Actual Infinity in Reality?

[polymath257]

Again, the definition of 'infinite' that you are using isn't the one that others use. That infinite sum does, in fact, add to be 1/3. The *limit* is exactly 1/3. We can, in fact, evaluate the answer without going through the whole process.

Yes, you can, in fact, add an infinite number of distances and obtain a finite distance. That is precisely what limits do. 1/2 + 1/4 + 1/8 +...=1. Exactly.

Yes, the infinite aspects do come to completion in a finite time. That only shows your definition isn't working.

There was another post, where I was going to mention this, but this seems like a good one as well.

There have been a number of times where you do the typical atheistic thing where you dismiss logic and philosophy (seemingly to avoid it).  You question the definitions of infinity, even the use of the terms actual and potential infinities.  And demand that everything to be changed to dealing with infinities in math. 

If math has something to add to the discussion, then that is good.  However the OP was not about mathematical infinite sets that exists only in the abstraction of the mind.   It is about actual infinity, and infinity in regards to philosophy.   That you keep wanting to change things, says to me, that you are not talking about the same ideas....   I also think this is why you do not see the obvious contradictions.

1/2 + 1/4 + 1/8 +...<1     It is never equal to 1.    If you where to reach 1, then you would stop your infinite chain, and it would not be infinite.

Well, perhaps part of the problem is that philosophers have chosen the wrong things to focus on?

And you are wrong about that inequality. Each stage is less than 1, but the sum is equal to 1. it isn't a problem of 'reaching'. The infinity is completed and the answer is 1.

I would suggest that math is a much better way to look at reality than philosophy. This is demonstrated by the lack of progress in the sciences when philosophy was dominant and the progress exactly when math became central.

I don't avoid Aristotelian philosophy. I dismiss it as invalid. In particular, the distinction between potential and actual infinities is a false one. There are only infinities and all infinities are completed. Individual processes may not terminate, but that is irrelevant.  The infinities themselves are actual.

[GrandizerII]

1/2 + 1/4 + 1/8 +...<1     It is never equal to 1.    If you where to reach 1, then you would stop your infinite chain, and it would not be infinite.

1/2 + 1/2 = 1

1/2 + 1/4 + 1/4 = 1

1/2 + 1/4 + 1/8 + 1/8 = 1

If you hypothetically keep going with this, then you should conclude that:

1/2 + 1/4 + 1/8 + ... = 1

If not, then something must have changed the equation, and yet the left hand side of the equation has always been the same value and 1 is always equal to 1. So where's the change in value, pray tell?

[SteveII]

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Since (2) is of the class of axioms that are not self-evident, they are assumptions on which further mathematical equations can be developed (useful in calculus for example). To be clear, this axiom is not reasoned into--it is just assumed as a foundation for the subset of infinite set theory in mathematics. See this earlier post. 

This is CLEARLY a question-begging argument and therefore invalid.

That, or you still haven't grasped (or maybe you don't want to grasp) the exact argument we're making. We're not arguing that infinity is logically possible, therefore it is. We're arguing that you haven't provided any good reductio ad absurdum arguments to disprove the logic of actual infinity. You've failed with all the analogies and paradoxes you've posted about thus far.

And even if it was a question-begging argument, which it isn't, it would still be a valid argument anyway. Circular yes, invalid no.

And about the B-theory of time, William Lane Craig himself said the KCA is predicated on the A-theory of time and that if the B-theory of time is true, then the argument is useless. Well, we know which theory of time is backed by the science, and it's not the A-theory of time.

This is getting silly--try to keep up. 

First, there is no "logic of actual infinity" for me to assail. There is no non-question-begging argument for it. 

Second, you can't answer Hilbert's Hotel without invoking set theory. I have not yet been supplied a reason why we have to invoke a mathematical assumption used only in mathematics to discuss rooms and guests. We wouldn't if there were 100, 1000 or even 10^10 rooms/guests. Poly has tried that tack that set theory is necessary for basic math operations. This is utterly ridiculous and I will point that out shortly. 

What makes you think I am arguing KCA? Stop--I am not going to respond because that is not the topic here. 

I see you have dropped your infinite causes is possible because there are no causes argument--good for you! It was a lousy argument.

[Edwardo Piet]

Do you mean that 1 = 0.99999......

I think that says it all right there.

What do you mean?

Don't you agree that 0.999999... actually is equal to 1? And not just potentially?

Lol I suck at maths and even I know that 0.99999999... = 1 because it makes logical fucking sense.

[SteveII]

Not only are you correct when you say "you don't *have* to" put the rooms in sets, but why would you? The desk clerk is not pulling out paper and using {G1, G2, G3...} to move the guests around. He is making changes with real rooms and real guests and does not have to resort to creating abstract objects by grouping them together. 

You do not need sets to preform any basic operations like addition, subtraction, multiplication or division. I'll give you a chance to back away from that assertion. 

The only reason you desperately want to hang on to putting those rooms into sets is so you can apply unwarranted external constraints (set theory) to them and dismiss the contradiction and absurdities that would otherwise surface.

