there still needs to be enough commonality between your meaning and my meaning of a given word for us to understand one another. — Olivier5

So...

sufficiently similar for my purposes. — Isaac

...then

... then. — Isaac

Then, you need to think in terms of meaning, not just glyphs.

Then, you need to think in terms of meaning, not just glyphs. — Olivier5

I have no idea what you mean by this.

You said...

There is likely very little difference between what you conceive as Pi and what I conceive as Pi. Nevertheless, there will always be one guy or another out there who has a different conception, e.g. who thinks that Pi is equal to 3, or that it's a rational number.

Therefore the term "universal" is not really correct, even for Pi. I guess the word "concept" is better here, as it expresses the possibility of a personal or personalized concept, whereas a "universal" cannot logically be "personal". — Olivier5

Which is precisely what I've been saying (and you've been arguing against) all along. Same's true of triangles, spellings, numbers, letters and every other damn thing you've raised these last God knows how many posts in opposition to my making this exact point.

Indeed you made a similar argument and I did recognise the limits of the term "universal" but that does not imply that no such thing exists as concepts or ideas and their abstract meaning... It just means that concepts, while being "universal enough" within the folks speaking a given language for the language to work, do not need to have exactly the same meaning across that population. Slight variations may apply to their boundaries, that's all.

You must still think in terms of the meaning of letters, words, and sentences if you care to understand language. And this meaning is not to be found in the letters or in the words themselves (which are arbitrary symbols). This meaning is often not about any individual thing, but about sets of things (e.g. "I don't like cats"), and relations between sets of things (e.g. "Dogs often don't like cats"). Thinking involves spotting and constructing generalities.

Take the example of the number Pi, defined as the constant obtained by dividing the circumference of any circle by its diameter. The number Pi is a concept, an abstraction, and it is different from the many ways one can in practice write down "Pi".

Does the number Pi exist? I don't know, not even sure the question has a meaning other than the trivial: "some people conceive of the number Pi".

Can we compute Pi? Not exactly.

Is it useful? Certainly yes, Pi is a very useful concept, in spite of its value being forever an estimate.

This is all fair enough, but the matter at hand is the existence of non-physical objects. The key factor here is that nominalism allows for each of these concepts to be exactly the neurons on which they are coded in each individual's brain. A different entity in each brain, just very, very similar to each other example. To require a non-physical stuff you need a true universal, something which cannot reside in each individual's brain because it is mind independent, so identical in each instance that it is one entity (law of identity), which means it cannot reside in each person's brain (otherwise each instance would have a different location and so be a separate thing).

If what you're arguing for is concepts which are very, very similar yet still reside in each individual's brain, then there's no argument for non-physical matter and so no necessity for dualism. I have not and would not deny the existence of concepts. Contrast that with someone like Wayfarer who actually thinks there's an existent form for numbers etc outside of the individual minds for whom it is a concept - a proper dualist.

I have not and would not deny the existence of concepts. — Isaac

Okay then. Concepts have some ontological status, we agree, at least as "subjective approximations of absolutes residing in people's mind".

I like to define a concept as a set. There are fuzzy sets/concepts and neat ones. A well defined concept is a well defined set. But there is always a residue of ambiguity in human concepts. Witty said it best: concepts have fuzzy boundaries. Which is why they are often difficult to define precisely: they are not precise objects but categories of objects with many borderline cases.

Mathematical concepts are a bit better defined. Pi is a concept that any averagely intelligent student is expected to grasp in a rather precise, operational manner. They might ask: What's the circumference of the trigonometric circle? If she answers "a little more than 6", it's technically correct but not mathematically satisfying. The answer can be exact (2*Pi) so it needs to be exact. The concept of Pi is mathematically precise.

Of course, nobody will ask her: where does Pi reside: in the pure realm of eternal mathematics, in physical circles, or in your head? My answer to that question would be: why choose? Can't it be in all three?

If concepts are "subjective approximations of absolutes residing in people's mind", doesn't it follow that the absolutes which concepts approximate, these absolutes also exist, at least as "limits" or "directions" or "horizons" of human thought?


Once you start to learn trigonometry, you have to agree that 1) there exists the concept of circle (as a concept in people's minds); 2) physical circles exists, that approximate the concept; 3) the human mind can forge additional concepts that are useful for thinking about circles and measuring them, such as the number Pi; 4) etc. etc... It may be okay to remember all these caveats ("in people's minds") for whatever metaphysical reason, but it is heavy. Very soon, you find yourself speaking of Pi as if it was a real number...

