Date: Mar 17, 2013 8:20 PM
Subject: Re: Matheology § 224
On 3/17/2013 2:57 PM, Virgil wrote:
> In article
> WM <firstname.lastname@example.org> wrote:
>> On 17 Mrz., 00:25, Virgil <vir...@ligriv.com> wrote:
>>>>> Can WM provide any definition for natural numberss which doe not state,
>>>>> or at least imply, that every natural must have a successor natural?
>>>> Numbers are creations of the mind. Without minds there are no numbers.
>>> Which is not a relevant answer.
>> By definition of a matheologian.
> Which is a non-response to my original question:
> Can WM provide any definition for natural numberss which doe not state,
> or at least imply, that every natural must have a successor natural?
> WM's failure to respond positively I take as a "no" answer.
>>> Can WM provide an definition for natural numbers which doe not state,
>>> or at least imply, that every natural must have a successor natural?
>> It is always stated or at least implicitly assumed in classical
>> mathematics that we are able to add 1. In reality this is an erroneous
>> assumption as has been shown in MatheRealism.
> Unless you can produce such a natural, which even in your alleged
> "mathrealism" you have not done, your claim is, as always, unfounded.
>>>> you are not able to write aleph_0 digits of a real numbers like 1/9.
>>> So what? There are lot of things in mathematics one cannot do, but that
>>> should not keep us from doing what we can do, the way you would limit us.
>> But the claim of matheology is that all digits exist and can be
>> determined - for instance all digits of pi.
> I do not make the claim that all the digits of the number pi can be
> found, but I do claim that the number pi has a definition, as do
> infinitely many other reals whose exact decimal representations cannot
> be found.
> E. g., the square roots of each of the infinitely many primes are all
> defined, though none can be given exactly as decimals.
And, necessary to the proof of an algebraically closed field.
But when one 'knows' such things 'by reality' there is
no need of definition or proof.