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 <vir...@ligriv.com> wrote:
>> In article
>> <39dd320b-1f56-4cf7-bb03-f0f634420...@l5g2000yqe.googlegroups.com>,
>>
>> WM <mueck...@rz.fh-augsburg.de> wrote:

>>> On 24 Mrz., 20:39, Virgil <vir...@ligriv.com> 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.


http://plato.stanford.edu/entries/logic-free/

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.


http://en.wikipedia.org/wiki/Idealism#Idealism_in_the_philosophy_of_science

http://en.wikipedia.org/wiki/Philosophy_of_science#Scientific_realism_and_instrumentalism

http://en.wikipedia.org/wiki/Scientific_realism

http://en.wikipedia.org/wiki/Instrumentalism


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