Pun aside, it is more convenient theoretically to forgo the realist caveats, or just suspend them temporarily while learning trigonometry. Just assume numbers exist, Pi exists, and perfect circles exist. It may take a leap of faith, but it's worth it as it makes for easier, less encumbered learning. And what do you got to lose anyway? If they poke fun at you for "reifying Pi", send them to me.

As you said: une façon de parler, mais utile!

If we take a mathematical example, I think we can agree that the number Pi (singular) is not "physical" in the sense that it is not an individual thing out there that people can see or take in their hand, and that the number Pi is therefore an idea. But we can also agree that it is a very precisely defined idea that leaves very little room, if any, for personal interpretation. — Olivier5

Insofar as it translates from linear things like radii to radial things like circle circumferences, pi is pretty important to us, but it's just another real number, one of a category of things we can talk about, in particular an irrational number, something we had to talk about not because the idea revealed itself to the chosen, and certainly not because it is a priori (as a species we've gone most of our existence without any concept of it, something I'm sure that rationalists would opportunistically take as a win for their team), but because of music and astronomy, the study of physical things.

The interest in geometry comes ultimately from defining categories of things in the real world. Circles are all around us, from observations of the Sun and the Moon, to the invention of the wheel which predates Euclid, Archimedes and Pythagoras by millennia. None are perfect, but their _average_ is. Dealing with the category of circles, taking perfection -- the average shape of a circular thing irl -- as a symbol of any referent (generalisation), was a way of making predictions about physical objects and processes (how long does my bike tyre need to be if my wheel radius is R?). Taking this category, or its symbol, to be more fundamental than the real things seems back-to-front to me. It would be like defining all the hues if blue as some imperfection of the more or less arbitrary category of blue.

Dealing with the category of circles, taking perfection -- the average shape of a circular thing irl -- as a symbol of any referent (generalisation), was a way of making predictions about physical objects and processes — Kenosha Kid

Which is a good thing, right?

(setting aside that circles have a precise conceptual definition, not based on an average of approximate circles)

(setting aside that circles have a precise conceptual definition, not based on an average of approximate circles) — Olivier5

The former doesn't contradict that our experiences of real, imperfect, circular things is prior to our concepts of circles. A perfect circle is precisely what every near-perfect circle we ever see has in common.

our experiences of real, imperfect, circular things is prior to our concepts of circles. — Kenosha Kid

Yes, existence precedes essence. But even if essences (of concepts) are arrived at by successive approximations and refinements of mental and sense experience, it doesn't make them less interesting to precise and refine...

In that sense I agree that precise concepts are not fundamental to our experience. They are derived from it, but in my mind precise concepts are nevertheless useful, and to the degree that they are useful, they aquire reality, if only as useful hypotheses.

it doesn't make them less interesting to precise and refine... — Olivier5

Oh, of course.

In that sense I agree that precise concepts are not fundamental to our experience. They are derived from it, but in my mind precise concepts are nevertheless useful, and to the degree that they are useful, they aquire reality, if only as useful hypotheses. — Olivier5

Agreed, they are real. Really modelled in your real brain.

The key factor here is that nominalism allows for each of these concepts to be exactly the neurons on which they are coded in each individual's brain. A different entity in each brain, just very, very similar to each other example. — Isaac

That cannot be the case. As has already been shown, neural activity shows no such regularities or patterns that can be discerned when the brain is exposed even to a simple stimulus. You're arguing for brain-mind identity, but there is nothing like 'logic' in brains, or 'syntax', or 'symbols', or anything of the kind. Rather, the brain is able to capture such ideas, because of intelligence, whose job it is to identify differences and to represent with abstractions, and so on.

To require a non-physical stuff you need a true universal, something which cannot reside in each individual's brain because it is mind independent, so identical in each instance that it is one entity (law of identity), which means it cannot reside in each person's brain (otherwise each instance would have a different location and so be a separate thing). — Isaac

Which is just what universals are.

