I agree that ideas are not physical, but I rather prefer a dualist interpretation, whereby humans are able to interface between the Platonic realm of abstractions, and actual objects, to produce neat things like:
— Wayfarer

Say that L is the set of all possible expressions in language, then Lr is a subset of L in which the language expressions seek to be isomorphic with the real, physical world R.

I agree that:

Lr ⊂ L and Lr ≈ R

Let's call Lr "the map" and R "the territory".

One major problem is, of course, that R is actually unknown. As Immanuel Kant famously quipped: Das Ding an sich ist ein Unbekänntes. (The thing in itself is an unknown).

We often use Lr and R interchangeably, and that is often no problem, but in the cases in which it is a problem, we may soon run into an abstraction leak, because ultimately the map is not the territory:

The map–territory relation describes the relationship between an object and a representation of that object, as in the relation between a geographical territory and a map of it. Polish-American scientist and philosopher Alfred Korzybski remarked that "the map is not the territory" and that "the word is not the thing", encapsulating his view that an abstraction derived from something, or a reaction to it, is not the thing itself. Korzybski held that many people do confuse maps with territories, that is, confuse models of reality with reality itself. The relationship has also been expressed in other terms, such as Alan Watts's "The menu is not the meal."

As coined by Joel Spolsky, the Law of Leaky Abstractions states:

All non-trivial abstractions, to some degree, are leaky.

Not only do abstract models not represent reality at all, unless you painstakingly expend effort to maintain such isomorphism, they do not even need to do so, in order to be useful. Mathematical axiomatizations, for example, never represent reality, while theorems must not be considered to be mathematical unless they belong to such axiomatization. They could be something else, however; such as scientific, for example.

In other words, a theorem can be mathematical or can be scientific, but can never be both at the same time. — alcontali

The problem is that I think this is a false dichotomy. I don't think abstractions such as language and number exist each in an hermetically-sealed realm; to say so is taking the idea of 'abstraction' too literally.

Part of post-Galileo science is the role of quantification. Remember 'the book of nature is written in mathematics'? The genius of Galileo and the modern scientific method that grew from there, is the emphasis on quantitative analysis. This was greatly expedited by Cartesian algebraic geometry. So those, along with all the other great breakthroughs of early modern science, enabled the precise application of mathematical logic to physical properties. Of course, this also has a huge downside, a shadow, so to speak, which is the bracketing out or rejection of the 'qualitative', although that's a separate issue.

So, I can't see how you can argue that abstraction and symbolic representation do not represent aspects of the real world. The whole success of mathematical physics in the last several hundred years is inextricably connected with the ability to apply mathematical methods to actual experiments and real data. Hence the 'unreasonable efficiency of mathematics in the natural sciences', Eugene Wigner's classic essay on just this point.

A pragmatist might ask why 'the physical world' is not also 'a language object'. Why is 'physicality' not merely 'a set of experiential expectancies' associated with those aspects of human physiology we call 'the senses'?

A pragmatist might ask why 'the physical world' is not also 'a language object'. — fresco

I think a legitimate distinction can be made. Indeed in the thread this was copied from, I noted this quotation:

If you can translate it into other languages, then it must be a language object. For example, "5" is a language object, because you can also write "five", "cinque", "fünf", or "101" (binary). Therefore, it has nothing to do with the real, physical world. It is an idea instead of something physical. — alcontali

I agree that '5' is a symbol, but what I'm inclined to say is that the symbol is not the thing signified (which roughly corresponds with the 'map is not the territory' analogy).

But what is the thing signified? Why, that's a number! And 5 = 5 (or 4+1, or 3+2, etc) in any language or system, or even in any possible world.

So I'm of the view that numbers (etc) are indeed 'intellectual objects', or ideas, as alcontali says. They're only grasped or known by a mind that capable of counting, but for any such mind, then 5 = 5. It's the symbol that is physical - the symbol is the physical representation of an idea. So there is a kind of dualism there, between (physical) form and (intelligible) meaning. That's what interests me.

But I *don't* agree that '5' has 'nothing to do with the real, physical world', for what I thought would be the obvious reason that applied mathematics is an ubiquitous feature of our day to day life.

I suggest '5' is merely the ubiquitous cultural expectancy involved of a verbal utterance associated with a human activity we call 'counting' used for other human activities like 'sharing'. In apocryphal 'less sophisticated cultures' whose counting system is '1, 2, many' our notion of '5' would be meaningless, Further more, 'counting' is already predicated on ' naming a thing' , a linguistic activity (the nominal level of measurement) so 'thinghood' is an ontological issue which precedes that of 'the physical world'.

I think we could interpret natural numbers as properties, or attributes, of physical objects: "5" is an attribute of a physical object that is made of 5 parts. At the same way as "red" is an attribute of an object that reflects red light.

One major problem is, of course, that R is actually unknown. As Immanuel Kant famously quipped: Das Ding an sich ist ein Unbekänntes. (The thing in itself is an unknown). — alcontali

Maybe if you folks stopped treating Kant like a religious messiah.

Kant was wrong. Philosophers, including the most famous philosophers, were just people like anyone who posts here. They can and often did say things that were just as wrong, stupid, misconceived, etc. as anyone says on the board, or as anyone says around the watercooler at your place of work, etc.

When someone says something, don't just accept it. Ask, "Is this correct? What's the argument or evidence for it (and what's the argument or evidence for the claims made in the argument for it? And for the argument or evidence for that . . . .) Does this analysis make any sense? Is this coherent/clear/etc.?" And so on.

A pragmatist might ask why 'the physical world' is not also 'a language object'. Why is 'physicality' not merely 'a set of experiential expectancies' associated with those aspects of human physiology we call 'the senses'? — fresco

Because there was a physical world a billion years ago.

You're not a young Earth creationist or something, are you?

Because there was a physical world a billion years ago.

You presumably mean that in your current human mind's eye with your current language and current psychological construct of 'time', your sentence 'makes sense' to 'like minded' humans ?
Correct !... for those humans a philosopher might call 'naive realists'.

As for 'creationism', I don't even know what that means except in terms of the imagined actions of a hypothetical anthropomorphic entity.

You presumably mean that in your current human mind's eye with your current language and current psychological construct of 'time', your sentence 'makes sense' to 'like minded' humans ? — fresco

No, I didn't "mean" anything like that.

LOL. I know you didn't...but I did !
Naive realists think that what we humans call 'the physical world' has nothing to do with the active perceptual needs of us as a species. They don't understand that a picture of 'a world devoid of humans' is a current human construction useful for current purposes. As those purposes evolve, our perceptual states evolve, and with them the picture of what we call 'the world' (or 'universe').

Are you prepared to stick your neck out and say that potential solutions to current enigmas, like 'dark matter', will not not radically change are current concept of 'physicality' ? Or do you deny that current research in quantum gravity implies that 'things' are merely 'repetitive events' ?

Remember that what we call 'science' has only been going for a few hundred years...the blink of eye in the history of humanity.

I agree that ideas are not physical, but I rather prefer a dualist interpretation, whereby humans are able to interface between the Platonic realm of abstractions, and actual objects, to produce neat things like: — Wayfarer

If imagination is simply the mind combining prior sensory data or rearranging it to make up imaginary objects that are not correlated to the real world, then this sort of Platonic realm of abstractions is deflated to simply imagination which is a sort of mechanized reflection of our sensory world by our mind. There would be no Platonic realm more than this. Certainly, the Hard Problem of Consciousness remains, but this in no way proves that the internal/imaginary state is in some way linked to an ethereal realm of Platonic forms and what not.

Naive realists think that what we humans call 'the physical world' has nothing to do with the active perceptual needs of us as a species. — fresco

Drop the labels and maybe we can make some headway. Labeling someone a "naive realist" and then attaching naive realism instead of what someone actually says is not productive.

Our "active perceptual needs" do not create the world ex nihilo. We are each of us born into a world that is not of our own making. It was here before any of us were and will be here after all of us.

When someone says something, don't just accept it. Ask, "Is this correct? What's the argument or evidence for it — Terrapin Station

What we see, i.e. the input signals we receive, create some kind of model in our heads, i.e. an abstraction of the physical world. With all complex abstractions being leaky, this process inevitably, occasionally produces unexpected results, i.e. situations where the perception as a model is out of sync with what it is trying to model.

We are not necessarily aware of when these perception errors take place. Therefore, I agree with Kant that we have no guarantee that the "appearance" that we see is a faithful representation of the thing-in-itself. In that sense, it is legitimate to declare the thing-in-itself to be an unknown.

Hence, you can even argue in favour of Kant's unknown thing-in-itself view using the law of leaky abstractions, with perception itself being the leaky abstraction.

Prolegomena, § 32.And we indeed, rightly considering objects of sense as mere appearances, confess thereby that they are based upon a thing in itself, though we know not this thing as it is in itself, but only know its appearances, viz., the way in which our senses are affected by this unknown something.

Maybe if you folks stopped treating Kant like a religious messiah. — Terrapin Station

I just think that Kant is often surprisingly spot on. I do not believe that he was infallible or so ...

Foolso4

Fine if we discount the fact that 'before' and 'after' are also parochial human constructs.
We were born into a world of concepts which WERE of our own making. Start from there if you want to see 'productivity'.

With all complex abstractions being leaky, this process inevitably, — alcontali

Ah, the leaky abstraction, which is itself a leaky metaphor. I understand it to mean that abstractions sometimes fail to perfectly hide the complexity, allowing it to occasionally leak through, creating difficulties in understanding.

So if a computer program has a leaky abstraction, that means the low level details matter in some way that might be unknown to the programmer, who's trying to figure out why their program isn't working as expected.

Which makes me wander about the role of metaphor in conceptual schemas and whether Aristotle took that into account. Plato clearly uses a metaphor for sense impressions being shadows on the wall of the cave, and the forms being the objects clearly seen outside. But all that is a non-literal use of visual imagery, and could potentially mislead us.

Can a metaphor be a platonic form? Are platonic forms leaky metaphors, hiding the messy physical details, while sometimes letting them through? Didn't Plato have difficulty deciding whether some things had forms, like mud?

What we see, i.e. the input signals we receive, create some kind of model in our heads, i.e. an abstraction of the physical world. — alcontali

So when someone says something like this, I ask--is this correct? What's the argument or evidence for it? And the answer to that is?

Fine if we discount the fact that 'before' and 'after' are also parochial human constructs. — fresco

I think it may rather be the case that theories of time are the constructs and time as we experience it and what occurs in time - getting older, for example, are pre-cognitive events, which in time we developed concepts of.

We were born into a world of concepts which WERE of our own making. — fresco

We are born into a world in which there is light and noise and motion and, if we are fortunate, a breast to latch onto, although the nipple of a bottle will do.

As Goethe said, and Wittgenstein quotes approvingly:

In the beginning was the deed.

Concepts come later.

Can a metaphor be a platonic form? Are platonic forms leaky metaphors, hiding the messy physical details, while sometimes letting them through? Didn't Plato have difficulty deciding whether some things had forms, like mud? — Marchesk

Well, there is that part of Plato's Parmenides where the question was asked if "participation" of a particular being in a form was more like being covered by a sail or happening in the same day. That is quite a range of speculation.
The status of mud is that it is not in danger of not being itself. The "participation" element seems to be related to beings that are in danger of losing themselves.

If imagination is simply the mind combining prior sensory data or rearranging it to make up imaginary objects that are not correlated to the real world, — schopenhauer1

Umm, there's this thing called 'science'..... :yikes:

Can a metaphor be a platonic form? Are platonic forms leaky metaphors, hiding the messy physical details, while sometimes letting them through? Didn't Plato have difficulty deciding whether some things had forms, like mud? — Marchesk

Interesting question! The idea of forms is intimately connected with the idea of universals, which in turn underwrite a theory of meaning. But it is hugely complicated by the fact that Plato's dialogues concerning the forms are very unclear in many respects, and littered with aporia; as if he himself had not perfectly intuited what the forms are, but had an overwhelming sense of their reality.

Thus, in the Euthyphro, Socrates, in asking for a definition of piety, says that he does not want to know about individual pious things, but about the "idea itself," so that he may "look upon it" and, using it "as a model [parádeigma, "paradigm" in English]," judge "that any action of yours or another's that is of that kind is pious, and if it is not that it is not" [6e, G.M.A. Grube trans., Hackett, 1986]. Plato concludes that what we "look upon" as a model, and is not an object of experience, is some other kind of real object, which has an existence elsewhere. That "elsewhere" is the "World of Forms," to which we have only had access, as the Myth of Chariot in the Phaedrus says, before birth, and which we are now only remembering. ...

Plato himself realized, as recounted in the Parmenides, that there were some problems and obscurities with his theory. Some of these could be dismissed as misunderstandings; others were more serious. Most important, however, was the nature of the connection between the objects of experience and the Forms. Individual objects "participate" in the Forms and derive their character, even, Plato says in the Republic, their existence, from the Forms, but it is never clear how this is supposed to work if the World of Forms is entirely separate from the world of experience that we have here. In the Timaeus, Plato has a Creator God, the "Demiurge," fashioning the world in the image of the Forms, but this cannot explain the on-going coming-into-being of subsequent objects that will "participate" themselves. Plato's own metaphorical language in describing the relationship, that empirical objects are "shadows" of the Forms, probably suggested the Neoplatonic solution that such objects are attenuated emanations of Being, like dim rays of sunlight at some distance from the source. — Kelly Ross

The way that I interpret forms is revisionist - that the forms represent 'the form of real possibilities'. So, for instance, the 'form' of a wing must have certain attributes if it is to fulfil the function of flying; but this doesn't prohibit the fact of very different evolutionary pathways to the development of wings (i.e. bats, birds, pterosaurs, flying lizards, aeroplanes). So the 'form' of goodness, or of justice, or of vision/seeing, is not for a minute like an actual shape or even an object; it's considerably more abstract than that. Perhaps, then, 'eyes' are instantiations of the 'form of seeing'; not of some 'ethereal eye' object.

But I have no trouble envisaging that the world of real particulars as a reflection or a striving towards ideal forms. The question will come up, 'where do these forms exist'. To which the answer is: they don't exist! They don't need to exist! Things do the hard work of actually existing! The forms inhere in the realm of timeless possibility, above all change and decay. But they're not 'existing things'.

What was lost in the battle between medieval realism and nominalism was just this sense of there being a realm of real possibility. To us, possibilities are something that exists in minds, minds in brains, brains in bodies, and bodies are physical; modernity seeks to 'ground' everything in this narrative. Whereas

The Platonic ideas are not in our mind; we are in them. They are not our servants; they are our masters. That’s why we experience awe and wonder at them. Most philosophies don’t have that power over our souls. When we speak of "awe" and "wonder" we don’t usually think of modern philosophers. — Eve Keneinan

She ain't kidding.

To my way of thinking the real world is knowable; it is always already interpreted and in conceptual shape, so to speak. It is what Wittgenstein referred to with his 'The world is the totality of facts, not of things". So, the real world is the factual world (in Kantian terms it would be the empirical world).

The "in-itself' which gives rise to that factual world is what I would call the "actual Real" ('actual' here has a different sense than the common sense: it should instead be read as 'the indeterminate which acts", kind of like Schopenhauer's "Will"). The actual Real is not a world, it is indeterminate. (It might be thought of it as sheer physicality or the Mind of God, but any definition must be thought to be inapt or merely a matter of taste) We determine the actual Real as world by factualizing it.

the real world is knowable; it is always already interpreted and in conceptual shape, so to speak. — Janus

You must mean unknowable, right? Otherwise your post reads very oddly. (Which I realised after starting to respond to it.)

Umm, there's this thing called 'science'..... :yikes: — Wayfarer

Not sure your non-sequitor there. The point is why would imaginary objects be equated with Platonic realm?

Well, there seems to be some fundamental disconnect here between how you and I understand this issue. So I'll go back to this comment:

If imagination is simply the mind combining prior sensory data or rearranging it to make up imaginary objects that are not correlated to the real world, then this sort of Platonic realm of abstractions is deflated to simply imagination which is a sort of mechanized reflection of our sensory world by our mind. There would be no Platonic realm more than this. Certainly, the Hard Problem of Consciousness remains, but this in no way proves that the internal/imaginary state is in some way linked to an ethereal realm of Platonic forms and what not. — schopenhauer1

What is at issue in all of this is the reality of certain kinds of ideas. As we are discussing, platonism (small 'p') maintains that numbers are real, that is, they exist independently of any particular mind. But at the same time, they're only perceivable by a mind that is capable of counting, namely, a rational intellect. So they are described as 'intelligible objects' - real, but not material. So in that sense, not 'products of the imagination' at all. (Mathematical platonism is controversial and not universally accepted, but it's still maintained amongst at least some current mathematicians - Godel and Penrose often named in this respect.)

So the philosophical question is, what kind of reality or being do numbers have? Are they simply in individual minds, and therefore ultimately explicable in terms of 'what that the brain does'? (which would be the materialist view.) Because if they're both real, and not material, then this is obviously a defeater for materialism, which holds that everything is reducible to, or supervenes on, matter. So there's no room in that view for real numbers.

And they're not 'made up', evidence for which is the uncanny degree to which mathematical logic has advanced physics and science generally in the last several centuries. In other words, it enables real and testable predictions about the real world, which could not be known by other means.

There's quite a good SEP article on mathematical platonism, particularly the paragraph on it's philosophical significance.

I should also add that scholastic philosophy maintains there's a distinction between imagination, perception, sensation, and conception. Ed Feser has a blog post on that which is germane to this discussion.

No, I meant "knowable". I am drawing a distinction between the real world and the actual Real that gives rise to it. It is not different than the distinction between the empirical world and the noumenal (which cannot be rightly thought as a world).

But at the same time, they're only perceivable by a mind that is capable of counting, namely, a rational intellect. So they are described as 'intelligible objects' - real, but not material. So in that sense, not 'products of the imagination' at all. (Mathematical platonism is controversial and not universally accepted, but it's still maintained amongst at least some current mathematicians - Godel and Penrose often named in this respect.) — Wayfarer

I see. Certainly this goes to the idea that humans have pattern recognition. Quantification is one of these.

So the philosophical question is, what kind of reality or being do numbers have? Are they simply in individual minds, and therefore ultimately explicable in terms of 'what that the brain does'? (which would be the materialist view.) Because if they're both real, and not material, then this is obviously a defeater for materialism, which holds that everything is reducible to, or supervenes on, matter. So there's no room in that view for real numbers. — Wayfarer

I guess the question to you is whether abstractions have to be "Platonic"? What does that mean to be Platonic? What would an abstraction be that is not "Platonic"?

And they're not 'made up', evidence for which is the uncanny degree to which mathematical logic has advanced physics and science generally in the last several centuries. In other words, it enables real and testable predictions about the real world, which could not be known by other means.

There's quite a good SEP article on mathematical platonism, particularly the paragraph on it's philosophical significance. — Wayfarer

Yes, I had a thread going about mathematical realism. The idea that we are sort of patterns seeing the patterns. The patterns cannot help but create pattern-recognizers, sort of thing. This is a sort of neo-Pythagoreanism.

What is at issue in all of this is the reality of certain kinds of ideas. — Wayfarer

Attributes and numbers are real insofar as recognizable objects are categorizable and numerable, and insofar as we are able to symbolize those generalities and quantities. In that sense attributes and numbers are independent of any particular mind, but of course it is true that it takes a mind to recognize, categorize and enumerate objects. What further reality do you imagine attributes and numbers might have?

The patterns cannot help but create pattern-recognizers, sort of thing. This is a sort of neo-Pythagoreanism. — schopenhauer1

But it's not. You can't explain mathematics in terms of patterns, because patterns are by their very nature regular and repeatable. Reason and rational inference are of a completely different order. (There's a guy who posts on this and other forums about epistemology based on pattern recognition.) It's just one of the typical assumptions of naturalism that numerical ability evolved and is therefore understandable in terms of its biological antecedents. It's a lot closer to neo-darwinism than neo-pythagoreanism.

(Actually that book Emperor's New Mind is about this topic. I bought it, but Penrose is way over my head. Anyone wants a copy, they can have mine.)

What does that mean to be Platonic? What would an abstraction be that is not "Platonic"? — schopenhauer1

They're good questions.

You can't explain mathematics in terms of patterns, because patterns are by their very nature regular and repeatable. — Wayfarer

Mathematical operations are not "regular and repeatable"? Take the simplest operation: counting, for example...