well it's obviously a deep question and probably a controversial subject matter. But I think there's a theme in world philosophy of there being 'mind' in a sense more general than 'the individual mind', yours or mine. Actually I'm embarking on a course of studying the current philosopher, Bernardo Kastrup, who has this kind of philosophy. Finding a way into it is challenging, however.

But let's go back to the question in the OP. Why is it that the human ability to grasp mathematical relationships is so effective in respect of discovery? For that matter, consider the word 'discovery' - something previously concealed becomes revealed or clear. And mathematics has played a central role in that, as far as mastery of nature is concerned. A classic case in point I often refer to, is Paul Dirac's discovery of anti-matter. He predicted it, long before it could be detected, because it 'fell out of the equations'. And years later, lo! there it was. That's why I can't buy into this idea that it's simply something humans thought up, it's the discovery of something deep about nature herself. When Galileo said the book of nature is written in mathematics, he wasn't simply employing poetic allegory..

That's the 'romance of mathematics'. Actually it's very unpopular in mainstream academic circles today, because it's very hard to reconcile against Darwinian evolution. The fashion is always to rationalise such abilities in terms of adaptation, when it seems to be so much more than that.

But, on that note, take a geez at one of my favourite online essays on this theme, A Fabulous Evolutionary Defense of Dualism, Clay Farris Naff.

I never really bought the idea that reducing the number of forms and making actualities be the product of mixtures of a smaller set of forms solved the Third Man problem. Plato himself gets at this in the Parmenides when he says there aren't forms for dirt and mud, but that there might be for more essential items. However, you still have the problem of infinite regress with the form of the large or small. The only solution I find particularly appealing there is to boot out the forms that are necissarily comparisons (e.g. small, large, bright, etc.), but then you still have to deal with them in some way.

Aristotle's categories seem to get around this issue in a much better way. I mentioned Hegel before because I think the synthesis there provides an explanation of how the universal and the particular can interact in being in a "circle of circles," while avoiding the Third Man Problem, through rejecting epistemological realism entirely.

I could never get my head around 'the form of largeness' either. When I first encountered it, it was pretty near a show-stopper for me, but I'm continuing to investigate. Still, a long way from abandoning the basic idea of 'the forms'.

I think this to mean that bits of matter somehow represent ideas, in the same way that codes represent objects in, say, computer systems. It seems natural, even obvious.

The problem is that even very simple mental operations can generate enormously divergent patterns of neural activity. Very simple stimulus and response patterns in mice are subject to what is called 'representational drift' - the same stimulus evokes responses in very different regions in the brain over time. Same thing happens with humans, albeit even more complicated. I read that long neurological studies attempted to trace characteristic patterns of activity in human brains when learning simple tasks, like memorising a new word, but that the activities were so divergent that researchers could detect no consistent pattern despite years of studies (see Why Us?, James le Fanu.)

Furthermore, consider the way in which a divergence of symbolic forms can be used to convey the same idea. A number can be represented by a variety of symbols, but they all specify the same idea. So the meaning of the idea is in some sense separable from its physical form. The mind, of course, can recognise such equivalences and translate one form to another - but again, can that be understood as a physical process? I think rather that it's a pretty cogent argument for dualism.

Right, when memes are said to live in the host, it isn't in a particular set of synapses we're talking about, it's a set of processes that give rise to a corresponding, similar-enough, set of mental phenomenon. Memes are abstractions that live as part of the emergent system of conciousness in their hosts. However, I think memes can still be understood as physical processes. The evidence for this is that people with damaged brains stop being able to understand ideas. If there is a powerful idea in a society, one that dominates their conciousness, and that society and its texts are destroyed, the meme vanishes until some lost text is found and translated by archeologists. It doesn't hang out in the ether, or if it does, no empirical evidence for it can be produced. So maybe it is the case that the idea lives on in an eternal realm, but the eternal realm is not necissary to explain ideas.

That you can't pinpoint the physical location of an idea, and that the activity that makes up the idea changes from moment to moment isn't at all incompatible with the findings of neuroscience, it's what we should expect. If ideas corresponded to hardwired structures then we'd have a finite memory capacity and would loose very specific bits of information with age and neuronal death, which isn't what we see. I would also disagree with the code analogy. I think brains as computers analogies generally do more harm than good in explaining things. When you write code, the meaning of your operations doesn't shift over time. Individual strings remain constant. That's not how brains work. The pattern of neuronal activity associated with something as simple as a smell varies over time, eventually corresponding to entirely different sets of neuronal activity. Since the subjective mental phenomena don't appear to change over time, this appears to suggest that the process, not the medium in which it occurs, creates the mental phenomena.

