the Dharmakaya is nevertheless real - but never to be made the subject of dogmatic belief. But that is definitely another thread (or forum!) — Wayfarer

Yes! Anyway, I believe that strictly carried through empirical idealism leads either to an Advaita-like system (there is only one Reality) or to a Madhyamaka-like one (there is neither-one-nor-may ultimate realities, but ultimate reality is wholly beyond concepts).
Also, I don't think that it is a chance that these systems posit (at least as provisional truths) a beginningless mental continuum. If that is the case, there is no problem of explaining how the mind and the empirical world 'arose' in the first place.

Kant’s T.I. does just that, to my understanding anyway. As in his statement that the proud name of ontology must give place to the modest title of analytic of the pure understanding, which is to say it is useless to inquire of the being of things, or indeed their possible nature, when there is but one a posteriori aspect of any of those things for our intellect to work with, and consequently supplies the rest from itself. — Mww

Ok, thanks!

The empirical world doesn’t ‘arise’’; it is given, to the extent its objects are our possible sensations. — Mww

But, in fact, it does, right? Before I was born, for instance, the empirical world that I am now cognizing didn't really exist. If there was a point in time that my mind didn't exist, then, given that the empirical world is not 'independent' from it, it would seem that the empirical world arose. So, it seems to me that the question is worth asking.

If there is no answer to that question is either because we can't know it or becuase there is, indeed, no answer because, perhaps, what is 'beyond' the empirical world cannot be known conceptually.

Would it be the same to say, within, or under the conditions of, e.g., transcendental idealism, an ordered, intelligible representation of our empirical world is constructed, in relation to our understanding? — Mww

The problem is that even asking this question and assuming that we can, indeed, answer it seems to go beyond transcendental idealism. A consistent transcendental idealist IMO would simply say: "I cannot answer this question".

I can’t get behind the notion of an intelligible world, is all. Just seems tautologically superfluous to call the world intelligible, or to call all that out there an intelligible world, when without our intelligence it would be no more than a mere something. Just because we understand our world doesn’t mean the world is intelligible; it, more judiciously, just means our understanding works. — Mww

I disagree. If we say that the world is intelligible we are saying something non-trivial. That is, it has a structure/order that can be grasped by our faculties of understanding.
The empirical world of transcendental idealism can be grasped because it is constructed by the mind via sensibility and other mental faculties. On the other hand, if the 'external reality' is intelligible, we are saying that it has a structure that is graspable. This structure/order is not imposed by the mind but it's 'there'.

So, I would say that it is an explanation of why our understanding works not just a mere recognition that it does.

Anyway, thanks for getting back to me. I’m kinda done with it, if you are. — Mww

Thanks to you too! I hope I clarified a bit more.

Recall the koan, 'first there is a mountain, then there is no mountain, then there is.' 'First, there is a mountain' refers to before training, before initial awakening, the state of everyday acceptance of appearances. 'Then there is no mountain' refers to the state of realisation of inter-dependence/emptiness and the illusory nature of appearance. 'Then there is' refers to the mature state of recognising that indeed mountains are mountains, and rivers are rivers, but with a balanced understanding. — Wayfarer

Well, appearances are not negated but they must be recognized as 'mere appearances'. So, the 'mountain' seems to be an entity but, in fact, it isn't. But this doesn't mean that the there is no 'appearance of a mountain'. The mountain is illusion-like. So, I guess that one might attach some ontological status to the 'mountain' but it is very tenuous.

Anyway, as you know, most Buddhist schools regard the 'self' as illusion-like/mere appearance. Of course, there are various strands of Buddhist thought. I believe that Madhyamaka and Yogacara come close to transcendental idealism. But, in both case, both the 'self' and the 'world' (and thus every thing) are illusion-like, mere apperances. When all conceptual constructs are removed, 'what remains' is neither 'something' nor 'nothing' (because, after all, apperances cannot be negated).

In Advaita, the reasoning is similar but Advaitins affirm that recognizing the apperances as 'mere appearances' actually leads one to the conclusion that only Brahman is real. It's no chance that IIRC that both Advaitins and Madhyamikas argue that the when we anlyse the world correctly, we come to the conclusion that no thing ever arose. For the Advaitin this means that there is, ultimately, only the unarisen Brahman. For the Madhyamika, ultimately, both oneness and plurality don't apply - 'Suchness' is not a unity, nor a collection of things but not even nothing. Our concepts do not apply (Kant would IMO say that we can't know if they do not apply or they do...).

Nowadays I am less persuaded by these views even if I am still very fascinated by them. I do believe that multiplicity is real. Even if we and the things in the world are ontologically dependent, it isn't true that we and them are ultimately illusion-like. We maintain our identity as distinct from what is not us. And the distinction is real.

I don't understand what you mean by the idea that structure of the world needs explaining. Its like asking why there is anything at all, which is a question not resolved by any perspective. — Apustimelogist

I disagree, unless you think that existence involves intelligibility (which is something that classical metaphysics asserts but I'm not sure physicalists generally would say). In any case, if you assume that the world is intelligible and its existence must be intelligible too, then it would be meaningful to ask if the world is contingent or not contingent and discuss the consequences of such statements.

Its entirely prediction. You see the words, you infer the kinds of behaviors you expect to see in that context and act appropriately. Words and meaning is about association which is just what anticipates a word, what comes after a word, what juxtaposes words - that is all I mean by prediction. prediction is just having a model of associations or relations between different things. Like a map that tells you how to get between any two points. Fictional stories are included. Everything we do is included. — Apustimelogist

I'll need to think about this. This is also because it includes things that I would never classify under the term 'prediction'. Not saying that you are wrong in calling that way.

Here's where I explained it to Wayfarer: — Relativist

Ok, thanks for the clarification. But note, that, however one can still say that we have been proven wrong in our assumptions many times, even by science itself. It's obvious, for instance, the Sun and the stars revolve around us.
Of course, the existence of a 'physical world' is something more fundamental than the motion of celestial objects but the point is interesting regardless.
Furthermore, note that even the most radical of the ontological idealist often assumes that the minds interact. So, even for them, there is an external world. It's just very, very different from what we tend to think.

So, I'm not sure if your argument here is compelling. But I agree that denying the 'physical' seems to much of a stretch. But this isn't something that all ontological idealist do anyway. Neither neoplatonists nor Hegel nor classical theists (if we consider them as 'idealist') deny the existence of the 'physical'.
Berkeley and Bradley apparently did but ontological idealism is a very wide spectrum.

This is unarguably true, but it doesn't imply the framework represents a false account. Consistent with evolution, it's plausible that our mental faculties came into being in order to interact with the world that we perceive and "make sense" of. Were these faculties to deceive us, we wouldn't have survived- so it is reasonable to maintain our innate trust in these faculties. Perfectly fine to keep the truism in mind, and adjust our inferences, but extreme skepticism seems unwarranted. — Relativist

But note that, however, pragmatism doesn't imply truthfulness. For instance, it is useful for me to 'know' that the Sun rises in the east and sets in the west even if, in some sense, it's false. So, even if I believe that the Sun truly revolves around the Earth this can be still an useful belief for me.
That said, of course, unwarranted skepticism can be dangerous. So, the best might be to not claim 'sure knowledge' and be open to revision of one's own beliefs, especially those that we can't have 'direct access' to a verification or falsification.
I would say that, however, the existence of an external, partially intelligible physical world is a reasonable belief to be mantained. But I do not claim certainty about this.

This still relies on mere possibility. This is like a conspiracy theorist who comes up with some wild claim which he clings to because it can't be proven wrong. Only this is worse because there's no evidence to support the hypothesis. — Relativist

I see what you mean but Bradley's argument is at least different in character. While I don't buy the conclusions it is still interesting. Saying that it's like a conspiracy theory is a disservice to it.
IMO it raises interesting questions also about the nature of the 'physical', even when we assume that it is real.

Yes, the law of contradictions is semantics: it applies to propositions, not directly to the actual world.

How can it be that the physical world can produce physical beings that make sense of the world? The survival advantage explains the causal context. Can something physical experience meaning? I can't prove that it can, but it seems plausible to me. If you're inclined to think it cannot, then what would you propose to account for it? The problem you have is that you need to make some wild assumptions about what exists to account for it - and then I'd ask if those assumptions are truly more reasonable than physicalism? — Relativist

Again, I can even agree with this. But note, that 'meaning' seems something that relates to mind. So, if meaning is something that relates to the physical too (and, in fact, it is something fundamental), it would seem that the 'physical' is not that different from the 'mental'. In other words, we land to a physicalism that seems not to far from a panpsychism (or at least quite open to the 'mental').

I suspect that I don't understand what you mean. — Apustimelogist

Well, I believe that it's simply becuase for you it is a fact that needs no explanation. So, you don't see a problem (perhaps I am the one that sees a problem where there is none. But I am not persuaded by that).

Yes, meaning is just more prediction. Nothing different, nothing special. — Apustimelogist

Not sure about this. Let's say you encounter the words "one way" in a traffic sign. How is that 'prediction'? It seems to me that here meaning is not predictive.

The meaning of 'word' just comes from its associations with other aspects of our experiences which become apparent in how we use the word 'word'. Nothing more than prediction. — Apustimelogist

Do you believe that, say, fictional stories (like, say, fantasy novels) are still 'predictions'? How is that so? They are certainly meaningful, but I am not sure that we can say that their meaning are instances of predictions.

What do you mean? — Apustimelogist

I meant that if the world is completely devoid of intelligible structure it might still be possible for us to make good predictions. It just doesn't seem plausible. It would seem to me an incredible amount of 'luck'. I can't, however, exclude with certainty that possibility.

