The Mathematics of Idealism

Do form and structure require a passive observer, or do they require an active participant which intervenes , alters and transforms? If observation is intervention, performance, constitution, then it is not mind which is intrinsic to the cosmic order but intra-action within configurational patterns. This implies that the world, thought independently of mind, consists of no preexisting forms, laws or substances. Not matter or energy, but phenomena which matter in differ ways in the different configurations that their intra-actions produce.

Matter and energy are nothing without relevance. Relevance doesnt require a human subject but is already at work in the agential, intra-active nature of configurative phenomena that produce and reproduce a world through their reciprocal inter-affecting.

To say something is already to objectify, to single out, to identify.

In the unobserved state, there are no boundaries. A rock is not separate from the dirt it rests upon; a star is not a discrete sphere isolated from the vacuum around it. The forms that we presume are inherent in the objects we see are imputed by those cognitive acts which identify and separate them from their backgrounds. In the unseen cosmos, there is only a vast dynamic matrix of quantum fields and energetic interactions. Of course it continues to exist, but not in any way that is meaningful to an observer ~ Mathematics of Reality

This is why I think Kant’s expression ‘ding an sich’ (thing in itself) is misleading, as to designate a ‘thing’ is already to objectify it. But the in-itself retains its usefulness as a placeholder or limit, designating ‘what exists totally outside of any awareness or consciousness’.


Time is also observer–dependent, in that it has no reality without there being a sense of duration and the awareness of the intervals between temporal events which only a mind can bring to it. Subject of another essay, About Time.


In Charles Pinter’s book, cognitive gestalts are, if you like, the basic units of cogniton:

When life appears on the scene — whether it is a human being, a bird, or an insect — the organism’s nervous system acts as a highly specialized sieve. In order to survive, the organism’s cognitive system must carve boundaries into this continuous flux. A frog must distinguish a “fly” from the leaf on which it rests, or it will perish. A human must distinguish a “cliff edge” from the path, or she will fall. These are, in Pinter’s terminology, examples of the “Gestalts” which comprise the basic units of cognition. What we instinctively grasp as “shapes,” “wholes,” “edges,” and “identities” are structural invariants constructed by the architecture of perception.

The physical world provides the material basis, but it is the mind that draws the boundaries, differentiates objects, and identifies features. These Gestalts represent the constraints that define what is possible, and what is not, for an evolving organism. On the basis of these constraints, the brain constructs its life- world, the world to which it is adapted and has its being. Pinter makes the point that all of this is shaped by purpose:

“If creatures did not have goals then no action would be possible: Indeed, without a purpose there would be no such thing as activity at all, because activity would then be nothing but aimless random movement.” (Mind and the Cosmic Order, p. 63)

This is the sense in which the mind or consciousness is ‘all pervasive’. Not that it is some subtle, objectively–existent entity, but that it is the indispensable ground of awareness (although the very attempt to name it or identify it distorts that understanding.)

But I have no wish to displace mind as fundamental (subject to the above caveats about objectification). I don’t hold to a flat ontology. What I’m continually protesting is the tendency to believe that what is real is what exists in the absence of any subject. It is an oxymoronic conception.

Well Kant is a tricky one, but he makes it easy for some readers to take him as an indirect realist.

The indirect realist agrees that the coffee cup exists independently of me. However, through perception I do not directly engage with this cup; there is a perceptual intermediary that comes between it and me.

source

Idealism consists in the assertion, that there are none but thinking beings, all other things, which we think are perceived in intuition, being nothing but representations in the thinking beings, to which no object external to them corresponds in fact. Whereas I say, that things as objects of our senses existing outside us are given, but we know nothing of what they may be in themselves, knowing only their appearances, i.e., the representations which they cause in us by affecting our senses. Consequently I grant by all means that there are bodies without us, that is, things which, though quite unknown to us as to what they are in themselves, we yet know by the representations which their influence on our sensibility procures us, and which we call bodies, a term signifying merely the appearance of the thing which is unknown to us, but not therefore less actual. Can this be termed idealism? It is the very contrary.

