Philosophy Now Forum

It means that the arithmetical line works fine as a fiction, but as a fundamental phenomenon it is paradoxical. What is the paradox? Same as saying that set-theory is fine for everyday life but doesn't work when we try to make sets fundamental. Making sets fundamental works very well in math. And m...

Our approaches may both be reasonable and functional. It seems your interest is formal and not fundamental. So set theory for you floats free of the world and its paradoxical features are of no interest. I get this. But as a metaphysician I'm more interested in how set theory may be axiomatised for...

By shrinking I mean to take the limit. Then at any stage the shrinking interval has a length greater than zero. Any two intervals of real numbers with nonzero length can have their points put into one-to-one correspondence. There is a one-to-one correspondence of the points in a tiny tiny interval ...

And points are parts, which is the confusion of Mathematicians to think they are ever speaking about continuums. Mathematicians do not make that category error. They know that they are talking about the set of real numbers, which is a particular technical construction carried out in the framework o...

There may be a deeper issue. Weyl suggests not just that the numbers are unreal but that extension is not real. He endorses the Perennial view for which time and space are fictional. The basic issue may be that a continuum has no parts. In this case there can be no such thing as an extended continu...

What if we shrink AB to zero? Then AB is a point and the theorem no longer applies. Do you understand that we can match up the points of any two finite line segments in a one-to-one correspondence? I feel wtf is correct to say that there is some confusion here between what Hermann Weyl calls the 'a...

The number of points for any line is similar! That sounds absurd to me. Here is a classic visual proof for two finite line segments. You can pair up the points on each line segment by drawing a line from p through a point on the upper segment that then hits some point on the lower segment, and vice...

and null? Are you saying that a line is made of these number of points? If yes where is the length dependence? Aleph-0 (or Aleph-null) is the smallest infinite cardinal. It's the cardinality of the integers. 2^(Aleph-0) is the cardinality of the real numbers; that is, the number of points on a line...

I see. Therefore what you are saying is that there is no mathematician who believe that the largest natural number doesn't exist. The opposite. There is no mathematicians who does believe a largest natural number exists. Of course there are a lot of mathematicians and some of them might believe cra...

A point is that which is absent of any form or volume, it can only be observed as the change of one phenomenon to another. Phenomenon composed of points are composed of change. That's an interesting philosophical point of view. It is not the contemporary mathematical view, for what it's worth. I do...

Cool story bro'.

All I am saying in simple word is that if a line exists, continuum, then it is divisible no matter how many times you try to divide it otherwise you get a point after some divisions, lets call it Ω times, which leads to absurd result. You're correct that you can always divide a line segment in half...

The number of points on a line must be bigger than Lambda What is Lambda? Is this what you were earlier calling Li, and what Cantor called Ω? otherwise we are dealing with a contradiction: Consider a line of length X. Consider that the largest integer number also exist, so-called Lambda. No largest...

bahman wrote: ↑Tue Aug 18, 2020 9:37 am By Li I mean the biggest number, bigger than all trinsfinte. There is no number bigger than this. This number exists according to Cantor.

How does Cantor's idea of the absolute infinite, which he thought was God, bear on the discussion of points on a line?

To identify each point as a number is to equivocate 0 to 1 given the point is absent of any qualities. If you prefer, each point is identical and we associate it with the number that is the location of the point. So there is a point at 2, and a point at pi, and a point at 47, and so forth. You are ...