Consider that when you think about triangularity, as you might when proving a geometrical theorem, it is necessarily perfect triangularity that you are contemplating, not some mere approximation of it. Triangularity as your intellect grasps it is entirely determinate or exact; for example, what you grasp is the notion of a closed plane figure with three perfectly straight sides, rather than that of something which may or may not have straight sides or which may or may not be closed. Of course, your mental image of a triangle might not be exact, but rather indeterminate and fuzzy. But to grasp something with the intellect is not the same as to form a mental image of it. For any mental image of a triangle is necessarily going to be of an isosceles triangle specifically, or of a scalene one, or an equilateral one; but the concept of triangularity that your intellect grasps applies to all triangles alike. Any mental image of a triangle is going to have certain features, such as a particular color, that are no part of the concept of triangularity in general. A mental image is something private and subjective, while the concept of triangularity is objective and grasped by many minds at once. — Feser

It is largely the very peculiar kind of being that belongs to universals which has led many people to suppose that they are really mental. We can think of a universal, and our thinking then exists in a perfectly ordinary sense, like any other mental act. Suppose, for example, that we are thinking of whiteness. Then in one sense it may be said that whiteness is 'in our mind'. ...In the strict sense, it is not whiteness that is in our mind, but the act of thinking of whiteness. The connected ambiguity in the word 'idea'...also causes confusion here. In one sense of this word, namely the sense in which it denotes the object of an act of thought, whiteness is an 'idea'. Hence, if the ambiguity is not guarded against, we may come to think that whiteness is an 'idea' in the other sense, i.e. an act of thought; and thus we come to think that whiteness is mental. But in so thinking, we rob it of its essential quality of universality. One man's act of thought is necessarily a different thing from another man's; one man's act of thought at one time is necessarily a different thing from the same man's act of thought at another time. Hence, if whiteness were the thought as opposed to its object, no two different men could think of it, and no one man could think of it twice. That which many different thoughts of whiteness have in common is their object, and this object is different from all of them. Thus universals are not thoughts, though when known they are the objects of thoughts. — Bertrand Russell, The World of Universals

Really modelled in your real brain. — Kenosha Kid

Not only in mine, that's the hick. There's a certain universal dimension to concepts. Language depends on it.

Not only in mine, that's the hick. — Olivier5

Didn't we just play this tune though?

What you are saying is that "universals" are not as universal as we may think, their limits are hazy, which is true and indeed an important point in that the verification of universals by interviewing locutors is never perfect. You can always find a guy who disagrees somewhere. — Olivier5

Yes, but more than this: we define demarcations of categories individually. Homogeneity of environment, pedagogy, similar objects of experience, and feedback help to make our models similar, while differences in experience and minor differences in hardware will ensure that no two models are identical. It's like DNA... yours is yours, individual enough to convict you of a crime, but similar enough to mine to make us the same kind of object. — Kenosha Kid

I agree that much too much is made of "universals", that they are not as universal as they seem, and they only need to be sufficiently universal, or somewhat homogenous across individuals, not perfectly equal, like in your example of human DNA. — Olivier5

Didn't we just play this tune though? — Kenosha Kid

Sure. This tune are us, essentially.

So it's being on a plane is not a property of your ideal triangle? — Isaac

If you think about it, being on a plane is implied in the definition. Any three points are always on a plane.

Would a non-euclidean object with those properties still be a triangle? — Isaac

If it’s non Euclidean it wouldn’t have straight edges.

What about shapes matching that description but in non-standard topologies? — Isaac

If it’s not on a standard topology it wouldn’t have straight edges.

They could not simply derive the answers by comparing their new objects to some ideal form — Isaac

False, that’s exactly how they found the answer. They had the ideal form, and checked if a non Euclidean “triangle” can have its proprieties. It can’t. Then they checked if non standard topologies can. They can’t. Etc.

It’s the same thing you do when asked when a square is a triangle or not. You compare the properties of what you’re looking at to the properties of a triangle. You find they don’t match.

So are we mis-naming the things we commonly call triangles? — Isaac

Technically yes.

There's only yours, mine, everyone else's. — Isaac

If someone’s idea of a triangle includes that it is comprised of 4 vertices, don’t we have justification to tell them they’re wrong? From where do we get that justification?

All, no doubt very similar to your ideas, since we share a culture, language community, biology etc. — Isaac

So there is a unified shared idea of a triangle? That’s what I’m saying.

And no “very similar” is not enough. When speaking of geometry, it has to be exact. Or you’ll fail your math test. And if it’s NOT exact we have justification to call that person wrong. Meaning there is some universal standard we all abide by.

There is a reason math is called the universal language.

and plenty of evidence from developmental psychology that we use our own personal models to identity objects, not ethereal universal ones. — Isaac

What you’re debating is the source of the idea of triangle. Either it’s just a shared social thing, or it somehow predated society, and all we did was discover it. I’m leaning towards the latter, but in any case you do admit there is a unified idea of “triangle” that we all (basically) share.

