To infinity and beyond.

[Walt Zingmatilder]

Came across some new thinking on the existence of actual, metaphysical infinities as opposed to abstract mathematical infinities.
Apparently certain infinities throw up contradictions, multiple solutions etc.
Since these are not seen in concreto as it were, or in physical reality, it gives us grounds to doubt the existence of those infinities.

[splashscuba]

Link please

[Stranger]

Came across some new thinking on the existence of actual, metaphysical infinities as opposed to abstract mathematical infinities.
Apparently certain infinities throw up contradictions, multiple solutions etc.
Since these are not seen in concreto as it were, or in physical reality, it gives us grounds to doubt the existence of those infinities.

Link please

^^^ What splash said.

Also, calculus assumes an infinity of points between any two other points (the continuum), and that isn't even the smallest infinity.

[Walt Zingmatilder]

Link please

https://youtu.be/7j4qJIWbfZ0?si=c7Jy1XI95NydyKiY

[Walt Zingmatilder]

I think the arguments have been along the lines of infinities cause contradictions and therefore cannot be and the opposing there is no reason to believe that there is anything preventing them from being actual.

A revised line is that the contradictions are not observed in actuality and therefore the existence of those infinities is doubted.

Presumably, as an example, if there could be a Hilberts hotel then there would be an infinite number and yet alas nary a one.

[Walt Zingmatilder]

^^^ What splash said.

Also, calculus assumes an infinity of points between any two other points (the continuum), and that isn't even the smallest infinity.

I don't think any one is arguing that infinities do not exist in maths or the abstract and a platonic might argue that maths is real but are we actually observing infinitesimal small points or even distances. I'm not sure.

You'd have to examine each infinity on it's own merits and see what contradictions are actually observed and evidenced.

[Stranger]

https://youtu.be/7j4qJIWbfZ0?si=c7Jy1XI95NydyKiY

Oh dear, a video from a Christian apologist. The first mistake is that the Hilbert Hotel (yawn!!!) is not contradictory, just counterintuitive, compare with the continuum. There is literally the same 'number' of points in the interval -∞ to +∞ as there are between 0 and 1. This is not a contradiction.

You couldn't do the mathematics of transfinite numbers if there were actual logical contradictions involved because you'd end up being able to prove literally anything (The Principle of Explosion).

If there are no logical contradictions, then there can be no contradictions in physical realisation (even if it's impossible in practice, like an infinite hotel).

There are many scientific hypotheses that involve real infinities in past and future time, and nobody throws them out with the absurd dogma of "you can't have real infinities" except people who disagree on religious grounds because it spoils their arguments. What's more, the limited evidence we have actually suggests infinite space. As an aside, there are also hypotheses that say past likelike paths are cyclical and lead back to the present.

To go back to the video, some credit is due for pointing out some of the more obvious objections to the KCA, but I skipped through to the relevant points according to the table of contents, and then lost interest when he started wittering on about time travel. If you think there is some other stunning point later on, please point out where. I'm not spending a full half hour of my time watching yet another apologist make the same old mistakes.

[Walt Zingmatilder]

Oh dear, a video from a Christian apologist. The first mistake is that the Hilbert Hotel (yawn!!!) is not contradictory, just counterintuitive, compare with the continuum. There is literally the same 'number' of points in the interval -∞ to +∞ as there are between 0 and 1. This is not a contradiction.

You couldn't do the mathematics of transfinite numbers if there were actual logical contradictions involved because you'd end up being able to prove literally anything (The Principle of Explosion).

If there are no logical contradictions, then there can be no contradictions in physical realisation (even if it's impossible in practice, like an infinite hotel).

There are many scientific hypotheses that involve real infinities in past and future time, and nobody throws them out with the absurd dogma of "you can't have real infinities" except people who disagree on religious grounds because it spoils their arguments. What's more, the limited evidence we have actually suggests infinite space. As an aside, there are also hypotheses that say past likelike paths are cyclical and lead back to the present.

