I've read one physicist claiming that this means that existence, time, space, everything must be finite, because infinite sets are logically contradictory, as you can apparently change their ratios by changing the order in which you look at them. — Fuzzball Baggins
What do you guys think? Anything wrong with my reasoning? Anything I've missed? — Fuzzball Baggins
I've read one physicist claiming that this means that existence, time, space, everything must be finite, because infinite sets are logically contradictory, as you can apparently change their ratios by changing the order in which you look at them. — Fuzzball Baggins
Perhaps with numbers and mathematics one should stick to the logic of math itself and not bother about physical time and physical doing, of what kind of numbers our present day computers or computers of the future can handle. Even a atural number that is one hundred thousand digits long can be problematic for us to handle and our Computers to handle, yet the logic of the number is totally similar to a natural number that is two digits long, basically one between 0 and 99. Otherwise you will start looking for the quite illogical "first too big number that cannot be handled by a computer".However it has occurred to me that the measure problem would apply equally well to a large finite set, say a set of a billion integers which it would take a very long time to actually count in order to determine the correct ratio of odd-to-even. — Fuzzball Baggins
However it has occurred to me that the measure problem would apply equally well to a large finite set, say a set of a billion integers which it would take a very long time to actually count in order to determine the correct ratio of odd-to-even. — Fuzzball Baggins
in the second half he starts extrapolating a bit too much from the measure problem, and seems to think that any set that has the measure problem can't actually exist. — Fuzzball Baggins
I suppose this is really more a discussion of the definition of the word set rather than whether the universe could be infinite, so I'll agree with you that with the definition that humans have given the word set, the term 'infinite set' is illogical :P — Fuzzball Baggins
A "collection" in the sense of a noun implies having been collected, so an infinite collection is impossible — Metaphysician Undercover
I have them collected in my mind. But I do not understand your claim. A large number of grains of sand of sand is certainly collectible. But in terms of your apparently empirical criteria, they're uncountable - I guess you can't have a large pile of sand, yes?I haven't collected them all yet in my mind. — Metaphysician Undercover
Says who besides you? Your opportunity to educate.Furthermore, "all the positive numbers" does not qualify as "well-defined" — Metaphysician Undercover
I have them collected in my mind. — tim wood
A large number of grains of sand of sand is certainly collectible. — tim wood
I guess you can't have a large pile of sand, yes? — tim wood
Your opportunity to educate. — tim wood
Which ones would you like me to list?You have all the positive numbers collected in your mind!? Can you list them then? — Metaphysician Undercover
I know the difference - I'm by no means sure you do. And your "if you listen" in response to my question to you as to who besides you says so - your answer in response to that question - is simply an example of what I've experienced as your toxic style of discussion. You made a claim,Do you understand that there is a significant difference between "a large pile of sand", which obviously has a finite number of grains of sand, (as any pile of sand does), and "an infinite number of grains of sand"? The latter is not a pile of sand.
Your opportunity to educate.
— tim wood
If you will listen, I will oblige. — Metaphysician Undercover
My claim is quite simple. A large number of grains of sand is collectible. An infinite number is not. — Metaphysician Undercover
Which ones would you like me to list? — tim wood
I know the difference - I'm by no means sure you do. And your "if you listen" in response to my question to you as to who besides you says so - your answer in response to that question - is simply an example of what I've experienced as your toxic style of discussion. You made a claim, — tim wood
I ask you who besides you says so. And you do not answer. Answer or Hitchen's razor awaits you. — tim wood
So it appears, at first glance, that there may be an issue with self-contradiction, because it is suggested that a multitude of objects is a single object. However, we do commonly speak of a multitude of objects as a single object, that's what happens in arithmetic; 2, 3, 4, etc., are each representative of a single object, a number, but each number defines a multitude as well. What happens with "infinite" is that the multitude is undefined, and even specified as undefinable. But the object, the particular number, 10, 15, 25, or whatever, only has existence because it defines a multitude. Its very existence, as a number, is completely dependent on its capacity to define a multitude. If any such number which is signified by a numeral, "6", "7", "8" etc.,, did not define a multitude, it would not exist as an object. "Infinite" signifies an undefined multitude. So by the very fact of what it signifies, the possibility of it being an object is denied. What "infinite" signifies is "it is impossible that I am an object like a number", because a number necessarily defines a multitude while "infinite" necessarily does not.. — Metaphysician Undercover
Your claims seem a little arbitrary. Especially your claim that the multiverse being seen on the one hand as a multitude and on the other as a single object makes it self-contradictory. A bunch of bananas is both a single object and a multitude of bananas. — Fuzzball Baggins
Do you have any logical reasoning (not involving human intuition, but based on the laws of physics or mathematics) for why an infinite thing could not exist in reality? — Fuzzball Baggins
I don't think the concept of a set having to be 'collected' quite applies to what can and cannot exist in reality. — Fuzzball Baggins
I may not be able to create an infinite collection, or even imagine all the members of an infinite set, but reality doesn't have to 'collect' anything - infinite things can exist simultaneously without having to be created one by one. — Fuzzball Baggins
All of them of course. I want you to prove to me what you claimed. "I have them collected in my mind." — Metaphysician Undercover
I ask you who besides you says so. And you do not answer. Answer or Hitchen's razor awaits you.
— tim wood
I'll take the razor, and here's my proof. I'll reproduce from above, as it appears like you haven't read the thread. Tell me which part you dislike — Metaphysician Undercover
all positive numbers of the form 2n, n being any integer. — tim wood
The razor, then. "What is averred without evidence can be dismissed without evidence." Btw, a request for a respectable source is perfectly reasonable. — tim wood
I went through this already. It is unreasonable to assume that any thing is infinite because such an assumption impedes our capacity to know that thing, and it is also impossible to know that a thing is infinite. So it's not the case that it is impossible that an infinite thing exists, in reality, but it is impossible to know that any given thing is infinite, and detrimental to the understanding of that thing, to assume that any given thing is infinite. Therefore it is unreasonable to assume that there is an infinite thing in reality. — Metaphysician Undercover
I think that is a reasonable way to define an infinite set of numbers, it is used all the time in mathematics. Just because he didn't list all those numbers separately doesn't mean they don't all exist. You were complaining earlier that infinite sets are inherently undefined. '2n, with n being any integer' is an example of how to define an infinite set.I asked for the list, not a description of it. — Metaphysician Undercover
You may not be able to observe through empirical evidence that an infinite thing exists, but that doesn't mean it's unreasonable to infer that it exists. Take numbers, for example. I cannot count all the way to infinity, but I can infer that there are infinite numbers from the fact that if there were a finite biggest number then asking 'what is that number plus one' would break that limit. — Fuzzball Baggins
I think that is a reasonable way to define an infinite set of numbers, it is used all the time in mathematics. Just because he didn't list all those numbers separately doesn't mean they don't all exist. — Fuzzball Baggins
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