It's like how ecosystems exist but aren't located in a singular location as well. The movement of ideas works the same way that a terraforming operation could recreate an ecosystem in any physical space using none of the same material.

So I don't think you need non-material ideas to make sense of ideas. You just need a model where there are myriad ways to represent the same idea. The other problem for eternal ideas is that, if they are not material, how do they interact with our material brains? It seems like you'd need some version of Decartes pineal gland in place for that.

Which is not to address that the "material world" is itself a subjective abstraction made up of ideas, and that, in every sense, our understanding is the product of ideas. I find valid arguments for forms of idealism or dualism in that direction, just not in Plato's original direction of pointing to seemingly eternal ideas.

Does God being physical/material affect theism in any significant sense? Speaking for myself, I'm totally ok with God being physical. — TheMadFool

I think that "God", if he exists at all, could be anything.

The point is not to decide in advance what ultimate reality is. The point is to have an experience of it.

In the meantime, there can be nothing wrong with referring to it as "the unfathomable, ineffable, One".

The modern translation is ‘intellect’ but it’s a bit starchy to convey the gist. The Wiki entry is a good intro. ‘nous’ is preserved in vernacular English as being cluey or having a kind of insight — Wayfarer

I think "intellect" can be misleading. To understand Plato we need to understand the Greek terms he is using.

The word nous comes from the root gno- (PIE *gneh, “to know”) from which gnoos > noos, and it signifies the knower, i.e., that within us that is aware, knows, and understands.

Therefore:

A. The nous is the knower.
B. The nous is our true self.
C. Being a knower is our natural or true self.
D. Knowledge is of two kinds, of oneself and of things other than oneself.
E. Knowledge of other things is impossible without reference to the knowing self.
F. The highest form of knowledge is self-knowledge.
G. To attain self-knowledge we must rise from objectivity to pure subjectivity.

There are the following levels of awareness:

1. Perceptible object “out there”.
2. Mental image of object.
3. Thought about object.
4. Ideal object conceived in the mind.
5. Form of the object or combination of Forms (Size, Shape, etc.) constituting the ideal object, intuitively grasped by the nous or subject.
6. Nous or subject being aware of itself (pure subjectivity).

As subjectivity refers to the knowing self, we may use the question “Who am I?” which can be answered as follows:

1. (Gazing at the external object): “I am the knower or perceiver of the object”.
2. (Closing the eyes): “I am the knower or perceiver of the image of the object”.
3. (Thinking): “I am the knower of the thoughts about the image”.
4. (Conceiving the ideal object): “I am the knower of the ideal object”.
5. (Contemplating the Forms): “I am the knower of the Forms”.
6. (Contemplating the consciousness from which the Forms arise): “I am that”; “I am myself”; “I am”; “I”, etc.

In this way, we progress from the distant perceptible object "out there" to increasingly closer layers of awareness until awareness itself (or something as close to it as possible) is reached.

Clearly, this requires systematic mental training, that can be a life-long endeavor, in order to reach the final goal. However, a few hours or days of practice should at least give us an idea or intuition of what it is about.

At any rate, if Plato is right about the soul, Forms, the One, etc., then I think this would be one way of testing it for oneself.

A distinction needs to be made between the discussion of mathematical objects in the works of Plato and mathematical objects as they are thought of by mathematical Platonists.

Aristotle claims that Plato regarded them as intermediates, between Forms and sensible things.

Further, apart from both the perceptibles and the Forms are the objects of mathematics, he says, which are intermediate between them, differing from the perceptible ones in being eternal and immovable, and from the Forms in that there are many similar ones, whereas the Form itself in each case is one only. ( Metaphysics 987b14-18)

One issue of contention is the ontological status of these intermediates. Another is the relationship of intermediates to Forms. An insightful discussion of this and the importance of mathematical objects and the limits of logos for Plato's philosophy can be found here:

https://pdfs.semanticscholar.org/9a77/b70f6a93af7cc665bbac3fc64e5bfaffd1c6.pdf

From the article:

... the pure arithmetical units and perfect geometric exemplars hinted at in the Divided
Line passage or at Philebus 56d-e are, in fact, not onta at all. Rather, they are the way Forms appear, or are thought and related to, in the medium of mathematical διάνοια – a medium by its very nature incapable of thinking Forms directly.

