can something exist literally 'infinitely' far away?

Originally posted by humy
I could be completely wrong here, but I suspect you may have subtly misunderstood his exact intended meaning.

Which of the meanings you guessed at, would make any kind of sense in the context of what he said?

Originally posted by twhitehead
Which of the meanings you guessed at, would make any kind of sense in the context of what he said?

within the very narrow context of his quote that mentions 'electrons', the possibly intended implied meaning involving 'there exists a finite number of electrons but doesn't exists an infinite number of electrons'.

Originally posted by humy
within the very narrow context of his quote that mentions 'electrons', the possibly intended implied meaning involving 'there exists a finite number of electrons but doesn't exists an infinite number of electrons'.

I really can't see how you get that from what he said.

Originally posted by twhitehead
I really can't see how you get that from what he said.

"...Some mathematicians called ultra-finitists claim that there are no numbers larger than - for example - the number of electrons in the universe - numbers larger than that have no meaning and so do not really exist. Other mathematicians will happily accept that a number can be infinite. ..."
I assume the latter "...Other mathematicians will happily accept that a number can be infinite. ..." implies what he actually meant by the former " ...numbers larger than that ... " was " ...numbers larger than any finite number like that ... " i.e. he intended to imply infinity.
We could simply ask him.

Originally posted by humy
"...Some mathematicians called ultra-finitists claim that there are no numbers larger than - for example - the number of electrons in the universe - numbers larger than that have no meaning and so do not really exist. Other mathematicians will happily accept that a number can be infinite. ..."
I assume the latter "...Other mathematicians will happily accept th ...[text shortened]... any finite number like that ... " i.e. he intended to imply infinity.
We could simply ask him.

I don't know the argument the ultra-finitists use, but I'd guess it's along the lines of the following. I think the question of what I meant by "exists" earlier is basically the point they're making, in this kind of context when I say "exists" I normally mean exists in the way (perfect) circles exist. The concept clearly exists, and they're approximated in nature, but there are no actual perfect circles. What I assume the ultra-finitists are thinking is that there is a problem with using "exists" in this way. I think for them for the words "there exists" to have any meaning it actually does have to exist. So that because number is a term for a collective property of things for a number to exist one has to be able to point to a set of actual real world objects whose order is that number. Blueness is a property of a thing not a thing in itself so that were there no blue things there wouldn't be much point in the concept of blueness. So any number larger than the order of any set which is actually realized in nature isn't real. So if you start counting things, when you've run out of things to count then you've reached the biggest number there is because any larger number would apply to a set that doesn't exist so you can't make a sensible sentence with it. I used the number of electrons in the universe as an example of a big real set of things that can be counted. Numbers larger than that don't count anything that actually exist (is realized in nature) and so aren't real (here by real I mean denotes something that actually exists). Basically they are adjectives without any nouns to modify.

Originally posted by DeepThought
So if you start counting things, when you've run out of things to count then you've reached the biggest number there is because any larger number would apply to a set that doesn't exist so you can't make a sensible sentence with it.

Well they sound like nutters to me. Counting is not the only sensible way to use numbers in a sentence. Nobody could even count the atoms in the head of a pin, so the whole idea that counting relates to the usefulness of numbers at scale is ridiculous. I really don't see why such people would be counted as 'mathematics philosophers' or why you think the question is undecided.