I recognise that, it's David Bentley Hart's latest All Things are Full of Gods. And he states exactly what I was about to write, which is the vexed relationship between logical necessity and physical causation. I've been drafting some material on this question, which I'll present below.,

Once again, I'll situate this historically. Pre David Hume, there was an assumption that the world was intelligible — that is, there was an intrinsic link between the order of nature and the order of reason. Causes were understood in terms of formal and final causes, which often carried logical or conceptual necessity. For example, water flows downhill because that is part of its nature — a blend of formal and final causation. More from Hart:

In the pre-modern vision of things, the cosmos had been seen as an inherently purposive structure of diverse but integrally inseparable rational relations — for instance, the Aristotelian aitia, which are conventionally translated as “causes,” but which are nothing like the uniform material “causes” of the mechanistic philosophy. And so the natural order was seen as a reality already akin to intellect. Hence the mind, rather than an anomalous tenant of an alien universe, was instead the most concentrated and luminous expression of nature’s deepest essence. This is why it could pass with such wanton liberty through the “veil of Isis” and ever deeper into nature’s inner mysteries.

David Hume broke this supposed relationship. He argued that causation is not something we can deduce from reason alone — it's only ever inferred from constant conjunctions: "We see A followed by B, and infer causation." Hence, causation is not logically necessary but contingent and habitual.

All reasonings concerning matter of fact seem to be founded on the relation of cause and effect. But... the connection between cause and effect is not a product of reasoning, but of custom. — An Enquiry Concerning Human Understanding

This cleaved the empirical from the rational, leading to the so-called Humean bifurcation: facts (contingent, empirical) vs. norms/logical truths (necessary, conceptual). And that is still writ large in so many of the dialogues on this forum. Many of the contributors I will talk to here - Apustimologist, Relativist, Philosophim, to name a few - assume that, as the brain is physical, and the brain is the source of throught, then thought too has a physical basis. In fact they can't even conceive of there being an alternative to that, it is so firmly a tenet of modern culture.

I think one way to address this rupture is through what John Vervaeke calls relevance realization — a contemporary cognitive science account that begins to heal the divide Hume opened between logical structure and physical causality.

Vervaeke argues that cognition — especially human intelligence — is not a matter of brute computation or mechanistic stimulus-response. Rather, it's grounded in our dynamic ability to interpret what is relevant in a given situation, from among an almost infinite range of possible inputs, actions, and interpretations. This isn’t something that can be fully formalized or predicted — it’s emergent, self-organizing, and constrained by the organism's goals, embodiment, and interaction with the world.

In this light, cognition is not just caused — it's structured. That is, our awareness of the world is shaped by a salience landscape, a kind of lived topography of what stands out, what matters, and what calls for action. And this is not imposed on a passive agent; it is co-constituted by organism and environment ('co-arising'). The world does not merely act on us through physical causes — it is disclosed to us through a structure of intelligibility that is tied to our biological, emotional, and social existence.

What’s significant here is that this structure of salience and relevance is normative and existential in character — it allows for truth and error, insight and illusion, precisely because it is not just reducible to efficient causes. Vervaeke’s insight is that intelligence is the capacity to realize what is relevant — and this is not simply a logical deduction nor a chain of physical causes, but an enacted form of knowing by being, to borrow Hart’s phrase.

This begins to undo the Humean bifurcation. Relevance realization is causal — grounded in the biological dynamics of neural networks, evolution, and interaction — but it also has logical structure, in the sense that it underwrites all higher-order cognition, including our grasp of concepts, categories, language, and truth itself. But the normative aspect recognises that for us, as intelligent rational agents, the fact that things matter cannot be captured in reductionist or physical terms.

In a way, it returns us to something like the Aristotelian sense of logos as both reason and structure — where mind is not a ghost in the machine, but the expression of nature’s capacity for self-disclosure. The very idea of a "veil of Isis" only makes sense if there is something behind the veil that is able to be seen — and something within us that is capable of seeing it. That is the intuition the pre-modern world preserved — and one that Vervaeke’s work is attempting to recover in post-cognitive-scientific terms.

