People like Kurt Godel, however, apparently thought that a Platonic world exists. As it turns out, Godel was also crazy, but that alone does not make his thinking dismissable. — tim wood

Bashing on Godel, his incompleteness theorems points towards the noetic faculties of the mind that are capable of perceiving beyond that of which would be limited by his incompleteness theorems. That's actually a powerful argument for Platonic ideals, and/of which nobody really phrases the question about Platonic idealism in this way; but, I find the argument ad hoc persuasive.

On the question of the status of Platonic ideals, where are we? Where should we be? — tim wood

I feel your essay is somewhat tendentious although I hasten to add that I don’t feel sufficiently qualified to properly criticise it. It’s inevitable when you try and compress thousands of years of intellectual history into a few paragraphs, and all conditioned by your prior conclusion as to what the platonic ideas might be.

I am hamstrung by the fact that I didn’t receive an education in The Classics - well, one year of Latin although that hardly suffices. But later in life I feel as though I have reached a kind of synoptic understanding of some important aspects of Platonism - which, I’m sorry to say, is not evident in what you’ve written above.

The central issue as I see it, is not what we understand as ‘ideas’, but universals. Platonism is realist about universals, and universals are not simply ‘ideas’ as you or I might think of them. The main point about universals is that, whilst they are only perceptible to a rational intelligence, they are not the product of the individual mind.

Actually for an effective short primer on such matter, have a peruse of Edward Feser’s blog post, Think, McFlly, Think (I think that’s a movie reference). He discusses the distinction between concepts, intellection, sensation and imagination.

I think the key point about your approach is that it subjectivises ideas i.e. sees them as the attribute of individual minds. Whereas in Plato, you see the origin of objective idealism, that is, the understanding that ideas in the form of universals are intrinsic to the fabric of the cosmos. But they are so in a way which is unintelligible to enlightenment rationalism, for the precise reason that this outlook inherited the attitude of the early nominalises, e.g. Ockham, Bacon et al. This is the subject of a very good long read, What’s Wrong with Ockham: Reassessing the Role of Nominalism in the Dissolution of the West.

All of this is a deep study, and as much a matter of intellectual history as of philosophy per se. Or perhaps you could say it’s a study in meta-philosophy.

On the question of the status of Platonic ideals, where are we? — tim wood

Not in college.

Where should we be? — tim wood

In college.

:up: Nailed it.

Are you bashing on Godel? I'm not. As to his incompleteness theories, I do not think you understand them - maybe at all. In brief, they concern what can be said within a specific and well-defined system, as compared to what can be observed about that system from "outside" of it. If you a find and read his proof (and it is very readable) in English, you will see that it is built from the ground up with requisite rigor - that is, all rigor, nothing whatever mystical about it in any way. As such, there is no "powerful argument" in it for anything beyond its proper sphere of application. But there is no end of people who, thinking perhaps poetically, think that there is.

As to his incompleteness theories, I do not think you understand them - maybe at all. — tim wood

No, I have a pretty good understanding of Gödel's incompleteness theorems. But, don't take it from me, by all means... I actually understood his work in regard to reading about it from Tarski's undefinability theorem, who arrived at the same conclusions somewhat latter (another case of Newton vs Leibniz wrt. to truth, in my mind).

https://arxiv.org/ftp/arxiv/papers/1509/1509.02674.pdf
https://academic.oup.com/philmat/article-abstract/2/3/177/1455520?redirectedFrom=PDF
https://www.cairn.info/revue-internationale-de-philosophie-2005-4-page-513.htm#

Are you bashing on Godel? I'm not. — tim wood

Well, you made the annoying quip about him being crazy. He was paranoid about food and starved himself to death; but, not "crazy".

. He was paranoid about food and starved himself to death; but, not "crazy". — Wallows

Uhhhhh .... sure.

Uhhhhh .... sure. — Marchesk

Great. Have at it, a guy who was best friends with Einstein taught at Princeton and completely demolished Hilbert's program is... crazy. Is this shitposting taken to a new level on TPF?

Well, you made the annoying quip about him being crazy. He was paranoid about food and starved himself to death; but, not "crazy". — Wallows

He was arguably a paranoid schizophrenic. He apparently thought that he was being poisoned and thereby, as you say, starved himself to death. I'm easily persuaded that the truth of the matter probably is not that simple. Mine was not a quip; it was a statement of generally excepted fact. If there was any annoyance to it, it's in the mind of the reader. For it to be an annoying "quip," it has to be a quip, and it has to be annoying and intended to be such. In as much as neither is the case, the quippiness and annoyance are all yours. Attributing them elsewhere is usually called projection. So we might ask, except that I'm not because this is a complete waste of time, why you're hostile to Kurt Godel?.

