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Topic: How do you prove that 2+2=4? Is it enough to consider 2 objects,
then 2 more then put them together and count them and get 4, or do you have
to resort to fancy-schmancy methods?

Replies: 8   Last Post: Nov 18, 2012 7:45 PM

 Messages: [ Previous | Next ]
 Charlie-Boo Posts: 1,635 Registered: 2/27/06
Re: How do you prove that 2+2=4? Is it enough to consider 2 objects,
then 2 more then put them together and count them and get 4, or do you have
to resort to fancy-schmancy methods?

Posted: Nov 17, 2012 9:23 PM

On Nov 16, 1:05 am, William Hale <bill...@yahoo.com> wrote:
> In article
>
>
>
>
>
>  Charlie-Boo <shymath...@gmail.com> wrote:

> > On Nov 16, 12:33 am, William Hale <bill...@yahoo.com> wrote:
> > > In article

>
> > >  Charlie-Boo <shymath...@gmail.com> wrote:
> > > > On Nov 15, 11:22 pm, donstockba...@hotmail.com wrote:
> > > > > Just askin.
>
> > > > Principia Mathematica BS says it takes 100 pages.  I don't know
> > > > anybody who has tried to explain what is going on there (everyone just
> > > > sits in awe at the number of pages), but Peano Arithmetic proves it in
> > > > a few steps where 2 is 0'' and 4 is 0'''', based on the axioms x+0=x
> > > > and x+y' = (x+y)' where x' is x+1 ("successor of x").

>
> > > > C-B
>
> > > You can view "Prinicpia Mathematica" at the link:
>
> > > incipiaMathematicaVolumeI#page/n95/mode/2up

>
> > > More is being done than just proving that "2+2=4". For example, logical
> > > propositions like "q implies (p implies q)" are being proved.

>
> > People always say "It takes 100 pages to prove 1+1=2!" as if it's
> > cool, contrary to Occam's Razor.  So how many pages are needed for the
> > ultimate derivation of 1+1=2 (or 2+2=4 whatever)?

>
> > C-B
>
> Principia Mathematica is not trying to just prove "2+2=4". I believe
> that its original purpose was to show that all of mathematics could be
> derived from just logical principals (which I think even Whithehead
> himself eventually rejected). Principia Mathematica is developing
> theorems about logic and sets. From there, it shows how standard
> mathematics like arithmetic might be derived. Principa Mathematica is
> starting from axioms that are much more primitive than Peano's axioms
> for the natural numbers,

You cannot prove the 2 axioms for addition because they are the
relation after having defined it and its properties, then you can
multiplication, and as a result when a+b=c we can prove that a+b=c.
This is because the relation a+b=c is recursive so truth coincides
with provability.

How do you think they derived the fact that x+0=x for all x? How many
pages does that take? Can you substantiate your claim?

It is just silly to brag about taking 100 pages to prove a trivial
fact that is nothing more than by definition of the numbers 1 and 2
(or 2 and 4.)

C-B

> so it takes longer to reach the point where you
> can prove "2+2=4".
>
> Here's a tinyURL for "Principia Mathematica":
>
> http://tinyurl.com/cgmfzfb
>
>

Date Subject Author
11/15/12 donstockbauer@hotmail.com
11/15/12 William Elliot
11/16/12 Charlie-Boo
11/16/12 William Hale
11/16/12 Charlie-Boo
11/16/12 William Hale
11/17/12 Charlie-Boo
11/18/12 harold james
11/18/12 William Hale