It doesn’t mean reverting to pre-scientific metaphysics, but it does mean questioning the flattening effect of a purely mechanistic view of causality. In a salience-structured world, causation isn't just physical interaction — it’s also the enactment of meaning. And meaning, far from being a subjective gloss on an indifferent universe, becomes a central feature of how the world comes into presence at all.

the Aristotelian sense of logos as both reason and structure — Wayfarer

Everything you wrote about Hart and Vervaeke is fascinating and on point for me (though I don't see Hume as the diabolus ex machina they do). My particular m2m problem is a bit different, but can hardly be addressed without taking account of the perspectives you're describing.

I was especially struck by the quoted phrase. I've long held out for a difference between causes and reasons. If we can speak meaningfully about m2m causation, then I think causation has to be understood, or interpreted, as a type of reason, not a physical cause. And the logos concept has a lot to offer here. How can a mere structure also provide reasons that cause/influence/lead to mental events? And yet, when we entertain a syllogism, isn't this what happens? But the problem begins even before thought is seen as syllogistic: Somehow, what we call the "content" of a thought (be it propositional or imagistic) appears to provide causes (or reasons) for other thoughts. A reductively psychological explanation involving "associations" will not suffice, as I hope to argue.

You really need to have a look at Alicia Juarrero Dynamics in Action. The book starts with the question ‘what is the difference between a wink and a blink?’ and then proceeds to review ‘action theory’ in the context of that question. (I’ll add that I haven’t finished the book nor really assimilated it yet but it seems directly relevant.) Also see https://www.meaningcrisis.co/episode-6-aristotle-kant-and-evolution/

Thanks, on my list.

David Hume broke this supposed relationship. He argued that causation is not something we can deduce from reason alone — it's only ever inferred from constant conjunctions: "We see A followed by B, and infer causation." Hence, causation is not logically necessary but contingent and habitual. — Wayfarer

IMO, the Law Realists improved upon this by proposing that laws of nature entail a necessitation. They define a law of nature as a causal relation between types of things (AKA "universals"). Hume would notice the empirical evidence that every observed pair of electrons repelled each other, and label this a "constant conjunction", while law realists would say that electrons (a type of thing) repel each other - and this is constitutes a law. If A and B are electrons, then they it is physically necessary that they will repel, given that that this law exists.

So I'm curious if you agree that law realism is a better explanation of empirical evidence than constant conjunction?

the Law Realists — Relativist

Such as?

I’d say that “law realism” really just smuggles Platonism back in through the side door. It appeals to universals to ground necessity, but universals are not observable particulars — they are grasped only by reason. That makes them, in effect, intelligible structures postulated to explain phenomena, which is a Platonic move, whether admitted or not. Kant on the other hand accepted that these lawful relations are indispensable for science, but located them in the activity of the mind as a priori conditions of experience. They were not ‘in re’ but ‘in intellectus’

The difficulty is that law realists won’t acknowledge it, because it thinks mind itself is simply the product of those same physical processes which it situates ‘in things’. But that is circular: the only way we ever know about universals or laws is through the activity of reason, the mind’s ability to discern likeness within diversity and to infer necessity where the senses show only succession. To explain mind as product of the very processes whose necessity it is positing is to fall into a circularity. The scientific realist appeal to universals already presupposes rational relations that cannot be explained away as a physical mechanism, and it’s here that the Platonic and Kantian implications reassert themselves.

the only way we ever know about universals or laws is through the activity of reason, the mind’s ability to discern likeness within diversity and to infer necessity where the senses show only succession — Wayfarer

What's wrong with that? It's a metaphysical hypothesis with broad explanatory scope, and consistent with the success of science.

