Ultrafinitism: Infinities, both potential and actual, do not exist and are not acceptable in mathematics. Finitism: Potential infinities exist and are acceptable in mathematics. Actual infinities do not exist and we must limit or eliminate their role in mathematics. Predicativism: We may accept the natural numbers, but not the real numbers, as a completed infinite totality.. Quantification over ℕ is acceptable, but quantification over ℝ, or over the set of all subsets of ℕ, is unacceptable. Infinitism: Actual infinities of all kinds are welcome in mathematics, so long as they are consistent and intuitively natural. Of these four positions, the finitist one seems to be the most objective. [...] The real world contains many potential infinities. [...] However, the real world does not appear to contain any actual infinities. For this reason, actual infinities are suspect. In order to maintain objectivity in mathematics, it seems necessary to limit the use of actual infinities. We introduce them only as "convenient fictions". [...] There is no clear way to integrate ZFC-based mathematics with the rest of human knowledge. The unity of mathematics is good, but the unity of human knowledge would be even better. [...] both set theory and religious faith can claim to be in a "strong" position vis a vis skeptics, by avoiding reliance on facts which can be questioned. I reject such claims on grounds of lack of objectivity. [S.G. Simpson: "Potential versus actual infinity: Insights from reverse mathematics" (2015)]

Regards, WM

måndag 29 november 2021 kl. 10:30:17 UTC+1 skrev WM:
> Ultrafinitism: Infinities, both potential and actual, do not exist and are not acceptable in mathematics. Finitism: Potential infinities exist and are acceptable in mathematics. Actual infinities do not exist and we must limit or eliminate their role in mathematics. Predicativism: We may accept the natural numbers, but not the real numbers, as a completed infinite totality. Quantification over ℕ is acceptable, but quantification over ℝ, or over the set of all subsets of ℕ, is unacceptable. Infinitism: Actual infinities of all kinds are welcome in mathematics, so long as they are consistent and intuitively natural. Of these four positions, the finitist one seems to be the most objective. [...] The real world contains many potential infinities. [...] However, the real world does not appear to contain any actual infinities. For this reason, actual infinities are suspect. In order to maintain objectivity in mathematics, it seems necessary to limit the use of actual infinities. We introduce them only as "convenient fictions". [...] There is no clear way to integrate ZFC-based mathematics with the rest of human knowledge. The unity of mathematics is good, but the unity of human knowledge would be even better. [...] both set theory and religious faith can claim to be in a "strong" position vis a vis skeptics, by avoiding reliance on facts which can be questioned. I reject such claims on grounds of lack of objectivity. [S.G. Simpson: "Potential versus actual infinity: Insights from reverse mathematics" (2015)]
>
> Regards, WM
why do you keep citing shit instead of actually learning logic?

On 29/11/2021 10:30, WM wrote:

> Infinitism: Actual infinities of all kinds are welcome in mathematics,
> so long as they are consistent and intuitively natural.

So long as *logically valid*, which is what and all mathematics needs.

> Of these four positions, the finitist one seems to be the most objective. [...]
> The real world contains many potential infinities. [...]
> However, the real world does not appear to contain any actual infinities.

Nope: for a starter, that is forgetting all abstract constructions, in
science and not only. It is also forgetting things that have been
meanwhile obliterated, from the infinity of Cosmos to that of Man and
everything. But, back to Earth, the very answer to Achilles and the
Tortoise *is* *already* *infinitary*!

> We introduce them only as "convenient fictions". [...]

Rather call yourself a "naturalist" of the naive and misplaced kind.

> There is no clear way to integrate ZFC-based mathematics with the rest of human
> knowledge.

It rather appears that standard mathematics is broken re *anything*
infinite, potential or otherwise.

> I reject such claims on grounds of lack of objectivity. [S.G. Simpson: "Potential
> versus actual infinity: Insights from reverse mathematics" (2015)]

I'd suggest you reconsider.

Julio

WM wrote:

> Ultrafinitism: Infinities, both potential and actual, do not exist and
> are not acceptable in mathematics. Finitism: Potential infinities exist
> and are acceptable in mathematics. Actual infinities do not exist and we
> must limit or eliminate their role in mathematics. Predicativism: We may

they are. The stupidity of people on this planet is infinite:

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Julio Di Egidio wrote:

> On 29/11/2021 10:30, WM wrote:
>
>> Infinitism: Actual infinities of all kinds are welcome in mathematics,
>> so long as they are consistent and intuitively natural.
>
> So long as *logically valid*, which is what and all mathematics needs.

the monarchy, at the recent meeting, said openly that countries on this
planet, have to introduce *militarized_forces*, to curve the carbon
emission to zero. The carbon emission is you.

PROF. SUCHARIT BHAKDI: THE COVID "VACCINES" WERE DESIGNED TO FAIL
https://www.brighteon.com/39255c9d-a5be-4fa2-a212-b0afd16a43e1

On Monday, November 29, 2021 at 4:30:17 AM UTC-5, WM wrote:

> Quantification... over the set of all subsets of ℕ, is unacceptable....

What problems if any arise from the well-ordering principle that, for all subsets S of N, if S is non-empty, then there exists as least element in S? (Hint: NONE).

Dan

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On Monday, November 29, 2021 at 1:30:17 AM UTC-8, WM wrote:
> Ultrafinitism: Infinities, both potential and actual, do not exist and are not acceptable in mathematics. Finitism: Potential infinities exist and are acceptable in mathematics. Actual infinities do not exist and we must limit or eliminate their role in mathematics. Predicativism: We may accept the natural numbers, but not the real numbers, as a completed infinite totality. Quantification over ℕ is acceptable, but quantification over ℝ, or over the set of all subsets of ℕ, is unacceptable. Infinitism: Actual infinities of all kinds are welcome in mathematics, so long as they are consistent and intuitively natural. Of these four positions, the finitist one seems to be the most objective. [...] The real world contains many potential infinities. [...] However, the real world does not appear to contain any actual infinities. For this reason, actual infinities are suspect. In order to maintain objectivity in mathematics, it seems necessary to limit the use of actual infinities. We introduce them only as "convenient fictions". [...] There is no clear way to integrate ZFC-based mathematics with the rest of human knowledge. The unity of mathematics is good, but the unity of human knowledge would be even better. [...] both set theory and religious faith can claim to be in a "strong" position vis a vis skeptics, by avoiding reliance on facts which can be questioned. I reject such claims on grounds of lack of objectivity. [S.G. Simpson: "Potential versus actual infinity: Insights from reverse mathematics" (2015)]
>
> Regards, WM

Modern is something that is always in the new now...
We really want to get past it instead.. imagine future worlds

Our Modern does not make it objective.
Critical thinking does...