My answer would be that the in-itself—the world as it is entirely apart from any relation to an observer—cannot be said to be non-existent. Of course something is, independently of our perception of it. But precisely insofar as it is independent of any possible relation to perception or thought, it is beyond all predication - hence, also, not really 'something'! Nothing can truthfully be said of it—not that it is, nor that it is not, for even non-existence is itself a conceptual construction.

In this sense, and somewhat in line with certain strands of Buddhist philosophy, the in-itself is neither existent nor non-existent. Any claim otherwise would overstep what can be justifiably said, since even the concept of "existing" or "not existing" already presupposes a frame of conceptual reference that cannot be meaningfully applied to what is, by definition, outside such reference. (The proper attitude is something like 'shuddup already' ;-) ) — Wayfarer

Yes, I would say that this is a possibility and perhaps it is the most consistent one if one accepts epistemic idealism. The 'in itself' is 'beyond concepts'. If this is so, then, it's not nothing because, if it would be nothing then, well, we could not experience anything. It can't be 'something' in the sense that it isn't something that we can conceive.

My problem with this is the following. If the 'in-itself' is so 'beyond concepts' it would imply IMO that, ultimately, the plurality is illusory. Either all reduces to 'one' (as in Advaita) or to 'neither one nor many' (as non-dualism is conceptualized in Buddhist schools). It just seems that we can, say, speak of 'boundless that is writing' but, in fact, there is no 'boundless' and the whole thing is illusion-like. If one wants, instead, to assign some reality to us and the world it seems to me that one must assume that the 'external world' has some intelligible structure. So IMO if one wants to follow the epistemic idealism model to its inevitable conclusions, then, it seems to me that, ultimately, one must say that selves, minds, the external world are illusion-like (not completely equivalent to illusions, perhaps, because when all that is ordered in conceptual representation is removed it's isn't true that nothing remains...). To be fair, some who say that the 'in itself' is beyond concepts accept just these things, so it's not a criticism, I guess. I am just not persuaded by these views.

IMO many empirical/transcendental idealists underestimate the implications of their model (I think that you do not BTW).

Most in fact, naturalism being one of them. Pretty much anything except materialism and idealism respectively. — noAxioms

Naturalism generally explicitly denies anything 'supernatural' (there is nothing outside the 'universe' or the 'multiverse'). Unless it is something like 'methodological naturalism' I don't see how it is metaphysically neutral.

I am aware of this wording, but have never got it. How can a perspective not be first person by the thing having the perspective, even if it's a tree or a radio or whatever? Sure, it might not build a little internal model of the outside world or other similarities with the way we do it, but it's still first person.

An internet intelligence might have thousands of points of view corresponding to widespread input devices. That's not a single perspective (just like our own isn't), but again, it's still first person. — noAxioms

Well, I believe we would disagree here about what is a 'first-person' perspective (see our discussion about 'perspectives' before). Anyway, the 'third-person perspective' is said to more or less be equivalent to a view from anywhere that makes no reference to any perspective.
I guess that you would say that there can't be any true 'third-person perspective', though.

I kind of lost track of the question. Classify the ontology of the first and third person ways of describing what might be classified as an observer? — noAxioms

I meant: is it dualistic to assume that there is indeed consciousness and 'the material world' and none of them can be reduced to the other with the proviso, however, that any of them are 'ontologically fundamental'?

OK, I can go with that, but it implies that 'stuff' is primary, interaction supervenes on that, and laws manifest from that interaction. I think interaction should be more primary, and only by interaction do the 'things' become meaningful. Where the 'laws' fit into that hierarchy is sketchy. — noAxioms

I actually agree with that. 'Stuff' requires both interactions and laws/regularities of how these interactions happen. You can't have 'stuff' before interactions and regularities, which both seem more fundamental (after all, every-thing in this world seems to be relational in some way...).

Depending on one's definition of being real, I don't agree here. A mind-independent definition of reality doesn't rely on describability. By other definitions, it does of course. — noAxioms

Well, is it interesting, isn't it? I believe that, say, someone that endorses both materialism and scientism would actually tell you that the world is 'material' and totally describable. It would be ironic for him to admit that this implies that is not 'mind-independent'.
I am open to the possibility that something mental is fundamental also because of this: if the 'physical world' truly has a structure that is describable by concepts and must have such a structure, then, it seems that 'something mental' is fundamental.

Anyway. If, in order to be mind-independent a definition of reality must not rely on describability would not this mean that, in fact, we can't conceive such a definition of reality?

There were no sensations in the universe before life came into being. — Relativist

Not sure if you understood Bradley's argument and similar. The point is: can you conceive a world that has absolutely no relation to 'sentient experience'?
Remember that our knowledge certainly starts from our experience. If we don't experience we don't know. And the point here is that we can't conceive anything except withing the framework of your experience and the mental faculties that 'make sense' of it.

This seems to entail abandoning our innate sense of a world external to ourselves. If one really believed this, why wouldn't one stop interacting with the world we're allegedly imagining? Why eat? Why work? — Relativist

It depends on the 'ontological idealist'. Ontological idealists of this kind, for instance, are generally not solipsists and they would affirm that there is something outside our minds: other minds and their mental contents. So, perhaps, while there is no 'material' world, there is still something external of us and, in fact, there are still other minds with which/whom can interact.

Understanding can only be from our perspective (it's like a non-verbal language - a set of concepts tied directly to our perceptions), but that doesn't mean it's a false understanding. And it has proven to be productive — Relativist

Right but this doesn't undermine neither idealism (epistemic or ontological) nor the argument that Bradley makes. There might be some kinds of sentient experience that we can't know but are in principle knowable.

Ironically, epistemic idealists would actually assert in a rather strong manner that our understanding can only be from our perspective. Certainly, a metaphysical physicalism asserts something 'more' than what empirical idealists claim we can know.

It is a necessary fact that survival entails successful interaction with the external world. Our species happened to develop abstract reasoning, which provided a "language" for making sense of the world- a useful adaptation. There may very well be aspects of the world that are not intelligible to us. Quantum mechanics is not entirely intelligible -we have to make some mental leaps to accept it. If there's something deeper, it could worse. — Relativist

I disagree that QM isn't intelligible. The predictions are certainly intelligible. The problem is with the interpretation. But, after all, even in newtonian mechanics there are various things that are matters of interpretation (such as how to understand 'forces').

Anyway, you are still asserting that there is intelligility without explaining it. That is, the very fact that evolution happened in a way that is intelligible to us means, to me, that the world is intelligible. 'It makes sense' that, say, language and reasoning allow us to adapt in a very flexible way to our environment. And this suggests that the world is intelligible (at least partly). My point is: why is it so? can we understand the 'structure' in purely physical terms?

Exactly. We can consider a universal by employing the way of abstraction: consider multiple objects with a property in common, and mentally subtract the non-common features. This abstraction is a mental "object", not the universal itself. — Relativist

Ok, thanks for the clarification. I am myself not sure if 'universals' are concepts or not.

What IS ontologically fundamental? Isn't it a brute fact? Even if it is mathematical, it's a brute fact that it's mathematical, and a brute fact as to the specific mathematical system that happens to exist. — Relativist

Well, at a certain point explanations do stop. Agreed. But IMO physicalism stops before the time. That is, I think that the intelligibility of the physical world has an explanation. Not that we can explain everything.

A physicalist perspective is that we abstract mathematical relations which exist immanently. There are logical relations between the pseudo-objects (abstractions) in mathematics, and logic itself is nothing more than semantics. — Relativist

So, the 'law of non-contradiction' is semantics?

Anyway, I believe that intelligibility also implies meaning ('making sense'). So, that's another reason why I don't understand how to explain (without assuming it from the start and leaving it de fact unexplained) how a purely physical world is intelligible.

Not too sure what form the problem is supposed as having, but at first glance:
So if the ordered world of experience arises from the interaction between the mind and representations of the external domain….the problem disappears? — Mww

No, actually, I meant that from a Kantian perspective it's just difficult to explain, without assuming the intelligibility of the 'external world' (in the thing-in-itself), how the empirical world 'arises'. Of course, one might think to leave this unexplained, as perhaps the most consistent forms of transcendental idealism do.

For instance, Schopenhauer argued that the 'thing in itself' must be 'one' because plurality arises in the empirical world. That is, the will, according to him, as the thing-in-itself wasn't characterized by the properties that categories understand. But IMO this is self-contradictory. First of all, if the thing-in-itself is one, then, it can be understood by the concept of 'unity'. Secondly, he tried to explain how plurality arises by saying that it is 'imposed' on the will by the mind. But the minds are many, not one. So, at the very least Schopenhauer either had to say that plurality was ultimately an illusion (as in Advaita Vedanta, if you are familiar) or that the minds (and, therefore, plurality) are ontologically distinct from the will (while dependent on it). In both cases, however, I would say that Schopenhauer had to resort to 'pre-Kantian metaphysics' (either by denying the reality of plurality or by affirming it one must make a metaphysical statement). I don't think that this is 'bad'. But on this he was inconsistent.

IMO Kant was more careful here. He tried to assert nothing about the 'noumenon'. But, again, it is difficult to me to see transcendental/epistemic idealim as a stable position, especially in practice.

That which is mind-independent cannot be represented. With respect to Kant’s view alone, reality is not mind-independent, by definition hence by methodological necessity, the content of which remains represented not by the cognitive faculties, but sensibility. From which follows the ordered world of experience arises from that which is always truly presented to the mind, and from that, appearances to the senses are not merely assumed, but given. — Mww

I agree that 'reality' for Kant is not mind-indepedent if by reality we mean 'empirical reality'. In my post I didn't make a distinction between cognitive faculties and sensibility, which was wrong in terminology from a Kantian perspective. I do believe, though, that sensibility is also cognition (and IMO 'cognition' as generally understood shares some analogies with 'sensibilities'). If we want to stick to Kant's terminology, however, ok.