The difficulty is that law realists won’t acknowledge it, because it thinks mind itself is simply the product of those same physical processes which it situates ‘in things’. — Wayfarer

You're conflating law realism with physicalism. One could accept the reality of laws, while choosing to believe "the mind" is not the product of natural law - whether by faith (as religious scientists do), or by hypothesis - including whatever hypothesis of mind you are drawn to.

You're conflating law realism with physicalism — Relativist

From our previous discussions, I presumed you had D M Armstrong in mind, who is an avowed physicalist. Are the 'law realists' who are not physicalist? (Coming to think of it there would be.)

Law realism works well with physicalism, but it doesn't seem dependent on physicalism being true. The notion that there exist laws of nature seems (to me, at least) a better explanation of regularities than Hume's constant conjunctions.

I want to comment on this:

Many of the contributors I will talk to here - Apustimologist, Relativist, Philosophim, to name a few - assume that, as the brain is physical, and the brain is the source of throught, then thought too has a physical basis. In fact they can't even conceive of there being an alternative to that, it is so firmly a tenet of modern culture. — Wayfarer

I am open to alternatives to a physicalist metaphysics, but I haven't seen any viable proposals from you or anyone else. You've merely pointed to the hard problem of consciousness as a reason to be skeptical of a physicalist theory of mind. The alternatives are as speculative as they are numerous, so they do no more than raise possibilities. You seem interested in exploring these possibilities, but I am not. I'd be interested if you (or someone) felt he had a persuasive argument to support one of them, but my impression is that each theory gets embraced purely on subjective grounds.

Of course, physicalist metaphysics deals with much more than theory of mind. So if you think one should abandon physicalism because of the explanatory gap with mind, I'd need to see a metaphysics that is equally comprehensive and parsimonious. You've never proposed one, and my impression is that this is not something you're particularly interested in. I can respect your point of view on that, but I have a different one.

You seem interested in exploring these possibilities, but I am not. — Relativist

I understand that you’re looking for a comprehensive alternative metaphysics. That’s a high bar — one that most philosophers don’t clear. My interest is less about constructing a new system and more about questioning the adequacy of physicalism and pointing out why it can't be understood as complete (or even completable!)

Besides, it is common practice in philosophy to show the way in which a framework is inadequate without immediately offering a replacement. Kant didn’t resolve every metaphysical puzzle; he set limits. Chalmers doesn’t provide a worked-out metaphysics of consciousness, but his argument still shifted the debate. Plato's dialogues contain many more questions than answers. For that matter, philosophy may be better understood in terms of asking questions than providing answers.

In addition to pointing out the so-called 'hard problem of consciousness' (which is the irreducibility of firrst-person experience) I've also argued along other lines, such as that information is not reducible to matter or energy (Norbert Wiener); that what exists and what is known to be real are not coterminous (C S Peirce); that the placebo effect and neuroplasticity as cases of top-down causation are inconsistent with neuro-physicalism; that constraints, forms, and intelligible structures (laws) play a real role, which physicalism as substance-ontology fails to recognise. I often raise these with various physicalist interlocutors. Anyway we went through it all in in this thread.

I understand that you’re looking for a comprehensive alternative metaphysics. That’s a high bar — one that most philosophers don’t clear. — Wayfarer

And yet, physicalism does comprise a comprehensive metaphysics. My eyes are wide open: I recognize that it's imperfect; I want to understand it's weaknesses, because that comprises an area where it can't be applied. But it can be applied to most everything I'm interested in.

It dovetails my epistemology. My epistemology justifies utilizing physicalism as a pragmatic framework for evaluating new information. Conversely, physicalism grounds that epistemology, in terms of a theory of truth. As I've recently discussed in another thread, I think that most of our rational beliefs are the product of inference to best explanation: draw conclusions (form beliefs) based on evidence (interpeted through my world-view, of course) and strive for that conclusion to be the best interpretation of that evidence.

