Can we use Euclid's second postulate ("A terminated line can be produced indefinitely") to say that the universe is infinite?

Question

Euclid's second postulate says

A terminated line can be produced indefinitely.

Can we use this and say, Universe is infinite?

I have read this post but if we consider universe as a three dimensional space, the universe will fall in to the postulate's domain (geometry).

What do you mean by "Universe"? Are you talking about something mathematical here? — xxxxxxxxx, Nov 19 '19 at 03:34
I think the Universe existed before Euclid formulated his postulates — Vasili, Nov 19 '19 at 03:35
Euclid's second postulate is an assumption that is made for mathematical purposes. I'm not sure of the connection to what we can or cannot say about the world around us; at best you can say that Euclid was possibly assuming that the universe he lived in was infinite. — xxxxxxxxx, Nov 19 '19 at 03:38
So any theory which may use (exploit) this infinitely term in this postulate can go wrong? (If our universe is finite..) — Madhusoodan P, Nov 19 '19 at 03:41
It would seem you should be reading Immanuel Kant. Recent comments: http://jur.byu.edu/?p=9200 — Will Jagy, Nov 19 '19 at 04:13
Will Jagy, no, haven't read his work. But good to know that someone thinks in the same way as me. — Madhusoodan P, Nov 19 '19 at 04:34

score 1 · Accepted Answer · answered Nov 19 '19 at 03:46

1

Euclid's postulates were an attempt to represent the world as he experienced it, but of course experience does not include extending a line to infinity. I would guess (but I didn't ask him) he noticed that you could extend lines very far, assumed space was homogeneous, and made the postulate. From the wording it is not clear whether extending a line many times around a circle counts or not. If it does not, this one will rule out geometry on the surface of a sphere, where lines are great circles. I suspect his experience was not sufficient to distinguish the geometry of the surface of the earth from an infinite plane, even though there were famous Greek proofs that the world was round.

answered Nov 19 '19 at 03:46

Ross Millikan

374,822

Here is an interesting theory which we can disprove if the lines around circles can be counted "Two distinct lines cannot have more than one point in common." – Madhusoodan P Nov 19 '19 at 04:51
Also is there a branch of geometry which doesn't use these postulates? – Madhusoodan P Nov 19 '19 at 04:52
I am only aware of absolute geometry, which is geometry without the parallel postulate. It seems to many people (and I agree) that the rest are "obvious". Without the postulate you mention the universe could have a hard edge. – Ross Millikan Nov 19 '19 at 05:00

score -1 · Answer 2 · answered Nov 19 '19 at 05:10

It seems to me that this postulate should be imagined (Euclid didn't relate his postulate to Universe). So, we shouldn't exploit this postulate in proving theories on Universe.

In simple words, Universe doesn't fall in the same domain where this postulate is defined.

Can we use Euclid's second postulate ("A terminated line can be produced indefinitely") to say that the universe is infinite?

2 Answers2