The Stanford Encyclopedia of Philosophy’sRussell’s Paradox entry has the following.

Russell’s paradox is the most famous of the logical or set-theoretical paradoxes. Also known as the Russell-Zermelo paradox, the paradox arises within naïve set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself. Hence the paradox.

Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves “R.” If R is a member of itself, then by definition it must not be a member of itself. Similarly, if R is not a member of itself, then by definition it must be a member of itself.

Did Russell’s paradox exist before he . . . discovered it? Or . . . invented it? Which is it, discovered or invented? If discovered, then yes, the paradox was there since before the Big Bang, just waiting to be found. If invented, then no, the paradox came into existence the moment Russell first thought of it.

The paradox exists. For how much longer? Can an idea stop existing? That doesn’t seem right. It seems if all humanity vanished tomorrow, Russell’s paradox would still exist. But if an idea cannot cease to exist, then it obviously must exist for all eternity into the future. If Russell created the paradox, that would mean the idea is half-eternal, having a start time in the finite past but no end time in the future. It seems rather odd to say a mortal human being can create something which will exist for all eternity. It seems to make more sense to say that Russell’s paradox was discovered, not invented; that it has always existed.

Existed where? One answer is: in the mind of God. But this answer assumes an all-good, all-powerful, all-knowing being, which are more assumptions than we need. The minimum is merely to stipulate a place where all thoughts exist, without saying anything more about the place. I call the place the “mindscape.” [reference to this thread omitted]

I don’t claim the above is a proof; any of the steps in thinking can probably be disputed. But it’s a train of thought—an interesting train, at least, for me—that leads to the idea of the mindscape. — Art48

The paradox exists. For how much longer? Can an idea stop existing? That doesn’t seem right. It seems if all humanity vanished tomorrow, Russell’s paradox would still exist — Art48

I merged this thread with the older OP because they're substantially about the same question. You're dealing with the reality of abstract objects, such as ideas, numbers, universals, and so on. I agree with you that it's a valid question and an important question, and I also agree that such things as ideas, numbers, universals, and the like, are real. But they're not existent as phenomena, they are not real in the sense that tables and chairs and trees are real. That's the conundrum you're outlining - how can these ideas be real if they don't actually exist? It is a metaphysical question par excellence.

So in my view, you're asking a question about the fundamentals of metaphysics. But I think that metaphysics as understood by classical philosophy has been more or less forgotten or abandoned in philosophy as whole except for in the case of classes and books specifically about that subject. I mean, the subject still exists, but it is not appreciated that the real basis of metaphysics as a living subject revolves around the very question you're asking. Because it asks us to deeply question what we take for granted as what is real, what exists. It introduces a wholly other dimension to the question.

Russell, apparently, regards thoughts differently, as acts. He writes: “One man's act of thought is necessarily a different thing from another man's.” — Art48

Yes - but look at the context! He says 'universals are not thoughts, but when they're known, they appear as thoughts'. He distinguishes thoughts from universals, because he says that universals (such as whiteness) must be the same for all. Which is just the same for mathematical and geometrical proofs! They too are the same for all who can grasp them. So they can only be grasped by thought, but they're not the product of thought. I hope you can see this distinction. They exist as what tradition would call 'intelligible objects' i.e. they are real only as objects of reason, not as sense-able phenomena. But that distinction is largely lost in modern philosophy because of its exclusive emphasis on empiricism (what can be sensed).

I'm trying to situate your ideas within the context of the debate about the reality of universals, because that's what I think you're actually talking about. I don't claim to be an expert but I'm someone who has noticed that it *is* a question, and also someone who believes that it is a central question of philosophy.

You're just misusing the word "exists".

You've taken the way we talk about the common stuff around us existing in a place and a time and applied it unjustifiably to Russell's paradox.

Paradoxes are not just like trees and rocks. — Banno

Do ideas exist or not? Would you rather the world "subsist"? Or some other word?

Wayfarer,

You make interesting points.

