What is it that you would contrast mathematical elements to? What is it that completes the sentence "mathematical elements are real, not..."? — Banno

When I first noticed the reality of numbers, it was an epiphany. The idea suddenly occurred to me: everything material is composed of parts, and is temporally de-limited. But this doesn’t apply to numbers: numbers do not come into or go out of existence, and they’re not composed of parts (although later I realised that this strictly only appeals to primes, but even then, numbers are only ever composed of other numbers.) So I thought aha! This is why the ancients believed that numbers were of a higher order of reality than sensable objects. (That was the epiphany.)

At the time, I didn’t think much more about it, until I joined philosophy forums and started asking questions about it. Recently fooloso4 pointed to Jacob Klein’s book, Greek Mathematical Thought and the Origin of Algebra, from which I quote:

Neoplatonic mathematics is governed by a fundamental distiction which is indeed inherent in Greek science in general, but is here most strongly formulated. According to this distinction, one branch of mathematics participates in the contemplation of that which is in no way subject to change, or to becoming and passing away. This branch contemplates that which is always such as it is and which alone is capable of being known: for that which is known in the act of knowing, being a communicable and teachable possession, must be something that is once and for all fixed.

That was the exact intuition which I had had in that epiphany. In my view it is central to the tradition of Western philosophy, but it’s been abandoned. I trace that back to the conflict between scholastic realism and nominalism in the later medieval period. The significance of it is, that the ‘intelligible objects’ (universals, numbers, principles, and the like) belong to a higher order than do the objects of empirical discovery - they belong to the ‘intelligible domain’ (which is not some place.) With the loss of that intuition, then there is the loss of the vertical dimension, the qualitative dimension, and a real metaphysics. This is what I’ve been painstakingly researching the last 10-12 years. Hence my (somewhat unwilling) discovery of Augustine, Aquinas and neo-Thomist philosophy.

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

Yep, I can see how arriving at this conclusion might be problematic. We might end up back in a world similar to scholasticism and its transcendentals of truth, goodness, beauty. Is idealism popular with conservatives? I remember reading Roger Scruton, who argued that an awareness of the transcendentals wasn't necessary in life, unless you wanted a full understanding of reality and of each other. :chin:

I am not sure I understand how one is supposed to access or understand 'pure ideas' such as truth or beauty in order to appreciate them in our reality.

I am not sure I understand how one is supposed to access or understand 'pure ideas' such as truth or beauty in order to appreciate them in our reality. — Tom Storm

Don't we understand them only in terms of feelings or intuitions we have in respect of real things? A beautiful person, or landscape, a true friend or situation, and so on? How else could we understand truth and beauty? Remember Keat's chiasmus at the end of 'Ode to a Grecian Urn':

"Beauty is truth, truth beauty,—that is all
Ye know on earth, and all ye need to know."

No idea - none of this language resonates with me, so I apologise. I am trying to understand how such 'judgements' might work from an idealist model. Idealism is a type of objectivism, isn't it? So presumably an idealist, who makes judgements about beauty is identifying how an instantiation of something (a sculpture or painting, say) reflects an ideal form. Ditto ethics.

So presumably an idealist, who makes judgements about beauty is identifying how an instantiation of something (a sculpture or painting, say) reflects an ideal form. Ditto ethics. — Tom Storm

It seems to me that the underpinnings of ethics are easy enough to comprehend in terms of the understandable desire social animals have for social harmony; a pack, troupe, group, community or society riven with conflict does not benefit the collective.

The idea that beauty in painting or sculpture consists in reflecting an ideal form doesn't seem plausible to me. Take the human form, for example; how, on the basis of what criteria, would an ideal form become established that actual forms might be related to? Or a landscape; what is the ideal form of a mountain? Can we invoke symmetry, or is that not too simplistic?

I remember reading Roger Scruton, who argued that an awareness of the transcendentals wasn't necessary in life, unless you wanted a full understanding of reality and of each other — Tom Storm

Unless, that is, you wanted to be a philosopher.

Sure. I specifically am asking for an idealist account of this so I can better understand the thinking.

Unless, that is, you wanted to be a philosopher. — Wayfarer

So much could be contained in this one statement.

Sure. I specifically am asking for an idealist account of this so I can better understand the thinking. — Tom Storm

The only idealist accounts I am familiar with invoke a higher realm of some kind; a realm of absolute goodness, beauty and truth, which is only ever partially reflected in this fallen world of ours. But I don't see how this could have much potential for being an account that anyone who lacked the kinds of intimations this understanding springs from could be persuaded by.