Anyway, the point is that within transcendental idealism you have an ordered, intelligible empirical world that is related to a mind. It seems evident - albeit we can't have a 'total certainty' - that this 'empirical world' is the result from an interaction between the subject and the 'external world' and the latter might be unknowable. But even if it is unknowable, the 'best guess' is that it somehow must have a structure/order that allows the 'arising' of the 'empirical world'.

Frankly, I still don't see how transcendental/epistemic idealism avoids the pitfall of 'epistemic solipsism', which might in a sense 'correct', in the sense that we have no 'certain knowledge' of anything outside us and 'the world as it is represented by us'. But I am my misgivings when this is taken to mean that we can't know anything about the 'thing in itself'.

From whence, then, does the interface arise? If the represented world of experience is all with which the human intellect in general has to do, there isn’t anything with which to interface externally, interface here taken to indicate an empirical relation. And if the only possible means for human knowledge is the system by which a human knows anything, the interface takes on the implication of merely that relation of that which is known and that which isn’t, which is already given from the logical principle of complementarity. Does the interface between that out there, and that in here, inform of anything, when everything is, for all intents and purposes, in here? — Mww

I am not sure about the point you make in this paragraph. The interface is the 'empirical world' itself, which is ordained by cognitive and sensitive faculties. The point is that the 'interface' is supposed to be a representation of something 'outside' of our minds which never 'appears' in the interface itself. Can we avoid an epistemic solipsism, however, if we deny that we can say anything about that 'something'.

Empirical/experienced world, and the variated iterations thereof, is a conceptual misnomer, though, I must say, a rather conventional way of speaking, not fully integrating the development of the concepts involved. That, and the notion of “intelligibility of the world”. Which sorta serves to justify why the good philosophy books are so damn long and arduously wordy. — Mww

Intelligibility of the world merely means that the world has a structure that can be 'understood' in terms of some conceptual categories, principles and so on. That is, that it has a structure that can be 'mirrored' to some conceptual order.

Not sure however what is your point about empirical/experienced world. It is IMO a somewhat clear concept to me. It is the world as it appears to a given mind.

Alright, sure. I just think those things come from a brain that has evolved able to infer abstract structure in the information it gets from the environment. There is a kind of pluralism in the sense that depending on how the brain relates to the environment, different information appears on its sensory boundary and so different structures are inferred. Like say if you are looking at an object from different angles and it looks different. — Apustimelogist

Ok. The problem for me, however, is to explain from a purely physicalist point of view why there are these 'structures' in the first place.

For the world to intelligible imo just means that it has structure. To say the world has structureis just to say something like: there is stuff in it and it is different in different places, which is kind of trivial. — Apustimelogist

Not just that. It also means that the 'stuff' behaves in a certain manner and so on. And this 'order'/'strucure' is such that it can be understood (maybe only in part, but the point remains) by a rational mind.

Furthermore, it seems to me that intelligibility also conveys meaning. And I am not sure meaning is something you can explain in purely physical terms. For instance, the meaning of the word 'word' is difficult to explain just in physical terms. But, again, I assume that if one accepts that intelligibility is just a 'fact', then, also the associated meaning is assumed to be a 'fact'. I don't see both of them as trivial. But I think we have to agree to disagree here.

Yes, this doesn't make sense to me. If we can fit coherent models to reality, even if they turn out to be erroneous after some limit, it would suggest they capture some subset of the intelligible structure (at the very least intelligible empirical structure) of reality. This just happens to be embedded in a model whose wider structure is erroneous. — Apustimelogist

:up: I guess that the negation of this isn't 'impossible' but it doesn't seem plausible.

How do they justify believing this? — Relativist

Imagine 'how the world looks like' without any kind of sensations. Here's a quote I found from F.H. Bradley (who BTW wasn't a Berkeleyan idealist but is said to be more like Hegel apparently... I actually don't know Bradley, I just use this quote because I find it a good way to put it and here he looks quite the 'Berkeleyan' or possibly the 'epistemic idealist' - this depends on how you interpret his conclusion):

"Sentient experience, in short, is reality, and what is not this is not real. We may say, in other words, that there is no being or fact outside of that which is commonly called psychical existence. Feeling, thought, and volition (any groups under which we class psychical phenomena) are all the material of existence, and there is no other material, actual or even possible. This result in its general form seems evident at once; and, however serious a step we now seem to have taken, there would be no advantage at this point in discussing it at length. For the test in the main lies ready to our hand, and the decision rests on the manner in which it is applied. I will state the case briefly thus. Find any piece of existence, take up anything that any one could possibly call a fact, or could in any sense assert to have being, and then judge if it does not consist in sentient experience. Try to discover any sense in which you can still continue to speak of it, when all perception and feeling have been removed; or point out any fragment of its matter, any aspect of its being, which is not derived from and is not still relative to this source. When the experiment is made strictly, I can myself conceive of nothing else than the experienced. Anything, in no sense felt or perceived, becomes to me quite unmeaning. And as I cannot try to think of it without realising either that I am not thinking at all, or that I am thinking of it against my will as being experienced, I am driven to the conclusion that for me experience is the same as reality. The fact that falls elsewhere seems, in my mind, to be a mere word and a failure, or else an attempt at self-contradiction. It is a vicious abstraction whose existence is meaningless nonsense, and is therefore not possible."

F.H. Bradley
- Appearance and Reality

To the 'Berkeleyan idealist' the fact that we struggle to conceive 'what the world looks like' when all 'mental content' is removed is an evidence for denying the existence of a 'mind-independent matter'.

Physicalism is epistemically grounded in our perceptions of the world - presumably our senses deliver us a reflection of reality (so there is a bit of distinction between perceived reality and actual reality) and the success of science. It's logically possible for these assumptions to be false, but the grounding beliefs are innate - basic beliefs. Possibility alone doesn't justify abandoning them. — Relativist

As I said in my previous post, physicalism seems content to claim that intelligibility (which you assume here) is just a 'brute fact' that doesn't need to be explained. I disagree. So, for me, it isn't enough.

I can actually agree with what you said here, despite not being a physicalist. I do not deny the existence of a 'physical world', independent from our minds (i.e. which is not just mental content), but IMO it isn't ontologically fundamental.

This framework reflects, and accounts for, the structure that we see in the world. It's not a causal account, it's a structural account. — Relativist

To be honest, I actually think that your view is similar to Aristotle's account of the physical world.

I believe that the structure is intrinsic to physical reality, i.e. there would be no physical reality without structure. But the structure itself, however, is not 'physical'. I do adimit, however, that if there were no physical reality, we might conclude that the structure itself would disappear. However, while I admit that this is true for some of it, the nature of logical and mathematical principles (their seemingly being necessary and eternal) leads me to think that is not wholly 'immanent' in the physical world. That's why I think that the ontological status of math/logic is actually important in this discussion.

No. It doesn't fit into a physicalist paradigm, ontologically. — Relativist

And yet, I do find your talk about universals quite close to it. I mean, not the same as it. But similar. The only difference I can think of is that you think that universals are immanent and, therefore, nothing is independent of physical reality. Still, you seem to assume that universals aren't just 'figments of imagination' but they do have an ontic status, independent from us.
I may be wrong but I don't think you are an anti-realist about universals.

"Physical" is just the label attached to the things that exists that is causally connected to everything else. Causally disconnected things are logically possible, but because of an absence of causal connections, their existence is moot and there is no epistemological justification to believe such things exist. — Relativist

Ok. In other words, do you believe that universals/structure can be considered 'physical' because their 'existence' is immanent in the physical world?

If you still believe there's an equivocation, please describe it. — Relativist

Well, I have my difficulties to label universals as physical for instance. But I think I understand why you would do (I hope I didn't however misunderstood your view).

I am not sure what this means: the interpretative structure of following a ball and catching it? — Apustimelogist

More or less. My point is that in order to even think to follow and catch a ball, you need some interpretative mental faculties. Same goes for some basic innate concepts (like a basic notion of 'thing', 'change' and so on).

What kind of answer you want? I don't understand why you want me to explain how the world can be structured. It seems self-evident to most people. — Apustimelogist

Well, yes, but my question is how to understand why the physical world is intelligible in the first place. A physcialist might well aswer as you do. It is just a 'brute fact'. But IMO it would be ironic. The very intelligibility of the world is left unexplained (and perhaps unexplainable).

For instance Aristotle mantained that all physical things are composed of matter and form. By 'form' he meant, well, the same as Plato's forms. So concepts for him were an intrinsic part of the 'physical reality'. That would a possible answer to my question. But I doubt that a physicalist might find it congenial. It's difficult, after all, to think about Aristotle's ontology of physical things as 'physicalist'.

I don't need a platonic realm to do this, I just need a brain that can infer quantity in the sensory world and extrapolate. — Apustimelogist

Perhaps you don't need a platonic realm. But that intelligibility is left an unexplained 'brute fact'. I am not saying that physicalism is necessarily wrong because of this (even if I believe it would be a reasonable conclusion to make).

You can have an intelligible model that is incorrect. Like people used to have models of the solar system that were intelligible, gave correct predictions and turned out to be completely wrong. — Apustimelogist

Yes, the model is incorrect and intelligible. But I guess that one could then say that if, even in principle, we could not make any correct model, then the world would be in fact intelligible for us.