Hostile to Kurt Godel? Are you kidding me? I idolize the man in many regards. I see we're on completely different wavelengths here, so I'll stop the projecting, which (according to you and your "consensus" about him being a paranoid schizophrenic is entirely made up in my mind).

Look, I see you edited your post two or three times, about him being a paranoid schizophrenic at it being an established "fact". So, I rest my case. This discussion seems to have evolved into giftedness and "craziness", so it's up to you to either take it in that direction or not.

Great. Have at it, a guy who was best friends with Einstein taught at Princeton and completely demolished Hilbert's program is... crazy. Is this shitposting taken to a new level on TPF? — Wallows

Hey, I've watched A Beautiful Mind. Being crazy doesn't mean you can't also be an accomplished genius. And I was only referring to the part about starving yourself to death out of food paranoia. That sounds like an untreated mental illness.

On the question of the status of Platonic ideals, where are we? Where should we be?

It turns out the nominalists were right. Ideas are as fragile as the parchment they’re written on. They are carried in our artifacts, not in some other realm.

Hey, I've watched A Beautiful Mind. Being crazy doesn't mean you can't also be an accomplished genius. And I was only referring to the part about starving yourself to death out of food paranoia. That sounds like an untreated mental illness. — Marchesk

It could be, don't really know. I tend to suspend judgment calls on such matters.

I feel your essay is somewhat tendentious although I hasten to add that I don’t feel sufficiently qualified to properly criticise it. — Wayfarer

I did not write an essay, I wrote an OP to TPF in which I asked a question, gave some background, and sketched my own views. In sum, really, a question. So what's to criticize?

which, I’m sorry to say, is not evident in what you’ve written above. — Wayfarer

Why would an understanding of yours "be evident" in my OP?

The central issue as I see it, is not what we understand as ‘ideas’, but universals. Platonism is realist about universals, and universals are not simply ‘ideas’ as you or I might think of them. The main point about universals is that, whilst they are only perceptible to a rational intelligence, they are not the product of the individual mind. — Wayfarer

Questions abound here: First, I'm pretty sure you're not back-reading anything Christian into Plato's thought, yes? Second, "they are not the product of the individual mind." What is not the product of an individual mind? Universals? Or the ideas of universals? You appear to claim that universals themselves exist; is that your claim? If they exist, were they produced (somehow)? By what agency if not mind? (And currently the only minds we have any knowledge of is animal minds - subject to adjustment when the spaceships arrive, but not until, except as a matter of speculation.)

I readily agree that universals, and lots of other ideas, are ideas, productions of thinking by human minds plural, the ideas being in course of time influenced and informed by the contributions of individual minds. I take this to be a statement of fact. People, on the other hand, can believe what they like - belief being one of the benefits of having a mind that can think "outside the box." But outside-the-box is not inside the box. Outside-the-box, anything goes. Inside the box, in my understanding, are facts, as best we an determine them, truth, as best as that can be determined, and reason that thinks about facts and truth as best it can. Call it, with such rules as pertain at a given time, the rational world, which includes the natural world and everything in it. Outside-the-box, then, is not of this world. To get from out to in, there are criteria. Usually encapsulated in the phrase, "Prove it," meaning neither more nor less than demonstrating that the thing in question that's outside, has a proper place inside, in an appropriate form.

This is the subject of a very good long read, What’s Wrong with Ockham: Reassessing the Role of Nominalism in the Dissolution of the West. — Wayfarer

It's useful to read the "editorial statement" of the source, an apparently respectable journal. It's not overly long, but I've shortened it. Anyone can go to the site you listed above and read both it and the article.

"ANAMNESIS is both an interdisciplinary, peer-reviewed, academic journal and an intellectual online journal dedicated to the study of Tradition, Place, and ‘Things Divine.’ ....

Place is an existential category, like the human body, that connotes focus on the limits of human scale, the value of human attachment to historical community and locality, and the value of human connection to nature and the land. Issues of agrarian values, decentralization, localism, and other such concerns are themes that the journal hopes to explore.

’Things Divine’ is Cicero’s phrase, and it is part of his famous claim that “wisdom” entails “knowledge of things divine and human.” The expression is intended to encompass a broad swath of meanings. On the one hand, it connotes openness to theological and philosophical inquiry into what is thought to be ultimate and unconditioned; and so we welcome exploration of topics related to Logos, natural law theory, and other such themes. On the other hand, we are also open to the mythos view of culture—i.e., that many basic truths about reality, which people experience, are often expressed in myths." Italics mine.

