Date: Mar 25, 2013 1:40 PM
Author: fom
Subject: Re: Matheology § 224

On 3/25/2013 7:07 AM, WM wrote:
> On 25 Mrz., 00:49, Virgil <> wrote:
>> In article
>> <>,
>> WM <> wrote:

>>> On 24 Mrz., 20:39, Virgil <> wrote:
>>>> But if David had left out the world "all", and said merely
>>>> "In fact, Aleph_0 lines are required
>>>> (necessary sufficient) to contain all of the naturals."
>>>> then David would have been correct, since EVERY set of aleph_0 lines is
>>>> sufficient but no set of less than aleph_0 lines is sufficient.

>>> We know your statements of faith. But where do you get aleph_0 lines
>>> without using lines of the infinite set of aleph_0 lines that, as
>>> provable in mathematics, are not sufficient?

>> Which infinite sets of lines does WM claim are provably not sufficient?

> All FISONs are not sufficient, because forall F in the set of FISONs:
> There are infinitely many natural numbers not covered by F and all its
> predecessors and all its followers.

That is why 'all' means something different from 'one'.

That is the genius of what happened in the nineteenth century.
Mathematics was seen to be a form of logic that could refer to
parts of individuals as individuals in contrast to the classical
logic that preceded that period.

>> THEOREM: To have a subset of the infinite set of lines(FISONs) whose
>> union is |N, it is both necessary and sufficient that that subset of
>> lines also be infinite.

> Nonsense. All FISONs cannot be sufficient, since no FISON is
> necessary.
> Corollary: To catch a unicorn it is both necessary and sufficient to
> ask an infinity of horses to help.

There is a logic for that.

By the way, you have yet to justify any of your philosophical
statements concerning the "reality" that grounds your philosophy
of mathematics.

After all, "proof by reality" is not belief. Is that not
the basis of your criticisms of classical mathematics?