But, again, the very fact that we can make predictions suggests to me that, at least in principle, we could make a 'correct model'. It might be beyond our reach but still a possibility in principle. Otherwise, it seems to me that our predictions would be completely right for 'luck': that is, we get incredibly good predictions in the absence of an intelligible structure of reality. Weird.

That’s it. This is what I believe Kant means by the ‘in itself’, as distinct from ‘the phenomenal’. The issue is, empiricism tends to take what exists in the absence of any observer as the hallmark of what is real, but that entails an inherent contradiction. — Wayfarer

Note, however, that there is IMO a problem with Kant's and similar views. So, intelligibility of the world is 'brought into' by the organizing activity of the mind. Of course, epistemic idealists hold that what mind brings in is just order. So, the question becomes: how can we understand this 'ordering'?
It seems in fact to assume that there is, indeed, a mind-independent reality which is then 'represented' by the cognitive faculties of the mind. Hence, it seems that the 'ordered world' of experience arises from the 'interaction' between the mind and 'the mind-independent reality', which is never truly presented 'as it is itself' to the mind. The 'represented' world of exprience is thus like an interface (as Donald Hoffman puts it, but the idea is much older) and for the knowing subject it is impossible to know what the world is like independent from the mental categories.

But even asserting that there is an interaction that, ultimately, is what 'triggers' the interface is to suggest a minimal degree of intelligibility of the 'mind-independent world', other than giving to it an ontological status. So, I wonder if epistemic idealism doesn't in fact necessarily collapse into some variants of either indirect realism or other types of 'idealism' or whatever else, except perhaps strict physicalism. Even, say, Bernard d'Espagnat's view isn't empirical idealism, after all. He believed that we can acquire some knowledge of the mind-independent reality, which he described as 'veiled' (just like, say, by touching a statue hidden by a veil we can know some of its characteristics). Not sure if his view can be called 'epistemic idealism' (of course, he, like others, incorporates some parts of the epistemic idealist thesis, without however fully subscribing to it IMO).

In any case, to the strict epistemic idealist, I would ask: how do you explain the 'arising' of the 'empirical/experienced world' without positing an intelligible mind-independent reality (let's consider the minds here as those of sentient beings not some 'higher' Mind, which would in fact be, in a certain sense, a mind-indepedent reality, at least from the epistemic idealist point of view)?

My point that "measurement is an essential element of duration" stands. In a relativistic universe, duration isn't an absolute, pre-existing quantity that merely needs to be "counted" by an observer. In other words, it is not transcendental, but phenomenal. The duration of an event itself is dependent on the observer's frame. Therefore, the act of measurement, by defining the observer's frame of reference, is intrinsically linked to the definition of that particular duration for that observer. You're not just measuring a pre-defined duration; you are, in a sense, participating in the definition of its duration by being in a specific frame. — Wayfarer

Well, I guess that one can even say that in order to even think to make a measurement you have to assume that the 'world' is intelligible in terms of mental categories (and 'time' might be one of them). The epistemic idealist would then say that such an assumption of intelligibility is only valid when the world is analysed in the context of experience, i.e. we can't make any claim about how 'the world is' without any kind of reference to experience. So the 'perspectival' character of physical quantities might even be an indication of this.
If duration is quantized, it would still not 'falsify' epistemic idealism IMO. It would simply tell us how 'the world as is presented' is best understood.

So this modern materialism then, what does it suggest, especially above and beyond what naturalism does? — noAxioms

If I am understanding your question correctly, that 'modern materialism' would be the thesis that fundamental reality is 'physical', 'natural' etc.

It's how I use the word, but mostly just to identify 'not dualism', and I prefer to use naturalism to describe that, so I admit that the term needs something else, perhaps said ontological stance. — noAxioms

My problem with this is that there are also philosophical models that do not make any 'stance' about whether 'the physical' or 'the mental' is fundamental. Some phenomenological approach conceptualize this by saying that the 'first-person perspective' (the 'mental') and the 'third-person perspective' (the 'physical') are not reducible to one another but you need to take both into account even if it is not possible to make a synthesis of them (think about 'complementarity' in QM). To none of them, however, an ontological status is actually granted. Both are ultimately 'point of views'.
How would you classify this? It is obviously not 'dualistic' in the sense that an ontologiy is not even presumed.

No, but I don't suggest that I am composed partially of principles and laws either. Those things are the means by which physical stuff interacts. — noAxioms

Sort of agree. They are not 'parts' that we are composed of. That would be a 'materialistic' interpretation of principles and laws. But even saying that they are 'means' is wrong IMO. I would say that they 'manifest' in the way physical stuff interact. If they weren't 'there', there would be no 'way' in which physical stuff would interact.

I am trying to understand all the terms being used here. Some examples would help, perhaps of something unstructured, and how exactly speaking about a physical reality contradicts materialism.
Something unstructured would seem to not stand out to anything, and in that sense it wouldn't be intelligible. Not sure if that's what you mean though. — noAxioms

Mmm it's difficult to make an example of something unstructured... because making a description would actually assume an intelligible structure!

I am not even sure that it even makes sense to think about an 'unstructured reality'. So, probably, this implies that, after all, intelligibility is sometinh essential to anything real.

Regarding my point about 'physical reality' and materialism, think it this way. If one posits that, say, the fundamental reality is, say, the Platonic 'world of Forms' it's possible to explain why the physical world presents to us regularities. They are, so to speak, 'moving images' of the Forms or 'manifestations' of them. And physical things are instantiations of the forms.
But materialism would simply assume that there is an 'order' in the world without having a conceptual category that explains it. Is being intelligible intrinsic/essential to be material? Is the 'order' material? etc

OK, but I've always associated that with just 'idealism'. Perhaps I should ask what non-ontic idealism is then. I mean, epitemic idealism makes sense, but almost in a tautological way. You only know what you know. — noAxioms

I quote my previous post which tries to explain 'epistemic idealism':

Then, of course, we have epistemic idealists. These would say that, in fact, we can only know the world as it is represented by our own mental categories. For them, it isn't at all surprising that the world seems intelligible: our experience is structured by our own mental categories. This specific type of idealism, however, makes no claim about how the world is 'outside' of experience. — boundless

Assuming a reality to make a case for a reality? — noAxioms

Assuming some kind of reality of mathematical and logical principles to make a case for the intelligibility of physical reality.

It seems to me that it makes more sense to believe it IS physical, because otherwise we must make some unparsimonious assumptions about what else exists, besides the physical. — Relativist

Viceversa, I just don't understand why many physicalists are so sure that using the term 'physical' is appropriate for the 'structure'/'order'. To me it's just equivocating the term.

I just don't get why so many are embracing idealism- it seems to depend on skepticism about the perceived world, and then makes the unsupported assumption that reality is mind-dependent. I see no good justification for believing that. Sure, our perceptions and understandings are mind dependent, but I see no justification to believe that's all there is to reality. The innate, basic belief has not been defeated, and if we merely apply skepticism- we should also be skeptical of the hypothesis of idealism. — Relativist

Note that unlike an idealist thinks that the 'physical world' is just mental content they also believe that there is something 'outside'. And, in fact, even someone like Berkeley would say that the order is 'mind-dependent' if 'mind' is taken to be the individual mind.
Of course, Berkeley would probably say that mental content and minds are all there is. But 'idealism' includes a much more diverse picture.

That is, only some idealists would claim that the physical world is reduced to perceptions and understandings. They would probably agree with you that, instead, the world is 'external' from the mind and it is intelligible. They would probably contend that its intelligibility is an indication that shares a common structure with the mind and, therefore, it is (for them) an indication that it is ontologically secondary to Mind (I use the capital letter because these types of ontological idealists often believe in a higher 'Mind' as the ground of the physical world).

Then, of course, we have epistemic idealists. These would say that, in fact, we can only know the world as it is represented by our own mental categories. For them, it isn't at all surprising that the world seems intelligible: our experience is structured by our own mental categories. This specific type of idealism, however, makes no claim about how the world is 'outside' of experience.

The metaphysical physicalist, on the other hand, assumes that the physical world is primary and intelligible and mind is derived from it. But how can a purely physical account explain its intelligibility without just assuming it as 'taken for granted'?

And, yes, skepticism works in both ways. But note that I was thinking about the consequences of accepting the assumption that the physical world is intelligible.

No, I'm being consistent with physicalism in terms of what a property is: properties are universals that exist immanently where they are instantiated. — Relativist

Aristotle for instance agreed with this and he wasn't a physicalist.
Anyway, assuming that a 'hylomorphic' physicalism holds (i.e. a Aristotelian picture of reality without the 'super-natural' aspects of his worldview), do you believe that formal causes exist? I mean if there is an 'order' in the physical world, it just seems that the world has a 'form' in a quite Arisotelian way.
Note that this is different from saying that math can be used to make predictions. It assumes that we can truly understand something 'essential' of the world.

In the case of properties (universals) - you can recognize that two or more things have it. It's true that we aren't visualizing redness as a thing- we're visualizing a red surface, but we are intellectually just identifying the sameness that red things have. — Relativist

Note that this wasn't my point. I said that reductionism cannot explain a structured world because 'structure' is a property (if it even can be considered a 'property') of the whole, not of the parts.
It was something separate from universals.

I don't think so, because I don't explicitly need concepts for the world to be intelligible. I can see the trajectory of a thrown ball, predict where it will end up and catch it without overt need for any concepts. We apply concepts after the fact, mapping them to what we see. Much of the time they are wrong and make false predictions. The ones that happen to be empirically adequate may survive, generally. — Apustimelogist

And yet, on the other hand, probably even in order to 'see' the trajectory, you need to have already some kind of interpretative structure. So which comes before which?
And BTW, you are assuming that the 'world' to be structured but you are not explaining how it can be. If you did, you would use precisely those concepts you think are totally derived from experience.