The article itself appears to scant without regard the history of Christian Realism. And it's odd, because the author cites Étienne Gilson, which, had he read any of his books, esp. The Spirit of Mediavel [sic] Philosophy, he could not have fashioned the article he did write.

Christian Realism, per Gilson, is the result of a conscious choice of the church fathers in putting together Paganism and early Christianity. In so putting together, they created problems that blew up c. 1325 AD. For details, Gilson's account is a marvelous read, at Amazon or AbeBooks or your public library.

But the article's author just assumes out of whole cloth that the problem is one of the existence of universals (not to be confused with the question as to whether they exist). It is not. The problem is correct thinking about the history of the thinking about universals and how, in the light of that history, one ought to think about them now. And it makes a difference. Christian Realism means (is intended to be understood as the doctrine) that God is good. Nominalism, that God is omnipotent. Most folks do not understand that the two are different. Martin Luther certainly did. I, however, had to learn it from Gilson.

Finally, from the article:
"A first problem with this characterization becomes evident when we realize that, on this account, Thomas Aquinas would count as a nominalist. Aquinas is supposed to be the exemplary medieval realist—indeed, it is most often from Thomist quarters that Ockham’s nominalism is criticized—and yet Aquinas is very clear that nothing exists as a universal; all existing things are individuals. Universals, as such, do not exist, not even on some “different metaphysical plane.”

I recommend reading the rest of the article.

These all are take-offs from Godel's theorems. E.g., "The aim of this paper is to review and evaluate various philosophical interpretations of Godel's theorems and their consequences, as well as to clarify some confusions." Italics added.

"In this paper I argue that it is more difficult to see how Godel's incompleteness theorems and related consistency proofs for formal systems are consistent with the views of formalists, mechanists and traditional intuitionists than it is to see how they are consistent with a particular form of mathematical realism." Italics added.

"Many physicists beleive [sic] in a materialistic metaphysics,.... If we apply this theorem to
a TOE, it means that there will exist statements, i.e. physical phenomena, that cannot be explained
within this theory. The first person to point out this was S. Jaki [2] in the 60's, and later it was also
discussed by S. Hawking [3]. Although GIT prevent the existence of a TOE...." Italics added.

What you appear to be familiar with is derivative literature, the sort that says, "Well, if this, then that." Entertaining and thought-provoking to be sure, if it's not too ridiculous.

If you would care to present any of these arguments other than by reference, please go ahead. My difficulty is the number of times I've read such references and found they do not say what what they are supposed to have said.

I recommend reading the rest of the article. — tim wood

Please do, and let us know what you think.

The passage that strikes me in this essay is the following:

Thomists and other critics of Ockham have tended to present traditional realism, with its forms or natures, as the solution to the modern problem of knowledge. It seems to me that it does not quite get to the heart of the matter. A genuine realist should see “forms” not merely as a solution to a distinctly modern problem of knowledge, but as part of an alternative conception of knowledge, a conception that is not so much desired and awaiting defense, as forgotten and so no longer desired. Characterized by forms, reality had an intrinsic intelligibility, not just in each of its parts but as a whole. With forms as causes, there are interconnections between different parts of an intelligible world, indeed there are overlapping matrices of intelligibility in the world, making possible an ascent from the more particular, posterior, and mundane to the more universal, primary, and noble.

In short, the appeal to forms or natures does not just help account for the possibility of trustworthy access to facts, it makes possible a notion of wisdom, traditionally conceived as an ordering grasp of reality.

The main thrust of the essay is indeed 'how to conceive of universals'. It notes:

In doing away with forms, Ockham did away with formal causality. Formal causality secures teleology—the ends or purposes of things follow from what they are and what is in accord with or capable of fulfilling their natures.

As to whether Joshua Hothschild would agree with Gilson or not, I do not know, but his credentials are impressive (and include being a founding member of the Society for Medieval Logic and Metaphysics.)

As for Godel's Platonism, there's an excellent article by Rebecca Goldstein (who happens to be married to Steve Pinker):

Gödel was a mathematical realist, a Platonist. He believed that what makes mathematics true is that it's descriptive—not of empirical reality, of course, but of an abstract reality. Mathematical intuition is something analogous to a kind of sense perception. In his essay "What Is Cantor's Continuum Hypothesis?", Gödel wrote that we're not seeing things that just happen to be true, we're seeing things that must be true. The world of abstract entities is a necessary world—that's why we can deduce our descriptions of it through pure reason.