You're dealing with the reality of abstract objects, such as ideas, numbers, universals, and so on. I agree with you that it's a valid question and an important question, and I also agree that such things as ideas, numbers, universals, and the like, are real. But they're not existent as phenomena, they are not real in the sense that tables and chairs and trees are real. That's the conundrum you're outlining - how can these ideas be real if they don't actually exist? It is a metaphysical question par excellence. — Wayfarer

I perceive thoughts, ideas, and emotions directly in consciousness. I perceive the external world indirectly, via the five physical senses. The ideas I perceive definitely exist. The water I perceive may be a mirage, or I may be a brain in a vat. It seems odd (and wrong) therefore to say tables and trees have more reality than thoughts, ideas, and emotions, although I admit it's a widespread and understandable view.

He distinguishes thoughts from universals, because he says that universals (such as whiteness) must be the same for all. Which is just the same for mathematical and geometrical proofs! They too are the same for all who can grasp them. So they can only be grasped by thought, but they're not the product of thought. — Wayfarer

So, universals pre-exist in what is called the mindscape? It's a short step to say all thoughts exist there, although, of course, the step has to be justified.

I just thought a thought. Thoughts must come from thoughts then. It’s a causal chain of thoughts. When thoughts stop happening we stop thinking don’t we ?

When thoughts stop happening we stop thinking don’t we ? — invicta

Yes, if you consider thoughts a process.
On the other hand, the mindscape idea says thoughts are pre-existing and we encounter them, just as we encounter the pre-existent tree in a landsacpe.

It's a short step to say all thoughts exist there, although, of course, the step has to be justified. — Art48

As I said earlier, I think you need to distinguish thought in the sense of random neural chatter from the formal aspects of thought.

I also think the basic problem with the 'mindscape' is that it is trying to project the activities of reason onto a kind of external or objective landscape, like the so-called 'ethereal realm' of Platonic objects. It draws on the sense of being located in physical environment as an analogy, as if there is a literal 'realm of ideas'. But that is a reification - there is no literal 'realm of natural numbers', although it is conceptually real.

But that is a reification - there is no literal 'realm of natural numbers', although it is conceptually real. — Wayfarer

Now I am curious, what is an example of something that is conceptually unreal?

Do ideas exist or not? Would you rather the world "subsist"? Or some other word? — Art48

The trouble is you haven't set out what it is you are asking; how you are using the word "exist".

It's a word that can be parsed in several quite different ways. It can be a quantifier, or indicate membership of a class, or set out membership of a domain, just for starters.

"Exists" in "Anthony Albanese exists" is not being used to do the same thing as "exists" in "The largest prime less than 1000 exists". One you might meet in the street, the other, no so much.

Your failure to notice these distinct uses leads you to propose absurdities.

Now I am curious, what is an example of something that is conceptually unreal? — Richard B

The point I'm trying to make is simply that to depict the denizens of 'the realm of ideas', such as logical principles, or natural numbers, in terms of 'mindscape', suggests a 'landscape' - which is spatially and temporally extended. Whereas the 'domain of logical principles' or 'the domain of natural numbers' are neither. So my argument is that they're real, because they're the same for all who think, but they're not strictly speaking existent. They are real as the constituents and objects of rational thought. (I think this is the original, as distinct from the Kantian, meaning of 'noumenal'.) So this is a distinction which I am trying to make between the nature of the existence of perceptible objects (or phenomena), and the nature of intelligible objects, which are perceptible only to reason.

Good post ! Rucker is great. Let me throw a wrench into the machine. What is an idea ? One approach, that might save us some trouble, is that it's an equivalence class of expressions.
https://en.wikipedia.org/wiki/Equivalence_class

I'm happy to explain the concept of an EC if you are interested.

In short, I don't think ideas always existed. Or always will exist. I don't think it makes much sense to try to 'get around' the historical 'space of reasons.'

The trouble is you haven't set out what it is you are asking; how you are using the word "exist". — Banno

:up:

Ah, solving that question
Brings the priest and the doctor
In their long coats
Running over the fields.