Yes, of course you need sets for addition (for example). Without them, how do you even define addition? Try to define the notion of addition without using collections. You cannot do it. The same goes for multiplication. Subtraction and division require *extensions* of those notions and the way to extend them is by careful consideration of the sets involved.

So, a challenge: how do you *define* addition? Use *only* those logical axioms that you have accepted prior to this. They are just not sufficient to the task. For that matter, even to define the concept of number requires the use of collections.

And *you* were the one wanting to get results like infinity+infinity=infinity from moving people around. YOU were the one claiming subtraction needs to be well defined for infinite quantities (with no reason).

You don't need sets for addition (or any other basic arithmetic operation). If you think so, it should be easy for a math student to post a link that explain it. Until I see an article from a recognized source of such things, I will assume you are wrong.
What is your fascination with what axioms I am using? It does not really matter, because we are not arguing about two logic systems. We are arguing using propositional logic. If you think that is the wrong logic system to use, make an argument why. Until then, stop thinking this is a point that needs to be made. Regarding addition and multiplication:

The operations of arithmetic on real numbers are subject to a number of basic rules, called axioms. These include axioms of addition, multiplication, distributivity, and order.
http://science.jrank.org/pages/505/Arith...z58VfUtp8b

Lest you think there is an argument to be made that HH example doesn't contain real numbers, the rooms are numbered--with real numbers.

[GrandizerII]

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That, or you still haven't grasped (or maybe you don't want to grasp) the exact argument we're making. We're not arguing that infinity is logically possible, therefore it is. We're arguing that you haven't provided any good reductio ad absurdum arguments to disprove the logic of actual infinity. You've failed with all the analogies and paradoxes you've posted about thus far.

And even if it was a question-begging argument, which it isn't, it would still be a valid argument anyway. Circular yes, invalid no.

And about the B-theory of time, William Lane Craig himself said the KCA is predicated on the A-theory of time and that if the B-theory of time is true, then the argument is useless. Well, we know which theory of time is backed by the science, and it's not the A-theory of time.

This is getting silly--try to keep up. 

First, there is no "logic of actual infinity" for me to assail. There is no non-question-begging argument for it.

Ok, but you can still use a certain type of argument to disprove it. You get that, right? And in fact, that's what you have been trying to do anyway ... but you keep failing.

Second, you can't answer Hilbert's Hotel without invoking set theory. I have not yet been supplied a reason why we have to invoke a mathematical assumption used only in mathematics to discuss rooms and guests. We wouldn't if there were 100, 1000 or even 10^10 rooms/guests. Poly has tried that tack that set theory is necessary for basic math operations. This is utterly ridiculous and I will point that out shortly.

Every grouping of stuff that can be mathematically represented as a set.

What makes you think I am arguing KCA? Stop--I am not going to respond because that is not the topic here.

We're not dumb, Steve. The KCA requires that an actual infinity of time moments be logically impossible. We all know why you made this thread. The problem is that, as WLC rightly confessed, the argument from beginning to end depends on the A-theory of time. With the B-theory of time, the KCA is easily debunked.

I see you have dropped your infinite causes is possible because there are no causes argument--good for you! It was a lousy argument.

I didn't drop it. You just didn't respond to the argument last time I referred to it. Plus, you seem to have forgotten Sean Carroll's causality is derived, not fundamental, quote. You do know that's what physicists believe, right?

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What do you mean?

Don't you agree that 0.999999... actually is equal to 1? And not just potentially?

Lol I suck at maths and even I know that 0.99999999... = 1 because it makes logical fucking sense.

Don't worry, they're worse from what I'm seeing.

[Edwardo Piet]

I suck at maths because my short term memory and concentration is too poor to hold numbers in my head and focus on abstract symbols. I'm more than intelligent enough... which is why I'm good at logic but if the premises start to get replaced with stuff like "P" and "Q" I suddenly can't cope because I keep forgetting what each symbol stands for.

I'm fantastic at abstract concepts... not so good at abstract symbols.

[GrandizerII]

I suck at maths because my short term memory and concentration is too poor to hold numbers in my head and focus on abstract symbols. I'm more than intelligent enough... which is why I'm good at logic but if the premises start to get replaced with stuff like "P" and "Q" I suddenly can't cope because I keep forgetting what each symbol stands for.

I'm fantastic at abstract concepts... not so good at abstract symbols.

I'm guessing writing them down wouldn't help either?

[Edwardo Piet]

I suck at maths because my short term memory and concentration is too poor to hold numbers in my head and focus on abstract symbols. I'm more than intelligent enough... which is why I'm good at logic but if the premises start to get replaced with stuff like "P" and "Q" I suddenly can't cope because I keep forgetting what each symbol stands for.

I'm fantastic at abstract concepts... not so good at abstract symbols.

I'm guessing writing them down wouldn't help either?

It might a bit perhaps but I think I'd still fail to concentrate.

My spelling is awesome but I suck at Scrabble too. I can't do the rearranging the letters in my mind bit.

[SteveII]

Do you mean that 1 = 0.99999......

I think that says it all right there.

What do you mean?

Don't you agree that 0.999999... actually is equal to 1? And not just potentially?

That's ridiculous. 0.99999... will NEVER equal 1. Not even potentially

In no world does that make any sense to assert that.