This outlook comes full circle when reconsidering physicalism: I'm not going to drop it unless there is a better explanation. I haven't encountered one. The "explanatory gap" simply comprises an area where no rational position exists - and judgement should be withheld. I observe a variety of (unnatural) guesses about the mind , all of which seem purely speculative and depend on enormous assumptions. There seems to be no "best" one because they aren't epistemologically grounded in objective evidence. This "enormity" has two forms: 1) treating mind as ontologically primitive; 2) negating much else of what we know about the world.

"Possible" is about all we can say about the various enormous speculative hypotheses. There are more modest speculations that address the explanatory gap, that build upon what we know about the world - rather than supplant it. Still, they aren't grounded in evidence, so none are worthy of accepting them. But they support the view that naturalism is also possible - and therefore, I see no rational reason to drop it.

I've written this solely to outline my point of view, not to convince anyone else to change their mind. I'm happy to answer questions and to address any weakness one may perceive.

You say physicalism “comprises a comprehensive metaphysics,” but I would challenge that. It seems to me that physicalism doesn’t so much seek to provide a metaphysic as to negate it.

Remember that “metaphysics” as a term originates with Aristotle: it referred to those writings placed after his Physics — his “first philosophy,” where he addressed questions that physics, by its nature, cannot. The role of metaphysics has always been to ask about the principles and presuppositions of physics itself: what it means for something to exist, what kinds of causation there are, what “being” means in the most general sense.

Physicalism, by contrast, insists that all there is to reality is what the natural sciences study. But that is not “first philosophy”; it is the refusal to consider a first philosophy (and I note this refusal is often made explicit in modern philosophy). It begins by adopting the methods and categories of physics as metaphysically basic — which is precisely the point under dispute. It begins with exclusion and abstraction: bracketing off the qualitative features of experience as ‘subjective,’ leaving only those precisely measurable properties which, not coincidentally, are exactly what our scientific instruments can register.

As for the explanatory gap: it’s not a scientific theory, nor a temporary lack of evidence. It is the observation that third-person, objective description (the stock-in-trade of science) cannot in principle account for the first-person nature of existence — the fact that there is 'something it is like to be....' To say “withhold judgment” is fair enough; but to act as though physicalism is therefore the only “rational” option is to bury the the problem in the very premisses that it's exposing.

This is exactly what Thompson, Frank, and Gleiser call the blind spot of science: the inescapable fact that experience itself — the standpoint from which all science is done — cannot be brought into the picture by the very methods of objectification that make science possible. The point isn’t that it’s “subjective” in the narrow sense, but that it is constitutive: it is what allows there to be an “objective world” in the first place. So when you say you don’t see the issue, that’s not a neutral stance — it’s part of what the “blind spot” diagnosis itself explains. So if physicalism seems comprehensive to you, perhaps that’s because the very standpoint from which you judge it—lived experience itself—has already been screened out by the framework. You're not seeing what it is you don't see.

When you lump everything else under “enormous speculative guesses,” you’re effectively classifying any framework that doesn’t begin from physicalist premises as irrational. The whole sweep of philosophy other than physicalism! But that’s precisely what’s at issue. That’s why other traditions—Platonic, idealist, Buddhist, phenomenological —are vital: they provide principled accounts of experience and intelligibility, precisely what physicalism has excluded from its field of vision.

Remember that “metaphysics” as a term originates with Aristotle... — Wayfarer

The meaning of "Metaphysics" has broadened:

"One might almost say that in the seventeenth century metaphysics began to be a catch-all category, a repository of philosophical problems that could not be otherwise classified as epistemology, logic, ethics or other branches of philosophy. ...
...Whatever the reason for the change may have been, it would be flying in the face of current usage (and indeed of the usage of the last three or four hundred years) to stipulate that the subject-matter of metaphysics was to be the subject-matter of Aristotle’s Metaphysics."