So my argument is that they're real, because they're the same for all who think, but they're not strictly speaking existent. — Wayfarer

And it would be unreal if they’re different for all who think? But this would just be different ideas. Or, someone is thinking the same thing but the idea is different compared to someone else thinking the same thing? This does not make sense. Austin said the following about “real”, “Real, is also a word whose negative use “wears the trousers” (a trouser-word)”

Apologies for not having explained the point with sufficient clarity.

Good post ! Rucker is great. Let me throw a wrench into the machine. What is an idea ? One approach, that might save us some trouble, is that it's an equivalence class of expressions. — green flag

I'm familiar with equivalences classes. The same idea can be expressed in different ways (for instance, in different languages). But I'd give logical priority to the idea itself so defining the idea in terms of its expressions seems backwards.

In short, I don't think ideas always existed. Or always will exist. — green flag

Can you describe how and when an idea goes out of existence. For example, 2+2=4 is an idea. Will it ever cease to exist.

Do ideas exist or not? Would you rather the world "subsist"? Or some other word? — Art48
The trouble is you haven't set out what it is you are asking; how you are using the word "exist". — Banno

Ideas exist. Tell me if there's a sense of "exist" where you think the statement is true and maybe we can go from there.

So my argument is that they're real, because they're the same for all who think, but they're not strictly speaking existent. — Wayfarer

A few posts seem to be quibbling over the word "exists". What word would you prefer instead? Subsist? Something else?

A few posts seem to be quibbling over the word "exists". What word would you prefer instead? Subsist? Something else? — Art48

It's far more than a quibble but I can see it's useless to try and explain why, so I give up.

\

Ideas exist. — Art48

"There are ideas" just places ideas in the domain of the discussion. But you erroneously take this to mean that they have a place or a time or some such. That doesn't follow. You take "P exists" to imply that P has a spatial location, then when they are not found down the back of the lounge you invent a magical space for them to exist in.

But I'd give logical priority to the idea itself so defining the idea in terms of its expressions seems backwards. — Art48

But that's exactly the step that I'm questioning (I go into this in my Semantic Finitude thread.) It is arguably the basic superstition and the basic confusion of Western philosophy, tangled up with the complementary immaterial subject for whom such beings are supposed to be mysterious and immediately present.

Can you describe how and when an idea goes out of existence. For example, 2+2=4 is an idea. Will it ever cease to exist. — Art48

If we stick with the equivalence class metaphor (with a blurry substitute for the mathematical version), then the idea dies with its last representative, just as it was born with its first.

It's conceivable that we'll include 'Klingon' expressions in such an equivalence class, if we last that long and someone finds us.

"There are ideas" just places ideas in the domain of the dicusion. But you erroneously take this to mean that they have a place or a time or some such. — Banno

:up:

It's way too easy to use words like 'idea' and 'exist' without hearing their hollowness, their elusiveness, their contextdependence, ...

I'd say the sense data is not in the mindscape, but the idea of shit is. — Art48

To me there's a relatively reasonable interpretation of 'mindscape' along the lines of 'geist' or 'spirit' or culture. We humans live together in a symbolically articulated lifeworld. We have marriages and milkshakes and murder and mud here. We are held responsible for what both what we say and what we do and their relationship. The language we are "in" does transcend the individual, but you seem to want to make it transcend the species.

Some philosophers pretend they can break up this unity into components without talking nonsense, but I don't think it's so easy. The confusion is various versions of secret insides, like ideas that hide inside or behind expressions, ghosts that hide inside meatsuits and drive them around with nothing but willpower and a pineal periscope, the the really really stuff that hides beneath every namable floor.

Off the top of my head...

Maybe I can go along with an ontological pluralism in which ideas can be said to exist in their own domain, but they would exist in a different way from stars and brains (which is just/also to say that "exist" has different meanings in different domains, as @Banno has pointed out).

As @green flag said, we can use concepts like lifeworld or culture, and maybe the manifest image is along the same lines. I'll add another one that's more granular and ontological: fields of sense. This is Markus Gabriel's concept: a field of sense is a context, domain, or background in which or against which something stands out, and thereby exists.

