The Philosophy Now Forum

Do numbers really exist? And if so, in what sense of “really” and “exist”?

RickLewis wrote: ↑Tue Sep 29, 2026 9:50 pm Do numbers really exist? And if so, in what sense of “really” and “exist”?

As nouns? Or merely adjectivally?

Do they exist the way bricks exist, or the way "red-ness" exists, or some other way?

RickLewis wrote: ↑Tue Sep 29, 2026 9:50 pm Do numbers really exist? And if so, in what sense of “really” and “exist”?

as much as any other mental representation...

-Imp

Hmmm … I’ll start by suggesting that numbers are real because they aren’t imaginary (although there are what mathematicians call … but let’s not go there!)

RickLewis wrote: ↑Tue Sep 29, 2026 9:50 pm Do numbers really exist? And if so, in what sense of “really” and “exist”?

Well, as usual in philosophy, no one knows. What anyone believes depends on where they find themselves on the physicalist - idealist spectrum. Anything from definitely not, because you can't fill a bucket with 4, to absolutely yes, because like other ideas, they are examples of the only things we know definitely exist.
My own view, which I am making up as I type, is that anyone on the absolutely yes end, is confusing ideas with sensations. 4 is different to blue; at least I have no immediate sensation of 4 that is analogous to my perception of blue. I might just be weird though.

Will Bouwman wrote: ↑Wed Sep 30, 2026 8:44 pm

RickLewis wrote: ↑Tue Sep 29, 2026 9:50 pm Do numbers really exist? And if so, in what sense of “really” and “exist”?

4 is different to blue; at least I have no immediate sensation of 4 that is analogous to my perception of blue.

But the number of something is a sort of "-ness," in that one senses "two-ness" when there is a pair of something, and "three-ness" when there is one more; but the specific "noun-ness" of the thing can change: one can have two-ness manifested in two ocelots, or two earlobes, or two aqualungs. The quality of "being two" is the only thing that's really the same. And that's what I mean by numbers having an "adjectival" quality: they seem to be attachable to any particular objects.

But here's the weird thing: one cannot calculate with "redness," because the quality of being red must attach to an object in order to be attributable. But numbers can be separated from any particular referent, and they still function very well: 2+2 of anything or nothing continues to yield a product of 4. And this makes pure mathematical manipulations possible; yet when we return the results to reality, they still work -- whatever is happening within the system of pure mathematical concepts, it also works whenever we take it out again to reality.

It's almost as though mathematics are somehow "written into" reality in some very unexpected way, something not analogous to other adjectival attributions like "redness."

At its most fundamental, I think of numbers, whether given or derived, as defining the extent of objects in space and their separations within that space. In that context, numbers are variables defined within the frameworks in which they're applied...mostly within the context of time or, as mentioned space itself. Without that context, numbers exist in a purely abstract domain, in terms of primes, factorials, etc., which indicates how numbers can internally organize once their paradigms are discovered not unlike atoms, proceeding from quarks, organizing into molecules in ever layered complexities.

RickLewis wrote: ↑Tue Sep 29, 2026 9:50 pm Do numbers really exist? And if so, in what sense of “really” and “exist”?

Yes, numbers exist. They are detected by mind.
Rocks also exist and they are detected by the body.

Numbers and rocks, and everything else known and unknown, exist within infinite potentiality.

Numbers really exist when detected by mind.
Rocks really exist when detected by the body.

Numbers really existing, independent of detection by mind, is an inference.
Rocks really existing, independent of detection by the body, is an inference.

Everything exists in potentiality.
Manifestation is really existing.
Particular conditions cause particular manifestations.

Awareness detects numbers and rocks in different ways, although both can be inferred to exist (potentiality) if not detected, and really exist (manifestation) if not detected, because both have been discovered in the past.

Immanuel Can wrote: ↑Wed Sep 30, 2026 9:18 pm

Will Bouwman wrote: ↑Wed Sep 30, 2026 8:44 pm

RickLewis wrote: ↑Tue Sep 29, 2026 9:50 pm Do numbers really exist? And if so, in what sense of “really” and “exist”?

4 is different to blue; at least I have no immediate sensation of 4 that is analogous to my perception of blue.

But the number of something is a sort of "-ness," in that one senses "two-ness" when there is a pair of something, and "three-ness" when there is one more; but the specific "noun-ness" of the thing can change: one can have two-ness manifested in two ocelots, or two earlobes, or two aqualungs. The quality of "being two" is the only thing that's really the same. And that's what I mean by numbers having an "adjectival" quality: they seem to be attachable to any particular objects.

