Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

On 10/11/2024 11:02 AM, Jim Burns wrote:

On 10/11/2024 7:06 AM, Richard Damon wrote:

On 10/10/24 11:19 PM, Chris M. Thomasson wrote:

On 10/10/2024 6:38 PM, Richard Damon wrote:

On 10/10/24 2:32 PM, WM wrote:

>

If not all do exist,
te doubling yields larger natnumbers,
some of which have not existed before.
But that means potential infinity.

>
But there aren't any natural numbers that
have not existed before. That is just showing that
your "actual infinity" is a finite set that you grabbed on the way
to infinity,
but didn't get there yet.

>

Actual infinity means
you need to wait until you get there.
The problem is
finite creatures can't do that,
so can't handle actual infinity.

>

What do you mean?
I can say all the natural numbers.
That was pretty fast for all of them. ;^)

>
Which names the set,
but not actually list the contents of that set.

>
Is a set
without a finite list  but
with a finite description
potential or actual?
>
It looks to me as though the consensus is:
we don't care what the answer is.
>
We have a description of ℕ and its elements,
free of mentions of 'potential' and 'actual'.
 From its description,
we can reason about it and its elements.
"Potential ℕ" vs. "actual ℕ" leaves unchanged
which claims we reason to.
>
I see them as in the same vein as
weekday.mathematics and Sunday.mathematics.[1]
A distinction without a difference.
>
And I see that indifference as there _by design_
It is why unwelcome mathematical results are accepted
not because mathematicians are paragons of rectitude
(no offense)
but because there is no weasel.ability in mathematics.
>
⎛ Not everyone appreciates that lack of weasel.ability.
⎝ Those who don't self.select to be non.mathematicians.
>
[1]
⎛
⎜ Most writers on the subject seem to agree that
⎜ the typical “working mathematician” is
⎜ a Platonist on weekdays and a formalist on Sundays.
⎜ That is, when he is doing mathematics,
⎜ he is convinced that
⎜ he is dealing with an objective reality
⎜ whose properties he is attempting to determine.
⎜ But then, when challenged to give
⎜ a philosophical account of this reality,
⎜ he finds it easiest to pretend that
⎜ he does not believe in it after all.
⎝
https://core.ac.uk/download/pdf/82047627.pdf
Some Proposals for Reviving the Philosophy of Mathematics
REUBEN HERSH
Department of Mathematics, University of New Mexico,
Albuquerque, New Mexico 87131
>
>

I'm familiar with that you tend to repost that,
yet platonism and formalism don't necessarily
contradict nor preclude each other, with regards
to neither necessarily being fictionalism.
https://www.youtube.com/watch?v=PnO-eLyGjBw&list=PLb7rLSBiE7F4eHy5vT61UYFR7_BIhwcOY&index=37&t=1065s
Mathematics is not "pretend", though it's fair to
say that humans are finite creatures then though
there's that we conceive the limitless and infinite,
that there is an object sense for reason for a real
mathematical infinity in the _de re_ and _de res_
and _de natura_, each. Then, that may be a conceit,
and it may be pretentious, of each being his or her
own _science_, yet that's conscious, and it's in
accords to some ultimate ontological commitment to
the _truth_ of the mathematical _facts_, not "make-believe".
It's kind of like the old "great minds think alike /
the greatest minds think the same".
Recall the discussions here like "Aristotle agrees:
potential is actual and actual is potential, and it's
easy to bring the same argument and assert the same
equivalency", or, for example, "Zeno demands you
account what side of the bridge you are on".
Or, for example, "Cantor happily considered counting
backward until a conundrum led him to quit and throw
away the idea of a universe", or "Russell quite torpedoed
Frege then wished it away and won't accept his own
criticism".
So, you can go all the way back to Anaximander and get
into the limitless then as with regards to Aristotle
about the actual, infinite, then that at least these
days, I can always refer you to Goedel who _assures_
you that your ordinary fragment of theory is at best
incomplete, and thusly that there are relations about
it and relations around it, and, that Cohen _assures_
you that there are ordinals and cardinals and cardinals
and ordinals and quite all more an extra-ordinary than
that blessed by the Russell's retro-thesis, who, though,
not all worship.
And some find profane, ....