Long before Locke’s time, but assuredly since him, it has been generally assumed and granted without detriment to the actual existence of external things, that many of their predicates may be said to belong not to the things in themselves, but to their appearances, and to have no proper existence outside our representation. Heat, color, and taste, for instance, are of this kind. Now, if I go farther, and for weighty reasons rank as mere appearances the remaining qualities of bodies also, which are called primary, such as extension, place, and in general space, with all that which belongs to it (impenetrability or materiality, space, etc.)—no one in the least can adduce the reason of its being inadmissible. As little as the man who admits colors not to be properties of the object in itself, but only as modifications of the sense of sight, should on that account be called an idealist, so little can my system be named idealistic, merely because I find that more, nay, all the properties which constitute the intuition of a body belong merely to its appearance.

source

OK, but above you seem to insist on an “external world” that exists “without form” until form-bestowing consciousness emerges. So you seem to use “subjective time” beyond the limits of subjectivity as an “absolute” time that is prior to subjectivity.

Another approach is to rethink what statements about the “pre-sentient past” can mean for creatures like ourselves.

This is clearly a reference to Berkeley, who had written “there is not any other Substance than SPIRIT, or that which perceives” Part 1, Section 7, A Treatise Concerning the Principles of Human Knowledge.

Kant was compared to Berkeley (much to his great annoyance) after the First Edition of CoPR was published, so he subsequently added ‘the refutation of idealism’ in the B edition to differentiate his transcendental idealism from what he termed the dogmatic idealism of Berkeley (and Descartes ref).

This is pretty well what the OP says verbatim:

…on the one hand, scientific explanation requires us to say that conscious beings emerge only after a long causal sequence unfolding in time. On the other hand, time itself — understood as succession or temporal sequence — exists only as a form of representation, and therefore presupposes a knowing subject. Schopenhauer insists that both are undeniable facts, and that neither can be eliminated without incoherence.

It is in this context that he writes that the world comes into existence only with the “first eye that opens" (ref). The emergence of the first perceiving being does not occur in time in the ordinary sense, because time itself becomes meaningful only with the possibility of perception. And yet, once time appears, it necessarily presents itself as having an infinite past stretching behind that first present moment. The entire temporal history that science reconstructs is therefore simultaneously dependent upon, and explanatory of, the emergence of consciousness.

Schopenhauer does not treat this as a defect of reasoning, but as an antinomy³ inherent in our faculty of knowledge. “Time has no beginning”, he writes, “yet all beginnings are in time”. The world, considered as appearance, cannot exist without a knowing subject; yet the knowing subject, considered as phenomenon, appears only within the world. The contradiction dissolves only when time is recognised, with Kant, as belonging to the form of representation rather than to things as they are in themselves. Likewise, minds only appear in sentient beings such as ourselves and the higher animals within the world, but the world itself — as a meaningful, temporally ordered whole — is something that is only intelligible in relation to a mind, and can’t really be understood as if from a standpoint somewhere outside of it ~“About Time”, excerpt.

A question has occurred to me. Let’s assume we have fully grasped the intricacies and nuances of idealism. Let’s assume we have either accepted or rejected the idea that the structure of the world and the structure of the mind are identical.

But what new knowledge or necessary course of action follows from this?

Does this mean that all our thoughts are now equivalent to reality? Does it mean that every person’s thought structure is essentially an extension of the world’s structure?

Yet, even if that were the case, people still wouldn’t think alike; they would still argue about the truth and continue searching for something else. I simply cannot wrap my head around it. What is the actual outcome?

I should perhaps explain that what I mean by the term ‘idealism’ may not be what it is often taken to mean. In my essay on the subject, I state at the outset that I don’t take idealism to mean that ‘the world is all in my mind’, nor that mind is a constituent of objects. What I mean is closer to the Kantian point that the mind is not a passive recipient of an already-existing external reality. It actively synthesises and organises sensory experience into the unified world that we experience as objective reality.

That doesn’t mean that my thoughts are equivalent to reality, or that each person’s individual thought structure is an extension of the world’s structure. Quite the contrary: the distinction between what I think and what is objectively the case remains essential. I can be and often am wrong about all kinds of things! But the Kantian point is about the conditions under which there can be an objective world for us in the first place. In practical terms, what I’m criticising is that aspect of empiricist philosophy which identifies reality with what exists independently of any apprehension or knowledge on our part. I’m questioning the assumption that the world is simply ‘there anyway’, fully constituted as it is independently of any possible experience of it, and that our minds merely receive information about that pre-existing world. ‘Scientism’, in a nutshell, which is still a major influence in today’s world.

That view can also be described as metaphysical realism, and I think it characterises much of modern philosophy. My objection isn’t that there is no reality beyond my individual thoughts; it is that the notion of a reality completely independent of the mind has become a kind of yardstick for what counts as real. But if we understand the ‘synthesising activity’ of the mind we will see that this is a self-contradictory yardstick.

