On Oct 6, 12:04 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 04 Oct 2011, at 21:59, benjayk wrote:

> > The point is that a definition doesn't say anything beyond it's  
> > definition.
>
> This is deeply false. Look at the Mandelbrot set, you can intuit that  
> is much more than its definition. That is the base of Gödel's  
> discovery: the arithmetical reality is FAR beyond ANY attempt to  
> define it.

Can't you also interpret that Gödel's discovery is that arithmetic can
never be fully realized through definition? This doesn't imply an
arithmetic reality to me at all, it implies 'incompleteness'; lacking
the possibility of concrete realism.

>
> > So, the number 17 is always prime because we defined numbers in the  
> > way. If
> > I define some other number system of natural numbers where I just  
> > declare
> > that number 17 shall not be prime, then it is not prime.
>
> No. You are just deciding to talk about something else.

I think Ben is right. We can just say that 17 is also divisible by
number Θ (17 = 2 x fellini, which is 8.5), and build our number system
around that. Like non-Euclidean arithmetic. Primeness isn't a reality,
it's an epiphenomenon of a particular motivation to recognize
particular patterns.

Craig

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