Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-standard)

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Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-standard)
De : ross.a.finlayson (at) *nospam* gmail.com (Ross Finlayson)
Groupes : sci.math
Date : 16. Nov 2024, 05:08:27
Autres entêtes
Message-ID : <XWKdnXoQbf4oh6X6nZ2dnZfqnPadnZ2d@giganews.com>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
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On 11/15/2024 06:52 PM, Ross Finlayson wrote:
On 11/15/2024 02:37 PM, Jim Burns wrote:
If it is true that
our domain of discourse is a model of ST+PQ
then it is true that
our domain of discourse holds a standard integer.model.
>
What is Mirimanoff's argument that
it doesn't exist?
>
Mirimanoff's? Russell's Paradox.
>
>
That "If it is true that our domain of discourse
is a model of ST+PQ then it is true that our
domain of discourse holds a standard integer.model"
is a pretty long axiom - why not just say
"infinity", that's the usual approach.
>
>
>
>
People want to learn philosophy and theory,
then it's like "well you have to study Kant,
he was considered the best". Then it's like,
"well what's his point?", and there's, "well,
he's got that there's in a thing in itself, and
there's a thing bigger than itself". "Well that
doesn't seem according to those words ..."
and it's like "yeah some people don't get it".
It's fair to say for some people "there's no
infinity", and that's sane, "logically consistent",
yet, it's also small. It's finger counting, and
anybody can do it, and it's sane, and it's small.
Then, we know since ancient times that there's
either Archimedean "infinitely-many and no
infinitely-grand", and that's sane, and then
there's Democritus, "infinitely-small and
makes one whole", that's sane, and then
there's Euclid, "it's axiomatized if necessary
between any two points is a shortest, straightest
line", that's sane.
Then it's like, "well I put together Euclid and
Democritus and Archimedes, now there's
infinitely-grand to be infinitely-small",
then it's like "well, now you see how Kant
is stood up as a great philosopher".
Then it's like "you point at Duns Scotus,
he read enough Aristotle to put together
Aristotle on Archimedes and Democritus
and Euclid because of Zeno, so, infinity is
in".
How can that all be sane? Well, it's simple,
it's called "resolving the paradoxes of logic",
and it involves a dialectic from either side
of "so" and "not so", "finite and infinite",
why there's a theory and philosophy at
all, that's sane.
Then, for people who haven't gone through
all that, then it's like, "well, there's Kant",
"according to Kant's idealism there's a sane
infinity even if it's non-standard". I.e. they
lean on that in case not having all together
made a theory for themselves from the axiomless
natural deduction how it's arrived at.
Then there's that, and it's like, "well how's that",
then it's like, "well, you see there's Hegel, and,
he refers to Kant, then points out there's nothing,
then he gives it a proper name, Nothing, and
then it's a reflection on points and their spaces of
geometry as continuous and infinite and words
and their spaces of algebra as finite and discrete
and then that's enough sane for pretty much all of it".