Its almost trivial to observe the world around you and be able to identify that there can be more of something or less of something, bigger things and smaller things. — Apustimelogist

So, where 'more or less' comes from? Isn't that evidence, then, that concepts do map 'reality' in some way? How is that so?

I am not presuming some exclusive dichotomy of invented or discovered. Something can be both. You can invent a system of rules and then discover implications of following those rules that you did not know before. — Apustimelogist

Fine!

If math was an extremely small field that entirely described physics exclusively then I would say you have a point but math can describe thing that are physically impossible or physically don't make sense. — Apustimelogist

Actually, the history of physics clearly showed us how some 'obscure' mathematical concepts have been used in physical theories. Moreover, I do believe that this property of math as being 'more' than what is actually employed in physics gives more credence to platonism. If math wasn't so 'broad', its truths would be accidental. And, frankly, I am not even sure in a purely physicalist perspective how can we even conceive something that has no relation to '(experienced) reality'. What would even the point of that?

Even if your models are wrong beyond some limit, the fact that you can construct models that give correct predictions suggests that there is an intelligible structure to that part of reality which is being captured. If reality wasn't intelligible, you wouldn't be able to do that. — Apustimelogist

Agreed. More precisely, if reality wasn't intelligible and still we can make successful predictions this would imply that we can do that due to sheer, inexplicable luck. It is sort of possible, I guess. We can't exclude that. But it just doesn't seem 'right'.

Intelligibility is about understanding and comprehension, it isn't about being right or wrong. I would say something is unintelligible when you cannot create any model that gives correct predictions; even then, I am skeptical that such a thing even exists except for say... complete randomness... even paradoxes and contradictions are intelligible and understandable... even the concept of randomness itself to some extent. — Apustimelogist

Not sure how can you understand something without being 'right'. In a way, one might even say that 'reality isn't intelligible' is self-refuting: in order to be true, it must correctly 'describe' reality. But if it does describe reality, then...

Why do I need aome special explanation for the fact that I can count things that I see in the world (under the assumption of identifying those counted things as the same)? — Apustimelogist

Partly it's psychological...because, well, for me it isn't 'obvious'. It isn't something I would take for granted. BTW, personally I also marvel at 'existence' itself.

And, in fact, I guess these two things are related. Why reality is 'ordered' when it could be otherwise? Is it even conceivable to speak about 'order'/'structure' without assuming some mental categories? Does this have implications?

Again, was not aware of that, but there is probably more than one view lumped under the term. — noAxioms

I did some googling and it does seem that you are right, in fact. It does seem that physicalism is used to denote some positions that are not about ontology.
Since this thread is about ontology, however, it would be probably more appropriate to refer to 'materialism', then, without using that term to indicate a specific form of 'materialism' that, say, is equated to ancient atomism or a literal interpretation of newtonian mechanics but it is compatible with modern physical theories.

Still, I am not sure why people would call 'physicalism' a non-ontological view, but that's me.

The definition of 'physical' definitely gets shaky when one steps outside of our own particular universe. — noAxioms

Yes, that's the problem that I have with using that term. Anyway, personally, I would not call principles, laws and so on as something physical.

In fact, they are more like the transcendental conditions for the existence of something physical. Personally, I would not say that they are 'physical'. To me that leads to an equivocation of the term 'physical' that renders it meaningless, in fact.

A purely 'unstructured' (i.e. intelligible) 'physical reality' is not a 'physical reality' at all. And the structure is more like a 'principle' than an 'object'. To me this means that the mere assumption that 'physical reality' is intelligible (which seems to be in fact necessary to speak about a 'physical reality'), contradicts materialism (and hence 'physicalism' as a metaphysical/ontological position).

I perhaps am one open to accepting structure as more fundamental than physical. — noAxioms

:up: Nice! I am also of the same opinion. An unstructured world is IMO a contradiction in terms. But the structure is more like a 'transcendental' for the world (i.e. a precondition of it).

Which may just bring it back to an objective truth, yes. — noAxioms

Right!

Is there such a thing as ontic idealism? — noAxioms

Well, it is often referred to the position that reality is exclusively mental and, therefore, there are only minds and mental content as we know them (a position that is most often attributed to Berkeley, but I think that he was more sofisticated than how it is often presented). In a sense, however, I would sat that even positions as diverse form that like, say, classical theism, neoplatonism, and other metaphysical positions which accept the existence of a 'material' world (which is not assumed to be fundamental, of course, but intelligible), are 'ontological idealist' because they assume that some kind of 'Mind' is the most fundamental reality (and mathematical/logical truths are concepts in that 'Mind'). But generally, these positions are not included under the label 'idealism'.

Anyway, I was not trying to 'make a case' for any of these 'idealist' positions. I was more like 'making a case' for the 'reality' of 'mathematical and logical truths' by simply assuming that there is an intelligible physical/material reality.

Roger Penrose, for instance, endorsed the existence of a 'platonic realm' which for him is independent from both the material/physical and the mental 'realms' (see this video, for instance: https://www.youtube.com/watch?v=ujvS2K06dg4). I would distinguish Penrose's positions that the ones mentioned before. Plato himself seemed to me unclear about whether the 'forms' are 'concepts' (and are in some kind of 'eternal Mind') or if they are 'independently real' and, in fact, something ontologically different and independent from either minds/souls and 'matter'. I guess that those mathematicians that are deemed platonists are in both camps (for instance, Kurt Godel was both a platonist and a theist, so I would suspect that he considered mathematical 'forms' as concepts (in the Divine mind). The early Bertrand Russell was an atheist but a platonist, so I would imagine that he held a similar view to Penrose. Also G.H. Hardy mantained a similar view). In any case, if one assumes the 'reality' (and the 'indipendence' from the physical world and our minds) of math and logic, then one cannot be a 'materialist' and possibly even endorse some forms of ontological idealism, for that matter.

I don't agree. Set physicalism aside and just consider the evolutionary advantage of associating effect with "cause" (something preceding) with "effect" - even in nonverbal animals. This mirrors "if....then", the most basic form of inference. — Relativist

As I said in my previous post, if one speaks about 'evolution' and 'evolutionary advantage' as an explanation and, indeed, if one thinks that explanation is true, I don't see how one can escape the conclusion that the 'process' considered is intelligible. If it is intelligible, this means that our concepts do mirror the regularities of that which is 'happening'. Of course, if one embraces a quite radical skepticism where this evolutionary explanation is not considered true but 'useful', then, yes, one can avoid to attribute intelligibility to the 'evolutionary story'.

Such a 'skeptic' attitude, however, IMO goes against every 'physicalism' I can think of. Ironically, it's closer to epistemic idealism and some forms of phenomenology.

If the world does have structure/order, then it would be amenable to rational description. — Relativist

If it doesn't, then, I doubt that one can have a coherent form of physicalism. After all, a minimal degree of intelligibility is IMO assumed to talk about coherently of a 'physical reality'.

My only point here is that the capability of recognizing patterns is consistent with physicalism, so it doesn't require magic. — Relativist

My point stands, however. If the world does have structure/order which is intelligible and amenable to rational description, how we have to understand that 'order'? Is it something 'physical' (in a sense of the word that is not equivocal)? If there is not, how can we speak of 'physical reality'?

I mean even saying "there are objects that interact" assumes basic concepts like 'sameness', 'diversity', 'oneness', 'plurality' and so on. So, I guess that any account of 'physical reality' must be intelligible. Which to me raises the question of how to understand that intelligibility, that order in purely physical terms.

Or, consider the spectatular success of mathematics in predicting physical phenomena. How is that even possible without the assumption that mathematics does indeed enable us to 'capture' the structure of a physcial world (again, let us set skepticism aside)?

Order is not a property, per se. It is a high-level intellectual judgement. Properties are not parts. "-1 electric charge" is not a part of an electron, it's a property that electrons have. I don't see a problem with identifying an aspect (a property or pseudo-property) that 2 or more distinct objects have and then focusing attention on that aspect. Explain the problem you see. — Relativist

IMO you are oscillating between a position that requires some degree of intelligibility (the assumption that there is a physcial reality) and a skeptical position which would require to abandon all attempts to rational understanding of reality.
I would say that the 'order', if we take it seriously, would not be just a 'judgement' but also a property of physcial reality itself.

Yes, properties are not parts.

My point was that, if intelligibility of physical reality is assumed, then, you can't 'conceive' the more elementary parts of physical world independent of anything else. Mine was a criticism of reductionism rather than physicalism in that case, I should have clarified better.

From this standpoint, I don't really see the problem you raise. I don't need to assume rational knowledge for my brain to do stuff... it just does stuff in virtue of how it evolved and developed. And none of what the brain does os strictly arbitrary because it depends on its interactions with the outside world. — Apustimelogist

My point is that the 'story' you're telling presupposes intelligibility in order to be 'right'. If you admit that the physical world - at least in some features - is intelligible (apparently enought intelligible to be certain of these things), then, at least the most basic concepts that ground describe the order of the physical world, which seem to imply that they are actually also part of the order of physical reality itself.

Also about predictions: unless one adopts a quite skeptical approach (for instance the one about 'perspective' I mentioned earlier), these extremely accurate predictions seem to imply that, indeed, mathematics does describe the 'structure' of reality. But if that is true, mathematics isn't invented (at least, the part that describes the structure of the world).

