# Logical argument using infinity

Discussion in 'General Philosophy' started by arfa brane, Mar 19, 2019.

1. ### NotEinsteinValued Senior Member

Messages:
1,986
Well, for one, it's well-defined, so it passes the hurdle where the infinite circle idea seems to fall flat.

Probably something along the lines of taking the set of all points that have two real numbers as their orthogonal coordinates, or something along those lines.

Again, you seem to be laboring under severe misconceptions about limit taking. You didn't start with a finite plane that you extended to infinity, so no, you didn't take a limit here.

3. ### arfa branecall me arfValued Senior Member

Messages:
7,832
No I'm extending the circle indefinitely, without limit. I don't need a function that relates the radius to the curvature. All I need is indefinite extension (hell, I don't even need infinity, because that's implicit).
And you seem to be unable to distinguish between the modern concept in calculus, of the limit of a function, and the ancient Greek concept of indefinite extension.
I didn't start with a finite plane, because I can't--the plane is infinite.

But your orthogonal coordinates and pairs of real numbers is a construction, right? In the infinite plane? So how do you know where to put the origin (I know that's a stupid question, but here we are).
The answer to the stupid question is: it doesn't matter; the plane is infinite in extent. So then it doesn't matter where you stand (anywhere will do), it doesn't matter where you point, there is a circle of directions over every point.

Where is the circle of directions? It doesn't matter where it is because you can prove it exists . . .
Since it doesn't matter where it is, the circle can be at infinity.

Last edited: Mar 28, 2019

5. ### NotEinsteinValued Senior Member

Messages:
1,986
More misconceptions. Please look up what "taking the limit to infinity" means.

Actually, you already have set that up in your OP. That you didn't realize that doesn't mean you didn't do it.

Which is exactly what limit taking is...

If you don't need infinity, you can't have an infinite circle. Are you now abandoning your infinite circle claims completely?

7. ### arfa branecall me arfValued Senior Member

Messages:
7,832
If you construct an actual circle around a point and call it a circle of directions, does it need to have a finite radius?
Yes, if you need to construct the circle.

What if you just need to prove there is a circle of directions? Where does the circle "need" to be?
What, if anything, does this have to do with taking a limit?

8. ### NotEinsteinValued Senior Member

Messages:
1,986
I don't know; "circle of directions" is something you came up with, so why don't you answer your own question?

Well, there you go, I guess?

I have no clue what a "circle of directions" is, so I can't provide you with any answers regarding that.

9. ### arfa branecall me arfValued Senior Member

Messages:
7,832
Oh bullshit.
You know what a direction is I assume? And what a circle is?
Stand at the centre of a given circle. How many directions can you point in? Is there a semantic problem with calling this set of directions "a circle of directions"?

No? Well, there we are then. You can also call the set of circles of directions, on some manifold, a circle bundle (whoa, I just did!).

10. ### NotEinsteinValued Senior Member

Messages:
1,986

Since I understand that limit taking can be seen as an generalization of indefinite extension, I'm perfectly capable of distinguishing the two, thank you very much.

So why were you talking about limit taking there then?

I suppose, yes.

Wrong. It's "of the infinite plane". I'm constructing it; that was the task you asked of me. One cannot construct a thing inside the thing that one is trying to construct; that's ridiculous.

What do you mean, "where"? It's not like I'm placing points into an already existing space. In fact, the origin is an arbitrary choice, so I guess you could answer "anywhere you want"?

How can you have an infinite plane when you are still busy constructing it? You are making no sense.

What is a "circle of directions"?

The more I read "circle of directions", the less coherent the term becomes. How can a circle be constructed out of directions?

Please provide that proof then! I've asked you multiple times for proof now, and you continue to refuse while also continuing to claim the proof exists. It's approaching intellectually dishonesty, to be frank.

A circle being located at infinity doesn't mean the circle is infinite in size, so I don't know why you are bringing this up?

11. ### NotEinsteinValued Senior Member

Messages:
1,986
Well, obviously.

360 degrees, obviously.

Yes, because if you read the definition of circle I gave earlier, this obviously isn't one.

Please stop redefining words mid-conversation without telling anybody.

Actually, not "no".

Why do you feel the need to start defining things that are irrelevant to the discussion at hand? Are you trying to pull this thread off-topic?

12. ### arfa branecall me arfValued Senior Member

Messages:
7,832
There's a difference between "in the infinite plane", and "of the infinite plane"? That's pretty cute.
And you are "constructing" the infinite plane? That's even cuter.
Ha ha hah . . . etc

13. ### arfa branecall me arfValued Senior Member

Messages:
7,832
You aren't very well-read, are you? A circle of directions isn't that common a term, but it is well understood (and not really hard to understand, unless you're too cute to be bothered).
Why should I accept what you say about relevance? Who TF are you?