Date Sujet#  Auteur
3 Nov 24 * Re: Incompleteness of Cantor's enumeration of the rational numbers505Jim Burns
4 Nov 24 `* Re: Incompleteness of Cantor's enumeration of the rational numbers504WM
4 Nov 24  `* Re: Incompleteness of Cantor's enumeration of the rational numbers503Jim Burns
4 Nov 24   +* Re: Incompleteness of Cantor's enumeration of the rational numbers481WM
5 Nov 24   i`* Re: Incompleteness of Cantor's enumeration of the rational numbers480Jim Burns
5 Nov 24   i +* Re: Incompleteness of Cantor's enumeration of the rational numbers4Jim Burns
5 Nov 24   i i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (re-Vitali-ized)3Ross Finlayson
5 Nov 24   i i `* Re: Incompleteness of Cantor's enumeration of the rational numbers (re-Vitali-ized)2Ross Finlayson
5 Nov 24   i i  `- Re: Incompleteness of Cantor's enumeration of the rational numbers (re-Vitali-ized)1Chris M. Thomasson
6 Nov 24   i +* Re: Incompleteness of Cantor's enumeration of the rational numbers470WM
6 Nov 24   i i`* Re: Incompleteness of Cantor's enumeration of the rational numbers469Jim Burns
6 Nov 24   i i +* Re: Incompleteness of Cantor's enumeration of the rational numbers466WM
6 Nov 24   i i i`* Re: Incompleteness of Cantor's enumeration of the rational numbers465Jim Burns
6 Nov 24   i i i `* Re: Incompleteness of Cantor's enumeration of the rational numbers464WM
6 Nov 24   i i i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers463Jim Burns
7 Nov 24   i i i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers462WM
7 Nov 24   i i i    +* Re: Incompleteness of Cantor's enumeration of the rational numbers7Jim Burns
7 Nov 24   i i i    i`* Re: Incompleteness of Cantor's enumeration of the rational numbers6WM
7 Nov 24   i i i    i `* Re: Incompleteness of Cantor's enumeration of the rational numbers5Jim Burns
7 Nov 24   i i i    i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers4WM
7 Nov 24   i i i    i   +* Re: Incompleteness of Cantor's enumeration of the rational numbers2Jim Burns
7 Nov 24   i i i    i   i`- Re: Incompleteness of Cantor's enumeration of the rational numbers1WM
7 Nov 24   i i i    i   `- Re: Incompleteness of Cantor's enumeration of the rational numbers1Chris M. Thomasson
7 Nov 24   i i i    `* Re: Incompleteness of Cantor's enumeration of the rational numbers454Jim Burns
7 Nov 24   i i i     `* Re: Incompleteness of Cantor's enumeration of the rational numbers453WM
8 Nov 24   i i i      `* Re: Incompleteness of Cantor's enumeration of the rational numbers452Jim Burns
8 Nov 24   i i i       `* Re: Incompleteness of Cantor's enumeration of the rational numbers451WM
8 Nov 24   i i i        +* Re: Incompleteness of Cantor's enumeration of the rational numbers18Richard Damon
8 Nov 24   i i i        i`* Re: Incompleteness of Cantor's enumeration of the rational numbers17WM
8 Nov 24   i i i        i +* Re: Incompleteness of Cantor's enumeration of the rational numbers2Richard Damon
9 Nov 24   i i i        i i`- Re: Incompleteness of Cantor's enumeration of the rational numbers1WM
8 Nov 24   i i i        i `* Re: Incompleteness of Cantor's enumeration of the rational numbers14joes
8 Nov 24   i i i        i  +* Re: Incompleteness of Cantor's enumeration of the rational numbers7Moebius
8 Nov 24   i i i        i  i`* Re: Incompleteness of Cantor's enumeration of the rational numbers6Moebius
9 Nov 24   i i i        i  i `* Re: Incompleteness of Cantor's enumeration of the rational numbers5WM
9 Nov 24   i i i        i  i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers4Chris M. Thomasson
9 Nov 24   i i i        i  i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers3Moebius
10 Nov 24   i i i        i  i    `* Re: Incompleteness of Cantor's enumeration of the rational numbers2WM
10 Nov 24   i i i        i  i     `- Re: Incompleteness of Cantor's enumeration of the rational numbers1Chris M. Thomasson
9 Nov 24   i i i        i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers6WM
26 Dec 24   i i i        i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers5Chris M. Thomasson
26 Dec 24   i i i        i    `* Re: Incompleteness of Cantor's enumeration of the rational numbers4Moebius