The reason I am impressed with Charles Pinter’s book Mind and the Cosmic Order, is because it recognises this while also being fully conversant with the facts of science. Pinter’s PhD was in mathematical physics and his other books are mathematics textbooks. He’s not a starrry-eyed idealist by any stretch, in fact, he doesn’t claim to be an idealist at all. I’m saying that I think cognitive science and even physics itself nowadays suggests the recognition of the ‘constructive role of the mind’ in a way that was anticipated by Immanuel Kant and so is idealist in that sense. So my own view might be actually a form of constructivism or phenomenology, but I prefer ‘idealism’ as I think it’s a perfectly respectable category.

1 Like

I find this observation fascinating, but what are we to do about it? Certainly we cannot deny that all living things are just as sentient and participating in the world and what is real as we individually are. If we eliminated every living thing down to the last one, would it make any difference? Would the world then conform to that one last living things perception of it?

Yeah, as my ol’ buddy James Hetfield is apt to say…..sad but true. But there are those who know better, so…….

Continuing with Prolegomena, is found in Remark 3, (just before Sec. 14), for those insisting, in some strict sense, that to be an indirect realist is to be an idealist…..

“…..My protestation too against all charges of idealism is so valid and clear as even to seem superfluous, were there not incompetent judges, who, while they would have an old name for every deviation from their perverse though common opinion, and never judge of the spirit of philosophic nomenclature, but cling to the letter only, are ready to put their own conceits in the place of well-defined notions, and thereby deform and distort them…..”

To imagine the universe as it would be with no life in it at all still demands a perspective. If you remove all perspective what would remain? Of course this is not to say it ceases to exist: that would be imagining it not existing.

None of which means we can’t explore the universe as if there were no observer.

I’ve concluded no distinction between these two cases. Yes, I read the OP, and I know the typical distinction made by realists. I’m just not one of them.

Context yes. Intentionality, well, I’ll probably admit to that as well, but I wouldn’t have chosen that word.

A purely physicalist ontology probably can account for structure, but you said ‘object’, not structure. Triangle is ‘object’. Structure is the way the matter is arranged, not what it is called or what bounds it is assigned.

You have to realize that the 2D shape that is observed (Mt Fuji say, essentially a triangle from the typical local PoV), or it’s 3D model (a cone) is not its shape at all. At best it’s a projection on a plane or a hyperplane defined by a selection of world, time, place, and bounds, none of which are defined without a reference and, in the case of bounds, something to assign them.

That also said, Mt Fuji having a shape is something assigned by a mind, and getting rid of the minds contradicts the question being asked of a mind, which already knows what ‘mountain’ means.
If we really got rid of the minds, there’d likely be nothing to ask the questions of unless you ask the non-living things that you personally don’t consider to be minds, in which case they’d perhaps answer ‘triangle’ or ‘cone’ since that’s what they observe.

Absent a PoV, but not absent the world or bounds definitions, Fuji (actual Fuji, not it’s projection) is shaped neither like triangle nor cone, but rather a very long 4D object kind of pointy at one end and abruptly truncated at the other. Sans the world reference, Fuji (even unnamed) is totally undefined.

I think Kant would reject the idea that the mind “carves boundaries” into an otherwise amorphous physical reality. For Kant, the forms of experience are not supplied by a particular biological organism interacting with a pre-existing physical world. Rather, space, time, causality, substance, and objecthood are transcendental conditions that make any experience of a world possible in the first place.

In Kant’s framework, there is never an encounter with a “continuous matrix of quantum fields” prior to conceptual organization. The notion of a matrix of quantum fields is already a highly structured object of possible experience. It is already constituted within the framework of space, time, quantity, causality, and substance. So Kant would say that Pinter is trying to describe what reality is like before the mind imposes form, but the description itself already relies on the very forms it claims to get behind.

We know that objects conform to the conditions of possible experience, but we don’t know whether things-in-themselves are structured, unstructured, continuous, discrete, mental, material, or anything else. Those determinations apply only within the domain of appearances.

“Higher” animals seem to form Gestalts, such as Flock or Herd or Mountain, but may not understand the collective in terms of an interrelated system. For example, your dog may see the moon and ball as spheres, but not the invisible forces that cause matter to take on that common physical Form. They see the physical Pattern, but not the formal relationships that produce the abstract structures that humans conceive. :slightly_smiling_face:

1.There’s No Such Thing as Triangles
This is the maddening paradox at the heart of mathematics. Every mathematical object is much like the triangle: inspired by reality, but idealized beyond any physical existence.
https://mathwithbaddrawings.com/2015/11/11/theres-no-such-thing-as-triangles/

“I’m frightened and I cannot sleep,”
the little child said.
“I fear there might be triangles
underneath my bed.”