--Stanford Article on Metaphysics

When you lump everything else under “enormous speculative guesses,” you’re effectively classifying any framework that doesn’t begin from physicalist premises as irrational — Wayfarer

My statements were not a judgement of anyone else's rationality. But it would be irrational for me to drop physicalist metaphysics in total just because of the negative fact you repeatedly discuss: the mind is not entirely physical. I do not insist the mind is necessarily 100% physical (I'm not dogmatic), but whatever else it might be seems unknowable - and therefore the possibilities I've seen discussed simply seem like speculative guesses. You certainly don't have to agree with me, but if you believe my judgement (rooted in my backrgound beliefs) is misguided (irrational), then please identify my errors. If you don't wish to, then just agree to disagree and stop reacting negatively when I describe my point of view.

I do not insist the mind is necessarily 100% physical (I'm not dogmatic), but whatever else it might be seems unknowable - and therefore the possibilities I've seen discussed simply seem like speculative guesses. — Relativist

I haven't seen any indication that you will consider any alternatives. If they don't fit with physicalism, you will declare them speculative or 'requiring enormous assumptions', but I haven't seen anything by way of detail as to why.

When you issue a challenge, you have to expect responses. Critique isn’t negativity; it’s the lifeblood of philosophy. I've made my opposition to physicalism clear since Day One. Furthermore the idea that physicalism works 'for you' is beside the point (although then again, your screen name is 'relativist'). Why? Because it reduces it to a matter of opinion. 'Oh well, other people have different ideas, but I advocate physicalism'. But if there's a truth of the matter, than it's not a question of opinion.

And physicalism is all-or-nothing, I'm afraid. Physicalism is monistic: there is only matter, so if mind is anything other than matter, then it fails - you can't have a partial monism.

As far as this discussion is concerned, the topic is 'mental to mental causation'. But it might be useful to discuss the subject in relation to mental causation, generally. Physicalism must insist that 'mind is what brain does' and that intentional thought is nothing more than the configurations of neural matter, ultimately amenable to neuroscientific reduction. D M Armstrong is quite explicit about that. But that 1960's style of neural reductionism has gone almost completely out of fashion, save for amongst a certain clique of academics, because it faces insuperable logical problems. How, for example, do you explain syllogistic logic, or for that matter general semantics, in terms of neural processing? Syllogistic logic and general semantics operate in a normative, rule-governed space ('the space of reasons'). To reduce that to neural processing is a category mistake. Neural firings may underlie thought, but they don’t explain validity, reference, or meaning. Materialist theory of mind has moved on since Armstrong, but these kinds of objections remain, in fact it is because of them that physicalist philosophy has to keep re-defining its terms.

there's naturally not a lot of literature because the ideas in that other thread are pure speculation - possibly worse than pure speculation.

It didn't seem as if the other "m2m" thread was going in the direction that interests me, so I haven't read it carefully.

I think the paucity of literature on m2m is for a different reason. The general assumption is that causal language ought to be reserved for interactions that have at least one physical component -- that is, physical-to-physical (p2p), physical-to-mental (p2m), or mental-to-physical (m2p). On this understanding, mental events can't cause other mental events. I'll have a lot more to say about this, if I ever get the darn OP written. But quickly: We can, and do, say that propositions provide reasons for holding other propositions -- but this is supposed to take place in the mysterious world where propositions exist and interact without any minds to think them. And/or, we can say that a thought -- understood now as a mental event and not a proposition -- associates with another thought. I find this also mysterious, or at any rate a mere sketch. But the idea is that any talk of causality can only be brought in if the mental is tied to a physical substrate of some sort. And of course it presupposes a mechanistic view of causality.

I don't think there's as much presupposition as you think - I think moreso, it's about the obvious fact that we can experiment on the physical world and come up with causal explanations in a way that we can't do with the "non physical mental world" you suppose exists.

