Russell Standish wrote:
On Fri, Jun 12, 2015 at 03:40:48PM +1000, Bruce Kellett wrote:
This is a false distinction. Arithmetical 'truth' is no more
fundamental or final than physical truth. Arithmetic is, after all,
only an axiomatic system. We can make up an indefinite number of
axiomatic systems whose theorems are every bit as 'independent of
us' as those of arithmetic. Are these also to be accepted as 'really
real!'? Standard arithmetic is only important to us because it is
useful in the physical world. It is invented, not fundamental.
Yes - but comp actually doesn't depend on standard arithmetic
either. What it depends on is the Church-Turing thesis to define what
is meant by computation. Standard arithmetic is convenient, as it
contains CT-thesis universal computers within it, but not
essential. Any other ontology supporting the CT-thesis will do.
The assumption of CT-thesis is not trivial, however. As David Deutsch
would point out, one could assume the Hilbert Hotel, and get a form of
hypercomputation. DD argues that lack of hypercomputers around us is
evidence that physical reality cannot support more powerful
computational models that the Turing one, but a more neutral way of
putting it is to say that ontology (which may or may not be physical)
cannot support more powerful models, effectively demarcating parts of
Platonia.
That is an interesting observation. One formulation of the CT thesis is
that a Turing machine can do any calculation that can be done with
pencil and paper. This relates Turing computations quite strongly to
what is possible in the physical world. Deutsch's observation about
hypercomputation is interesting here -- apart from some speculative
possibilities in rotating black holes, hypercomputation is not possible
in this physical universe. So is comp actually delineated by the
physical world? And not as /a priori/ as might otherwise have been
thought? The physical world determines comp, and not the reverse?
Bruce
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
