Bruno Marchal wrote:
> Le 06-juil.-06, à 23:32, 1Z a écrit :
> >
> >
> > Bruno Marchal wrote:
> >
> >> Remember that comp relies on arithmetical platonism.
> >
> > Your version does. Computationalism is standardly
> > "the thesis that cognition is computation."
> Could you define or explain "computation" without believing that the
> relations among numbers are independent of you?

I can believe that relations between numbers are epistemically
independent of me -- I cannot will them to be different -- without
believing they exist ontologically.

Furthermore the /locus classicus/ for computation is Turing's work,
which defines it in terms an idealisation of humans performing
pencil-and-paper procedures.

> >
> > In other words, your argument really has two premises -- AR and
> > (standard) computationalism.
> Standard comp, indeed, does not make AR explicit. But as Dennett and
> others standard comp cognitivists agree on, comp needs Church thesis
> (if only to be able to take into account negative limitative result),
> and church thesis need AR.

Why do you think the Curch thesis needs AR ?
Which misunderstanding are you subsribing to ? [*]

> I just make this explicit, if only because I
> got a sufficiently counter-intuitive result.
> Remember that AR is just the presupposition that arithmetical truth is
> not a personal construction. Put in anoher way, AR is just the non
> solipsistic view of elementary math.

Well, if it is just an epistemological claim, it is not
going to provide you with a universal dovetailer.

> > You have bundled them together into
> > "comp".
> Just to make some point clearer. I have not yet met someone who does
> not believe in AR.

Oh yes you have !

>  (I have met mathematicians who does not believe in
> AR during the week-end, and I have met some philosopher who pretend not
> believing in AR, but who does.
> Bruno



Misunderstandings of the Thesis

A myth seems to have arisen concerning Turing's paper of 1936, namely
that he there gave a treatment of the limits of mechanism and
established a fundamental result to the effect that the universal
Turing machine can simulate the behaviour of any machine. [...]

Turing did not show that his machines can solve any problem that can be
solved "by instructions, explicitly stated rules, or procedures", nor
did he prove that the universal Turing machine "can compute any
function that any computer, with any architecture, can compute". He
proved that his universal machine can compute any function that any
Turing machine can compute; and he put forward, and advanced
philosophical arguments in support of, the thesis here called Turing's
thesis. But a thesis concerning the extent of effective methods --
which is to say, concerning the extent of procedures of a certain sort
that a human being unaided by machinery is capable of carrying out --
carries no implication concerning the extent of the procedures that
machines are capable of carrying out, even machines acting in
accordance with 'explicitly stated rules'. For among a machine's
repertoire of atomic operations there may be those that no human being
unaided by machinery can perform.

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