Are Numbers Real?

[GrandizerII]

What say you? Are numbers real? If so, in what way are they real?

First answer:

Are you real?
Not facetious:  it raises the issue of defining "real".


Second answer:

Some numbers are indeed real.
Others are imaginary.
Others are complex.

<ducks>

All real and imaginary numbers are complex. Just saying

[Dr H]

First answer:

Are you real?
Not facetious:  it raises the issue of defining "real".


Second answer:

Some numbers are indeed real.
Others are imaginary.
Others are complex.

<ducks>

All real and imaginary numbers are complex. Just saying

Well, some are just hard to get to know . . .

[BrianSoddingBoru4]

I was once making a sign for a mate's shop, and it included a large, wooden '2'.  I dropped on my foot.  That number was real in every way I cared about.

Boru

[bennyboy]

I'd argue that no descriptive term is real in an existential sense. Redness is very real as an experience, but there isn't actually such a thing as red matter.

[vulcanlogician]

I'd argue that no descriptive term is real in an existential sense.  Redness is very real as an experience, but there isn't actually such a thing as red matter.

What is real to you then, benny? To me, descriptive terms refer to something. Something real. I'd love to hear your thoughts on the matter. If you could be bothered.

[Belacqua]

I'd argue that no descriptive term is real in an existential sense.  Redness is very real as an experience, but there isn't actually such a thing as red matter.

What is real to you then, benny? To me, descriptive terms refer to something. Something real. I'd love to hear your thoughts on the matter. If you could be bothered.

Have you ever looked into Karl Popper's Three Worlds theory? It's a sort of [kind of] non-supernatural update of Plato. 

For him, World 1 is the physical, material world. We assume this would exist even if no people existed. 

World 2 is mental phenomena. Color is in this category. Also emotions, private thoughts, all those things. Those are real to the person experiencing them. 

World 3 is more tricky -- but easier to accept than Plato's Ideal realm. This is stuff invented by people but now mutually shared as real entities. I think the example he gives is a Beethoven symphony. (Not the score or the recording, but the symphony itself.) This was made by a person, and it continues to exist even though he's dead. It continues to exist even when it's not being played at the moment. It's real, but it would also go away if no humans (or musical aliens) remained. What's important here is that people can make objective [oh god there's that word again] statements and judgments about a given symphony, and debate true facts about it. No physical existence, but more than just a mental phenomenon. 

I'm not expert, but I think a lot of things are in this category. For example, Sherlock Holmes is real in this way. We can say true and false sentences about him, even though he doesn't exist. "Sherlock Holmes comes from Peru," is a false sentence. 

Numbers, and all math, is in World 3, as I recall. Somewhere there's a video of Roger Penrose outlining the same structure -- he apparently accepts it. 

The main paper on the subject is surprisingly short:

https://tannerlectures.utah.edu/_documen...pper80.pdf

[downbeatplumb]

Numbers are a real as any other that's used to describe a thing.
Sadness is real but you cant touch it.
If you have more than one rock then you have that many rocks, how many is described by the number.

[Magilla]

Numbers are a real as any other that's used to describe a thing.
Sadness is real but you cant touch it.
If you have more than one rock then you have that many rocks, how many is described by the number.

I agree that numbers are descriptive of reality. Of course no one can show you the number two for example,
though we have symbols that can be used in language to write about the number two, among which are,
2 decimal,  or 10 binary etc., and words, (noises), to talk about numbers, such two, pair, duet and so on.
And Morse code can be both either written down, or transmitted audibly.

If I say I have two apples, (which you could not see - maybe we're talking on the 'phone), I'd say that almost all
listeners would know what is meant, and have an image of something real, (ie. that quantity of apples). But the
apples need not match, one may be a Granny Smith, and one a Red Delicious. So the apples may not match, but
I suggest that we all have the same concept of two-ness, and an image of an apple (A), alongside another apple (B).

If I was more precise, and said that I have two red apples, (again if the listener couldn't see the apples), still the concept
of two-ness would be much better defined, than the quality of apple-ness. People may disagree about what it is
valid to classify as red. They may dream up two identical red apples, or two similarly red apples, but the size and shape
may be quite different. But again, I suggest that we all have the same concept of two-ness, with an image of apple (X),
alongside another apple (Y), even if we'd not necessarily agree on whether or not the apples were both red enough to,
characterise as red, (that's if we could all see the apples in question).

We could keep on refining the characteristics of the apples, for size, shininess, weight, etc, etc. but we'd not have any
trouble with two-nees, even when the apples are unseen by one or more parties.

But as I said, no one can show you the number two itself, only symbols that we've invented, so that we can talk about
or otherwise communicate over the concept of two-nees, (or three-ness or four-ness etc.) Things get more complicated
if we are talking about numbers~other~than zero, or positive integers, I mean, can we all agree precisely on what is half
an apple, (my half an apple is smaller than Fred's half an apple  ).

To be honest, I don't much care if numbers are real things in a metaphysical sense, I can talk about them, use them etc.
and that's good enough. When I use numbers following the rules of mathematics, I come up with the same results as
anyone else, who does the same.

Magilla