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. -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- 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.