I think that "God", if he exists at all, could be anything.

The point is not to decide in advance what ultimate reality is. The point is to have an experience of it.

In the meantime, there can be nothing wrong with referring to it as "the unfathomable, ineffable, One". — Apollodorus

What Mary Didn't Know.

There are experiences we can't put into words: Qualia, allegedly.

There are words we can't experience: Engage the warp drive Lt. Worf. Definitely.

The knife, it seems, cuts both ways. My question is if the reach of language exceeds experience (2nd case above), doesn't this mean experience, all manners of experience, is, for that simple reason, always effable?

But I think there's a theme in world philosophy of there being 'mind' in a sense more general than 'the individual mind', yours or mine. — Wayfarer

How did you come to that thought? Do you have any explanation for that belief or thought or conviction? Just a feeling? Guess? Personal experience? Inductive or deductive reasoning? If there were such things as general mind, then again where is it? Who is owning the mind? Having a mind means the haver can perceive, feel, think, and act. Does the owner of the mind exist in physical form?

My question is if the reach of language exceeds experience (2nd case above), doesn't this mean experience, all manners of experience, is, for that simple reason, always effable? — TheMadFool

That isn't an entirely bad question. And, of course, we could call the Good, the One, or God a "Quale" if we really wanted to. :smile:

However, my point is that what matters is not to name the object of experience but to experience it. And if we choose to name it, we may equally go for one of the names used by Plato himself (or by later Platonists). "The One" seems fairly neutral (as opposed to "God", for example) and would fit an object of experience of this nature IMO.

That's why I can't buy into this idea that it's simply something humans thought up, it's the discovery of something deep about nature herself. When Galileo said the book of nature is written in mathematics, he wasn't simply employing poetic allegory.. — Wayfarer

Hmmm I am not sure if I could agree with that point.
Who can only write the book of nature in mathematics? Humans. (I don't believe God or the aliens or cats can do this.)

Who discovered the antimatter? Paul Dirac. What was he? A human. (I don't believe he was a God or the aliens).

If you woke up on the earth 20000 years back, and were standing on a field with no one around you.
Just field, sky and yourself. Would you have been able to imagine the antimatter? The book of nature? Calculus or the Relative Theory? :) I think they are all in human mind, and the maths, the laws, scientific knowledge and all the facts have been discovered, and manifested into information by humans. Well, the ancient Greeks started the ball rolling.

No matter where I looked, the platonic forms were not found. — Corvus

Well, Socrates says:

The man who as far as possible uses his thought in its own right to access each reality, neither adducing the evidence of his sight in his thinking nor bringing any other sense at all along with the reasoning, but using his thought alone by itself and unalloyed, and so attempting to hunt down each real thing alone by itself and unalloyed, separated as far as possible from eyes and ears and virtually from his entire body, for the reason that the body disturbs his soul and, whenever it associates with it, doesn't let it acquire truth and wisdom, is the man who will attain to the knowledge of reality (Phaedo 66a)

You hunt something down by following its tracks until you see it. The tracks of the Forms are the universals, the things whose properties can be perceived in particulars ....

You hunt something down by following its tracks until you see it. The tracks of the Forms are the universals, the things whose properties can be perceived in particulars .... — Apollodorus

The universals and particulars ring a bell. Yes, it was in the Introduction to Metaphysics book. I can remember vaguely.

I will read up it again, and the Phaedo too. The Form was always very tricky part in Plato.
Thanks for the info.

The Form was always very tricky part in Plato. — Corvus

Very tricky indeed. But nevertheless essential, I think.

But I think there's a theme in world philosophy of there being 'mind' in a sense more general than 'the individual mind', yours or mine. Actually I'm embarking on a course of studying the current philosopher, Bernardo Kastrup, who has this kind of philosophy. — Wayfarer

I feel that the only way minds can be universal is sharing knowledge and truths discovered by reason and logic, and keep passing them onto other minds.

Very tricky indeed. But nevertheless essential, I think. — Apollodorus

:ok:

That isn't an entirely bad question. And, of course, we could call the Good, the One, or God a "Quale" if we really wanted to. :smile:

However, my point is that what matters is not to name the object of experience but to experience it. And if we choose to name it, we may equally go for one of the names used by Plato himself (or by later Platonists). "The One" seems fairly neutral (as opposed to "God", for example) and would fit an object of experience of this nature IMO. — Apollodorus

In Rome Total War, a recommended formation for infantry is to keep veteran men on the right flank of your army - the experience making up for the fact that shields offer no protection, being as they are held in the left hand.