To go back to the video, some credit is due for pointing out some of the more obvious objections to the KCA, but I skipped through to the relevant points according to the table of contents, and then lost interest when he started wittering on about time travel. If you think there is some other stunning point later on, please point out where. I'm not spending a full half hour of my time watching yet another apologist make the same old mistakes.

I want to focus on infinities. No one is denying the maths works or that contradictions thrown up by them can't constitute valid conclusions or even that there may be no logical barrier to their being.

The issue is are these contradictions evidenced in concreto?
If not then are we not justified in being a-infinitist?

[Stranger]

I want to focus on infinities. No one is denying the maths works or that contradictions thrown up by them can't constitute valid conclusions or even that there may be no logical barrier to their being.

The issue is are these contradictions evidenced in concreto?
If not then are we not justified in being a-infinitist?

What contradictions? There simply aren't any.

[Walt Zingmatilder]

What contradictions? There simply aren't any.

So you are saying that there are no mathematical infinities that produce multiple conclusions?

[Walt Zingmatilder]

What contradictions? There simply aren't any.

https://reasons.org/explore/blogs/impact-events/do-infinities-produce-contradictions

[Stranger]

So you are saying that there are no mathematical infinities that produce multiple conclusions?

I said there were no contradictions. You really need to tell us exactly what you think the contradictions are. "Multiple conclusions" is ambitious. For example, you can have multiple solutions to an equation without contradiction.

https://reasons.org/explore/blogs/impact-events/do-infinities-produce-contradictions

Yet another faith-based site and somebody else who doesn't know what they're talking about. We get another yawn inducing reference to Hilbert’s Hotel, with some 'absurdities'. What somebody thinks is absurd is not necessarily contradictory. He even ends by contradicting himself by referring to an infinite God.

This points out another silly aspects of religion rejecting infinities for the universe, while accepting them for 'God'. Special pleading fallacy.

[jeremyp]

Yet another faith-based site and somebody else who doesn't know what they're talking about. We get another yawn inducing reference to Hilbert’s Hotel, with some 'absurdities'. What somebody thinks is absurd is not necessarily contradictory. He even ends by contradicting himself by referring to an infinite God.

This points out another silly aspects of religion rejecting infinities for the universe, while accepting them for 'God'. Special pleading fallacy.

Actually, you need to read the whole article, as does Vlad. It explains why the absurdities don't really exist (subtraction is not well defined for infinities). It's arguing our side of the point.

[jeremyp]

https://reasons.org/explore/blogs/impact-events/do-infinities-produce-contradictions

You didn't read the article to the end, did you?

[Stranger]

Actually, you need to read the whole article, as does Vlad. It explains why the absurdities don't really exist (subtraction is not well defined for infinities). It's arguing our side of the point.

My bad. Why did I assume Vlad had read what he posted. 

[jeremyp]

My bad. Why did I assume Vlad had read what he posted. 

Don't feel bad. We all overestimate the opposition from time to time.

[Walt Zingmatilder]

 

Actually, you need to read the whole article, as does Vlad. It explains why the absurdities don't really exist (subtraction is not well defined for infinities). It's arguing our side of the point.

I think the point is he admits to contradictions where there is more than one conclusion possible.
All you have today is provide a physical example of such a situation. Similarly you are proposing subtraction as not well defined for infinities. You need to show this in the physical realm to justify showing that infinities are real.

[Walt Zingmatilder]

You didn't read the article to the end, did you?

How does it detract from his earlier admission with working out
That Infinities can provide multiple conclusions?

It isn't that I'm saying they aren't logical it's you having to demonstrate that in the real physical world I.e. evidentially.

[Walt Zingmatilder]

Actually, you need to read the whole article, as does Vlad. It explains why the absurdities don't really exist (subtraction is not well defined for infinities). It's arguing our side of the point.

I agree wholeheartedly that you should read the posts and Jeremy should actually read up on what my argument is.

Which is I am justified in being an A-Infinitist vis a vis actual infinities until physical evidence is presented  even if they work in maths or logic.

[Nearly Sane]

Came across some new thinking on the existence of actual, metaphysical infinities as opposed to abstract mathematical infinities.
Apparently certain infinities throw up contradictions, multiple solutions etc.
Since these are not seen in concreto as it were, or in physical reality, it gives us grounds to doubt the existence of those infinities.

