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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 ]
 harold james Posts: 76 From: mission sd Registered: 11/8/10
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 18, 2012 9:13 AM

> On Nov 16, 1:05 am, William Hale <bill...@yahoo.com>
> wrote:

> > In article
> >

> groups.com>,

> >
> >
> >
> >
> >
> >  Charlie-Boo <shymath...@gmail.com> wrote:

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

> legroups.com>,

> >
> > > >  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
> >
> > >
> >http://archive.org/stream/PrincipiaMathematicaVolumeI
> > > > 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
> > 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
> definition of addition. You only prove something
> relation after having defined it and its properties,
> then you can
> derive further conclusions about it. Peano defines
> 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
> >
> >

>
>

I think this goes back to Russel and Whitehead taking over one hundred pages in their set theory book to prove 1+1 = 2

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