I can hit a ball into another ball and watch the second ball consistently and reliably react in physical space. If I know both of their masses and the first balls speed, I can fairly consistently calculate the next sequence of events - I can calculate, given the surface they're on, how far the second ball will roll before it stops, and I'll be pretty darn close to right if I'm using the right equations.

There's nothing comparable about this mental world. Nobody's even sure if there is a mental world separate from the physical world. Some people suppose there is, but nobody has the faintest idea about how it's supposed to work.

So of course there's no literature, right? What are they going to write about? Experiments they can't do on a substance they can't observe?

The closest we have is psychology, and there's no lack of literature on that.

M2M seems interesting. On the one hand, if I wrote 12 + 7 =, I expect quite a few people will soon have 19 in their thoughts. But it's not the physical properties of the characters, or spoken sounds, that lead you to have 19 in your mind.

If that was the end of it, I might judge it one way. But how often are our words misunderstood? Especially online? I say one thing, and the other person thinks I mean something else. Maybe they think I meant it sarcastically. Maybe they think I meant the opposite of what I meant. Maybe they anticipated, incorrectly, where I was going with my longer of thinking. Inn whichever scenario, the meaning they "received" is not the meaning I "sent".

If it was not the contents of my mind that put the contents of their mind into their mind in the latter case, can we be sure that's what happened in the former?

we can experiment on the physical world and come up with causal explanations in a way that we can't do with the "non physical mental world" you suppose exists. — flannel jesus

I think (non-behaviorist) psychologists would be surprised to hear this! And just to be clear, I doubt whether there's a "mental world" that exists apart from physical supervenience. The whole "worlds" metaphor gets a good discussion in Popper's Objective Knowledge.

But you're right that my question overlaps with the concerns of psychology.

And just to be clear, I doubt whether there's a "mental world" that exists apart from physical supervenience. — J

I quite agree.

I haven't seen any indication that you will consider any alternatives. — Wayfarer

So...you make the unwarranted assumption that I won't. What I would need would be reasoning to support an alternative. A couple months ago, you said:

As for the 'unknown immaterial ground' - what if that 'unknown immaterial ground' is simply thought itself? — Wayfarer

This was no more than raising a possibility, with no reasoning to show why one might think this to be the case. I replied:

Why should I believe that? Why do you believe this to be more than a bare possibility? Thinking is a process - a process that humans engage in. Referring to a "thought" as an object seems like treating a "run" (the process of running) as an object. There's no run unless there's a runner, and there's no thought unless there's a thinker. This is what seems to be the case, so explain how your alternative makes sense. — Relativist

So you had tossed out a bare possibility, and I explained why I reject it. Because I stated my reason, you had the opportunity to identify a flaw in my reasoning, or simply answered my question, "Why should I believe that?" Or at least explained why one might take this possibility seriously.

I don't even know if you believe it, but bringing it up suggests you considered it worthy of mention. Why DO you?

I've been forthcoming with what I believe and why I believe it. This affords you the opportunity to identify a flaw in my reasoning, or undercut something I believe. By contrast, you have only made vague statements about what you believe.

But just to be clear about this . . . I do think that Popper's World 3, which refers to abstracta in general, apart from any particular physical/mental instantiation (Worlds 1 and 2), has to be understood as independent. We're still seeking good explanations of exactly what that means -- how it can be the case that there is a N-teenth prime even if no one knows what it is, or has ever had the thought of it.

Well, I can't much comment. I'd never heard of Popper and his Worlds until you mentioned him a couple posts ago. But I don't see why a N-teenth prime is a problem. We know how mathematics works, whether we discovered it or invented it.

