Re: Turing completeness of the functional paradigm?

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?

I am sorry again. I mean that there are only spatial relations.

> 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.

I see. Still, it seems that they impart nothing else.

> > > > 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.

They all seem to be merely Peano sequences.

> Philosophy's a joke.

"The formalist conception of mathematics is free from metaphysical
bias, and is therefore compatible with any sort of philosophy (/
without the metaphysical bias which is a joke /). It is the only
conception so far proposed that has that character."

-- Haskell Curry, Outlines of a formalist philosophy of
mathematics

Which, imho, is precisely to say: mathematical = formal = symbolic =
geometrical = spatial = Peano like. Which in turn, is precisely to say,
just for a brief example, if I may, a (Peano) sequence is true of a
(Peano) sequence iff they are isomorphic, a correspondence theory of
truth Tarski advocated. Everything else seems to be a joke, like you
kindly remarked.

> If it isn't, you're taking like too seriously.

Yes, I am taking it all (too) seriously.

"The main problem of mathematics is the notion of truth." -- H.C.,
Outlines...

The assumption in question is extremely far reaching. It is so serious,
and it reaches so far, that I am incapable of making it on my own. I'd
rather get nowhere then astray. I am sorry.

Mr Elliot, please, did I ever tell you how GREAT this NG is?

Thank you.
Tom

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