But here's the weird thing: one cannot calculate with "redness," because the quality of being red must attach to an object in order to be attributable. But numbers can be separated from any particular referent, and they still function very well: 2+2 of anything or nothing continues to yield a product of 4. And this makes pure mathematical manipulations possible; yet when we return the results to reality, they still work -- whatever is happening within the system of pure mathematical concepts, it also works whenever we take it out again to reality.

It's almost as though mathematics are somehow "written into" reality in some very unexpected way, something not analogous to other adjectival attributions like "redness."

Can atheists believe numbers exist?

Gary Childress wrote: ↑Thu Oct 01, 2026 10:42 pm

Immanuel Can wrote: ↑Wed Sep 30, 2026 9:18 pm

Will Bouwman wrote: ↑Wed Sep 30, 2026 8:44 pm
4 is different to blue; at least I have no immediate sensation of 4 that is analogous to my perception of blue.

But the number of something is a sort of "-ness," in that one senses "two-ness" when there is a pair of something, and "three-ness" when there is one more; but the specific "noun-ness" of the thing can change: one can have two-ness manifested in two ocelots, or two earlobes, or two aqualungs. The quality of "being two" is the only thing that's really the same. And that's what I mean by numbers having an "adjectival" quality: they seem to be attachable to any particular objects.

But here's the weird thing: one cannot calculate with "redness," because the quality of being red must attach to an object in order to be attributable. But numbers can be separated from any particular referent, and they still function very well: 2+2 of anything or nothing continues to yield a product of 4. And this makes pure mathematical manipulations possible; yet when we return the results to reality, they still work -- whatever is happening within the system of pure mathematical concepts, it also works whenever we take it out again to reality.

It's almost as though mathematics are somehow "written into" reality in some very unexpected way, something not analogous to other adjectival attributions like "redness."

Can atheists believe numbers exist?

What has one's Atheism got to do with anything?

Immanuel Can wrote: ↑Wed Sep 30, 2026 9:18 pm

Will Bouwman wrote: ↑Wed Sep 30, 2026 8:44 pm

RickLewis wrote: ↑Tue Sep 29, 2026 9:50 pm Do numbers really exist? And if so, in what sense of “really” and “exist”?

4 is different to blue; at least I have no immediate sensation of 4 that is analogous to my perception of blue.

But the number of something is a sort of "-ness," in that one senses "two-ness" when there is a pair of something, and "three-ness" when there is one more...

Well, we know that in some ways, you and I are wired differently. This might be another example, because I can assure you that I have no more immediate sense of two-ness or three-ness than I do of four-ness. I can say wirh confidence that I can instantly recognise 1, 2, 3, 4 and probably 5 objects and the squares of those if they are conveniently so arranged. Much beyond that though, and any sense of number-ness is gone. Descartes, rather better at numbers than you or I, made essentially the same point with reference to chiliagons and myriagons; even he couldn't claim a sense of thousand-ness.

Immanuel Can wrote: ↑Wed Sep 30, 2026 9:18 pmBut here's the weird thing: one cannot calculate with "redness,"...

I can't say that strikes me as weird

Immanuel Can wrote: ↑Wed Sep 30, 2026 9:18 pm...because the quality of being red must attach to an object in order to be attributable.

I don't see that as the reason we can't do sums in redness; it doesn't even strike me as true. I can't be certain, because I was very little at the time, but I'm fairly confident that I did not attach my first visual experiences to objects; that was something I had to learn.

Immanuel Can wrote: ↑Wed Sep 30, 2026 9:18 pm It's almost as though mathematics are somehow "written into" reality in some very unexpected way, something not analogous to other adjectival attributions like "redness."

That's not how I see it. We don't agree about this, but to my mind the universe would do its thing in an orderly and predictable manner unless there were a supernatural being twiddling the knobs. We find patterns in this behaviour and attached numbers and relations to them. Sometimes we find patterns in numbers that we later find applications for in the real world. Unlike Wigner, I don't think that makes mathematics unreasonably effective.

Will Bouwman wrote: ↑Fri Oct 02, 2026 8:32 am

Immanuel Can wrote: ↑Wed Sep 30, 2026 9:18 pm

Will Bouwman wrote: ↑Wed Sep 30, 2026 8:44 pm
4 is different to blue; at least I have no immediate sensation of 4 that is analogous to my perception of blue.