I've been forthcoming with what I believe and why I believe it. This affords you the opportunity to identify a flaw in my reasoning, or undercut something I believe. — Relativist

And I've been forthright in my criticism of physicalist philosophy of mind. Above, I mentioned some of them:

In addition to pointing out the so-called 'hard problem of consciousness' (which is the irreducibility of first-person experience) I've also argued along other lines, such as that information is not reducible to matter or energy (Norbert Wiener); that what exists and what is known to be real are not coterminous (C S Peirce); that the placebo effect and neuroplasticity as cases of top-down causation are inconsistent with neuro-physicalism; that constraints, forms, and intelligible structures (laws) play a real role, which physicalism as substance-ontology fails to recognise. — Wayfarer

All of these could be elaborated, but in the context of mental causation, I noted the objection:

How, for example, do you explain syllogistic logic, or for that matter general semantics, in terms of neural processing? Syllogistic logic and general semantics operate in a normative, rule-governed space ('the space of reasons'). To reduce that to neural processing is a category mistake. Neural firings may underlie thought, but they don’t explain validity, reference, or meaning. — Wayfarer

Perhaps this would be a cogent example to concentrate on, as it is proximate to this topic.

how it can be the case that there is a N-teenth prime even if no one knows what it is, or has ever had the thought of it. — J

But the same can be said of the real numbers, generally. Do they exist prior to being discovered? My view is that they don't exist at all except for as intellectual acts, but at the same time, they are real for anyone who is capable of understanding them (and hence, discovered not invented.)

Many of the arguments about the reality of abstract objects revolve around the misconception that they are held by Platonism to exist in an 'ethereal realm', some 'place' that is 'other' to the domain of objects in space and time. But the expression 'the domain of natural numbers' is a figurative use of the term 'domain' - it is not referring to a domain in the sense of a place. But nevertheless, two and four are inside it, and the square root of one is not. It is real, even if not materially existent.

There is a vast domain of what used to be called such 'intelligible objects' - numbers, laws, principles, and many other things - but it's an 'ethereal place'. It is the domain of ideas that can only be grasped by a rational intelligence. But at least some of these are not generated or created but discovered by the mind. I think that's what Popper was driving at. Also Tyler Burge Frege on Knowing the Third Realm (which incidentally has some material on mental causation, or at least the relations of ideas.)

But the same can be said of the real numbers, generally. Do they exist prior to being discovered? — Wayfarer

Yes. I picked a number no one knows just to make the point clearer. And your "real/exist" schema works well to help keep things straight.

it is not referring to a domain in the sense of a place. — Wayfarer

Do some people think it is? A "place" without space and time? Hmm . . .

It is the domain of ideas that can only be grasped by a rational intelligence. But at least some of these are not generated or created but discovered by the mind. I think that's what Popper was driving at. — Wayfarer

Popper did think we created them. He didn't believe World 3 objects exist apart from being created by World 2 thoughts. I'm more inclined toward your idea, which is closer to (non-naive) Platonism. But then you do require the intellectual act itself in order to bring such an object into reality, so perhaps this is closer to Popper after all.

I don't see why a N-teenth prime is a problem. We know how mathematics works, whether we discovered it or invented it. — Patterner

Sure. It's only a problem if you're philosophically bothered by the question "discovered or invented?"

it is not referring to a domain in the sense of a place.
— Wayfarer

Do some people think it is? A "place" without space and time? Hmm . . . — J

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.” — What is Math? Smithsonian Magazine

Platonism, as mathematician Brian Davies has put it, “has more in common with mystical religions than it does with modern science.” — What is Math? Smithsonian Magazine

I suppose. But this is a little hard on modern science. "Tough-minded" empiricism, perhaps, has trouble with abstracta. But scientists commonly work with laws and math, neither of which can be perceived or measured. I agree that some scientists don't appear to see the contradiction between that and nonetheless denying any reality to non-space-time items.

Sure. It's only a problem if you're philosophically bothered by the question "discovered or invented?" — J

Is the problem that humans might have invented mathematics? If that's it, I don't see it as a problem. It seems to me physical things we've invented are as real as physical things we did not invent, and non-physical things we've invented are as real as non-physical things we did not invent.