27 Dec 24   i i i        i     `* Re: Incompleteness of Cantor's enumeration of the rational numbers3Chris M. Thomasson
27 Dec 24   i i i        i      `* Re: Incompleteness of Cantor's enumeration of the rational numbers2Moebius
28 Dec 24   i i i        i       `- Re: Incompleteness of Cantor's enumeration of the rational numbers1Chris M. Thomasson
8 Nov 24   i i i        +* Re: Incompleteness of Cantor's enumeration of the rational numbers (doubling-spaces)2Ross Finlayson
8 Nov 24   i i i        i`- Re: Incompleteness of Cantor's enumeration of the rational numbers (doubling-spaces)1Ross Finlayson
8 Nov 24   i i i        `* Re: Incompleteness of Cantor's enumeration of the rational numbers430Jim Burns
9 Nov 24   i i i         `* Re: Incompleteness of Cantor's enumeration of the rational numbers429WM
10 Nov 24   i i i          `* Re: Incompleteness of Cantor's enumeration of the rational numbers428Jim Burns
10 Nov 24   i i i           `* Re: Incompleteness of Cantor's enumeration of the rational numbers427WM
10 Nov 24   i i i            +- Re: Incompleteness of Cantor's enumeration of the rational numbers (exponential)1Ross Finlayson
10 Nov 24   i i i            +* Re: Incompleteness of Cantor's enumeration of the rational numbers389Jim Burns
11 Nov 24   i i i            i`* Re: Incompleteness of Cantor's enumeration of the rational numbers388WM
11 Nov 24   i i i            i `* Re: Incompleteness of Cantor's enumeration of the rational numbers387Jim Burns
11 Nov 24   i i i            i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers386WM
11 Nov 24   i i i            i   +* Re: Incompleteness of Cantor's enumeration of the rational numbers5FromTheRafters
12 Nov 24   i i i            i   i`* Re: Incompleteness of Cantor's enumeration of the rational numbers4WM
12 Nov 24   i i i            i   i +- Re: Incompleteness of Cantor's enumeration of the rational numbers1FromTheRafters
12 Nov 24   i i i            i   i `* Re: Incompleteness of Cantor's enumeration of the rational numbers2joes
12 Nov 24   i i i            i   i  `- Re: Incompleteness of Cantor's enumeration of the rational numbers1WM
12 Nov 24   i i i            i   +* Re: Incompleteness of Cantor's enumeration of the rational numbers2Jim Burns
12 Nov 24   i i i            i   i`- Re: Incompleteness of Cantor's enumeration of the rational numbers1WM
12 Nov 24   i i i            i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers378Jim Burns
12 Nov 24   i i i            i    `* Re: Incompleteness of Cantor's enumeration of the rational numbers377WM
12 Nov 24   i i i            i     `* Re: Incompleteness of Cantor's enumeration of the rational numbers376Jim Burns
12 Nov 24   i i i            i      `* Re: Incompleteness of Cantor's enumeration of the rational numbers375WM
13 Nov 24   i i i            i       +* Re: Incompleteness of Cantor's enumeration of the rational numbers2Jim Burns
13 Nov 24   i i i            i       i`- Re: Incompleteness of Cantor's enumeration of the rational numbers1WM
13 Nov 24   i i i            i       `* Re: Incompleteness of Cantor's enumeration of the rational numbers372Jim Burns
13 Nov 24   i i i            i        `* Re: Incompleteness of Cantor's enumeration of the rational numbers371WM
13 Nov 24   i i i            i         `* Re: Incompleteness of Cantor's enumeration of the rational numbers370Jim Burns
13 Nov 24   i i i            i          `* Re: Incompleteness of Cantor's enumeration of the rational numbers369WM
14 Nov 24   i i i            i           `* Re: Incompleteness of Cantor's enumeration of the rational numbers368Jim Burns
14 Nov 24   i i i            i            +* Re: Incompleteness of Cantor's enumeration of the rational numbers6FromTheRafters
14 Nov 24   i i i            i            i`* Re: Incompleteness of Cantor's enumeration of the rational numbers5Jim Burns
14 Nov 24   i i i            i            i +* Re: Incompleteness of Cantor's enumeration of the rational numbers3Ross Finlayson
15 Nov 24   i i i            i            i i`* Re: Incompleteness of Cantor's enumeration of the rational numbers (research)2Ross Finlayson