So why can’t the same be said of New York? Or “A”?

As has already been shown, neural activity shows no such regularities or patterns that can be discerned when the brain is exposed even to a simple stimulus. — Wayfarer

It's notable how often you reach for the "you don't understand the philosophy" argument when disagreeing with those who've not read the same texts as you, in a field entirely composed of armchair speculation, yet you seem quite happy to paraphrase the results from a paper in neuroscience as if you understood it without a hint of humility.

I don't know what you think the Schoonover-Fink paper concludes, but it is not that concepts are not carried on neurons. If you want to understand representational drift I suggest you start with Tim O'Leary's work, such as this paper here https://pubmed.ncbi.nlm.nih.gov/31569062/ where he explains some of the mechanisms.

To require a non-physical stuff you need a true universal, something which cannot reside in each individual's brain because it is mind independent, so identical in each instance that it is one entity (law of identity), which means it cannot reside in each person's brain (otherwise each instance would have a different location and so be a separate thing). — Isaac


Which is just what universals are. — Wayfarer

That'd be why I described them. And, as I've been discussing with Olivier, there's absolutely no necessity, or warrant to think such things exist.

Would a non-euclidean object with those properties still be a triangle? — Isaac


If it’s non Euclidean it wouldn’t have straight edges. — khaled

Right. and yet your definition stipulated straight edges.

What about shapes matching that description but in non-standard topologies? — Isaac


If it’s not on a standard topology it wouldn’t have straight edges. — khaled

As above.

False, that’s exactly how they found the answer. They had the ideal form, and checked if a non Euclidean “triangle” can have its proprieties. It can’t. Then they checked if non standard topologies can. They can’t. Etc. — khaled

But non-eucledian triangles are still called triangles. As are triangles in non-standard topologies. See https://www.cs.unm.edu/~joel/NonEuclid/area.html for example, or here https://math.stackexchange.com/questions/1035931/properties-of-triangles-in-non-euclidean-geometries where some mathematicians are quite comfortably discussing the properties of 'triangles' in non-eucledian space without being misunderstood.

So are we mis-naming the things we commonly call triangles? — Isaac


Technically yes. — khaled

Then how are we understood? And prior to the formal definition, in whose mind was the 'correct' use when no one on earth knew it, but many were using the term (or it's translation) in everyday language? What's more, on whose authority is 'correct' judged? We'd normally turn to a dictionary, perhaps, in matters of conflict, but mine has...

Definition of triangle

1 : a polygon having three sides — Merriam Webster

...which is not the same as yours.

While we're on the subject, I presume everyone in the world is also misusing the word 'straight', because they keep applying it to things which aren't 'really' straight?

My dictionary has...

Definition of straight

(Entry 1 of 4)
1a : free from curves, bends, angles, or irregularities

and then proceeds to give the example of "straight hair or straight timber". Neither of which are completely free of all curves, bends, angles, or irregularities at any scale.

So are you suggesting that even the world's dictionaries have it wrong?

There's only yours, mine, everyone else's. — Isaac


If someone’s idea of a triangle includes that it is comprised of 4 vertices, don’t we have justification to tell them they’re wrong? From where do we get that justification? — khaled

It's not similar enough for their current purpose to the definitions the rest of their language community are using.

“very similar” is not enough. When speaking of geometry, it has to be exact. — khaled

We've already established that your definition is not the same as the one being used in the maths papers I cited. Nor, in fact are their definitions exactly the same as each other. Nor is either exactly the same as the dictionary's, and again - each maths textbook will have slightly differing definitions. They just all have key things in common, but are not "exactly the same" as per the law of identity, which would be required to posit a single entity.

you do admit there is a unified idea of “triangle” that we all (basically) share. — khaled

No, not at all. I've demonstrated above that there is no such idea. Just several ideas which share common features.

you seem quite happy to paraphrase the results from a paper in neuroscience as if you understood it without a hint of humility. — Isaac

Fair point. I will read some more. Certainly will absolutely acknowledge no expertise in that field.

But the question I have is, don't you think the claim that ideas are 'represented in' or 'inscribed on' neurons is rather confused? Because it seems to me, amateur that I am, that both 'representation' and 'inscription' refer to semiotics or semantics. How could a physical state or disposition of elements 'represent' anything, in that sense? Do you see what I'm questioning?

in any case you do admit there is a unified idea of “triangle” that we all (basically) share.

So why can’t the same be said of New York? Or “A”? — khaled

Good development. So there exist what we could call "near universals", concepts that we all or nearly all agree about, like Euclidian triangles.