Anyway, I am not sure I understand your point here. The world is intelligible to us because we have a brain that is designed to model the world. — Apustimelogist

No, the world is intelligible because it is intelligible (if it is indeed intelligible). On the other hand, I can't exclude the possibility that it isn't really intelligible, in which case we evolved in a quite 'lucky' way that enables us to make useful predictions by using models that are in fact wrong.
The very fact that we speak of evolution - which is indeed intelligible as a concept - to explain why we can have knowledge presupposes that the world is intelligible in some sense (unless, as I said, one wants to embrace skepticism).

Two times two is two twos. Thats just two plus two. Its the same. If you are using the notion "equals", you are giving a numerical equivalence, a numerical tautology. — Apustimelogist

If 'equals' is only about the value, ok. But, in fact, the semantic content of the two expression is different. And this IMO shows that mathematics is more than 'tautologies'. It does enable to get access to non-trivial truths.

I would also add that the mathematics that is used in physics is becoming via via more abstract and general principles like symmetries tend to become more and more prominent. And that IMO suggests to me that it can't be a human invention because it is quite surprising how far it is from what one expects from immediate experience.

Good points. Curiously enough, if I had to pick a term based on etimology I would go with 'materialism'. The reference to 'mother nature' is just too poetic.

Physicalism necessarily requires mathematics to be a mental product only? I was not aware of that. Materialism, sure, but not physicalism. — noAxioms

Just a quick terminological point. I believe that 'physicalism' and 'naturalism' are treated as synonyms. But, I would say that 'materialism' also can mean the same thing, unless we call 'matter' only a subset of what is 'physical'. But considering that 'matter' etimologically comes from 'mother', i.e. 'Mother Nature', I find odd that physicalists, according to which ultimate reality is 'natural/physical' object to call themselves as 'materialists'. Maybe 'materialism' seems to be somewhat less 'sophisticated' as a term. But IMO, it isn't necessarily the case. After all, saying 'ultimate reality is material' or 'ultimate reality is physical' for me is equivalent.

We seem to have an innate, basic belief that there's an external world that we're perceiving and interacting with. As we develop from infants, we are making sense of the world. The process continues throughout our lives, and underpins our study of nature. Maintaining a basic belief is perfectly rational, unless there's some undercutting facts. It's of course possible that we're wrong, and it's fare to acknowledge that, but possibility alone is not a rational reason to drop a belief. — Relativist

I agree with you here. If we also give credence to the basic belief of the intelligibility of the world would imply that we assume that the world has a 'structure' that can be 'mirrored' by our mental categories.

But note that this does have implications, after all. If we say, for instance, that logical inference derives from physical causality, we are assuming that physical causality has the same character of 'necessity' that logical inference has. So, it would imply that physical processes 'follow' regularities that are the same as the formal structure of coherent reasonings. But this is more or less something close to 'hylomorphism', rather than a physicalism that tries to derive the rules of logical inferences from the 'physical'.

The big question remains in this case: why would the 'physical' follow the same 'rules' that make a coherent reasoning 'coherent'?

As I said, logic is semantics -a formalization, based on assigning sharply defined definitions to terms. You could question the grounding of our semantics, I suppose. But again, the grounding seems to be basic, innate beliefs. Of course we learn a language, but we have a common understanding that depends on our hardwired mechanism for perceiving the world - and similarly, rational to maintain. — Relativist

Note that I am questioning the 'grounding' here. All explanations we can possibly make must be coherent. If we realize that an explanation is incoherent, we reject it.

I've identified the specific way universals are connnected to reality, and how we manage to perceive them. This seems a better account than saying they are "somehow connected".

Regarding "laws of thought": an orderly world producing orderly thoughts, enabling successful interaction with it. — Relativist

If I am not mistaken, however, you are assuming that the world has a structure/order that is amenable to rational description. But here we get the same question that I raised before in the case of causality.

It seems a minor step from pattern recognition, which Artificial Neural Networks can do. — Relativist

Note that Artificial Neural Networks are still, ultimately, our inventions that are programmed by us. So, I am not sure that this can lead us to the conclusion that the world is 'orderly' in the same way as our thoughts are.

But IMO, assuming that is the case, I just find weird from a physicalist point of view that the order is the same.

Anyway, if one assumes that the 'order' is an intrinsic property of the world this would mean that reductionism is wrong. Parts can't be understood as 'abstracted' from their context of relations. In fact, parts must be understood as, well, being intrinsically 'parts' and, therefore, wholes are not reducible to them.

Physicalism necessarily requires mathematics to be a mental product only? I was not aware of that. Materialism, sure, but not physicalism. — noAxioms

Well, I believe that physicalism posits that the 'physical' is fundamental. It all depends, after all, on what we mean by 'physical'. If we 'stretch' the meaning of that world enough, I guess that a platonic realm of forms can be thought as 'physical'.

But the risk here is equivocation. For instance, if I say that there are really 'physical laws', it seems that we end up with something like 'hylomorphism', i.e. the position that the 'physical' is also something that has a structure that is intrinsically intelligible (at least, in part). Is that 'structure' also 'physical'. I guess one can say so. But note, for instance, that assuming that 'structure' is not merely something we mistakenly impose on 'physcial reality' would imply that something like 'reductionism' is false. After all, reductionism tells us that fundamentally parts are ultimately real. But if one accepts that 'structures' are as fundamental as 'physical things', it certainly implies that wholes are not really reducible to parts (as parts cannot be 'abstracted' from their context).

So, I guess that at the end of the day the problem can be terminological.

I do agree that such an assertion results in circularity. Logic cannot be used to derive logic as an end product instead of something far more fundamental. — noAxioms

:up:

Those aren't counterexamples, but rather examples to show that 2+2=4 requires context, and a context requirement seems like an awful big asterisk to the claim of the objectiveness of its truth. — noAxioms

I can agree with that. And yes, you need to posit the 'truth' of the whole context.

I do believe that natural numbers ultimately derive from very basic concepts like 'sameness', 'otherness', 'unity', 'plurality' and so on, which can't possibly be 'invented'.

If it's a mental construct, it would seem dependent on time. I don't think it's a mental construct, so I'll agree with your assertion of it being eternal. — noAxioms

:up: on the 'eternality' part. Actually, I do think that maybe logic and math are 'mental constructs'/'concepts' (I do have my sympathies with 'idealism'*), but not in the sense that they are conventional.

*By 'idealism' I mean a very broad category that includes epistemic idealism, or whatever position that posits 'mind' as (at least part of) fundamental reality. In fact, I moved towards the second category recently (albeit, I do recognize that epistemic idealism is a very interesting perspective). I do admit however that strictly speaking I can't make any logically compelling argument from that position.

Non-eliminativist physicalists don't assume the physical world to be totally mindless of course (unless the minds under discussion are defined as being incompatible with physicalism). — wonderer1

No, but they either have to 'derive' them from purely physical things. I think that many physicalists are emergentists. The problem with that view is that it seems impossible to pin down properties of physical things 'in virtue of which' conscious experience - and, I would add, logic - can emerge.
The problem is that, until now, I never encountered a fully satisfying physicalist account of consciousness, logic, math and so on.

Furthermore, from the perspective of many physicalists, 'laws of thought' of some sort are to be expected. And 'laws of thought' are expected to be consistent with the sort of information processing that occcurs due to the structure of our brains. — wonderer1

In other words, here there is the hidden assumption of intelligibility of the physical world, i.e. that there are regularities in physical phenomena that are more or less the same as 'laws of thoughts'.

To make an example, it seems to me that you can't derive logical inference from mere physical causality. Or, if you can, you either (1) end up assuming that physical causality is more or less the same thing as inference or (2) we 'invent' inference from our experience but we are mistaken that experience can really be described by our reasoning.

Although my definition of "the natural" precludes things existing that we can't infer, I don't preclude the possibility of things existing that we can't possibly infer. But if so, they are unknowable and therefore we're unjustified in believing any specifics beyond the basic ackowledgement that are are possibilities. — Relativist

Don't you think, however, that you are assuming that this 'natural' world is intelligible, though? That is, your model, actually presupposes the validity of inferences, logical explanations and so on?
The orderly structure you are attributing to the world mirrors the structure of rational thought.

The "laws of logic" are nothing more than a formalized, consistent semantics - for example, the meanings of "if...then...else", "or", "and", "not" - all sharply defined by truth tables. — Relativist

Problem is that any explanation presupposes coherence. If an explanation is incoherent we do not think that it can be true, or convincing. So, you can't ground logic without assuming it in the first place. It's just fundamental.

Suppose there were no intelligent minds to grasp them - in what sense do these transcendental objects actually exist? — Relativist

IMO one might say that transcendental objects are in some way connected to the regularities of phenomena. But I would assume that it would be somewhat inconvenient for a physicalist to admit that, say, the 'laws of thoughts' are actually an essential aspect of that physical world which is assumed to be totally 'mindless'.

From a physicalist's point of view, if some physical phenomenon is describable with mathematics, it is entirely due to the presence of physical relations among the objects involved in the phenomenon. — Relativist

And yet these 'physical relations' have a structure that can be 'captured' by mathematics. There is unmistakable 'affinity' between physical regularities and 'laws of thought'.
Problem is: can physicalism explain that without assuming that logical and mathematical principles are just an essential part of the world (and therefore, ironically, unexplainable in purely physical terms)?

To repeat: my qualms about physicalism is that it still requires to assume the validity of logical and mathematical principles that it wants to explain. After all, all explanations that we can think of must presuppose the validity of those principles. At the same time, however, physicalists seem to say that logical and mathematical principles are just 'inventions'.
But if are not, how can be they considered in any way as 'physical'?