That said, although I think goodness in the ethical sense can be related to social well-being and hence requires no transcendental account to understand its wellsprings; beauty and truth seem to be entirely resistant to accounts in terms of anything more fundamental.

So much could be contained in this one statement. — Tom Storm

Or so little...

I guess what I am wanting is someone to defend or steelman a version of idealism for me so that I can better understand its potential use in the quotidian world. If idealism is true, why should it matter to us? This is what @Wayfarer keeps pointing towards. My guess is that the idealist will argue (and I'm looking for details) that all good judgement is a reflection of transcendence (what's the word I am looking for here?) and the idea of morality (for instance) is to understand truth and goodness in something approaching pure form. On a slight tangent, I am assuming that in theory a mystic is someone who has some access to this, shall we say, realm of ideas (apologies to Plato).

For now, I'm not interested in critiques of this or debunking of idealism - I'm hoping for a more enhanced presentation of the ideas in practice. But just a few clues not a thesis....

As I see it the only argument for the importance of an idealist understanding might be that it better supports "spiritual" aspirations and intuitions. Personally, I don't think that is the case, but I guess it depends on the individual; and in any case if spiritual aspirations are not important to you, and you have no such desires, feelings or intuitions, then I think it certainly wouldn't matter. For me the whole debate just seems overly simplistic and misguided.

Any idealism worthy of the name goes further, insisting that there cannot even be a way that things are without mind. — Banno

This is right, an idealist would claim "that there cannot even be a way that things are without mind". But this is easy to understand, and accept. The way that things are, is commonly believed to be perspective dependent. The way things are is different dependent on one's spatial-temporal perspective, and only a mind cam have such a perspective. This is the fundamental principle of relativity theory. And it is why many modern sciences, especially the disciplines which employ physics, are inherently idealist. Look at "model-dependent realism" for example.

You apparently wish to be both an idealist and a realist. I can't see, on the logic offered, how you could make these compatible. — Banno

There is no basic incompatibility between realism and idealism, hence the common position of Platonic realism, which is compatible with idealism. This is because "realism" is very versatile, and used in many different ways. The extreme form of Platonic idealism, Pythagorean idealism, posits a real independent world which is composed of mathematical ideas (God's ideas or whatever), and this is a form of realism. You'll find this also in Berkeley. Wayfarer I believe is a Platonic realist, as most modern mathematicians are (mathematics employs axioms which assume the reality of mathematical objects). So there is no problem for Wayfarer to be both idealist and realist. It seems to me that you believe in the reality of mathematical objects as well, Banno.

The way things are is different dependent on one's spatial-temporal perspective, and only a mind cam have such a perspective. This is the fundamental principle of relativity theory. — Metaphysician Undercover

I have a rule not to reply to Meta, it's not worth one's while. But it is incumbent on me to point out that this is almost exactly wrong. The Principle of Relativity is that the laws of physics must be the same for every observer.

Google it.

This is the flaw in the notion that physics tries to find the "view from nowhere". It doesn't. It looks for the "view from anywhere".

The "way things are" is the same for all observers.

Anyway, back to ignoring Meta.

You're right, numbers are real. But not for the reason you think. Numbers are not free-floating entities that minds find and interact with. Numbers are particular patterns of synapse firings.

Assume you see 3 apples on a table and a neurologist takes a detailed scan of your brain at the same time. Should that neurologist be able to cause the exact same synapse pattern to fire an hour later, what do you think will happen? "3" is an activity of brains. So yes, numbers are real because active brains are real.

Numbers are not free-floating entities that minds find and interact with. — Real Gone Cat

‘Free floating’ is your description. You’re saying that because you think all real things can only be situated in time and space, so there’s no category available to you which maps against transcendentals such as number. But that’s not unique to you as the culture we’re in has a blind spot about it.

Should that neurologist be able to cause the exact same synapse pattern to fire an hour later, what do you think will happen? — Real Gone Cat

No. Read my argument again, especially the section on representational drift.

I am not sure I understand how one is supposed to access or understand 'pure ideas' such as truth or beauty in order to appreciate them in our reality. — Tom Storm

I understand your perplexity and, I think, what you’re asking for. I have another of my stock quotes from an essay which I’ve found very valuable in this respect.

A genuine (scholastic) realist should see “forms” not merely as a solution to a distinctly modern problem of knowledge, but as part of an alternative conception of knowledge, a conception that is not so much desired and awaiting defense, as forgotten and so no longer desired. Characterized by forms, reality had an intrinsic intelligibility, not just in each of its parts but as a whole. With forms as causes, there are interconnections between different parts of an intelligible world, indeed there are overlapping matrices of intelligibility in the world, making possible an ascent from the more particular, posterior, and mundane to the more universal, primary, and noble.