“There might be ghosts,” the mother mused.
“I cannot speak to those.
There may be ghouls and goblins
who will nibble on your toes.
There could be long-toothed monsters
with their eyes a gleaming red.
But there’s no such thing as triangles!
They’re only in your head.”

Of course! But then, Kant didn’t think that biology could even be a science, as there was no concept of recursive causality in Newtonian science. He didn’t think in those terms because those terms didn’t yet exist. But what I’m arguing is that the ‘continuous matrix of quantum fields’ is just another way of denoting the ‘in itself’. It is ‘the world’ unseen by any eye (and so, not a world!)

Many of Kant’s critics raised this exact criticism of the ‘ding-an-sich’. They said that designating the in itself as a ‘thing’ already objectifies ‘it’.

Pinter has a chapter heading Kant: The Philosopher of Gestalts, saying that his insight into the way cognition works anticipated ideas explored by later cognitive science (Andrew Brook has described Kant as ‘the godfather of cognitive science’). He then mentions Jacob Von Euxküll which introduces a more modern phenomenological perspective.

I see Pinter’s model as being generally compatible with Kant’s understanding of the ‘mind as active agent’ rather than as passive recipient of sense-data from an already-formed world.

One of the examples given in Pinter’s book (which I’m sure you’ve mentioned elsewhere) is the cognitive abilities of the fairyfly, a minute insect. Worth revisiting that, I won’t try and reproduce it here.

So, your argument rests on the hypothetical example of asking rocks questions and presuming them capable of observation and response.

As far as I can make out, you haven’t resolved a tension in your own claims.

As a “phenomenalist,” I’d say that I am more decisive on this issue. I don’t accept the usual notion of “the ( absolute-universal) past.” I don’t think that the (personal) past and the (personal) future are symmetric. I’d even say that consciousness “is” (personal) time.

This issue is crucial. Commitment to “Newtonion time” blocks access to certain exciting alternative frameworks.

Perhaps you are more prepared to respond to critics from the other side. For me, subjectivity “goes all the way down.” Consciousness is the being of “moments” of the objects themselves. The “true” object is not hidden “outside” of “consciousness-as-stuff.”

I’m surprised you don’t see what I see.

To me it’s obvious that he insists on indirect realism precisely to avoid being understood as an ‘idealist.’

I see J. S. Mill as having fixed Berkeley’s “system.” Mach further clarifies the issue. Berkeley is actually pretty great — if you wipe off the theological prejudice, etc. Berkeley identified as and indeed was — counterintuitively — a “commonsense” philosopher.

Phenomenalism is still easily misread as idealism, but that’s because it’s a tired trope in the tradition that “perceptions” are “internal stuff.” Kant was still stuck in this assumption, for all of his greatness.

The “problem” with “in your head” idealism is that it tries to “rescue the genuine empirical object” while clinging to “perception as inside stuff.” This doesn’t work. But a long time ago we had Mach clear this issue up. Of course people have to want the issue to be cleared up to care about a solution. For many, philosophy is religion by other means, so secular and proto-pragmatic Mach is not appealing. We need “mind stuff” as a bridge to “god.” Or “external Matter” as “absolute truth maker” for today’s scientistic deism of the 4-D Trooth Krystal.

We might look into this “idealism” anxiety. “I’m not saying the world is in your head.” Well, you are, when you put “time and space” in people’s individual heads. If it wasn’t famous profound so-and-so saying it, we’d call it schizophrenia. I rate Kant highly as a philosopher for what is strong in his work. On this point, he couldn’t help it. He was — as we all must be — a creature of his time. He enacted an inheritance mostly blindly, as we all must.

The situation is funny, because “perceptions are inside stuff” is an “idealistic” assumption that immediately violates common sense. So the philosopher repairs a ridiculous axiom by “taking it back” in a pretentious way. I don’t just mean Kant here. I mean that most “mind/matter” talk is even childish in its alienation from life.

I never suggested anything of the kind, if this is what you’re commenting on, so I don’t understand what you’re saying.

This is the salient point:

A thing is a thing because it is a thing.

It is called x because I say so, and what x is good for based upon what I have found use for it.

If a person did not know what a triangle is, they would not see it. Even if they see it, they may not have a name for it. Even if they see it, they may not know the use for it. This does not make it less real.