Re: Turing completeness of the functional paradigm?



Tom wrote:
>
> My intention was to say that all notions non-definable within Peano's
> system are a mistake.

PA does not define a unique notion of natural numbers. No formalism
ever will.

> In pure logic there is even no time.

One can imagine pure logic with or without time. In logic with
awareness, there is time.
When Brouwer cosiders basic propositional reasoning, he claims there
are states of affairs in violation of pv~p:

http://plato.stanford.edu/entries/brouwer/weakcounterex.html

If '*p' represents a weak negation meaning 'it is not known that p', a
classical logician will regard *p as an empty placeholder akin to an
unsolved variable in an algebraic equation, but we can also regard *p
as the state of affairs in violation of the supposition that p or ~p is
the state of affairs.

.

Relevant Pages

  • Re: Time to sign off - too much trash
    ... >> Given the current sad state of affairs with regard to the ... >> proliferation of postings and new subject lines which ...
    (rec.radio.amateur.policy)
  • Re: Time to sign off - too much trash
    ... > Given the current sad state of affairs with regard to the ... > proliferation of postings and new subject lines which ...
    (rec.radio.amateur.policy)
  • Re: Death on my local TT course
    ... No extended pain/goodbyes/getting your affairs in order. ... worst for the family who find someone suddenly gone, feelings of guilt and so much unsaid or undone. ... "I did make a mistake once - I thought I'd made a mistake but I hadn't" Anon ...
    (uk.rec.cycling)
  • Re: When did you listen?
    ... Given the current state of affairs with regard to laws, regulations, ...
    (borland.public.delphi.non-technical)