In short, the appeal to forms or natures does not just help account for the possibility of trustworthy access to facts, it makes possible a notion of wisdom, traditionally conceived as an ordering grasp of reality. Preoccupied with overcoming Cartesian skepticism, it often seems as if philosophy’s highest aspiration is merely to secure some veridical cognitive events. Rarely sought is a more robust goal: an authoritative and life-altering wisdom — Joshua Hochschild, What's Wrong with Ockham?Reassessing the Role of Nominalism in the Dissolution of the West

The problem is, the West parted ways with this understanding so long ago that we’ve forgotten what it means - as that passage says. But reflect on the commonly held belief that life arose by chance and that we ourselves are the outcome of chance, marooned in a Universe which has no intrinsic reason. It’s difficult to reflect on, because of its taken-for-grantedness. As Buddhologist David Loy says, ‘ The main problem with our usual understanding of secularity is that it is taken-for-granted, so we are not aware that it is a worldview. It is an ideology that pretends to be the everyday world we live in. Most of us assume that it is simply the way the world really is, once superstitious beliefs about it have been removed.’ And that is a consequence of the transition to modernity. Modernity (and post-modernity) has many strengths, and besides it’s an inevitable and unstoppable development, but this is an aspect of it that has to be questioned.

Yep - that's what I'm talking about. I'll mull over it. Thanks.

the particular synapse pattern associated with "3" that accompanies the 3 apples I see today is not exactly the same as the 3 miles I must drive tomorrow. But some commonality will exist. — Real Gone Cat

Yes, but it will be a commonality of function, not neural pattern. Each neural cluster involved will tend to fire toward clusters which might help form the word for 'three' in your language, others mights trigger images of generic 'threedom' (like three dots in a row, or a triangle), others might start chains which relate to compare 'three' (is it enough, too much?)... But different neurons might carry out this role at different times. Interestingly, they'd usually be in the same general area of the brain and this has to do with the brain's meta-structure, determined, we think, by the history of long term potentiation, but the point is, they couldn't be identified other than generally.

"Real" gets its meaning by being contrasted to what is not real. It's real money, not counterfeit; it's a real van Gogh, not a print; it's a real lake, not an hallucination.

What is it that you would contrast mathematical elements to? What is it that completes the sentence "mathematical elements are real, not..."? — Banno

This seems related to the question I posed @Wayfarer yesterday...

you seem to define what is 'real' as if the category were clear (in terms of its membership criteria) and we could assign certain things to it - numbers, logical laws etc. But I don't see how you've arrived at those membership criteria. The set {all things which are real} doesn't seem to be well defined. — Isaac

It seems to me that if 'real' is not to mean something like 'made of physical matter' (which I agree would be too restrictive), then the range of coherent alternatives is limited. To my mind something like 'that which has a state which might at some time be unknown' is one such. But as you say, nothing prevents constructed social concepts from entering this category.

Where and how do you draw the line here so as to be able to make the distinction you’re trying to make between what is constructed and what is prior to and independent of construction? — Joshs

If I may...

I don't think one needs to see this as a question of where the line is - I think that's an interesting question - more that the model requires such a line. The very idea of construction requires raw material from which to build, it's in-built in the model.

The moment you accept that data from outside you Markov Blanket affects the nodes within it, that data must be imbued with properties modulating that effect, those properties clearly do not determine the network's hypotheses from within the Markov boundary, but their parameters will affect the nature of any function of their distribution.

So we might have social constructions around pots, clay, even atoms, but the the distributions of those constructs will be bound by the parameters of the data from outside the Markov Blanket.

an authoritative and life-altering wisdom — Joshua Hochschild, What's Wrong with Ockham?Reassessing the Role of Nominalism in the Dissolution of the West

Within this quote is all that I fear about idealism.

Note how every instantiation of idealism is also a tool of power. It creates, in each instance, a class of people who can 'see' and those who cannot. Usually some barrier is set to 'seeing' (education, religious practice) which can then be used to control (supply of education), or de-humanise (lack of religion).

There's little about idealism not distastefully entangled with the exploitation of unequal power relationships.

Note how every instantiation of idealism is also a tool of power. It creates, in each instance, a class of people who can 'see' and those who cannot. — Isaac

I've wondered about this in the past. It certainly provides opportunity for some folk to claim that their appreciation of art or ethics is informed by access to a transcendent and foundational guarantor (a Platonic realm) and therefore they are intrinsically more aware or sensitive to truths.