What appeals to me, is that there *is* 'an abstract reality. Because, if true, then it turns out materialism is falsified, as there are real but immaterial things.

Look, I see you edited your post two or three times, about him being a paranoid schizophrenic at it being an established "fact". So, I rest my case. This discussion seems to have evolved into giftedness and "craziness", so it's up to you to either take it in that direction or not. — Wallows

My purpose was to note a fact about the man, and to disqualify that fact as being grounds for judging his thinking. But you didn't get that, did you. And so you'e gone off on something that is irrelevant, and annoying, and a waste of time. Do you have anything at all substantive to contribute to the discussion, or to get it off the ground?

You appear to claim that universals themselves exist; is that your claim? If they exist, were they produced (somehow)? By what agency if not mind? (And currently the only minds we have any knowledge of is animal minds - subject to adjustment when the spaceships arrive, but not until, except as a matter of speculation.) — tim wood

I'll enlarge a reply to this later.

I think required of us here, to make any sense of Realism (R) v. Nominalism (N), is to first determine what we are talking about. Religion? Or philosophy? Existence or the history of ideas? I wonder if you might start with this: do you see with respect to the nature of God, how R and N are incompatible? One's omnibenevolent and the other omnipotent. Some try to erase the distinction by saying, sure, omnipotent, but He cannot be bad. By whose standards? And why not, if he's omnipotent. Gilson points out - recounts - that just what is good for an omnipotent God is not well-defined for people (or would it be vice-versa?), and being omnipotent, He can change his mind.

Edit: there's an emoji in this piece I did not put there. Maybe it comes from the parenthesis-N-close-parenthesis (N). Yep, confirmed. Interesting. Anyway, disregard the emoji. please.

A genuine realist should see “forms” not merely as a solution to a distinctly modern problem of knowledge, but as part of an alternative conception of knowledge, a conception that is not so much desired and awaiting defense, as forgotten and so no longer desired.

If they're solutions as you indicate, then they need to be disconnected from philosophy, religion/theology, and history. You have placed then into a static, timeless bubble. I just don't happen to think that will work - except as a matter of belief. Or, when belief moves into science, it's called begging the question.

In my opinion, this thread hasn't exploded yet. Maybe some care and precision about our topic, including deciding what, exactly, it is, may prevent an explosion, and maybe even yield some neat insights!

Mirabile dictu, we agree! See, what did I tell you (in that other thread)!

By no means I am an authority on the matter; but, let's suppose that we could envision an uncountable alphabet, then doesn't that suppose a mathematical realm in some objective sense, hence Platonism?

I mean, this in the most abstract sense...

By no means I am an authority on the matter; but, let's suppose that we could envision an uncountable alphabet, then doesn't that suppose a mathematical realm in some objective sense, hence Platonism? — Wallows

And, in a sense this "bypasses" Godel's incompleteness theorems, which Wittgenstein sought to point out as far as my limited knowledge spans.

I think required of us here, to make any sense of Realism (R) v. Nominalism (N), is to first determine what we are talking about. — tim wood

Metaphysics. Neo-thomism (of which Gilson was an exponent) is a modernized form of classical metaphysics. The Feser blog article would help clarify these questions.

My own view is that the answer is obvious: Platonic ideals just are ideas of ideas. I have a pretty good idea of what a horse is. I can imagine the idea of a perfect horse, and I can also imagine that my ideas of such a perfection might themselves contain some imperfections, as judged by people who know more about horses than I do. — tim wood

I agree.

I have urged that our perceptual relation to the world is conceptual all the way out to the world’s impacts on our receptive capacities. The idea of the conceptual that I mean to be invoking is to be understood in close connection with the idea of rationality, in the sense that is in play in the traditional separation of mature human beings, as rational animals, from the rest of the animal kingdom. Conceptual capacities are capacities that belong to their subject’s rationality. So another way of putting my claim is to say that our perceptual experience is permeated with rationality. — McDowell

https://en.wikipedia.org/wiki/Conceptualism

The important point, for me, is that concept isn't private. Concept is essentially public and social. What obscures this is its dependence on particular human beings as its 'host.' The mature, rational human being has learned to live in a humanized life-world. A chair is seen automatically as something to sit on. A sidewalk is seen automatically as something to walk on. Of course we also learn about justice, fairness, appropriateness.