Even Euclidian geometry as a whole is a "near-universal" in that we still haven't met a human being whose default mental GIS was non-euclidian. We all model space as perfectly Euclidian, intuitively.

Sure. This tune are us, essentially. — Olivier5

Encore!

don't you think the claim that ideas are 'represented in' or 'inscribed on' neurons is rather confused? Because it seems to me, amateur that I am, that both 'representation' and 'inscription' refer to semiotics or semantics. How could a physical state or disposition of elements 'represent' anything, in that sense? Do you see what I'm questioning? — Wayfarer

What we're in the business of doing when we have 'ideas' is the modelling of the hidden states we assume are causal in respect to our sensations. Triangles, letter 'A's, some multiple of similar objects, a city... these are all postulates, models of the causes of the sensations we receive. The same is true of thoughts. Thoughts are all recalled post hoc. The concept you have in your conscious mind of 'a triangle' is not the one your brain actually used to bring the word 'triangle' to mind on seeing the object. We can prove this by observing people with damage to the Hippocampus who can reliably identify objects (like triangles) but cannot bring to mind the definition of one, or people with damage to one or more subsections within the prefrontal cortex who can distinguish triangles from squares but cannot count the sides.

So if the concept you have in mind is demonstrably post hoc relative the the actual mechanism your brain uses to identify triangles, then it must either be coincidental (possible), or it must be itself a model of the that process, an inference of what's going on (the hidden states) in the subconscious mind, that yields the sensation (interoception) - 'triangle'.

You receive sensations (including interocepted physiological states), you behave in response to them, you model the cause of that whole relation. The mistake is in reifying the model to the actual.

So when I talk about what 'ideas' really are, I mean to refer to a model of their hidden states. What causes the sensation that I'm possessed of an 'idea'. My model for that is that of neurons being in certain configurations and having reached threshold levels of activation. Just like if you felt wetness on your skin, your model for the hidden causes might be one of rain, weather systems, air pressure gradients etc.

I could even, should I so wish, develop a model of this model. What would cause the sensation that there is such a model. And so on...

So yes, I do get what you're questioning - at least I think so. But I don't agree with your choice to reify the model when it is clear to me that models are, by definition, within their own Markov blanket, and so have hidden states. It is, by my model, those hidden states which deserve (if anything does) to be reified.

in any case you do admit there is a unified idea of “triangle” that we all (basically) share.

So why can’t the same be said of New York? Or “A”? — khaled


Good development. So there exist what we could call "near universals", concepts that we all or nearly all agree about, like Euclidian triangles. — Olivier5

I don't see anyone yet disagreeing with this. The disagreement is over the existence of actual universals, not over things which are nearly, or quite like universals. The distinction is absolutely crucial for the argument at hand because the law of identity would have us hold that only where the concepts are identical in every way can they be said to be one entity, identical with itself. Otherwise we're talking about several entities, all very, very, very similar. No matter how many 'very's I put in there, it will not be enough to qualify as identical and so not one unity requiring it's own existence.

As you've said, it may well be convenient to talk about it as such, but only within context. If, when teaching maths, the teacher refers to the 'near universal' concept of a triangle as if it were an actual universal, that is most certainly convenient for both her and her pupils, but when we're discussing something like the physicality of the mind, that contextual convenience does not just carry over by default. The context has changed, it may no longer be convenient to use the façon de parler in this new context. In fact, I think it's quite clear that it isn't, because we already run into substantial problems with laws of physics (how these entities interact), neuroscience (how to explain the studies showing a disconnect between stated 'ideal forms' and the capability to interact correctly with, for example, geometric objects). I'd say it's demonstrated already that it is no longer useful in this context, in fact it's getting very much in the way.

What we're in the business of doing when we have 'ideas' is the modelling of the hidden states we assume are causal in respect to our sensations. Triangles, letter 'A's, some multiple of similar objects, a city... these are all postulates, models of the causes of the sensations we receive. The same is true of thoughts. Thoughts are all recalled post hoc — Isaac

But isn’t this a problem for science? I mean, science of all types must assume the basic rules of inference to even begin to hazard what such and such neural data means. And science has been doing that with respect to a vast range of subjects for hundreds of years. So there must be some a priori principles to even propose such a theory.

that yields the sensation (interoception) - 'triangle'. — Isaac

You think geometric objects such as triangles are defineable as ‘sensations’? What about blind geometers? What kinds of ‘sensations’ would they have?

