There Are No Part To Whole Actual Infinities

[GordonP]

What the heck, I’ll give it a try…

Actually, that’s counterproductive because he is going to conceive as “all” as a natural number, which it is not in this case, and “sum” as an integer, which is likewise false in this case.

He started out well. He tried to do arithmetic using infinity as a natural number and ended up with a result that was absurd, which is correct.

Instead of coming to the realization that infinity is not a number, though, he came to the conclusion that there is something wrong with arithmetic itself. The arithmetic is correct, and the result was absurd, which is also correct, but the conclusion after that point is where he went completely off the rails.

 

[IWantGod]

Instead of coming to the realization that infinity is not a number, though, he came to the conclusion that there is something wrong with arithmetic itself.

???

 

[TechieGuy]

Yeah, I was hoping to counter through the “truly distinct numbers” part of his claim, but I see what you mean about the bigger picture of not understanding that infinity isn’t a number.

But from his later remarks, it seems like he isn’t talking about math at all, but rather some sort of Thomistic philosophical concept.

 

[GordonP]

???

This is what you did, using Techies terminology:

If you have a set of five real numbers, then “all” equals 5, which is a natural number, and their “sum” is a real number. That is correct.

If you have a set of ten real numbers, then “all” equals 10, which is a natural number, and their “sum” is a real number. That is also correct.

If you have a set of one billion real numbers, then “all” equals 1,000,000,000, which is a natural number, and their “sum” is a real number. That, too, is correct.

But then you did this:

If you have an infinite set of real numbers, then “all” equals infinity, which is a natural number, and their “sum” is infinity, which is a real number. That correctly led you to a mathematically absurd result, as you yourself pointed out.

The fact that you came up with an absurd result should have led you to re-evaluate your assumption that infinity can be treated as a natural number or a real number in arithmetic. It can’t.

Your mission, should you choose to accept it, is to figure out why infinity cannot be treated as either a natural or real number without producing mathematically meaningless results. I gave you a link to a good article to get you started.

 

[IWantGod]

This is what you did, using Techies terminology:

Did i?

If you have an infinite set of real numbers, then all equals infinity, which is a natural number, and their sum is infinity, which is a real number. That correctly led you to a mathematically absurd result, as you yourself pointed out.

Okay.

The fact that you came up with an absurd result should have led you to re-evaluate your assumption that infinity can be treated as a natural number or a real number in arithmetic.

This isn’t about arithmetic per-say, i am not arguing for a mathematical theory. It is about the possibility an actually infinite regress (the idea that there is an actually infinite number of past events) in the real world.

With both real numbers and real world quantities (specifically states) this leads to absurdity.

 

[Dovekin]

1> If you stop anywhere in an infinite series, it’s regress remains actually infinite,

2> and you can continue to a number greater than an actual infinite,

3> which is a contradiction because the very notion of an infinite series is dependent on the idea that it’s parts altogether comprise an actually infinite number.

4> This is to say that each part of the series is intrinsic to it being an actual infinite.

5> In other-words you should be able to take one part away from the series and it should cease to be infinite, but it doesn’t.

6> Therefore what makes the series infinite cannot be due to how many parts it is comprised of ( the very thing that defines it as an actually infinite number in the first place );

7>which is incoherent, making the idea of an actually infinite series meaningless.

1. OK
2. Nonsense.
3. What? I cannot even tell if it is nonsense.
4. again, what does this mean. Amd what is the basis for saying it.
5. Why should you be able to do that?
6. OK
7. Maybe. Something is incoherent certainly, but I think it is your attempt to align infinity in terms of its parts in statements 3-5.

I tend to agree you are reaching for the paradox of Hilbert’s Hotel, but your revision of parts and infinity is confounding.

 

[IWantGod]

1. OK
2. Nonsense.
3. What? I cannot even tell if it is nonsense.
4. again, what does this mean. Amd what is the basis for saying it.
5. Why should you be able to do that?
6. OK
7. Maybe. Something is incoherent certainly, but I think it is your attempt to align infinity in terms of its parts in statements 3-5.

I tend to agree you are reaching for the paradox of Hilbert’s Hotel, but your revision of parts and infinity is confounding.

Thank you for your contribution.

 

[GordonP]

Did i?

Yes, you did. If you knew the mathematics behind it, it would be blatantly obvious.

This isn’t about arithmetic per-say, i am not arguing for a mathematical theory. It is about the possibility an actually infinite regress ( the idea that there is an actually infinite number of past events ) in the real world.

That is precisely what mathematics and arithmetic are about. There is no “philosophical” discussion on this matter that is not mathematical in nature. Nor has there ever been. Nor can there be.

Mathematics is the branch of philosophy that deals with matters like this. You seem to think of philosophy and mathematics as being separate fields, and that you can do “philosophy” on a question involving the concept of infinity without using mathematics. You can’t.

You have a faulty concept of what both philosophy and mathematics are. If you want to be able to understand either or have a fruitful discussion about either, you have to put in the work and hit the books.

Otherwise, like I said, you will just be spinning your wheels and getting nowhere.

 

[IWantGod]

There is no “philosophical” discussion on this matter that is not mathematical in nature. Nor has there ever been. Nor can there be.