The more perfect-exact forms are mathematical, like the perfect circle. These seem less local, less cultural than other forms/concepts and presumably have their foundation in our biology.

A last point is that forms/concepts structure philosophy itself. So while we know that concepts are 'only in our heads,' they also make such judgment possible. We have heads (as heads) because of concepts. So in some sense concepts/forms are prior to the mental/physical distinction as the condition of its possibility.

The more perfect-exact forms are mathematical, like the perfect circle. These seem less local, less cultural than other forms/concepts and presumably have their foundation in our biology. — Eee

See - biology. Evolution as philosophy. What evolutionary theory is intended to explain is the development of species. But now, as a matter (not to say "accident") of history, it has become a 'theory of everything' - well, everything about us.

But, a circle is a circle in all possible worlds, whether h. sapiens has evolved to understand it or not. And when we do understand it, then we understand something that is in no way 'founded in biology'; we've evolved beyond the exigencies of biology at that point (to become, in Greek terms, 'the rational animal', which is a difference that makes a difference - an ontological difference, I claim.)

From that article:

In metaphysics, conceptualism is a theory that explains universality of particulars as conceptualized frameworks situated within the thinking mind.

What does 'within' mean? Within what? What is the ontological status of ideas? That suits 'naturalised epistemology' very well, because evolution gives rise to brain gives rise to mind. But that is exactly what is at issue here. And furthermore, does evolution give rise to the 'furniture of reason'? Can the law of the excluded middle be "explained" as a consequence of, or on the grounds of, biology? I say not - that there would be no "science of biology" were we first not able to recognise the law of the excluded middle.

The Hothschild article talks about 'conceptualism'. It's too detailed and long a discussion to summarise, but it starts by saying of conceptualism that 'This middle position is usually characterized as holding that while universals are not real things, they are not mere words either, they are concepts.' There's then a discussion of the medieval debate about the ontology of universals, which shows that it became a discussion about 'mechanisms of meaning'.

But he goes on to say that Aquinas' theory of scholastic realism is grounded in the 'inherence theory of predication', to wit:

Words signify forms—this is the heart of Aquinas’s “realism.” It is not that these signified forms are universals or have any universal existence; they exist only as the individual acts of being characterizing individual things. (And, as we will see, even the sense in which they “exist” in individuals can admit of great qualification.) But as the individual forms of individual things, they have a potential intelligibility which can be abstracted by the mind; abstracting this potential intelligibility—making it actually understood by the mind—is the formation of the concept. It is by means of such a concept that a word signifies, and the mind is aware of, many things insofar as they all share that same form. This is why Aquinas said that universality is a feature of individual forms existing in the mind, insofar as those individual forms relate that mind to many things.

This is supported by a quote from another source:

if the proper knowledge of the senses is of accidents, through forms that are individualized, the proper knowledge of intellect is of essences, through forms that are universalized. Intellectual knowledge is analogous to sense knowledge inasmuch as it demands the reception of the form of the thing which is known. But it differs from sense knowledge so far forth as it consists in the apprehension of things, not in their individuality, but in their universality ² .

So that is close to how I understand the knowledge of universals: that when we see a particular being, we recognise its form to say it is 'man' (etc) - something which is true of all men (hence, universal.) That is where you can see the intuition alluded to in the OP still living and breathing. Whether universals exist is another matter. I say that they exist in a sense - but you will find, modern thinking has no scale along which that expression is intelligible. For us, things either exist, or they don't. And that too has its origins in medieval scholasticism - it is the loss of the sense of there being 'degrees of reality' which is at issue, in my view.

I note this passage:

Conceptual capacities are capacities that belong to their subject’s rationality. So another way of putting my claim is to say that our perceptual experience is permeated with rationality. — McDowell

Completely agree. Compare that with this claim by Jacques Maritain - that 'what the Empiricist speaks of and describes as sense-knowledge is not exactly sense-knowledge, but sense-knowledge plus unconsciously introduced intellective ingredients, -- sense-knowledge in which he has made room for reason without recognizing it.' Which I think is a precise characterisation of most modern empiricism. The 'rational subject' is bracketed out by the initial 'grand abstraction' of science, which purports to deal with 'ideal objects'; and then having been bracketed out, is forgotten about. Which is how you end up with Daniel Dennett.

He was paranoid about food and starved himself to death; but, not "crazy". — Wallows

If that doesn't count as being crazy... then nothing will.

Fantastically illuminating conversation about Godel. People ought to pay to get in.

Timely blog post from Edward Feser on Ur-Platonism.