Actual Infinity in Reality?

[polymath257]

Of course 'infinity' means every one of those things you say it does not mean! The very first sentence in the Wikipedia article:


Need more?

in·fi·nite
ˈinfənət/
adjective
adjective: infinite

1. 1.
   limitless or endless in space, extent, or size; impossible to measure or calculate.
   synonyms:
   boundless, unbounded, unlimited, limitless, never-ending, interminable; More
   • very great in amount or degree.
     "he bathed the wound with infinite care"
     
   • MATHEMATICS
     greater than any assignable quantity or countable number.
     
   • MATHEMATICS
     (of a series) able to be continued indefinitely.
     

Where are you getting your definition?

I think it's the same place as words such as "end", "contradiction", "assume", "never", "last" and the like.

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Yes, of course I am saying they can be completed. That is what it means to be an actual infinity, after all.

The problem is that you have two very different notions of having an 'end'. One uses a list of the elements. The other is based on the order properties. if you want to list the elements of an infinite set one by one, you won't ever end that process. But that isn't required in the Zeno paradoxes. ALL that is required there is that every position has a time associated with it. THAT'S ALL.


So, if you use 'infinity' to describe quantity, then 'not having an end' is NOT the description you can use. That doesn't describe a quantity: it describes a process.

So what is it about the order that makes a thing infinite?  Why is it, that you cannot list the elements, but you seem to think that you can go through them all sequentially?  Are not both a process?  When cutting in half in the dichotomy paradox, would that then demonstrate that the process; not the number of points is infinite?

Yes, that process is infinite. But the process of going through the points at a speed of .2 is NOT infinite.

[Amarok]

Wow Steve wikipedia  

And once again i thought he said he quit

[GrandizerII]

From the Internet Encyclopedia of Philosophy:

The term actual infinity is now very different. There are actual infinities in the technical, post-1880s sense, which are neither endless, unlimited, nor immeasurable. A line segment one meter long is a good example. It is not endless because it is finitely long, and it is not a process because it is timeless. It is not unlimited because it is limited by both zero and one. It is not immeasurable because its length measure is one meter. Nevertheless, the one meter line is infinite in the technical sense because it has an actual infinity of sub-segments, and it has an actual infinity of distinct points. So, there definitely has been a conceptual revolution.

https://www.iep.utm.edu/infinite/

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Of course time is a factor.

Heres the article which I linked to a few pages back, and which addresses Zenos motion paradoxes from a physics standpoint.

http://www.mathpages.com/rr/s3-07/3-07.htm

Read the second last paragraph at least, if you dont want to read the whole thing. Though the whole thing is an interesting read.

What do you think in that addresses the logical contradiction being presented in Zeno's paradox?

What logical contradiction specifically? Zeno's dichotomy paradox isn't an argument against an actual infinity. It's called a paradox of motion, not a paradox of infinity.

Did you read at least the first few and last few paragraphs from the article?

[polymath257]

From the Internet Encyclopedia of Philosophy:

https://www.iep.utm.edu/infinit

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What do you think in that addresses the logical contradiction being presented in Zeno's paradox?

What logical contradiction specifically? Zeno's dichotomy paradox isn't an argument against an actual infinity. It's called a paradox of motion, not a paradox of infinity.

Did you read at least the first few and last few paragraphs from the article?

That was a *very* nice article! All those arguing against actual infinities should read the whole thing.

In particular, the use of actual infinities in mathematics, especially the development of calculus, is vital and cannot be dispensed with. And calculus is central to our understanding of the universe via physics.

That alone is a very, very good reason to accept actual infinities. Every basic physical theory since Newton has been based on calculus. There is a strong sense in which the development of calculus was what produced the differences in science between the West and the rest of the world. And infinities are central to that field.

So, in a sense, the allowance for actual infinities is central to the development of our modern understanding of the universe. It is why Aristotelian philosophy is so little regarded by modern science: it fails to produce the results.

I want to point out that NOBODY has actually presented a *contradiction* in the logical sense to an actual infinity. Yes, they have produced things that seem strange if they are used to finite sets all the time, but there has been no actual contradiction.

[GrandizerII]

Funny thing is Aristotle actually did believe in an actual infinite time.

[SteveII]

@Polymath

Are you a platonic realist? Do you think abstract mathematical objects really exist independent of the mind?

[polymath257]

@Polymath

Are you a platonic realist? Do you think abstract mathematical objects really exist independent of the mind?

No. I am more of a formalist. But I think the formalism shows the logical possibilities.

After that, we use math as a language for understanding and modeling what we observe and formulating hypotheses about such.

[GrandizerII]

This one is rather hilarious:

The multiverse theories of cosmology in the early 21st century allow there to be an uncountable infinity of universes within a background space whose volume is actually infinite. The universe created by our Big Bang is just one of these many universes. Christian theologians balk at the notion of God choosing to create this multiverse because the theory implies that, although there are so many universes radically different from ours, there also are an actually infinite number of copies of ours, which implies there are an infinite number of Jesuses who have been crucified on the cross. The removal of the uniqueness of Jesus is apparently a removal of his dignity. Augustine had this worry when considering infinite universes, and he responded that "Christ died once for sinners...."

Even Jesus is not allowed to be infinite!

[Anomalocaris]

This one is rather hilarious:

The multiverse theories of cosmology in the early 21st century allow there to be an uncountable infinity of universes within a background space whose volume is actually infinite. The universe created by our Big Bang is just one of these many universes. Christian theologians balk at the notion of God choosing to create this multiverse because the theory implies that, although there are so many universes radically different from ours, there also are an actually infinite number of copies of ours, which implies there are an infinite number of Jesuses who have been crucified on the cross. The removal of the uniqueness of Jesus is apparently a removal of his dignity. Augustine had this worry when considering infinite universes, and he responded that "Christ died once for sinners...."

Even Jesus is not allowed to be infinite!

That’s because jesus is a zero.