So, chairs exists and numbers subsist? Is that a common understanding? — Art48

As an ex prof I never thought about it, and I don't recall hearing the expression, but I suppose it could be appropriate.

I've seen the word "subsist" to refer to the referent of the first statement. So, chairs exists and numbers subsist? Is that a common understanding? — Art48

I think this refers to the old debate about mathematical platonism - were numbers invented or discovered? It's one of those endless debates which ultimately circles back to the nature of reality and what counts as transcendental. There's an entire thread on this here somewhere and many references to this in idealism discussions. To subsist, I believe, is to 'exist' conceptually but not as an object located in space and time - like a chair. Or something like this.

I've seen some YouTube videos where it's said that numbers don't exist. — Art48

If numbers didn't exist, then you couldn't be writing about them, so they must exist somewhere.

Not existent, but real, I say. Precisely where that distinction shows up. See What is Math? Smithsonian Institute Magazine.

We know, have them in our mind, and use numbers to describe the physical objects in the world.
Numbers don't exist like the physical objects. Numbers are concepts.

3 doesn't make sense on its own, but 3 kings do, 4 apples do as well.
It took me 2 days to read the book. 2 itself is meaningless, but 2 days makes sense.

Same with good and bad. They don't exist. We know them have them in mind, and use them to describe things, actions and situations, and people ... etc.

Good itself doesn't make sense. Whatever definition you give to good, it would be a tautology.
Good person, good deed, good food, good books, and good feeling do. Diito with bad.

If numbers didn't exist, then you couldn't be writing about them, so they must exist somewhere. — RussellA

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So, then, if the first even prime greater than 100 didn't exist I couldn't be writing about it?

3 doesn't make sense on its own — Corvus

??? I"d say 3 makes perfect sense on its own. It's an integer, prime, odd, etc.

Fine. Let's not use the word "exist" — Art48

I think we should use the word "exist." Perhaps there are types of existence other than physical.

??? I"d say 3 makes perfect sense on its own. It's an integer, prime, odd, etc. — Art48

So are, 5, 7, 11, 13, 17 .... etc etc? Surely you would have been looking for something more than the textbook definitions of 3?

So, then, if the first even prime greater than 100 didn't exist I couldn't be writing about it? — Art48

Yes, if the first even prime greater than 100 didn't exist, you couldn't be writing about it.

But you are writing about the first even prime greater than 100, so it must exist.

If something doesn't exist, it is not possible to write about it. If something is being written about, then it must exist somewhere.

Similarly, in the expression "it's said that numbers don't exist", then if something doesn't exist, then how is it possible to write about it.

But you are writing about numbers, so they must exist somewhere, otherwise you couldn't be writing about them.

What is missing in the above is the location of the existence, whether in the mind or in a world outside the mind.

But you are writing about the first even prime greater than 100, so it must exist. — RussellA

So what do you think it means to you when someone said "100", or when you saw a writing on the wall "100" apart from the fact that it is a even number?

(First) the number 2 (Second) the first even prime greater than 100...The second statement refers to something which, I think we all agree, doesn't exist. — Art48

Well, no. We certainly don't all agree. "Existence" and "reality" mean different things to different people in different contexts, but you haven't defined what it means to you in this particular situation. We've had this discussion many times here on the forum and it usually derails for the lack of an agreed on definition.

True, we don’t usually get a consensus on this. Just to help the discussion along, suppose we took Quine’s formulation - “To be is to be the value of a bound variable” - and asked ourselves what that might say about the status of ideas and/or numbers?

“To be is to be the value of a bound variable” — J

I think that's a wonderful definition even though I have no idea what it means.

[Edited for aesthetic reasons]

I think that's a wonderful definition even though I have no idea what it means. Sounds all philosophical and stuff. — T Clark

Quine could generalize the general.

Well, yeah, it’s pretty philosophical - that was kinda the idea! You can find good explanations of it on SEP and elsewhere, I’m sure. Just a suggestion.

