Re: Turing completeness of the functional paradigm?

On Thu, 14 Jul 2005, Tom wrote:
> Mr Elliot wrote:
>
> > > Actually, having pondered Peano's axioms a little more carefully, I
> > > have concluded that there seem to be no nospatial relations whatsoever.
> > >
> > What's a nospatial relation?
>
> Oh, I'm sorry. I meant a non-spatial relation really. Well, I meant
> that no such thing can ever be (i.e. something inexpressible in Peano's
> system, since as Godel showed through his numbering scheme, even FOL
> can be expressed this way). Is that so? No nonspatiality whatsoever?
>
Still confused about what you mean. Oh the wondrous wonders of double
negatives: Do not double negative not leave you untied in knots?

Peano's axioms allows a well ordering, indeed a sequential ordering, of
the integers. So in this sense, Peano's axioms do impart a spacial
orientation, that the integers can be strung along a line like
cloth pins on a cloth line.

> > > Please, is my thinking erroneous (again, on the absolute scale of
> > > things, and not implementationally)?
> > >
> > Erroneous is a complement. I think it attains unto erudite gibberish.
> Mr Elliot, I am very happy you kindly cared to criticize me. Thank you.
>
Tho a man in the street, but not in congress or the White-Lie House,
will call a spade a spade, a philosopher will attempt to wax eloquent
beyond the compression of even the most abstruse poets.

Philosophy's a joke. If it isn't, you're taking like too seriously.
.

Relevant Pages

  • Re: Turing completeness of the functional paradigm?
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