What is an 'actual, metaphysical infinity'? Actual and metaphysical would appear to be an oxymoron here.

[Stranger]

I think the point is he admits to contradictions where there is more than one conclusion possible.

Where? What contradictions? Exact quote or your own example needed.

All you have today is provide a physical example of such a situation. Similarly you are proposing subtraction as not well defined for infinities. You need to show this in the physical realm to justify showing that infinities are real.

Nobody needs to show anything in the physical world to dismiss a claim for contradictions that they can't actually cite. As the article says, some operations are not defined for zero (division, for example), yet you can definitely have zero apples in a box.

I agree wholeheartedly that you should read the posts and Jeremy should actually read up on what my argument is.

You made an argument? Where? I see claims and links, but no hint of an argument. You can't even give an example of these supposed contradictions.

[Walt Zingmatilder]

Where? What contradictions? Exact quote or your own example needed.

Nobody needs to show anything in the physical world to dismiss a claim for contradictions that they can't actually cite. As the article says, some operations are not defined for zero (division, for example), yet you can definitely have zero apples in a box.

You made an argument? Where? I see claims and links, but no hint of an argument. You can't even give an example of these supposed contradictions.

F there is more than one conclusion and those conclusions are different then we have a contradiction. If you are defining contradiction differently then you need to explain it.
If we look at the citation I gave we see in his working out that he does indeed come up with more than one conclusion when performing the maths of infinity. While that may be logical, if one is arguing that there could be real infinities one has to demonstrate these multiple conclusions occurring physically. And that’s all I am saying.

From the link
However, some “absurdities” arise when groups start leaving. If a finite group of 5 checks out, the hotel still has an infinite number of rooms filled. But consider what happens when two different infinite groups leave the hotel. Having the infinite group in all rooms greater than 5 check out leaves only 5 rooms filled. Alternatively, when the infinite group of all even numbers checks out, the hotel has an infinite number of odd rooms filled. In equation form (paralleling the addition equations above), this gives:

a – b = c   Just like addition above
∞ – a = ∞   OK so far
∞ – ∞ = 5   First infinite group leaving
∞ – ∞ = ∞   Second infinite group leaving
The last two equations are contradictory! You can’t subtract one value from another value and get two different results. Thus, many people have used this contradiction to argue that actual infinities cannot exist in the physical world. However, mathematicians recognized this dilemma and solved the issue by noting that subtraction is not a well-defined operation for infinites. Lest this strike you as defining the problem away, you encounter a similar solution for a much more familiar mathematical idea. Let me illustrate with an interesting proof:”. How does noting that subtraction is not well defined for infinities help out in the argument that actual infinities could exist?

[Stranger]

F there is more than one conclusion and those conclusions are different then we have a contradiction. If you are defining contradiction differently then you need to explain it.
If we look at the citation I gave we see in his working out that he does indeed come up with more than one conclusion when performing the maths of infinity. While that may be logical, if one is arguing that there could be real infinities one has to demonstrate these multiple conclusions occurring physically. And that’s all I am saying.

Why do you keep running away from giving an explicit example?

Just cite one example of such a contradiction (or of different conclusions that you regard as contradictions), and I'll happily respond. Just stop being so deliberately and pointlessly vague.

[Walt Zingmatilder]

Why do you keep running away from giving an explicit example?

Just cite one example of such a contradiction (or of different conclusions that you regard as contradictions), and I'll happily respond. Just stop being so deliberately and pointlessly vague.

I have provided where he establishes a contradiction or apparent contradiction.
See previous. I am not saying these contradictory conclusions don’t logically follow, l just ask for a real world example and because they are not provided it may be reasonable to suppose actual infinities which would provide them do not exist.

[Nearly Sane]

Why do you keep running away from giving an explicit example?

Just cite one example of such a contradiction (or of different conclusions that you regard as contradictions), and I'll happily respond. Just stop being so deliberately and pointlessly vague.

Just to point out Vlad's edited his post that you are replying to here, after your reply, to provide what he sees as a contradiction.