15 Nov 24   i i i            i            i i `- Re: Incompleteness of Cantor's enumeration of the rational numbers (research)1Ross Finlayson
14 Nov 24   i i i            i            i `- Re: Incompleteness of Cantor's enumeration of the rational numbers1FromTheRafters
14 Nov 24   i i i            i            `* Re: Incompleteness of Cantor's enumeration of the rational numbers361WM
14 Nov 24   i i i            i             +* Re: Incompleteness of Cantor's enumeration of the rational numbers291Jim Burns
15 Nov 24   i i i            i             i`* Re: Incompleteness of Cantor's enumeration of the rational numbers290WM
15 Nov 24   i i i            i             i +* Re: Incompleteness of Cantor's enumeration of the rational numbers2joes
15 Nov 24   i i i            i             i i`- Re: Incompleteness of Cantor's enumeration of the rational numbers1WM
15 Nov 24   i i i            i             i `* Re: Incompleteness of Cantor's enumeration of the rational numbers287Jim Burns
15 Nov 24   i i i            i             i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers286WM
15 Nov 24   i i i            i             i   `* Re: Incompleteness of Cantor's enumeration of the rational numbers285Chris M. Thomasson
16 Nov 24   i i i            i             i    +- Re: Incompleteness of Cantor's enumeration of the rational numbers1Moebius
16 Nov 24   i i i            i             i    +* Re: Incompleteness of Cantor's enumeration of the rational numbers280Moebius
16 Nov 24   i i i            i             i    i+- Re: Incompleteness of Cantor's enumeration of the rational numbers1Moebius
16 Nov 24   i i i            i             i    i+* Re: Incompleteness of Cantor's enumeration of the rational numbers2Moebius
16 Nov 24   i i i            i             i    ii`- Re: Incompleteness of Cantor's enumeration of the rational numbers1WM
16 Nov 24   i i i            i             i    i`* Re: Incompleteness of Cantor's enumeration of the rational numbers276Chris M. Thomasson
16 Nov 24   i i i            i             i    i `* Re: Incompleteness of Cantor's enumeration of the rational numbers275Chris M. Thomasson
16 Nov 24   i i i            i             i    i  +* Re: Incompleteness of Cantor's enumeration of the rational numbers2Chris M. Thomasson
16 Nov 24   i i i            i             i    i  i`- Re: Incompleteness of Cantor's enumeration of the rational numbers1Moebius
16 Nov 24   i i i            i             i    i  +* Re: Incompleteness of Cantor's enumeration of the rational numbers13FromTheRafters
16 Nov 24   i i i            i             i    i  i`* Re: Incompleteness of Cantor's enumeration of the rational numbers12Chris M. Thomasson
16 Nov 24   i i i            i             i    i  i +* Re: Incompleteness of Cantor's enumeration of the rational numbers2Moebius
16 Nov 24   i i i            i             i    i  i i`- Re: Incompleteness of Cantor's enumeration of the rational numbers1Moebius
16 Nov 24   i i i            i             i    i  i +* Re: Incompleteness of Cantor's enumeration of the rational numbers7Moebius
17 Nov 24   i i i            i             i    i  i `* Re: Incompleteness of Cantor's enumeration of the rational numbers2FromTheRafters
16 Nov 24   i i i            i             i    i  `* Re: Incompleteness of Cantor's enumeration of the rational numbers259Moebius
16 Nov 24   i i i            i             i    +- Re: Incompleteness of Cantor's enumeration of the rational numbers1Moebius
16 Nov 24   i i i            i             i    `* Re: Incompleteness of Cantor's enumeration of the rational numbers2Moebius
14 Nov 24   i i i            i             `* Re: Incompleteness of Cantor's enumeration of the rational numbers69Jim Burns
10 Nov 24   i i i            `* Re: Incompleteness of Cantor's enumeration of the rational numbers36Chris M. Thomasson
6 Nov 24   i i `* Re: Incompleteness of Cantor's enumeration of the rational numbers (opinions)2Ross Finlayson
6 Nov 24   i `* Re: Incompleteness of Cantor's enumeration of the rational numbers5WM
4 Nov 24   `* Re: Incompleteness of Cantor's enumeration of the rational numbers21Chris M. Thomasson

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