it from the concept "relation".

Notice that in the case of "becoming", Aristotle gave exception to the law of excluded middle. We can take this to indicate that the two opposing terms which are essential to the concept "relation", become irrelevant in "becoming". We must completely free ourselves from the confines of such terms. That demonstrates how different "becoming" actually is from "relation". It is the "becoming" which may or may not create the terms, rather than the terms which define the "relation". I think we must be prepared to completely dismiss all terms of logic and mathematics, to understand the "primacy of becoming". That is why this route is prone to drawing one into mysticism. We might look into it, but maintain your footing because you wouldn't want to slip right in. Or would you?

this 'taking part' or 'participating in' is itself a relation - and it's no good to account for a relation in terms of a relation. — StreetlightX

terms themselves become defined by their relations — StreetlightX

This is possible, but I'm not sure what it buys you. For example, one can 'Montague-lift' an individual, to turn it into what's called a 'generalized quantifier -' that is, the set of properties true of that individual (which includes its relations to other things - these being properties once you saturate the first term). In fact, the originator of the device, Richard Montague, proposed that the meaning of say a proper name is not the individual which it denotes, but rather the set of properties that individual bears.

You could also create a logic in which properties are primary and individuals are secondary, reversing the role of function and object we've had since Frege. But I think ultimately this is a terminological quibble and it's unclear to me how it genuinely rephrases the problem. The point is that properties and individuals interact in a certain functional way: whether one takes individuals or properties/relations as fundamental probably won't change that.

"If relations are external to their terms, and do not depend on them, then the relations cannot change without one (or both) of the terms changing. A resembles B, Peter resembles Paul: [if] this relation is external to its terms, it is contained neither in the concept of Peter nor in the concept of Paul. If A ceases to resemble B, the relation has changed, but this means that the concept of A (or B) has changed as well. If properties belong to something solid, relations are far more fragile, and are inseparable from a perpetual becoming — StreetlightX

I still don't understand the special status granted to relations here. Again, a property is a relation, just with an arity of 1 rather than 2, and everything said about it here could be said of properties as well.

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

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

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

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

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

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

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

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

Again, a property is a relation... — The Great Whatever

I agree, to some extent, with apokrisis here, we cannot say that a property is a relation, because the relation is actually something else. We can say as apo does, that the property is related to the object in some way, such as habituation, or we can say that the property is related to the subject by predication, depending on how you categorize "property". In either case, the property is not the relation itself, the relation is some form of activity.

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

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

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

This is possible, but I'm not sure what it buys you. For example, one can 'Montague-lift' an individual, to turn it into what's called a 'generalized quantifier -' that is, the set of properties true of that individual (which includes its relations to other things - these being properties once you saturate the first term). In fact, the originator of the device, Richard Montague, proposed that the meaning of say a proper name is not the individual which it denotes, but rather the set of properties that individual bears.

You could also create a logic in which properties are primary and individuals are secondary, reversing the role of function and object we've had since Frege. But I think ultimately this is a terminological quibble and it's unclear to me how it genuinely rephrases the problem. The point is that properties and individuals interact in a certain functional way: whether one takes individuals or properties/relations as fundamental probably won't change that. — The Great Whatever

The point of much of this is to see how one would approach concepts from the point of view of genesis: that is, if we don't take for granted the individuality of any-one-thing and instead try and approach from the point of view of things-coming-into-being. From such a perceptive, basically the entire edifice of formal logic is more or less inadequate to the task, precisely because it can only 'think' in terms of a subject-predicate coupling, and consequently, in terms of the already-individuated. The very form of thought that it engages in is compromised. As such, it's not enough to 'swap' the priority from individual to property, which simply keeps the form in place while reversing out the contents, as it were. Every time a relation is treated as a property, one gives up on thinking relation.

From the point of view of genesis and individuation, to say something like: "The point is that properties and individuals interact in a certain functional way...", is basically anathema. There's no point in beginning with your set of properties, and your set of individuals, and then combining and breaking them apart, lego-like. Doing this takes for granted individuation, and no amount of combinatoric cleverness will ever attain the point of view of genesis.

Alright, sure. I guess it's not clear to me what's at stake or what you want, but I can sympathize with thinking outside of an established framework. It still doesn't make clear to me what is special about a relation that we cannot also say about a property, though, which is where your OP began.

Also, if you believe Plato, anyway, the becoming-privileging view, where relations precede individuals, is far more ancient than the substance view. It probably has mythological precursors as well. I'd be inclined to think about it in terms of suffering, but that's just me.