I suggest that it is justifiable to believe the physical world is at least partly intelligible - justified by the success of science at making predictions. I don't see how anyone could justify being skeptical of this. Nevertheless, we should keep in mind our limitations. The known laws of physics (which I contrast with the ontological laws of nature) may be special cases that apply in the known universe but are contingent upon some symmetry breaking that occurred prior to, or during, the big bang. If so, it's irrelevant to making predictions within our universe. — Relativist

Ok, I agree with that. But the problem of how to explain (even partial) intelligibility remains.

I don't see a problem with abstractions. The "way of abstraction" (see: https://plato.stanford.edu/entries/abstract-objects/#WayAbst) is a mental exercise associated with pattern recognition. This describes the process by which we isolate our consideration to properties, ignoring all other aspects of the things that have them. The properties don't ACTUALLY exist independently of the things that have them, IMO. And I don't see how one could claim that our abstracting them entails that they exist independently. — Relativist

Note, however, that in order to even recognize a pattern, you need to assume a basic capacity of recognition of 'sameness' and 'different', which actually means that a capacity of interpretation is assumed. So, how abstraction is even possible if we do not assume the validity of certain basic and seemingly fundamental mental categories (which seem to be unexplainable but, in fact, the ground of any explanation)?

What do you mean by 'eternal' here? I have two definitions of that, and neither seems appropriate. I seem to favor the idea of mathematics being fundamental, but not all would agree. — noAxioms

Time-independent in the case of math and logic.

I agree that physicalism is reactive but it's like a 'half-made reaction' when one wants to have his cake and eat it too. That is, one wants to retain the idea of intelligibility of the physical world and, at the same time, wants to avoid to posit also the necessary conclusion that, in this world picture, the structure of the physical world actually is similar to that of our reason and at the same time trying to affirm that math and logic are the products of our minds. The problem is, of course, that in order to explain anything you have to assume that the explanation and, therefore, logic (and at least some parts of math) must be assumed to be true. In other words, physicalism would like to have a 'physical' explanation of everything and, yet, if it were true there would be no explanation that assumes the very thing it wants to explain as its starting point.

It's seems to me, then, that if one doesn't assume that logic and (at least some part of) math are irreducible, one can't assume that any kind of rational knowledge is possible. If they were simply 'inventions', nothing would be truly intelligible. So, instead of a 'physicalism' we would have an extreme form of skepticism of some sorts.

...

I have no problem with people being skeptical with this description because its obviously not rigorous and comes a lot from my intuition. But I don't feel the need for anything added to explain things about how math or logic works. Once we pre-stipulate conditions for things to be the same or different, we are just extrapolating those properties in tautologous ways. These things can be gotten straight out of reality, or describe reality very well in suspicious ways, purely because reality has structure in which different parts of the reality act in the same way! And so there is nothing special about maths relation to reality if these are just tautologies. — Apustimelogist

But note that basic notions like 'oneness', 'plurality', 'same', 'different' seem to be innate and do not seem to be 'fabricated' by us as mere abstractions. They do seem to mirror the 'structure' of the world 'external to us' as far as we can know. So, while we can't 'prove' it (and, therefore, we can't have certainty about it), the physical world seems to be (in part) intelligible and, therefore, knowable.
Furthermore, these 'basic concepts' seem to be the very categories that we use to interpret our perceptions even before we are aware of that. We distinguish different things, we distinguish change, we discern sameness, regularities and so on. If we had not these 'innate categories', how could we be able to make any sense of out experience at all? And, everything suggests that, while they maybe not 'without error', they still give us an approximate picture of reality. Which would then mean that the world is intelligible, which would mean that its structure is like that of our reasoning...

The antinomy I was talking about is this: while it does seem to us that the world is intelligible, we can't verify it from the 'outside' of our perspective. So, we might presume that the structure of our thought mirrors (in part) the structure of the 'external world' but we can't just prove that.

Count two fingers, then another two fingers.

Now count four fingers. — Apustimelogist

I am surprised that you made this point, actually. 'Two plus two' is a different concept from 'four'. Just because the numerical value is the same it doesn't at all imply that it's a tautology.

Think about 'two times two' being equal to 'two plus two'. Of course the two mathematica operations are not the same. Conceptually they are different. It is an informative truth, not just a tautology.

Ah, I think I understood your point now. But note that neither solipsism nor physicalism can explain why mathematical truths aren't contingent.

Furthermore, physicalism(s), if true, can't derive mathamatical truths. And yet, these ontological systems seem to presuppose them. So, if we do not say that 'mathematical truths exist' we still have to explain IMO why they are needed and how we have to understand them in a physicalist ontology.

After all, mathematical and logical laws, truths etc seem to be 'laws of thought'. If thought is derived from physical entities, it would seem that even that that mathematics and logic should somehow derive from physical entities (Edit: in other words, if physical entities form the ultimate reality from which everything is derived, all the properties of thought - reasoning included - must be explained in terms of physical entities. I am not sure how physicalists can explain, say, why mathematical truths are true if physicalism is assumed to be true...).

Presumably, then, you also believe in the existence of propositional truths, e.g. if "bachelors are unmarried men" is true then the truth that bachelors are unmarried men exists? — Michael

Well, the problem here is that 'bachelor' means 'unmarried man' if I am not mistaken, so here we seem to have a tautology. '2+2=4', however, IMO isn't a tautology.

If so then if "only I exist" is true then this propositional truth exists, and if this propositional truth exists then "only I exist" is false, giving us a contradiction. — Michael

Unless, however, I say that 'only I exist' is wrong. For instance, that statement, if true, would contradict everything I think is true about 'reality'. I do believe that my being is dependent and, therefore, "only I exist" probably is a contradiction because, after all, I can't exist without something else.

It doesn't seem a 'contradiction', but I am actually not sure.
I am not sure about your point, though. Propositions (or even models, theories, philosophical systems etc) can be formally valid (i.e. coherent) but still wrong.

@noAxioms, @Relativist, @Apustimelogist, @Wayfarer

I actually believe that, often, physicalists equivocate the meaning of 'physical', in order to explain consciousness, abstract objects and so on. If by 'physicalism', we mean that the physical is fundamental and everything else is derived from it, we would like to find a reasonable definition of 'what is physical'.

If we mean 'physical reality' as whatever exists in space-time and space-time itself (a definition that IMO is not without criticism), we have to explain how the apparent eternity and necessity of mathematical and logical truth can be explained by such a system, without falling into equivocity.

One way is to try to explain mathematical and logical truths as 'abstractions' that we derive from particulars. The problem, however, is that mathematics and logic seems to be transcendental, i.e. truths that we have to accept to even construct explanations, models and so on. An explanation, for instance, should be logically consistent. If fundamental reality is, indeed, 'physical' how can we explain the laws of logic in purely physical terms?
The same actually goes for mathematics. Mathematical truths seem to be independent from any particular circumstance. They don't seem to be contigent. We can't 'prove' that "2+2=4" by testing it with experiments, no metter how many time, as induction doesn't give us any 'proof', at least in the way mathematicians use the term.
If they were contingent, we could not even imagine to write physical theories in a consistent way. We would always have the expectation that all the mathematical structures of our theories might someday become unreliable.
A very strong 'empiricist' approach to explain mathematics and logic IMHO fails because, after all, we formulate explanations by assuming that mathematics and logic are correct. The very assumption that physical reality might be at least in part intelligible seems to be based on the idea that, indeed, logical and mathematical truths are not contingent and eternal.

If, however, we do accept that mathematical and logical truths are eternal and not contingent, the next step is to ask about their ontological status. Do they possess some kind of 'reality'? The fact that we assume that we can know them strongly suggests to me that they do have some kind of reality. This would mean that they are either fundamental in themselves (as say Penrose IMO suggests) or depend on something else that is also not contingent and eternal.

Of course, a physicalist might argue that the physical world is not contingent and eternal but the problem here is that this would go against what many physicalists seek in physicalism, i.e. a 'view of reality' where there is no 'Absolute'.

Of course, one might reject the premise that the 'physical world' is at least in part intelligible. But that's hardly a 'physicalism' IMO. It is more likely some kind of radical forms of skepticism (there are more than one) where we have the illusion that 'reality' is intelligible by our reasoning. That it seems like so. But this appearance is a self-deception so to speak and, in fact, the 'ultimate reality' is in fact completely 'beyond knowledge'.

Personally, I find the problem of 'abstract objects' a very difficult for any physicalist worldview, at least if we mean that 'physicalism' means that 'ultimate reality is physical' in a comprehensible meaning of the term. Also, the very assumption that reality is (at least partially) intelligible by our conceptual knowledge is, as I said before, something that suggests that logical and mathematical truths are not contingent etc as they would be the preconditions for any kind of explanations. In other words, physicalism(s) seem to be unable to explain why physical reality is intelligible and at the same time the ultimate level of reality without also introducing the assumption of the non-contigency of logical and mathematical truths. But once that is given, then, how can we call such a philosophical position 'physicalism'?

So IMO physicalists seem to be in a difficult position between some radical forms of skepticism about our conceptual knowledge and, instead, give some ontological status to abstract objects (at least logical and mathematical truths) something that IMO would hinder the physicalist project itself.

Thanks for the words and for the answer. I'll actually leave you the last word for now, as I would repaeat myself in my answer and I doubt that it will be useful. Maybe in the future the discussion will restart. Before that, however, I want to study more about some topics that have been discussed here.

