Actual Infinity in Reality?

[RoadRunner79]

Ok... .so how would you answer?  Would you agree, that if there is a logical contradiction, that this would disprove the math?   Perhaps a problem in the assumptions or in the way things are being explained, that it is not an actual infinite but something else. 

This guy has a number of articles about Infinity and what he sees as philosophical problems underpinning this relatively recent theory.  The following observation is interesting. 

Awesome article. Explains with much more clarity some of my modest points (by comparison) I was trying to make between mathematics and the real world. But holy cow, he lays mathematicians out over the concept of infinity. I liked this summary near the end:

Impolite Implications

To be frank, if I were a mathematician, I would be embarrassed by the conceptual holes in Cantor’s argument. It’s worse than the Copenhagen Interpretation of quantum physics. It’s worse than blind faith in deities. At least blind faith does not demand accepting logical contradictions into your worldview.

Cantor’s argument isn’t ridiculous in isolation; the entire modern mathematics profession is also damned by association. Modern math, by not weeding out the illogical presuppositions of Cantor, has turned itself into modern Numerology.

Pure mathematicians, to use a phrase by Marcelo Gleiser, have relegated themselves to being “monks of a secret order”. They think they have special access to the magical and mysterious world of numbers, and the great infinity of infinities.

Many contemporaries of Cantor mocked and despised his work. Mathematician Henri Poincaré is famously quoted as saying, “Later generations will regard [set theory] as a disease from which one has recovered.”

Mathematician Leopold Kronecker wrote, “I don’t know what predominates in Cantor’s theory — philosophy or theology – but I am sure that there is no mathematics there.”

The philosopher Wittgenstein at one point said, “Mathematics is ridden through and through with the pernicious idioms of set theory” which he called “utter nonsense” and “laughable.”

This is the type of article I have asked from Grandizer and Polymath for 40 pages. Where are the philosophy articles that defend an actual infinite in the real world?

He has about 4-5 articles on the topic of infinity and one I beleive concerning Zeno's Paradox.    There is a lot of repetitiveness, but there are some different aspects to each one as well.  They could probably be reduced to a single article and be neater and more concise.   For the most part it's not about the math, but the underlying assumptions. 

A lot of the arguments do seem to be that there is a concept in math of an infinite, or that numbers can go on forever, so there is an actual infinite.   And I think we agree, that this is not about there being an repeating pattern to the decimal system (without inherent limitation) nor that math has rules for infinite sets.  I think that our interlocutors are confusing these with an actual infinite (one seems to not even like that language, although I don't know the reason why).  But it's not about the concept of an actual infinite.   Philosophy has long held to the concept of an actual infinite long before Cantor and his sets.   Your argument from the beginning (and I agree) is about an actual infinite number of physical things..

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If you are saying that you never reach the destination (A), then I would agree.  It was my understanding that you where saying that A was reached, as opposed to Zeno's conclusion that motion was impossible or you have your contradiction.

Here is my reasons for there needing to be an last point (note reasons, not an assumption). 

So we take a line between two points (0 and our destination) 
We'll define A as any point >= the destination, making any point less than the destination !A

We start at point 0 (!A)  and progress through the line of points (either finite or infinite) where the current point is always greater than the previous point.
1.If you reach the destination (A) then the last point you passed where !A is your final point.

I believe that your equation where you progress through where X<Y<A  is analogous to Zeno's paradox.   Where Y is the average between X and A;  and you keep repeating this sequence where then Y becomes X and you solve for Y again.

This involves the first principles of the Law of identity, the law of non-contradiction, and the law of excluded middle applied as we move along our line.  It assumes that we are progressing along the line, and that we do reach the destination.   We start off !A and progress through the point along the line until we reach A.

Now what myself and Steve have been saying, and that a number of people seem to not want to do the math on, is that given this approach; you will never reach A.  And I would agree, given that you never reach A, there will not be a last point prior to A (it's a nonsensical question in that case).  The contradiction would be in saying that both A and !A are true.  And what makes your claim of infinity also prevents you from ever ending at point A.

I think that we can take for granted, we are presented this in the middle.  Can I place another number in there... Sure.   However the problem arises when you start doing so on the ends, and realize that you either cannot finish or cannot start your journey with such thinking, and lead Zeno to conclude that motion is impossible.  Zeno according to the tale was a strict logician and even though it was demonstrated that motion was in fact possible, demanded that he be shown logically where he was wrong.

I hope that we are in agreement, that motion is possible. To me and others, Zeno's problem is not in that math, nor in his logic.  His problem was with his starting assumption of a continuum or having to cross an infinite.

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I think we reach the point A, but not by stopping at each point in that sequence. To stop would entail spending more than an instant at each point, and that would not allow us to reach the end, 1.

In that process, at no stage is the final point reached. But that isn't the complete description of how we get from 0 to 1. There is more there than just that process (which would finish in a finite amount of time).

In 1, you are assuming there is a last point. The proof above shows there is not. yes, we start at !A and proceed to A. But there is not a last point before A. Where is the contradiction?

There is no A and !A being true. We do reach that last point by going through each point in the sequence AND ALSO 1. If we limit ourselves to that sequence, we do not get to A, but we are not limited to being on that sequence. We do go through every point of the sequence *and* 1 also.

Well, I explained my reasoning for a last point (it's not an assumption).  Even with only two points on a segment if we start at zero and end at A, then zero would be the last point before A.  With more than one point and progression to A through these points, you will have a last point.  It is not dependent on time at or between points, as long as there is some sort of movement towards the destination.

However If you are not going to engage, and just keep repeating the claim, then I'm not going to repeat myself..... Now after numerous posts you admit that this process which shows your infinite points also prevents you from reaching the destination at all.  There is some mystery process which is added, and allows us to end the other process, which is being defined as infinite (without end or limit).    If you have something new to talk about, or wish to engage with something that I have said... I'm happy to discuss.   Otherwise I'll leave the last word to you if you desire.