So ideas exist in their own domain. Very well. But what is happening to this concept when it turns into the mindscape? What justifies this leap? On the face of it, it's a wildly speculative reification that attempts to turn, say, an analogical way of thinking about ideas, one that's familiar to artists and geniuses, into a mind-independent ontology: not only do ideas exist, but they have always existed, and we tap into the mindscape to think them. But in fields of sense or the lifeworld, we might say that ideas exist, but we do not thereby establish eternal existence independent of people, because these domains are strictly human and finite realities, and I can't see the justification for the leap, at least not in the OP (I haven't read all of Rucker's online presentation of the idea).

Is this what happens when you combine the thought of a universe of physical objects with the thought of universals and abstract objects like numbers, as I think @Wayfarer is suggesting?

So you end up with something like Platonism I guess, although as far as I can tell the existents of the mindscape seem to be concrete and/or particular, rather than being merely universal forms: in this mindscape there are instantiations, like Macbeth, and not only forms.

On the other hand, the idea of a shared landscape of ideas is an attractive one, but only as at least part-analogical--there may be a world of ideas that we are part of when we think, but it's more map than landscape (but this might be in conflict with ontological pluralism, I'm not sure).

You take "P exists" to imply that P has a spatial location — Banno

When I say the mindscape is the place where ideas exist, "place" is a spatial metaphor, not to be take too literally.

If we stick with the equivalence class metaphor (with a blurry substitute for the mathematical version), then the idea dies with its last representative, just as it was born with its first. — green flag

I'm asking how exactly does an idea like 2+2=4 cease to exist. You seem to say it dies when the last representative in its equivalence class dies, but don't address how the last idea (or any idea) could cease to exist.

Maybe I can go along with an ontological pluralism in which ideas can be said to exist in their own domain, but they would exist in a different way from stars and brains — Jamal

True, but isn't that obvious? I'm puzzled why there have been so many posts about the word "exist". The definition of mindscape would be essentially unchanged if "subsist" or some other word were used.

So ideas exist in their own domain. Very well. But what is happening to this concept when it turns into the mindscape? What justifies this leap? — Jamal

Mindscape says ideas exist in their own domain and, as you point out later your paragraph, that ideas are eternal.

it's a wildly speculative reification t — Jamal

I think the reification accusation can be avoided if for "exist" people substitute "subsist" or whatever word they like that allows ideas to be.

So you end up with something like Platonism — Jamal

Yes! I read the mindscape as applying Mathematical Platonism to all ideas, not just mathematical ideas, which is my opinion of what Rucker, a Ph.D. mathematician, has done. Before I posted, I would have thought it uncontroversial that 2+2=4 is an idea which has existed from all eternity, just as the square root of 2 has been an irrational number from all eternity, and always will be.I was surprised that some people took issue with the word "existed."

On the other hand, the idea of a shared landscape of ideas is an attractive one, but only as at least part-analogical — Jamal

I agree, and never intended for mindscape to denote a literal place in spacetime.



.

I agree, and never intended for mindscape to denote a literal place in spacetime — Art48

But you did intend it to denote a literal domain of existence in which ideas exist eternally and independently of minds, yes?

But you did intend it to denote a literal domain of existence in which ideas exist eternally and independently of minds, yes? — Jamal

Yes. Well said.

That's the bit I have trouble with. Establishing the mind-independent existence of abstract objects (numbers) might be hard enough, but establishing the same for particular ideas is a big step beyond even that, is it not?

It is a big step and probably the cause of much discussion in this thread. That 2+2=4 is eternal is one thing. That the play Macbeth is eternal is quite another. Which I argue for in the original post in two steps.

First, once we admit a thought exists (or subsists or "is" or whatever word someone wants to use), it's difficult to see how it could go out of existence or cease to be.As I wrote to green flag above, "I'm asking how exactly does an idea like 2+2=4 cease to exist. You seem to say it dies when the last representative in its equivalence class dies, but don't address how the last idea (or any idea) could cease to exist."

IF we allow that thoughts don't go out of existence, then we either say 1) a mortal man such as Shakespeare can create something eternal, or 2) the idea has always existed.

2) implies the mindscape.

Where do clouds come from? Where do ocean-waves come from? Where do sunspots come from? :roll: