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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

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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
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article
<cb47a428-b69f-4666-9c12-d82b83a12326@4g2000yql.googlegroups.com>,
Charlie-Boo <shymathguy@gmail.com> wrote:

> On Nov 16, 12:33 am, William Hale <bill...@yahoo.com> wrote:
> > In article
> > <17eeb626-2a35-4177-ad68-92cf18be5...@c16g2000yqe.googlegroups.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 link:
> >
> > http://archive.org/stream/PrincipiaMathematicaVolumeI/WhiteheadRussel...
> > 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
Read 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?
donstockbauer@hotmail.com
11/15/12
Read Re: How do you prove that 2+2=4?
William Elliot
11/16/12
Read 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?
Charlie-Boo
11/16/12
Read 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?
William Hale
11/16/12
Read 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?
Charlie-Boo
11/16/12
Read 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?
William Hale
11/17/12
Read 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?
Charlie-Boo
11/18/12
Read 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?
harold james
11/18/12
Read 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?
William Hale

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