So, chairs exist and numbers subsist? Is that a common understanding? — Art48

Yeah "common" for philosophers, iirc, since A. Meinong¹. Simply put: existents are causally relatable to each other and subsistents (which are only instantiable via existents) are logically / grammatically relatable but are not causally related at all.

https://en.m.wikipedia.org/wiki/Nonexistent_objects#Meinong's_jungle [1]

If numbers didn't exist, then you couldn't be writing about them, so they must exist somewhere.
— RussellA
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So, then, if the first even prime greater than 100 didn't exist I couldn't be writing about it? — Art48

I have to try to find a way to word this...

You're not writing about it. There is no even prime number greater than 100. Not hypothetically, not in theory. You're writing a list of characteristics that, when combined, do not describe anything. Not even something that can't be physically made, but can be envisioned and discussed. Same with a square circle. These aren't even paradoxes. They're logical impossibilities.

The Meinong link 180 provided likens the square circles to unicorns. I disagree. Unicorns aren't logically impossible. They just don't exist. But we can picture them in our heads, and even draw pictures and make models of them.

A hypercube is an interesting example. It can't exist in our reality. We can't picture it in our mind, and can't draw or build a model of one. But we can calculate how many sides and verticies it has. We understand how the idea of it came about.

Numbers denote the relationship a part has to the whole. As representations, they depend on human minds, but as existing relaitonships, they don't.
The whole is unity, which with the empty set, can produce all numbers.

The first statement refers to something which exists in some sense or other, even if we don't use the word "exist." I've seen the word "subsist" to refer to the referent of the first statement. So, chairs exists and numbers subsist? Is that a common understanding? — Art48

I Googled "exist vs subsist" and got this link*1 to a philosophical definition. According to that authority, both "exist" and "subsist" are "modes", or mental models. But "exist" applies to our model of presumably real material objects, while ""subsist" applies to universal concepts, which are not real but ideal. For example, the Chair you are sitting in exists, but the notion of chairness, which is a mental definition of a kind of object, is merely a conventional model or "common understanding". The computer screen picture of a chair {image below}, subsists in an abstract artificial sense, but another realer mode of it may unfortunately exist in your child's room.

I suppose that Numbers persist only in conceiving Minds as modes or symbols or "persistent illusions"*2, but their rational relationships exist in the real world as the information patterns that cause your mind to conceive of counting real or imaginary objects. Absent a meaning-searching Mind, there would be no evaluated Numbers, but the geometric ratios would exist in the empty space between sensable objects. Think of Gravity as the geometry of reality. The natural/physical relationship is real, but the mental concept of gravity is ideal. As John Mayer sang : "gravity is working against me, gravity wants to bring me down". If gravity didn't exist, we'd have to blame our falling on some other imaginary agent. :smile:


*1. What's the difference between exist and subsist?
Existence, we find it said, is the mode of being proper to "particulars" or "substances," whereas subsistence is the mode of being proper to "universals," i.e. (on the usual view), "qualities" and "relations," as such, or considered apart from the particulars which they qualify or relate.
https://www.pdcnet.org/wcp6/content/wcp6_1927_0261_0271?file_type=pdf

*2. "People like us who believe in physics know that the distinction between past, present, and future is only a stubbornly persistent illusion." ___ A. Einstein

If something doesn't exist, it is not possible to write about it. If something is being written about, then it must exist somewhere. — RussellA

You mean all the science fiction books are real stories? Or merely exist in the authors' minds.

Yes, if the first even prime greater than 100 didn't exist, you couldn't be writing about it. — RussellA

He could have said "the first even prime number greater than 2". No such thing, 2 is the only even prime number because all other even numbers are divisible by 2.

So, chairs exists and numbers subsist? Is that a common understanding? — Art48

Chairs are mental constructions; they do not exist in the mind-independent world.

Numbers are strange. They are discovered through our minds but seem to be independent of it.

But natural numbers are not constructed the way chairs are. For one thing they are among the simplest things one could image.

