Hi Eric,

> >>0xf2f75022aa10b5ef6c69f2f59f34b03e26cb5bdb467eec82780
> >> didn't exist in this universe (with a very high probability, it
being a
> >> 512 bit number, generated from physical system noise) before I've
> >> generated it. Now it exists (currently, as a hex string (not
> necessarily
> >> ASCII) on many systems
> (...)
> > You admit a base 16 notation for numbers - which means you allow
numbers
> > to be written down that aren't "physically realized" by the
> > corresponding number of pebbles etc.  So much for talking about
pebbles
> > in your previous emails!
> 
> I think that it doesn't matter what base you choose to write down the
> number.
> It is an integer, therefore it is physically realizable *in
principle*. If
> you write
> '1aa3' in base 16, it means '6893' in base 10, which corresponds to a
> given
> number of pebbles. We may think that there is somehow more "reality"
in
> 6893
> in comparison to 1aa3, but they are both in the same footing, except
that
> we
> are more used to the first representation. Why would one claim that
the
> corresponding decimal representation of Eugen's 512-bit number has any
> more
> reality that the hexadecimal one?

I agree with everything you say, but did you really think I was making a
point because Eugen happened to use hex?!

You say the given integer exists because "it is it is physically
realizable *in principle*".  That sounds like the platonic view to me -
because the number is *not* actually physically realized and yet the
number is purported to have an independent existence.  Are you saying
otherwise?

I think any form of symbolic manipulation of numbers is implicitly using
the platonic view.  To say they spring into existence as they are
written down (which in any case only means they are realizable in
principle) just seems silly to me.

> I have no formed opinion on arithmetical realism, even though I tend
to
> accept that there is some external reality to the integers. But is the
> "reality" that is assigned to numbers of the same kind that is
assigned to
> their physical representation? Are we not discussing just words
without
> any
> meaning?

The Platonic view just says that every mathematical system free from
contradiction exists.  Ie if it can exist then it does exist.  There is
no need to talk about different types of reality.

- David 



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