I think you’re equivocating sensations and reason. When you understand a logical principle, or algorithm, say, to make a prediction, or solve some arcane mathematical conjecture - how can this be possibly be categorised as a ‘sensation’?

But isn’t this a problem for science? I mean, science of all types must assume the basic rules of inference to even begin to hazard what such and such neural data means. And science has been doing that with respect to a vast range of subjects for hundreds of years. So there must be some a priori principles to even propose such a theory. — Wayfarer

Why would that be a problem for science? I use my a priori methods of inference to model these a priori methods of inference as being neural networks. I'm not seeing the problem.

When you understand a logical principle, or algorithm, say, to make a prediction, or solve some arcane mathematical conjecture - how can this be possibly be categorised as a ‘sensation’? — Wayfarer

I thought I'd just explained that. 'Understanding' a thing is a post hoc model of the actual link between sensation and response. We can prove this by lesion experiments, as I've described. So one senses, by interoception, that one is possessed of an idea. You may be limited by thinking of senses as being just the five we're taught about in primary school. This is just a simplification for children. There's scores of 'senses'.

So if the concept you have in mind is demonstrably post hoc relative the the actual mechanism your brain uses to identify triangles, then it must either be coincidental (possible), or it must be itself a model of the that process, an inference of what's going on (the hidden states) in the subconscious mind, that yields the sensation (interoception) - 'triangle'. — Isaac

You've reminded me of another concept that Kahneman talks about, WYSIATI: what you see is all there is. Despite it being patently obvious that babies don't come pre-loaded with a glossary of ideas for which to identify physical objects (hence the amount of time and money we spend teaching them and buying them brightly coloured toys of different shapes to investigate), we tend to ignore what's absent from us, however important. He talks about this in regard to System 2's refusal to credit System 1 with anything at all, but our insistence on treating educated adults as if they come shrink-wrapped and fully formed is particularly apparent in philosophy from the ancient Greeks to the Rationalists of the Enlightenment.

The disagreement is over the existence of actual universals, not over things which are nearly, or quite like universals. The distinction is absolutely crucial for the argument at hand because the law of identity would have us hold that only where the concepts are identical in every way can they be said to be one entity, identical with itself. Otherwise we're talking about several entities, all very, very, very similar. No matter how many 'very's I put in there, it will not be enough to qualify as identical and so not one unity requiring it's own existence. — Isaac

When asked what passes for an A you answered: "anything that has enough resemblance to other As".

Let us agree then that anything that has sufficient resemblance to universals is a universal, for all reasonable purposes.

when we're discussing something like the physicality of the mind, that contextual convenience does not just carry over by default. The context has changed, it may no longer be convenient to use the façon de parler in this new context.... in fact it's getting very much in the way. — Isaac

I doubt it, seriously. Science as a whole is but a façon de parler that happens to be useful... I think your quest here is not knowledge-driven. Rather, it is a self-defeating metaphysical crusade against concepts, i.e. against yourself. Like all naïve materialists, you are sawing the conceptual branch on which you sit.

our insistence on treating educated adults as if they come shrink-wrapped and fully formed is particularly apparent in philosophy from the ancient Greeks to the Rationalists of the Enlightenment. — Kenosha Kid

Yes, absolutely. And it permeates even through to psychology. You'd be shocked (or perhaps not) at the extreme resistance to experiential models of external-world theories in child development. Some of my wife's work was in that field and although well-accepted now, it was like wading through treacle getting it even considered.

Let us agree then that anything that has sufficient resemblance to universals is a universal, for all reasonable purposes. — Olivier5

Well then we'd have multiple, slightly differing universals, a definitional contradiction. Why are you insisting on redefining 'universal' to make the concept exist? Why not just discard it? When it became clear that phlogiston was not required, we didn't redefine it to make it true, we just discarded it.

The IEP has a pretty clear definition of 'universals'. It's clear that even you agree that nothing matching that description exists. Why are you so invested in rescuing the concept. Hundreds of philosophers are nominalist, there's a long history, why redefine universalism to resemble nominalism, why not just call it nominalism in the first place?

Well then we'd have multiple, slightly differing universals, a definitional contradiction. — Isaac

That seeming contradiction did not bother you that much when you explained at length why it is possible to have multiple, slightly different As. So you are ready to be a bit charitable with your concept of A but not with your concept of universal.

why redefine universalism to resemble nominalism, why not just call it nominalism in the first place? — Isaac

Because I believe we can do far better than nominalism.