Well, the ancient Greeks started the ball rolling. — Corvus

Right! Damned! Why don't you write things once in a while with which I don't agree?

It was Xenophanes who started the view of an objective unique reality, to be known by ratio. The scientific ratio, back then of course still primitive, though who knows what some Greeks were thinking. Archimedes found "his" law in bath, so... It was still the time of the gods and Xenophanes expressed this view of a human-independent unique reality by means of a horrible kind of god.The one and only. All knowing, all seeing, super in anything. It didnt posses a list of qualities as qualities are subjective. Plato beleived in a mathematical heaven of unchanging forms. I think it was this kind of thinking, together with Xenophanes' view became to be the reality that only science can adress or at least approximately komen. Falsificationalism is based on this. Popper "expanded" endless falsification as the real thing will never get reached; tiring indeed. Why not saying that after falsifying, criticizing, falsifying, criticizing, ...ad inf. that you theory is "it"?

Rather clever them Romans, weren't they? :grin:

No matter where I looked, the platonic forms were not found. Now I am guessing, they could be my intuition or pure reason. — Corvus

The Forms are hypothetical. In the Phaedo Socrates says:

... I feared that my soul would be altogether blinded if I looked at things with my eyes and tried to grasp them with each of my senses. So I thought I must take refuge in discussions and investigate the truth of beings by means of accounts [logoi] … On each occasion I put down as hypothesis whatever account I judge to be mightiest; and whatever seems to me to be consonant with this, I put down as being true, both about cause and about all the rest, while what isn’t, I put down as not true.” (99d-100a)

The Forms are an attempt to make sense of the world. In the Republic Socrates will tell a tale of the philosopher who escapes the cave and ascends to the sight of the Forms. But Socrates also indicates that he has had no such experience. Here too the Forms are hypothetical not things known. In the Republic we also find the promise of dialectic being able to move beyond hypothesis by the use of hypothesis. But nowhere in any of Plato's dialogues does he identify anyone, either an historical individual or a fictional character, whose journey ends in knowledge of the Forms. The journey always ends in aporia.

Rather clever them Romans, weren't they? :grin: — Apollodorus

Indeed!

The Forms are an attempt to make sense of the world. — Fooloso4

Plato's tetrahaeder, octohaeder, icosahaeder, an attempt to make sense of the world?

First, although there is some disagreement, mathematical objects, including Platonic solids, are not Forms. See above: https://thephilosophyforum.com/discussion/comment/585928 Second. they are, literally, fundamental to the cosmogony of the Timaeus. They are the mathematical or eidetic models of the elements fire, water, air, and earth.

They are the mathematical or eidetic models of the elements fire, water, air, and earth. — Fooloso4

The Platonic forms are materializations of the corresponding eternal forms in Platonic heaven. But they are approximations. Math describes them exactly but it doesn't privide an image of the forms. The forms are unknowable in principle. Seems reasonable that they correspond to the real elements used in the cosmogenesis. It would be nice if the Platonic solid were made from the five elements. There would be a bigger arsenal of real forms to chosen from in the construction of the solar system. Even better than atoms. ☺

The Platonic forms are materializations of the corresponding eternal forms in Platonic heaven. — Prishon

I don't know what this means. The Platonic forms are eternal forms, or so the hypothesis states.

Math describes them exactly but it doesn't privide an image of the forms — Prishon

According to Plato, it is not the objects themselves with which the mathematician deals but their images, that is, drawings or diagrams.

The Platonic forms are materializations of the corresponding eternal forms in Platonic — Prishon

Prishon must correct. With forms he probably meant solids.

According to Plato, it is not the objects themselves with which the mathematician deals but their images, that is, drawings or diagrams. — Fooloso4

Indeed. The forms can never be known. Like the elements of heaven. The images are not the forms, which have no form.

Prishon must correct. With forms he probably meant solids. — Prishon

Perhaps you could ask.

Perhaps you could ask. — Fooloso4

Prison, did you mean "Platonic solids"?

Prishon says: "Yes! How the f. did you know?"

The forms can never be known. — Prishon

I would say that they are not known. That they are is not known. What they are is not known. To ask what they are is problematic because they are supposed to be the answer to the question "what?". This amount to asking "what is what" as John Sallis has pointed out.