I certainly see this in the observations of philosophers like Roger Scruton who identifies what is beauty and what is not beauty - generally via a conservative aesthetic lens. But having said all this, just because there are powerplays doesn't make it ipso facto wrong.

This somewhat echoes my earlier suggestion that what motivates idealists is a god complex. Idealism gives the illusion of control and purpose. It takes away scary ideas, like "the universe is bigger than me" and "the universe is random".

Coupled with another motivation that I will mention in a moment, it leads to what you have identified as unequal power relationships. The second motivation is exceptionalism. I don't know if any surveys have been conducted but I am sure that idealism is not a widespread belief amongst the general population. So an academic esoterica is created which only a few will ever immerse themselves in.

This may well be true, but it doesn't go to whether idealism is right or wrong.

having said all this, just because there are powerplays doesn't make it ipso facto wrong. — Tom Storm

Absolutely. It does, however, go to a pet interest of mine which is strategies for making decisions in uncertainty (also to answer )...

If we cannot know for sure whether idealism is right or wrong, then we must decide whether to believe it on the basis of something other than the weight of evidence. Such a method is clearly insufficient otherwise our intellectual peers would have already done so.

Thus, factors such as undesirable social consequences become relevant, as actual evidence and rational arguments recede in importance.

It's like choosing between two cars, the most important factor is that they both get you from A to B efficiently. But they wouldn't even be in the car showroom if they didn't do that, so we start to consider the colour, the upholstery, the stereo...

Yep, this is how I generally organise my beliefs too. Nevertheless I am still keen to dip into idealism to better understand the model/s since this is an area I have shunned for many years.

I am wanting is someone to defend or steelman a version of idealism..... — Tom Storm

Steelmanning or otherwise, without granting....understood a priori as given.....the intrinsic duality of human nature, no defense of any version of idealism will be acceptable. Or, another way to put it, the only defense of any version of idealism is predicated on an intrinsic duality of human nature.

philosophy wants to get the roots, the total, the ultimate, the general, the universal. The problem is that philosophy gets the ultimate by using the primitive instruments I said before. — Angelo Cannata

:up:

The result is that we would define the universe by saying, for example, that it must be necessarily “a shouting banana on a chair”, or a “guitar shouting to a banana”. Why are these example ridiculous? It is because they try to define something extremely wide, great, extended, general, which is the universe, by extremely specific words like the ones I used. We don’t realize how ridiculous is to talk about “material”, “external”, “exists”, and so on, because we think that those concepts are wide, great, general, so that they are appropriate to talk about the universe. Once we realize that those great concepts are actually extremely rough, unclear, local, limited, then we can understand how ridiculous is to talk about “external material world”. — Angelo Cannata

I agree that those concepts are quite unclear, but I do not understand what do you mean by them being rough, local and limited. Also, what does it mean to say that they are wide, great and/or general ?

when we talk about such big things, like “space”, “time” and so on, we are actually moving inside the cage of our mental categories — Angelo Cannata

:up:

Don’t confuse science and materialism. Science assumes materialism for practical reasons, it’s when it becomes a philosophical ideology that it is problematical. There are many scientists who don’t hold to it. — Wayfarer

:up:

Or, another way to put it, the only defense of any version of idealism is predicated on an intrinsic duality of human nature. — Mww

Sorry I don't know what you mean by duality of human 'nature' or the connection of a 'dualism' to a monist ontology.

I agree that those concepts are quite unclear, but I do not understand what do you mean by them being rough, local and limited — Hello Human

Consider them as synonyms of unclear.

It all hinges on the meaning of the word "external" as used in the OP question, doesn't it? External in what sense, external to what? And precisely how is it external to the what? — charles ferraro

Actually, I think I chose the wrong words to express the issue. The word "internal" implies that there is some "external", and vice versa. So perhaps the question should be separated into two distinct questions: "Is there a world existing independently of the mind ?", and if the answer is yes, "Can that world be entirely reduced to matter and energy ?".

But we can watch others directly interact with things, and so need not assume that this is untrue of ourselves. — NOS4A2

What do you mean exactly by "directly interact" ?

But the cogito is NOT a view of idealism. Descartes is a dualist. — L'éléphant

:up:

Don't you exist independently of other conscious beings? — Luke

I don't know. I don't think I can know either.

Since those conscious beings each have material bodies, then there is something material which exists independently of you: other people. Otherwise, do you assume that we are each free-floating consciousnesses without material bodies? — Luke

I don't assume it, but I don't deny it either.

So, I would like to "hear" your own position on your own subject "Is there an external material world?" — Alkis Piskas

I have no idea at all. I don't think we can ever know for sure. I think the only way we can compare the different answers is how practical they are for other human activities like science and engineering.