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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 ]
 William Hale Posts: 49 Registered: 5/2/12
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 16, 2012 1:05 AM

In article
Charlie-Boo <shymathguy@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, 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