But the number of something is a sort of "-ness," in that one senses "two-ness" when there is a pair of something, and "three-ness" when there is one more...

Well, we know that in some ways, you and I are wired differently. This might be another example, because I can assure you that I have no more immediate sense of two-ness or three-ness than I do of four-ness. I can say wirh confidence that I can instantly recognise 1, 2, 3, 4 and probably 5 objects and the squares of those if they are conveniently so arranged. Much beyond that though, and any sense of number-ness is gone. Descartes, rather better at numbers than you or I, made essentially the same point with reference to chiliagons and myriagons; even he couldn't claim a sense of thousand-ness.

I'm afraid you've kind of completely missed my point, Will. I wasn't saying that I, or you, have "a sense of" two-ness or three-ness. Rather, the FACT of two-ness or three-ness adheres to situations with two or three objects of any kind in it...and hence, that numbers have this sort of "adjectival" relation to the objects to which they are adhered.

What you and I "sense" is neither here nor there. An object that has the quality of "two-ness" will still be but 2, even if you and I have double vision and perceive it as 4. Facts and perception are distinct categories.

Immanuel Can wrote: ↑Wed Sep 30, 2026 9:18 pm...because the quality of being red must attach to an object in order to be attributable.

I don't see that as the reason we can't do sums in redness; it doesn't even strike me as true. [/quote]
Then maybe you'll show me how. Let's see if we can do a "sum in redness." The idea strikes me as exceedingly odd, and almost certainly expressive of a category error. But I won't conclude until I see.

Go ahead, please.

Immanuel Can wrote: ↑Fri Oct 02, 2026 12:58 am

Gary Childress wrote: ↑Thu Oct 01, 2026 10:42 pm

Immanuel Can wrote: ↑Wed Sep 30, 2026 9:18 pm
But the number of something is a sort of "-ness," in that one senses "two-ness" when there is a pair of something, and "three-ness" when there is one more; but the specific "noun-ness" of the thing can change: one can have two-ness manifested in two ocelots, or two earlobes, or two aqualungs. The quality of "being two" is the only thing that's really the same. And that's what I mean by numbers having an "adjectival" quality: they seem to be attachable to any particular objects.

But here's the weird thing: one cannot calculate with "redness," because the quality of being red must attach to an object in order to be attributable. But numbers can be separated from any particular referent, and they still function very well: 2+2 of anything or nothing continues to yield a product of 4. And this makes pure mathematical manipulations possible; yet when we return the results to reality, they still work -- whatever is happening within the system of pure mathematical concepts, it also works whenever we take it out again to reality.

It's almost as though mathematics are somehow "written into" reality in some very unexpected way, something not analogous to other adjectival attributions like "redness."

Can atheists believe numbers exist?

What has one's Atheism got to do with anything?

I figured you might want to take an opportunity to take another jab at atheists since you don't like them much.

Gary Childress wrote: ↑Sat Oct 03, 2026 3:25 am

Immanuel Can wrote: ↑Fri Oct 02, 2026 12:58 am

Gary Childress wrote: ↑Thu Oct 01, 2026 10:42 pm

Can atheists believe numbers exist?

What has one's Atheism got to do with anything?

I figured you might want to take an opportunity to take another jab at atheists since you don't like them much.

Actually, I like them just fine. But there's all the difference in the world between liking a person and agreeing with his worldview. I don't hate people I disagree with; I just disagree with them. And sensible people use reason and evidence to arbitrate the conflict. It all remains perfectly polite.

Here, we discuss worldviews, not people. And nothing we said so far has the slightest thing to do with Atheism. The subject here is the nature of numbers.

Immanuel Can wrote: ↑Sat Oct 03, 2026 3:33 am

Gary Childress wrote: ↑Sat Oct 03, 2026 3:25 am

Immanuel Can wrote: ↑Fri Oct 02, 2026 12:58 am
What has one's Atheism got to do with anything?

I figured you might want to take an opportunity to take another jab at atheists since you don't like them much.

Actually, I like them just fine. But there's all the difference in the world between liking a person and agreeing with his worldview. I don't hate people I disagree with; I just disagree with them. And sensible people use reason and evidence to arbitrate the conflict. It all remains perfectly polite.

Here, we discuss worldviews, not people. And nothing we said so far has the slightest thing to do with Atheism. The subject here is the nature of numbers.

So it's not that you have any prejudice against atheists when you assert, without demonstrable proof, that an atheist cannot possibly say why something is moral or immoral. You just don't find demonstrable proof necessary in order to make an assertion; is that it?