You mean all the science fiction books are real stories? Or merely exist in the authors' minds. — jgill

If a science fiction adventure is being talked about, the science fiction adventure must exist somewhere, whether as print in a book, in the mind of the author or reader or in a world outside any book or mind.

Is a thought in the mind any less real than something in a world outside any mind?

Is a thought in the mind any less real than something in a world outside any mind? — RussellA

That sounds like a categorical mistake. It is not matter of real or unreal. It is matter of knowing or not knowing.

So, chairs exists and numbers subsist? Is that a common understanding? — Art48

I think that the important point here is that we notice the difference between these two types of "things". Notice that by categorizing them with the same name "things", I tend to negate that difference which I am trying to emphasize. So when we categorize them in ways like this, by calling them both "objects", it's counterproductive toward understanding the difference between them.

The law of identity (a thing is the same as itself) was intended as a means of recognizing, and upholding the difference between these two. A physical object, a chair, as an individual particular, has an identity within itself, which is independent from anything which we say about it. We can point to it, or sense it, and assume it's independent existence. This assumed independent existence supports the concept of "thing-in-itself", and it also supports the idea that what we say about a thing might be incorrect, false. A "number" does not have this type of identity, because if we remove everything which we say about it, there is nothing left to point to. The number's existence is necessarily within the context of a conceptual structure, and is therefore better known as "a subject", in the sense of a topic, or theme, to be studied or discussed.

So your use of "subsist" to describe numbers is problematic. "Subsist", especially in the sense of "self-subsistence" implies existence independent from the environment or context. But this is exactly what makes a physical thing different from an idea, the chair has independent existence, "self-subsistence" while the number is dependent on the conceptual structure, so it does not have self-subsistence.

There is a type of Platonism, derived from Pythagorean idealism, which assigns "self-subsistence" to numbers. Aristotle analyzed this type of ontology in his "Metaphysics" and found it to be problematic. The issue is, that if an idea, such as "the good" has self-subsistence, then the idea, and its essence are necessarily one and the same. This would be the same for all ideas, they would be one and the same as their essence. Accordingly, it would be impossible for us to understand any ideas, because understanding requires logical relations such as prior and posterior.

So for example, if it's stipulated that the number two has self-subsistence, then its essence, (which is the means by which we understand it), must be within the number two itself. This would make its relations to other ideas "one", "three", "the first even prime greater than 100", etc., accidental rather than essential. If that was the case, ideas would be impossible for us to understand.

Therefore, it is very important in our ontology, to maintain the proper principles of separation between assumed independent objects, which are assumed to have separate existence by the law of identity, and ideas, which are dependent on their environment, context, for their existence. The latter we can know with a high degree of certainty, that it is impossible for them to have a truly independent existence.

That sounds like a categorical mistake. It is not matter of real or unreal. It is matter of knowing or not knowing — Corvus

Thoughts exist, otherwise you couldn't have written your post.

Thoughts exist in the physical brain which exists in the physical Universe.

Thoughts must be real otherwise it wouldn't be possible to write posts on the Forum.

Thoughts exist, otherwise you couldn't have written your post. — RussellA

I had thoughts, but I wouldn't say the thought existed. You cannot use "exist" on the abstract concepts. Well you could, just like you have done, but it doesn't quite make sense, and could be classed as "unintelligible".

You have ideas and know the concepts, but ideas and concepts don't exist in the external world like the physical objects do.

I had thoughts, but I wouldn't say the thought existed. You cannot use "exist" on the abstract concepts. — Corvus

If thoughts didn't exist, then how can a thought affect the physical world, such that the thought of pressing the "t" key on the keyboard turns into actually pressing the "t" key on the keyboard.

If thoughts didn't exist, then how can a thought affect the physical world, — RussellA

You apply the thoughts onto the physical world i.e. typing, measuring, hammering, drilling, and driving ... etc. You have ideas how to use and manipulate the physical objects. But the ideas are in your head, not in the world.

the thought of pressing the "t" key on the keyboard turns into actually pressing the "t" key on the keyboard. — RussellA

Folks learn to type from the early age, and typing becomes their 2nd nature.