The view I’m gesturing at is closer to a post-Kantian critical realism: yes, intelligibility is disclosed only in and through acts of knowing, and yes our access is conditioned — but the norms and structures that govern knowing are not merely subjective “forms of consciousness.” They function as constraints that inquiry discovers and revises in response to being. — Esse Quam Videri

This sounds more pre-Kantian than post-Kantian to me.
Claiming that reality can force its revision” is classic critical realism. It presupposes a relatively clean distinction between a conceptual framework or set of norms governing inquiry and a mind-independent reality that can push back against that framework and falsify it. That’s Popper’s structure: conjectures are proposed; reality tests them; error and correction drive progress.

Post-Kantian idealists would find that picture too dualistic.
They would not say that we “legislate” the framework in a purely subjective way. But neither would they describe reality as something standing outside the framework and exerting pressure on it.

For Hegel, the very distinction between “framework” and “reality” is unstable. What counts as “reality” is always already articulated within a conceptual structure. When that structure breaks down, the breakdown is internal , it manifests as contradiction within experience itself. The revision is not imposed from an external tribunal called “the real.” It is a dialectical transformation of how reality is understood.

Phenomenology, especially in Maurice Merleau-Ponty, would say something similar but in a different register. The norms of inquiry are neither merely subjective forms nor external constraints discovered “out there.” They are sedimented structures of the lifeworld. When they shift, it is because our embodied, historical being-in-the-world shifts. Error is possible, but it arises within a shared field of meaning, not from a neutral reality battering a theory.

That’s a very fair critique, and I agree my “reality pushes back” phrasing can sound Popperian — as if there were a clean dualism between framework on one side and an external tribunal called “the real” on the other.

But I don’t think that picture is essential to what I meant. I’m happy to grant the Hegelian and phenomenological point that “reality” is never encountered except as already articulated within experience and within a horizon of meaning. In that sense, breakdown is indeed internal: it shows up as contradiction, tension, or the collapse of a previously stable way of making sense.

Still, I’m not sure the post-Kantian dissolution of dualism can go so far as to make constraint purely intra-conceptual. Even if the “pushback” is experienced as breakdown within a lifeworld, the very intelligibility of error seems to require that our articulation is not sovereign — that the world can disclose our inadequacy in ways that are not reducible to mere shifts in communal norms or dialectical self-repair.

So I don’t mean “neutral reality battering theory.” I mean something closer to what phenomenology itself often emphasizes: the recalcitrance of experience, the failure of anticipations, the non-fulfillment of our intentions — a constraint that shows up immanently, but is not constituted by us. That’s the sense in which I still want to say intelligibility is discovered in response to being, even if “being” is never given outside the conditions of disclosure.

In short: yes, post-Kantian thought rejects the crude framework/reality split — but I don’t think it can dispense with the asymmetry between truth and warrant without losing the sense of genuine error and correction.

The idea that mathematics describes the structures and truths of the universe because rationality is built into it seems potentially misleading, since mathematical realists would hold these structures exist independently of us. I'm interested in the idea that the regularities and patterns we see are shaped by the ways we interact with the world, and that our perception and interaction with the world co-create the intelligible structures we study. Can you explain what a postmodern perspective (recognizing there are various approaches) might say in response to Platonism or the idea that science describes or maps on directly to a reality “out there”? — Tom Storm

Yes, phenomenologists as well as postmodernists would agree that there is a world impinging on us in ways that cannot be swallowed up by our concepts and expectations. But our only access to this world is through our interactions with it. Our mathematical schemes depend on idealizations we construct that stabilize the world into convenient, standardized identities.

So I don’t mean “neutral reality battering theory.” I mean something closer to what phenomenology itself often emphasizes: the recalcitrance of experience, the failure of anticipations, the non-fulfillment of our intentions — a constraint that shows up immanently, but is not constituted by us. That’s the sense in which I still want to say intelligibility is discovered in response to being, even if “being” is never given outside the conditions of disclosure. — Esse Quam Videri

I wonder what you might make of Lee Braver’s ‘middle way’ which he calls transgressive realism.

Lately, I've become interested in these moments of revolutionary experience, when our whole sense of what the world is like gets turned inside out and we are forced to form entirely new concepts to process what is happening. These experiences overwhelm and short-circuit our normal understanding of things, calling for new ways or sometimes per-petually escaping them. According to what I am calling Transgressive Realism (for those counting at home, this is the fourth strain of realism), these are the paradigmatic points of contact with a reality unformed by human concepts, when a true beyond touches us, sending shivers through our conceptual schemes, shaking us out of any complacent feeling-at-home. These moments are what allow us to escape the stultifying enclosure within our own ways of thinking that the Anti-Realists set up, where everything takes place on the basis of transcendental anticipation.

Transgressive Realism emphasizes the way reality unsettles us. We can never settle down with a single way of understanding the world because it can always unexpectedly breach these. Such experiences do not get squeezed into our mental structures but instead violate them, cracking and reshaping our categories. This violation is the sign of their externality since everything we conceive remains the offspring of our concepts and so retains a family resemblance with them. Rather than the wholly independent noumenal realm that Hegel rightly rejects, these are experiences that we have but which shatter our ways of understanding experience, exceeding our comprehension but not escaping our awareness. Transgressive Realism, I believe, gives us a reality that transcends our ways of thinking, but not all access to it, offering a middle path that lets us have our ineffable cake and partially eff it too. These aporetic experiences enter our awareness, not through the pathways prepared by our minds but in spite of them, transgressing our anticipatory processes.

Sometimes these strange ideas transform our way of thinking, reshaping our categories around their non-Euclidean shapes, but some permanently escape attempts to classify them. These are the wild thoughts that buck all domestication, escaping stable categories; these are the ideas prized by many continental thinkers as the “other” to our normal ways of thinking, which helps explain what may look like willful obfuscation and a casual rejection of basic rational principles. Many of these figures do cultivate the irrational in a sense, but for eminently sensible reasons, once the full conceptual context has been laid out.

Kant makes the conditions of intelligibility primarily conditions of appearance; the realist alternative treats them as conditions of judgment and truth, and therefore as answerable to reality rather than merely imposed upon it. — Esse Quam Videri

I’m struggling to see a real distinction here, though. I don’t see Kant’s categories as being ‘subjective’ in the sense implied here, in that they don’t pertain to a particular subject, but are the necessary constituents of judgement for any subject. Likewise, I don't see the categories of understanding as 'imposed', as if 'the world' is one domain, and they another. They are, rather, the inevitable grounds of comprehension.

Thank you for those references, they’re very helpful. I particularly resonate with the closing sentence:

What was concealed from Galileo was the practical activities of the life-world making possible the abstractions of modern science.

:clap:

I feel you have made the systematic mistake of transposing a limitation of minds onto a feature of the world. That a mind must apprehend the world by mind does not imply the world is mind dependent. — hypericin

I'll refer back to Joshs' response immediately after your comment.

I'm interested in the idea that the regularities and patterns we see are shaped by the ways we interact with the world, and that our perception and interaction with the world co-create the intelligible structures we study. — Tom Storm

I don't think that "unintelligible structure" makes sense. So it would be better to say "co-create the structures we study". Then doesn't "study" suggests the structures exist independently of us? That's not inapt, so long as we don't forget that we co-create them.

That’s the sense in which I still want to say intelligibility is discovered in response to being, even if “being” is never given outside the conditions of disclosure. — Esse Quam Videri

Wouldn't it be better to say "intelligibility is our response to being"?

But our only access to this world is through our interactions with it. — Joshs

If one says that, doesn't it immediately generate more questions about why the world and we are is set up that way? Could things be any different? I guess the answer is "no", because we are part of the world that we interact with. Which is very confusing.

I wonder what you might make of Lee Braver’s ‘middle way’ which he calls transgressive realism. — Joshs

I have a lot of time for this.

These moments are what allow us to escape the stultifying enclosure within our own ways of thinking that the Anti-Realists set up, where everything takes place on the basis of transcendental anticipation. — Lee Braver

I hope he realizes that "stultifying" is a whole argument on another level. Many people would settle for stultification if it brings the peace that, for example, Wittgenstein longed for. Yet I'm sure he would also recognize that transcendental anticipation itself also generates the next phase of confusion.

Many of these figures do cultivate the irrational in a sense, but for eminently sensible reasons, once the full conceptual context has been laid out. — Lee Braver

Perhaps he should have said that "irrational" is not the right word for what they were trying to do. Surely, it cannot be classified, because they are trying to talk about what comes before and enables rationality. "Arational" would perhaps be better.

I want to suggest that we might do better by accepting that the issue here is set up on a model of "us" and the world. We can also say, and should also say that we are part of the world and our intellectual (and practical) struggles with it are part of how it is. There is no journey, or rather, there is no destination, because the journey is the destination. The Tractatus was right, though perhaps for the wrong reasons. That doesn't mean we can abandon our attempts to speak the ineffable - or should that be "that we will abandon our attempts ...".

I want to suggest that we might do better by accepting that the issue here is set up on a model of "us" and the world. We can also say, and should also say that we are part of the world and our intellectual (and practical) struggles with it are part of how it is. There is no journey, or rather, there is no destination, because the journey is the destination — Ludwig V

:100:

I don't think that "unintelligible structure" makes sense. So it would be better to say "co-create the structures we study". Then doesn't "study" suggests the structures exist independently of us? That's not inapt, so long as we don't forget that we co-create them. — Ludwig V

Good. Nice.

So who are these arguments for?

The only answer that makes sense to me—one where there would be genuine consequences for the success of the argument—is believers who have somehow become "natural science curious". Here, Hart's arguments could find real purchase, and keep that little sheep from straying, or, rather, bring the sheep that has already strayed back into the fold.

I can't think of anyone else who would be interested and would take seriously what he has to say. — Srap Tasmaner

I can: People who try to make sense of the traumatic experiences they've had with theists.

When I'm reading this thread, I feel relief, finally, especially as I read Joshs' earlier post:

Hart rejects naive naturalism in favor of an even more naive divine naturalism. — Joshs

This is the first time that I'm able to make sense of why my interactions as a non-theist with theists are so straining and frustrating (to say the least). (And I know I'm not the only one.)

To me, a crucial part about philosophy is looking into how holding a particular worldview, a particular philosophy plays out in interpersonal interactions. Because this is where it matters.

The odd part there is that in studying philosophy one can also learn to do the opposite -- to defend one's viewpoint from all possible objections and prove oneself right. — Moliere

Yes.

Wouldn't it be better to say "intelligibility is our response to being"? — Ludwig V

How is it that people typically prefer to say
"This doesn't make sense"
and
"You're not making any sense"

as opposed to
"I don't understand this"
"I don't understand you"
?

Why externalize and say that intelligibility is somehow "out there", immanent to things, as opposed to being something we do, or that it is simply possible for humans to understand things?

’m struggling to see a real distinction here, though. I don’t see Kant’s categories as being ‘subjective’ in the sense implied here, in that they don’t pertain to a particular subject, but are the necessary constituents of judgement for any subject. Likewise, I don't see the categories of understanding as 'imposed', as if 'the world' is one domain, and they another. They are, rather, the inevitable grounds of comprehension. — Wayfarer

That's fair — "subjective" and "imposed" were poorly chosen on my part. Kant's categories aren't psychological or arbitrary; they're the universal conditions of judgment for any finite discursive knower. I agree with that entirely.

The distinction I have in mind is subtler. For Kant, the categories govern objects as they can appear to us, and he explicitly denies that we can infer from this that things in themselves are structured accordingly. That's the whole point of the phenomena/noumena distinction. The categories are epistemically universal but ontologically noncommittal.

The realist alternative doesn't deny that intelligibility is accessed through judgment — it does deny that the structures of judgment are merely conditions of appearance. On this view, judgment is truth-apt precisely because reality is intelligible in itself and can therefore satisfy or frustrate the internal demands of inquiry. The possibility of genuine error isn't just a feature of experience's internal economy — it's answerability to what is the case.

So the issue isn't whether the categories are universal. It's whether their universality reflects the structure of any possible experience for us, or the structure of being as knowable. Kant says the former. I'm reaching for the latter.

I wonder what you might make of Lee Braver’s ‘middle way’ which he calls transgressive realism. — Joshs

Braver is interesting, and I think "transgressive realism" captures something phenomenologically real — the way experience can disappoint anticipation and force conceptual revision. That's a vivid articulation of the kind of constraint I was pointing to, without falling back into naive "reality batters theory" dualism.

But I don't think it lands quite where I want to land, because Braver treats the paradigmatic encounter with the real as precisely what breaks intelligibility — the moments of shock, rupture, conceptual short-circuit. The real is most real when it is most resistant to rational articulation.

That's evocative, but I think it risks turning realism into a kind of romanticism of the ineffable. What I'm after is something stronger: not just that reality can unsettle our frameworks, but that inquiry can be normatively answerable to being in a way that yields truth and correction — that intelligibility belongs to reality itself, not merely to our revisable schemes.

In other words, Braver gives a compelling phenomenology of how revision gets triggered, but not an account of why revision can converge on truth. The transgressive moment is the beginning of inquiry — the prompt — but it's not yet the answer. And without some account of normativity — of what makes one revision better than another, not just different — I think he's left with a realism of disruption rather than a realism of intelligibility.

So I'd say that Braver is a step in the right direction, but I don't think he provides the middle way on his own. The deeper question remains whether the asymmetry between truth and warrant can be grounded, or whether it dissolves into an endless series of conceptual reshufflings punctuated by shocks.

Wouldn't it be better to say "intelligibility is our response to being"? — Ludwig V

I would want to say something stronger than this: that intelligibility is there to be discovered — that being is the kind of thing that can be understood, and that our knowing is a response to that prior intelligibility, not its source. The evidence for this is precisely the experience of error and correction: when inquiry goes wrong and we're forced to revise, the revision isn't arbitrary. It's better — more adequate to what we were trying to understand. And that "more adequate" only makes sense if there's something there that our understanding is iteratively converging on.

If you remove all of the idealizations that minds impose on the world of appearances, there is not much to say about the nature of what is mind-independent. — Joshs

We know the world as perceived and conceived is a synthesis of objective and subjective, even though it presents phenomenologically as something unitary. To say there is nothing to say about the objective pole of this relationship is frankly ridiculous.

All I did was ask the question, "How do we know...? why would you jump straight to me being not OK with something? — Tom Storm

I apologize, if you were offended by my interpretation of your OP : that you are not comfortable (OK) with the postulated explanations --- supernaturalistic or naturalistic --- for the Intelligibility of the universe : "I’d like to better understand the argument that intelligibility cannot arise through purely naturalistic processes"*1. Personally, I think the ability to infer the Laws & Logic of Nature did indeed evolve naturally by means of evolutionary progress. But if you think evolution is not progressive, then human intelligence will remain a mystery.

If you reject Pre-modern (religious) views on such questions, and Modern (scientific) views don't sufficiently address the issue, then perhaps you have become unsettled by Post-modern critical analysis of both religion and science. Postmodernism "critiques the certainty of objective truth, universal reason, and the "grand narratives" of modernity". As I understand it, the point of postmodernism is to unsettle certainty : to be "not OK". And 20th century Quantum Physics did that in spades.

Nevertheless, I have developed my own theory of how a seemingly "mindless" Big Bang beginning could naturalistically evolve intelligent beings, who ask how & why questions, from nothing but a> Energy (low entropy) and b> Natural Laws (regulations & limitations on energy) and c> Chance (quantum randomness). But it's a long & complex story, not suitable for a forum post. That's why I put it in the form of an initial Thesis and expansion in an online blog. :smile:


*1. The claim that "intelligibility cannot arise through purely naturalistic processes"is
a central argument in philosophy of mind, metaphysics, and theology, often used to challenge physicalism (the view that all things are physical). This perspective argues that the rational, logical, and meaningful structure of the universe implies an intelligent source rather than blind, random chance.
https://www.google.com/search?client=firefox-b-1-d&q=+intelligibility+cannot+arise+through+purely+naturalistic+processes.

I apologize, if you were offended by my interpretation of your OP : that you are not comfortable (OK) with the postulated explanations --- supernaturalistic or naturalistic --- for the Intelligibility of the universe — Gnomon

I am rarely offended.

The point of this thread was to understand Hart’s reasoning. What does he mean? Is the reasoning any good? That’s the main thing I was looking for. Seems to me after 9 pages, the question may be unanswerable or perhaps, I just can't make sense of it.

Does the apparent fit between human reason and the world require grounding in some kind of greater mind or God — Tom Storm

No.

If the world were unintelligable, it is hard to understand how it could support something as complex as life. If the world is intelligable, it is hard to understand how the evolutionary refinement of intelligence would not tightly track that intelligibility.

I'm not sure how evolution can explain intentionality, but I'm no expert.

I don't remember the context of my question. It was probably to understand what a theist might offer by way of reasoning.

I'm not sure how evolution can explain intentionality, — Tom Storm

Symbols are intrinsically intentional. Models are intrinsically intentional. That evolution should arrive at advanced nervous systems demonstrating both doesn't seem inconceivable.

To say there is nothing to say about the objective pole of this relationship is frankly ridiculous — hypericin

Give it a try. What vocabulary can you come up with to talk about the objective pole that doesn’t already imply a contribution from the subjective pole? Husserl discussed this issue:

“The purely Objective consideration, which investigates the Objective sense of thingness, requires that things be dependent on one another as regards their states and that they, in their real existence, mutually prescribe something to one another, regarding, specifically, their ontological content, their causal states. The question now is whether a thing, which indeed remains one thing under all circumstances, is the identical something of properties and is actually in itself solid and fixed with respect to its real properties; that is, is a thing an identity, an identical subject of identical properties, the changing element being only its states and circumstances? Would this not then mean that according to the various circumstances into which it can be brought, or into which it can be thought to be introduced, the thing has different actual states, but that in advance-a priori - how it can behave, and, further, how it will behave, is predelineated by its own essence?

But does each thing (or, what is equivalent here: does any thing at all) have such an essence of its own in the first place? Or is the thing, as it were, always underway, not at all graspable therefore in pure Objectivity, but rather, in virtue of its relation to subjectivity, in principle only a relatively identical something, which does not have its essence in advance or graspable once and for all, but instead has an open essence, one that can always take on new properties according to the constitutive circumstances of givenness? But this is precisely the problem, to determine more exactly the sense of this openness, as regards, specifically, the "Objectivity" of natural science.”(Husserl, Ideas II)

So the issue isn't whether the categories are universal. It's whether their universality reflects the structure of any possible experience for us, or the structure of being as knowable — Esse Quam Videri

‘Structure of being’ is an interesting choice of words. We ourselves are distinguished as ‘beings’. If by it, you mean the physical universe — electrons, galaxies, quantum fields — then calling it 'being' is already anthropomorphizing. Such entities are not beings in the sense humans are; they just exist (or subsist, or occur).

And if they're knowable, it's only because beings like us can render them intelligible. A universe without rational consciousness wouldn't be 'knowable' or 'unknowable'; those categories wouldn't apply. (This is what I take the 'in itself' to actually mean: not a mysterious shadowy 'something' lurking around behind the scenes, but the world or object outside any act of comprehension. The world as it would be without any intelligence in it - which is something we can't know.)

So 'the structure of being as knowable' already presupposes rational consciousness. You haven't escaped the circle — you've just disguised it by equivocating the term 'being'.

