Re: Solidity is degree of justification (was: Mirror neurons at autopsy)

On 26 Dec 2012, at 13:56, David Deutsch wrote:

>
> On 24 Dec 2012, at 09:07, Bruno Marchal <[email protected]> wrote:
>
> >
> > On 23 Dec 2012, at 20:13, David Deutsch wrote:
> >
> >> an important (and
> >> unrelated) philosophical error, the one that is currently called
> >> 'justificationism', namely that knowledge is that which can be
> >> justified as true, or likely to be true, etc.
> >>
> > The Theaetetus theory of knowledge is "justified *and* true", not
> > "justified as true", as this is impossible.
>
> I stand corrected.
>
> > The nature of the "and" is let unknown, and with comp can be shown
> > unknowable.
> >
> > It gives an instance of the "classical theory" of knowledge, which  
> is
> > the theory that knowledge is well described by the modal logic S4,
> > that is, with Kp = I know p,: Kp -> p, Kp -> KKp, K(p->q) -> (Kp ->
> > Kq); with the modus ponens, the classical tautologies, and the
> > necessitation rule: p => Kp.
>
> I (and, I think, Popper) would say that the attribute expressed by  
> that predicate K cannot be possessed (or usefully approximated) by a  
> physical object with respect to scientific theories p, even though  
> it can be defined formally.
>
I think this too.




> Hence he uses the term 'knowledge' to refer to a different  
> attribute, one which does not require a knowing subject but which,  
> apart from that, corresponds at least as closely to the commonsense  
> meaning of the term as K does.
>

Yes. In fact, he takes a sort of provability predicate. Except that it  
can be a very simple one in case we want attribute that "K" to things  
like genes and thermostats. But I have no (big) problem with that.



>
> In my view, formalising *that* conception of knowledge is a task for  
> the future, equivalent to achieving Artificial Intelligence.
>
In my view the riddle has been solved in the past, by Theaetetus (and  
by the old Wittgenstein and probably many others).
It consists to add true, to the common sense definition.

If we do that mathematically with a notion of belief "Bp" defines as  
such that elementary arithmetic is believed, and by working on machine  
extending consistently those beliefs, we can define, or more exactly  
meta define knowledge, by defining knowledge explicitly on each  
(arithmetical) proposition p, by Bp & p. In that case it can be proved  
that it will obey to the classical theory of knowledge described in  
the quote (actually it will even be axiomatized completely with one  
more formula, the one by Grzegorczyk     B(B(p->Bp)->p)->p, which  
introduce somehow an antisymmetry in the possible evolution of the  
knowledge).

(Bp & p) is not definable in the language of the machine. We might try  
with Bp and true(p), but "true about the machine" cannot be defined  
*in* the language of the (ideally correct) machine, by a result of  
Tarski. Knowledge cannot either by a result of Scott and Montague, but  
we can still work out "meta definition", and understand why the  
machine cannot defined its own knowledge predicate, and still have one  
as seen "from outside" and "assuming it correct", which is impossible  
in any practical situation.

I think that "artificial intelligence" is achieved, and that a theory  
like Peano Arithmetic is already conscious, despite being a bit dumb  
and rather disconnected from our reality. Today, to have a talk with  
her, we still need to do hard work and learn technic, but this is an  
interface problem. Universal machine, especially those "sufficiently  
rich" to prove their own incompleteness theorem are already conscious.  
it is us who are still a bit limited, by billions years of "nature  
prejudices" and who take the time to notice. But women can vote since  
recently, so there is hope that *we* can still develop our mind and  
lessen our prejudices.

Bruno



>
> -- David Deutsch
>
> 

http://iridia.ulb.ac.be/~marchal/





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