↪boundless That's the debate between Aristotle and Plato in a nutshell: Plato has it that the ideas are real quite apart from any instance of them, Aristotle that they are only real as manifested in concrete particulars. — Wayfarer

Agreed! The problem with Aristotle's view is IMHO that at least some abstract concepts do seem completely independent from their particulars. Mathematical and logical truths are an excellent example of that. Incidentally, I believe that theistic philosophers mantained that God's mind was actually the 'receptacle' of those forms and we can understand them because we are also rational beings created by God (Christians would say 'created in image and likeness'). A middle way of sorts between Aristotelism and Platonism. So in this latter view ('conceptualism' I think it was called), these forms are neither ontological independent from anything else (as in Platonism*) nor dependent from the particulars (as in Aristotelism**).

*Of course there is the possibility that Platonism actually was closer to conceptualism that is often recognized. After all, there was a hiearchy of the Forms in Plato's thought, with the Form of the Good as the Highest. Neoplatonism, certainly, was close to 'conceptualism' and incorporated some of Aristotle's views.

**Similarly, one wonders how much Aristotle's thought was also far from conceptualism, given that Aristotle was also a theist.

But such principles as the law of the excluded middle would presumably obtain in any world. That is what 'true in all possible worlds' means - although that is not highly regarded nowadays, because, as we've been seeing, we're prepared to entertain the idea of 'other universes' where such principles may not hold at all, But the question I have about that is, how could a world exist, if such principles didn't hold? In a sense, such principles are like constraints. — Wayfarer

I think I agree with that. Mathematics, logic and so on seem 'transcendental' with respect of the world (at least if we assume that the worlds are at least partly intelligible).

In any case, the specific point of the Eric Perl quote is to show that the idea of a 'separate realm' is not referring to a literal place. 'They are thus ‘separate’ in that they are not additional members of the world of sensible things, but are known by a different mode of awareness.’ — Wayfarer

Agreed. It is useful to note that there are various forms of Platonism. Penrose's view seems to be indeed of a separate ontological realm, accessible to our reason, albeit certainly not a 'place'. Probably some platonists have a 'quasi-materialistic' view of the 'world of Forms', but generally do not.

How could they not be? I mean, OK, under idealism, mathematics is nothing but mental constructs. I get that, and there are even non-idealists that say something similar, but since they can be independently discovered, it seems more than just a human invention. — noAxioms

Well, it depends on the idealist, after all. Some idealists would contend that mathematical truths are concepts. But maybe there is an eternal and necessarily existing mind of some kind that always knows them.
A purely physicalist view, however, is difficult to reconcile with the existence of abstract objects. For instance, logical operations do not seem to be reducible to physical causality, which seems contingent.
Generally physicalists oppose platonism due to the fact that it posits an irreducible non-physical reality.

On the other hand, an idealist that doesn't posit any eternal mind shares the same difficulty.

If a mathematical structure is going to supervene on mathematical truths, then those truths are going to need to be accessible by far more than just reason, which sounds like a mental act or some other construct that instantiates the mathematics (such as a calculator). — noAxioms

It depends on what we call 'reason'. If by reason we mean the mental ability to make deductions, inductions, reasonings and so on, well, at least a good part of mathematical truths are accessible to our finite minds. Complex calculations do not but we do understand them. So, either mathematics transcends reason or reason at least potentially can understand everything in math.

I'm actually being moved by this reasoning, so yes. — noAxioms

:up:

I think not the point. Said intelligence would need to be presented with an environment where such tools would find utility. It need not be 'of any kind' for mathematics to be independently discoverable. — noAxioms

I take this as an agreement. I mean, the potentiality to understand 'our' mathematics would be there. So, at least in principle, that intelligence could understand our mathematics.

An approximation of it can be, yes. A classical simulation is capable of simulating this world in sufficent detail that the beings thus simulated cannot tell the difference. Another funny thing is that GoL is more capable of doing this than is our universe due to resource limitations that don't exist under GoL. — noAxioms

Well, to be honest, I don't think that conscious beings can be understood in purely computational terms. But, I still don't see how it can be considered a separate world from the one where the simulation is run (unless you mean from the 'perspective' of the simulated 'entities', assuming that such a concept makes sense).

A world is what it is, and a simulation of it is a different thing, sort of like the difference between X and the concept of X, something apparently many have trouble distinguishing.. — noAxioms

Ok! Yes.

I need more of a mathematics background to give an intelligent answer to that. — noAxioms

Don't worry, neither do I. It is an interesting idea nevertheless IMO.



I know that you do not expect a reply but thanks for the thoughts. Something you said is above my level. I'll think about your answer and maybe I'll write some thoughts about some parts of it.

Yes, that's a possible view and I sort of agree with it. But note that this raises the question: would those principles still 'exist' if they are not instantiated in the things they 'regulate'?

I believe that mathematical truths (and not only them BTW), would still 'exist' even if they were not instantiated. This of course would ask the question: how? What then would be their ontological support?

I believe that the problem with this discussion is that its scope is becoming too large. Originally, it was a discussion about a question of how to reconcile the idea of the traditional view of hell as (some form of) unending torment with the notion of justice. From this, we then talked about St. Thomas Aquinas' argument that the orientation of the will has a central role. But then our discussion touched different issues like evangelization (in particular how to view it in an universalist context), God's salvific will and so on.

As I said some time ago, I am an agnostic and I wanted to make this discussion philosophical/theological but not exegetical or mainly exegetical. Not because I don't believe that exegesis is unimportant, but because I simply I do not have the education to make a serious exegetical discussion. Also, I don't know all the Christian universalists' answer to the verses and passages you cite (which might vary BTW among the universalists). Finally, I don't think that I am going to be persuaded about these kind of arguments, unless I find a convincing philosophical defence of the traditional doctrine of hell. To me none of the defences that I read have been convincing, mostly due to the fact that, in my opinion, they are difficult to reconcile with other, in fact, traditional doctrines.
If you are right about your claims regarding Scriptures and/or Tradition either these two things are true: (1) the traditional doctrine of hell is true or (2) Scriptures and/or Tradition are wrong in this respect.

Having made this premise, let's consider again what we said before and the things about which we agreed upon.

First, about repentance. It seemed to me that we did agree that the possibility to commit mortal sins, orienting the will to sin, alone is not enough to explain the thesis that it is at a certain point it's simply impossible to repent.
(Incidentally, I believe that the dogma that during this life it's assumed that it's always possible to repent lends support for this conclusion. it's interesting that you seem to say that experience here suggests to us that in some cases even during this life repentance is not possible... to me this would contradict the dogma.)

So, either the future life will be quite different from this life and the orientation of the will, will be inalterable for the sinners or not. If it will be, then, the thing remains unexplained. You mention that change of the will is not possible while disembodied, but at the same time you also believe in the resurrection (why, however, change is not possible while disembodied is something not obvious to me). But, anyway, the orientation of the will alone isn't enough to explain that the damned are beyond any hope. I believed we did agree with this.

This leads, in my opinion, to the conclusion that something else is needed to explain the hopelessness about the fate of the damned, especially if one believes that God, indeed, has a universal salvific will. It would appear to me that if God's desire/will is to save everybody, then creating the conditions that someone might be beyond any hope of salvation at a given point is problematic. The only possibility here is to claim that the sinner can become incurable even for God.

A problem with classical theism, however, is that God is assumed to be omniscent and, if I recall correctly, God already knows how everything will end. So, in this case, it is weird to me to think that God would desire that everybody if He already knows that some will never be saved*. So, probably, this means that what God wants is just to offer salvation to everybody, rather than to save everybody (which however is difficult to reconcile with the view of a God that desires and actively acts for the best of the creatures He loves... also it is quite strange to say that God offers salvation of everybody but He doesn't want that those who He is offering salvation will accept it). Or, maybe, the classical conception of Omniscence has to be modified. Or maybe I did misunderstood the concept.

Regarding the 'cohercion' part, well, I am not sure that this is coercion. After all, if one believes that the human highest Good is communion with God, then, it simply part of the human nature to have some kind of inclination for that Good, which maybe at some point would orient the will to that Good. Anyway, even if you were correct, it would not exclude the hope in universal salvation.

FInally, regarding the evangelization, you continue to think that the traditional view of hell is essential for it. It might be. I don't know. But to me the traditional view of hell is necessary for evangelization if either (1) one believes that all the unevangelized will go to the traditional hell or (2) believing in the traditional view of hell is necessary to evangelize or (3) if a Christian doesn't evangelize will go to the traditional hell. Perhaps, there are other possible reasons that I am not understading right now.
I said that universalists generally allude to other possible motivation for evangelization, which you don't find convincing.

Anyway, I want to thank you for this discussion. It is has been an interesting discussion for me. Possibly, you are right that it's time to stop the conversation for now at least.


*Edit: or even if God expects that some will not be saved without 'truly' knowing it.

Well, there are infinitely many mathematical truths, so the realm they inhabit is going to be infinitely "large" (if that word even makes sense). Also, is some kind of interaction going on between our mental realm and the platonic realm? When you think 2+2=4, do you interact, in some way, with one of these mathematical truths, and that allows for the grounding of mathematical knowledge? If so, then the interaction between the specific mathematical truth and one of the infinite mathematical truths in this realm...how does that work, exactly? And if there is no interaction, why posit the existence of objective mathematical truths? To avoid contradiction? — RogueAI

Yes, that's the problem with platonism. If mathematical (and other types of) abastract concepts and truths abide in a separate realm from the physical world and the mental world (including our culture), how can we know them? How the realms 'interact'?

I don't think that there is a fully satisfying answer to this question. That's why I said that I think platonism is right, but I don't think that there are fully compelling arguments for it.
The strongest evidence is the apparent eternity and necessity of these truths. To me platonist positions are the best explanations. But I can't claim knowledge or certainty about this.