(This is also why I make frequent reference to Charles Pinter's 2022 book 'Mind and the Cosmic Order'. He shows in great detail how the mind structures experience through the formation of gestalts, meaningful wholes, which are the basic units of cognition (and not only human cognition). We 'pick out' specific 'things' and identify them as shapes and forms against backgrounds. Without this cognitive activity there would be no conscious awareness as such - that is what 'the world' is for us. The difficulty is becoming aware of these activities, as it is largely reflexive and unconscious.)

Give it a try. What vocabulary can you come up with to talk about the objective pole that doesn’t already imply a contribution from the subjective pole? — Joshs

Fair question.

But does each thing (or, what is equivalent here: does any thing at all) have such an essence of its own in the first place? Or is the thing, as it were, always underway, not at all graspable therefore in pure Objectivity, but rather, in virtue of its relation to subjectivity, in principle only a relatively identical something, which does not have its essence in advance or graspable once and for all, but instead has an open essence, one that can always take on new properties according to the constitutive circumstances of givenness? But this is precisely the problem, to determine more exactly the sense of this openness, as regards, specifically, the "Objectivity" of natural science.”(Husserl, Ideas II)

So if the essence of things is open and continually shaped by the conditions in which they appear to us, then objectivity cannot be a fixed feature of the world itself but must instead be something constituted through an ongoing unification of these shifting appearances across different perspectives.

(This is also why I make frequent reference to Charles Pinter's 2022 book 'Mind and the Cosmic Order'. He shows in great detail how the mind structures experience through the formation of gestalts, meaningful wholes, which are the basic units of cognition (and not only human cognition). We 'pick out' specific 'things' and identify them as shapes and forms against backgrounds. Without this cognitive activity there would be no conscious awareness as such - that is what 'the world' is for us. The difficulty is becoming aware of those activities, as it is largely reflexive and unconscious.) — Wayfarer

It interests me that you see maths (Platonically) as transcending contingent human experience, what do you make of Josh's observations:

If you remove all of the idealizations that minds impose on the world of appearances, there is not much to say about the nature of what is mind-independent. — Joshs

Our mathematical schemes depend on idealizations we construct that stabilize the world into convenient, standardized identities. — Joshs

David Bentley Hart) argue that the intelligibility of the universe requires more than a naturalistic explanation. — Tom Storm

I can't help you with Hart's reasoning*1, except to note that it is based on theology, and argues against Naturalism/Materialism. If you are committed to Materialism, his arguments won't make sense. However, my own philosophical solution to the Life & Mind mystery is completely natural, and evolutionary, given the axiom of a Big Bang beginning of unknown provenance. If you don't accept the BB theory or Evolutionary theory, it won't make sense. My thesis even has a role for Quantum randomness, that Hart argues against. :smile:


*1. David Bentley Hart argues that the universe’s intelligibility—the, “fitting” of the human mind to grasp rational, mathematical, and logical structures in nature — cannot be explained by, naturalistic materialism. He contends that because mind and matter are intrinsically linked, a purely mechanical, chance-driven universe cannot account for the conscious, truth-seeking ability of human reason. Hart proposes that the world is inherently teleological and meaningful, pointing toward a divine, intelligent source rather than, brute, unconscious material causes.
https://www.google.com/search?client=firefox-b-1-d&q=David+Bentley+Hart%29+argue+that+the+intelligibility+of+the+universe+requires+more+than+a+naturalistic+explanation.

I can't help you with Hart's reasoning*1, except to note that it is based on theology, and argues against Naturalism/Materialism. If you are committed to Materialism, his arguments won't make sense — Gnomon

No. Some arguments that theists raise are self‑contained. All the theist has to demonstrate in this instance is that intentionality can’t be explained by physicalism or naturalism (not materialism per say).

If he is right, this does not lead directly to theism by any means, any more than demonstrating the existence of UFOs leads to little green men.

And remember that the famous atheist philosopher Thomas Nagel presents arguments similar to Hart.