14. ### NotEinsteinValued Senior Member

Messages:
1,986
Post #59: You: "How can the infinite plane exist? How do you construct it?"

So yeah, I'm sorry I took up your challenge. It's becoming more and more clear you are just trolling. Have fun with that!

15. ### arfa branecall me arfValued Senior Member

Messages:
7,832
That's a response to one of your posts; you've taken this out of context so you can troll this thread.

Asshole.

16. ### Write4UValued Senior Member

Messages:
19,206
But the diameter of the circle also becomes infinite, no? Why not an infinitely large curved plane?

Take a small completed circle and expand the circle infinitely large. Does it cease to be a circle? Will the circle break at some point and become parallel lines?

17. ### NotEinsteinValued Senior Member

Messages:
1,986
A circle with an infinite radius would also have an infinite diameter, yes.

That would be non-Euclidean; I've explicitly stayed away from that in this thread.

That's what the whole discussion between arfa brane and me was about. It seems that both of us have come up with arguments why infinite circles can't exist, without having found any counter-arguments, so it seems that if such a thing is possible, then yes, it ceases to be a circle.

18. ### arfa branecall me arfValued Senior Member

Messages:
7,832
It seems that it's a matter of choice whether an infinite circle is still a circle; some say no it can't be, by definition, some say it is a circle "at infinity", but loses most of the properties of a circle.

However it does still have identifiable antipodal points; indeed, the infinite circle is different in that respect because the identifications aren't added, like you can add to a finite circle, but axiomatic. Calling the line at infinity in the projective plane a "circle" is technically incorrect; but given a context (infinite distance), it's well understood what is meant. Then you see there is a kind of logic to it. Oh well.

19. ### Write4UValued Senior Member

Messages:
19,206
So, what happens to the plane, it also disappears, no?

Are we looking at a change from a 2D plane to a 1D line. Is that not against some rule?
How about 3D space, inflated infinitely large? What happens to that? Does it change from 3D to an infinity of straight 1D lines in all directions. Originating from where?

Is our description of the universe incorrect or is it not infinite? That would solve the entire exercise, no?

Last edited: Mar 28, 2019
20. ### NotEinsteinValued Senior Member

Messages:
1,986
What plane do you mean, exactly?

I don't think there's any 2D plane changing into a 1D line in this situation?

Are you "inflating"/expanding the space itself, or things within the space?

Why would a 3D space change into 1D lines in all directions?

How is this related to anything? Also, are you suggesting you know whether the universe is infinite or not (in spatial size)?

No, because we are talking about abstract concepts, not physical reality.

21. ### Write4UValued Senior Member

Messages:
19,206
A circle forms a 2 D plane, no? All points equi-distant from the center?
Is the center of the circle not in the center of the plane as well as in the center of a sphere?
That would be an example of a 3D sphere inflated infinitely. If the surface expands infinitely, does the sphere cease to be sphere at some point?
Does a sphere not have an infinite number of circumferences, creating a "volume"? Unlike a circle which has just one circumference, creating a "circle"?
No, I'm posing the question. It seems related to the OP and to the current example of a circle, no?
The argument would still need to be logically sound, no?

If not, it would not be possible, seems to me....

Last edited: Mar 28, 2019
22. ### NotEinsteinValued Senior Member

Messages:
1,986
A circle lies in a plane, but it isn't one itself. Are you perhaps thinking of a disc?

Not of the plane the circle is in. If you are talking about a disc, then yes.

I guess if a sphere is defined as all the points with at certain radius from the center or closer, it would remain a sphere, but I'm not sure if that's the proper definition.

What do you mean? Are you talking about things like "great circles" ("orthodomes")?

It's not related as far as I can see? How do you figure?

Well, yes, obviously. But for that trick to work, you'd need to find an infinite circle in reality, and we know that currently can't be done (the observable universe being finite and all that).

Not being able to find a physical case of an infinite circle doesn't mean one can't be constructed in abstract, so no this part of your reasoning doesn't hold up.

23. ### Write4UValued Senior Member

Messages:
19,206
No, I just visualize a sphere as being an infinite collection of equal circumferences in all 3 dimensions, equi-distant from the center, completely enclosing the volume of the sphere?

Any single measurement of a circumference of a sphere yields a circle, no?

Last edited: Mar 28, 2019