On 10 Jun 2014, at 22:39, John Mikes wrote:
Irrational number?
Are 'angels' rational? if not you cannot count them anyway.
JM
Oops I miss this post, sorry John. (and thanks to Clark for reminding
it).
The answer is simple. In arithmetic, rational machines and rational
angels are a minority.
I identify roughly the machines to the sigma_1 set (and the universal
machine with the sigma_1 complete set), and I identify the angels with
sigma_i or pi_i complete sets. Those are mathematical being which
cannot be emulated by machines, and their abounds in the arithmetical
relation.
I recall that a sigma_5 arithmetical proposition is one equivalent
with a proposition of the shape
ExAyEzAtEr such that P(x,y,z,t,r)
With P a decidable predicate.It says that it exists a number x such
that for all number y it exists a number z such that for all number t
it exists a number r such that it is the case that P(x,y,z,t,r).
A sigma_5 complete entity is quite a "divine" being knowing much than
us, which might only be sigma_1 complete.
Yet a pi_5 complete being and a sigma_6 complete being know *much*
more than sigma_5 complete one.
Arithmetical truth contains all of that kinds.
Those set are quite "reasonable", or rational, but with a lose
definition of believer machine, and angels, have no reason to be
rational, and this can depend on the choice of definition of rational
(obeying which logics?).
Bruno
On Mon, Jun 9, 2014 at 9:59 PM, LizR <[email protected]> wrote:
Ah yes, that gives us another definition - the ability to do things
that aren't optimal / rational. I knew there were more definitions
lurking around, probably a lot of them!
(Plus we have yet to decide how many angels can dance on a pinhead.
I'm in favour of an irrational number...)
On 10 June 2014 13:42, Russell Standish <[email protected]> wrote:
On Tue, Jun 10, 2014 at 12:49:01PM +1200, LizR wrote:
> Depends what you mean by "free will".
>
> Reasoning based on past experience is one good definition (by which
> criterion a computer can have free will too, and without being
conscious).
>
> Another good definition is "first person unpredictability" (not
knowing
> what you will do next).
>
> Presumably random noise in the brain will influence a random
decision (i.e.
> one where there is no reason to prefer one outcome over another).
That
> appears to be what is happening in this experiment. I'm not sure if
> everyone would agree this is "free will".
>
I don't everybody will ever agree about "free will". Whilst I don't
fully agree with JC that "free will" is a meaningless string of ASCII
characters, I would agree that a lot of "hot air" is generated about
free will.
I personally don't think rationality makes for a good definition of
free
will. A perfectly rational being is constrained to always choose the
optimal course of action. Such a will can hardly be "free".
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