I think there's a distinction being compressed here that's worth pulling apart.

You're right that "knowable" implies a relation to a knower — nothing is actually known without someone doing the knowing. I'm not disputing that. A universe without rational consciousness wouldn't contain acts of knowing.

But the question is whether the intelligible structure that knowing discovers is constituted by the knower or merely disclosed by the knower. Those are very different claims.

Consider: the ratio between a circle's circumference and its diameter would have been the same whether or not anyone conceptualized it. Not because π was floating around as a Platonic object, but because the physical relationships that we render intelligible as π were already there constraining how circular things behaved. Our conceptualization doesn't create that constraint — it grasps it. And if it merely created it, it would be hard to explain why we get things wrong and are forced to revise.

So when I say "being as knowable," I don't mean "being as already-known" or "being as constituted by a knower." I mean: being has the character of being able to be understood — it is the kind of thing that admits of intelligible structure. That's a claim about being, not a disguised claim about us. And the evidence for it is the very thing you're describing — that we can form gestalts, that cognition works, that the world cooperates with our inquiries rather than being opaque to them. The Pinter point about gestalt formation is interesting precisely because it raises the question: why does the world lend itself to being organized this way?

You might say: "That's just how cognition works — it's what minds do." But that's the question, not the answer. Why does what minds do yield genuine understanding of what isn't mind? Either the world is intrinsically the kind of thing that can be understood — in which case intelligibility is a feature of being — or the fit between mind and world is a brute fact with no deeper account. I find the former more plausible, but I recognize that's where the real disagreement lies.

I don't see the Husserl passage that Joshs quoted in this post as being inimical to the way I interpret the meaning of Platonic realism.

I'm inclined to say that number (as an example) is a necessary and uniform structure within rational thought. When I ask what the sum of 1 + 3 is, the answer is constrainted by necessity to '4'. We are 'compelled by reason' to give that answer. But in what sense does '4' exist? This is the question sorrounding platonic realism which has generated centuries of argument. The implication is, if abstractions exist, in what sense do they exist?

A strong empiricist or reductionist naturalism inclines us to accept only those things that exist as phenomena as real - numbers and logical rules are, then, seen as being in the mind or the product of the mind, 'human inventions', and the like, 'projected' onto the world. But that belies the whole concept of mathematical necessity!

Numbers are not objects in space, but intelligible structures apprehended by reason. But nevertheless, the rules of mathematics are uniform and universal, they're not arbitrary or made up. There are imaginary numbers and imaginary number systems, but they are dependent on the ability of the mind to grasp the concept of number in the first place.

Where I see the resistance to Platonic realism is the suggestion that numbers arereal but not material.. As soon as you say that, you're into metaphysics, like it or not, and most don't. We have a hardwired tendency to believe that what is real must be 'out there somewhere', literally existing in time and space. For example, see below:

There was an article published in Smithsonian Magazine a few years ago, What is Math? which explored this topic. Some of the sceptics' sentiments expressed in that article really give the game away:

...scholars—especially those working in other branches of science—view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago.

Platonism, as mathematician Brian Davies has put it, “has more in common with mystical religions than it does with modern science.” The fear is that if mathematicians give Plato an inch, he’ll take a mile. If the truth of mathematical statements can be confirmed just by thinking about them, then why not ethical problems, or even religious questions? Why bother with empiricism at all?

Massimo Pigliucci, a philosopher at the City University of New York, was initially attracted to Platonism—but has since come to see it as problematic. If something doesn’t have a physical existence, he asks, then what kind of existence could it possibly have? “If one ‘goes Platonic’ with math,” writes Pigliucci, empiricism “goes out the window.” (If the proof of the Pythagorean theorem exists outside of space and time, why not the “golden rule,” or even the divinity of Jesus Christ?)

I'm inclined to say that number (as an example) is a necessary and uniform structure within rational thought. When I ask what the sum of 1 + 3 is, the answer is constrainted by necessity to '4'. We are 'compelled by reason' to give that answer. But in what sense does '4' exist? This is the question sorrounding platonic realism which has generated centuries of argument. The implication is, if abstractions exist, in what sense do they exist?

A strong empiricist or reductionist naturalism inclines us to accept only those things that exist as phenomena as real - numbers and logical rules are, then, seen as being in the mind or the product of the mind, 'human inventions', and the like, 'projected' onto the world. But that belies the whole concept of mathematical necessity! — Wayfarer

But isn't the view that numbers are idealizations we construct that stabilize the world into convenient, standardized identities, somewhat inimical to this thesis? I don't know the answer to this myself.

Where I see the resistance to Platonic realism is the suggestion that numbers arereal but not material.. As soon as you say that, you're into metaphysics, like it or not, and most don't. We have a hardwired tendency to believe that what is real must be 'out there somewhere', literally existing in time and space. — Wayfarer

I'm not saying anyone needs to resist the idea; I'm simply wondering whether the idea is more than speculative. I'm already familiar with the arguments, so I don’t need to see them again. What I’d like, perhaps, is a postmodern account of mathematics (something not too inscrutable) that unpacks this further. I don’t think we’ll get that from classical philosophy.

So when I say "being as knowable," I don't mean "being as already-known" or "being as constituted by a knower." I mean: being has the character of being able to be understood — it is the kind of thing that admits of intelligible structure. That's a claim about being, not a disguised claim about us — Esse Quam Videri

Whereas I see that as a claim about 'what exists'. I wouldn't use the term 'being' in that way. 'What exists' is external to us, and precedes us, plainly. I'm not disputing that.

Why does what minds do yield genuine understanding of what isn't mind? — Esse Quam Videri

When you ask why what minds do yields genuine understanding of what isn’t mind, I think that already presupposes a separation that may not be ultimate. As Ludwig said above:

We can also say, and should also say that we are part of the world and our intellectual (and practical) struggles with it are part of how it is. — Ludwig V

My suggestion isn’t that mind creates structure, nor that matter is “just an idea.” It’s that intelligibility isn’t something added from outside. What we call “the world” is always already given as structured, as determinate, as available to articulation. That isn’t an optional overlay — it’s the condition under which anything counts as something at all. (That “always already” is what I take the a priori to mean — not a mental imposition, but the prior intelligibility without which anything could appear as anything)

So when we say the world is intelligible, we’re not describing a fortuitous correspondence between two independently constituted domains (mind here, structured being there). We’re describing a more basic fact: that being and intelligibility are internally related. The fit isn’t something that needs to be explained after the fact; it’s built into what we mean by “world” in the first place.

Anyway, once again, thank you for your perceptive questions, but I am going to take a brief spell and return to my writing project (although experience shows me, I never end up staying away for too long.)

I think we’re actually very close here.

I’m completely on board with the idea that intelligibility isn’t “added from outside,” and that the world is always already given as structured and available to articulation — in fact that’s very close to what I mean by saying intelligibility belongs to being rather than being a contingent overlay.

I suppose the remaining question is just whether that “always already” should be understood primarily as a transcendental condition of appearance (Kant/Husserl), or whether it also licenses a modest metaphysical claim: that what exists is intelligibly structured in itself, even if our access is always mediated.

Either way, I think you’ve put your finger on the deepest point: the fit isn’t between two alien realms, but reflects an internal relation between being and intelligibility.

Good luck with the writing project — and thanks for the illuminating exchange.

But that’s exactly where the pressure point lies: if the semantic/normative side is genuinely real, then physical causality can’t be an exhaustive account of thought. — Esse Quam Videri

For me eliminative physicalism says that ultimately the constitutive reality is the physical causal with the semantic being an emergent phenomenon of a purely conceptual nature. Basically that the obvious fact that the semantic seems real to us due to our immersion in symbolic language and conceptual generalization does not point to any substantive non-physical reality over and above the physical. I don't say i agree with that, but I do argue against those who try to claim that it is self-refuting.