There is pure mathematics and applied maths. Yes one can say that mathematics is a philosophy, but how you are applying it and how i am applying it are in two different contexts. I am applying numbers to states and arguing that they cannot be an actual infinite number of states. You are saying that i am arguing against arithmetic itself which is a conclusion that is not only baffling but also suggests that you failing to grasp what it is that i am doing. You are conflating two subject matters and then saying i am wrong…

 

[GordonP]

There is pure mathematics and applied maths.

That statement is meaningless in the context of this discussion.

Yes one can say that mathematics is a philosophy

No, one can’t say that. Mathematics is NOT a philosophy, it is philosophy. No “a”.

And no, you are not engaging in “applied mathematics”.

Sorry, but without adequate knowledge of philosophy and mathematics, you are stuck. And since it is clear that you are very, very far from that state, and apparently have no interest in expanding your knowledge through serious study, further discussion is a waste of time.

I gave you a good starting point to get you on your way. It’s up to you to go forward. Or not, if you prefer.

 

[IWantGod]

That statement is meaningless in the context of this discussion.

(Please Note: This uploaded content is no longer available.) IWantGod:

Then you can you can show why, otherwise you are not actually contributing anything to anybody’s understanding.

 

[IWantGod]

Sorry, but without adequate knowledge of philosophy and mathematics, you are stuck.

Assertions are worthless. You cannot defeat the argument and so you are throwing accusations.

Thank you for your time.

 

[PetraG]

These concepts work in pure mathematics. But i am applying numbers to distinct ontological states.

What is there in reality that is infinite, save God, who is beyond understanding?

He started out well. He tried to do arithmetic using infinity as a natural number and ended up with a result that was absurd, which is correct.

Instead of coming to the realization that infinity is not a number, though, he came to the conclusion that there is something wrong with arithmetic itself. The arithmetic is correct, and the result was absurd, which is also correct, but the conclusion after that point is where he went completely off the rails.

Exactly.

The fact that you came up with an absurd result should have led you to re-evaluate your assumption that infinity can be treated as a natural number or a real number in arithmetic. It can’t.

Your mission, should you choose to accept it, is to figure out why infinity cannot be treated as either a natural or real number without producing mathematically meaningless results. I gave you a link to a good article to get you started.

Bingo.

This isn’t about arithmetic per-say, i am not arguing for a mathematical theory. It is about the possibility an actually infinite regress ( the idea that there is an actually infinite number of past events ) in the real world.

With both real numbers and real world quantities ( specifically states ) this leads to absurdity.

That’s what he wrote.

There is no “philosophical” discussion on this matter that is not mathematical in nature. Nor has there ever been. Nor can there be.

Yes again.

Then you can you can show why, otherwise you are not actually contributing anything to anybody’s understanding.

First, explain what you have said that would encourage him to take you on as a student? You’re asking for someone to be your professor for free, but you don’t seem like the sort that a teacher would take on for the pure joy of teaching. I say that because you’re not willing to let go of an idea that you have been told is mistaken. If that is your position, then of course a teacher is going to instruct you to chase your tail on your own time.

 

[IWantGod]

First, explain what you have said that would encourage him to take you on as a student? You’re asking for someone to be your professor for free, but you don’t seem like the sort that a teacher would take on for the pure joy of teaching. I say that because you’re not willing to let go of an idea that you have been told is mistaken. If that is your position, then of course a teacher is going to instruct you to chase your tail on your own time.

If a teacher cannot show you why an argument is mistaken then he is not a teacher.

 

[IWantGod]

That’s what he wrote.

So what’s the problem?

 

[IWantGod]

First, explain what you have said

If you stop anywhere in an infinite series, it’s regress remains actually infinite, and you can continue to a number greater than an actual infinite, which is a contradiction because the very notion of an infinite series is dependent on the idea that it’s parts altogether comprise an actually infinite number. This is to say that each part of the series is intrinsic to it being an actual infinite. In other-words you should be able to take one part away from the series and it should cease to be infinite, but it doesn’t. Therefore what makes the series infinite cannot be due to how many parts it is comprised of ( the very thing that defines it as an actually infinite number in the first place ); which is incoherent, making the idea of an actually infinite series meaningless.

 

[PetraG]

If a teacher cannot show you why an argument is mistaken then he is not a teacher.

A student who refuses to believe that he is the one who is wrong, who rejects a beginner’s attitude, has not come to class ready to learn. If the horse is lead to water and doesn’t want to drink it, the wise person doesn’t waste time trying to force him. (When he gets thirsty enough, he’ll come around.)

 

[IWantGod]

A student who refuses to believe that he is the one who is wrong,

Show me why i am wrong.

 

[PetraG]

Show me why i am wrong.

Oh, no… life is too short for students who want to argue instead of learn!
You’ve been given an explanation, but you don’t want to hear it.
If you want to know, you’ve been pointed in the right direction. The rest is up to you.

 

[GordonP]

If a teacher cannot show you why an argument is mistaken then he is not a teacher.

I did. In spades. When I referred you to the article on the topic, which answers your questions in great detail, and told you to hit the books.

A good teacher is not someone who spoon feeds you. They are there to tell you to do the work on your own, and point out how to do it. You aren’t in elementary school anymore.