Wyman wrote: Seremonia wrote:
Philosophy Explorer wrote:Seremonia said:
"Secondly, infinity is 'not limited by another thing'."
Are you aware there are different levels of infinity? There's Aleph null, Aleph one, Aleph two, etc. So, in a sense, infinity limits itself where Aleph null, e.g., is limited by Aleph one. So let me ask you what you mean by limited?
As previously stated, limited means, it's dependent upon (in any possible ways) something else.
Seremonia, have you ever studied calculus? Between any two real numbers (or any two points on the real number line), there are infinitely many numbers. And yet, one can determine exactly what the area bounded by a curve is, or the volume of any bounded solid (or on the differential side, instantaneous velocity, or the slope of a curve at any point, or a thousand other applications) by calculations involving quantities that approach infinity or approach infinitely small quantities. So mathematics, even at the level of calculus, deals extensively with infinity - infinite sets, open and bounded, infinite series with finite values, etc., etc., etc..
Hahaha, yes, it's like zeno paradox.
Let me put this way, suppose there are infinitely many numbers in between two pointers. Well, those (infinitely) many numbers must be considered as real. In the sense, there are real things as much as those represented by infinite numbers in between two pointers (things). Now, can you calculate total length (content or something) of all of them? Consider we can do it, then we found the result that it has length (content or something) as far (much) as "X". It has limitation indeed. But looking inside them, "the infinite" says "there are unlimited numbers of (content or something).
An axiom: something (without additional assertions) can’t transcend beyond something itself. From one liter water (without additional assertions) can’t be poured as much as 1 gallon water.
So we have an understanding here. There is such unlimited inside a limitation. It's like there is a glass of tea and we can pour a tea from it as much as 1 gallon, which is impossible (unless there is something -tea - from outside the glass adding continuously to the glass).
The point is, while we are doing philosophical analysis, it must be relied on reality. Although we can think about it but we can't bring it.
But, although it's a tricky thinking, for me, we can still associate it with reality, as long as we could understand it properly. For me, this kind of understanding, actually it must be associated to another kind of understanding. I accept that kind of zeno paradox as an understanding that we are all one, and there is no separation in between all (but it takes another explanation which is irrelevant in this discussion).