On 18 Aug 2011, at 20:02, meekerdb wrote:
On 8/18/2011 10:50 AM, Bruno Marchal wrote:
On 18 Aug 2011, at 19:05, meekerdb wrote:
On 8/18/2011 7:24 AM, Bruno Marchal wrote:
I agree with that sentiment. That's why I often try to think of
consciousness in terms of what it would mean to provide a Mars
Rover with consciousness. According to Bruno the ones we've
sent to Mars were already conscious, since their computers were
capable of Lobian logic.
I don't remember having said this. I even doubt that Mars Rover
is universal, although that might be serendipitously possible
(universality is very cheap), in which case it would be as
conscious as a human being under a high dose of salvia (a form of
consciousness quite disconnected from terrestrial realities). But
it is very probable that it is not Löbian. I don't see why they
would have given the induction axioms to Mars Rover (the
induction axioms is what gives the Löbian self-referential power).
You didn't say it explicitly. It was my inference that the
computer's learning algorithms would include induction.
Yes, and that makes them universal. To make them Löbian, you need
them to not just *do* induction, but they have to believe in
induction.
Roughly speaking. If *i* = "obeys the induction rule", For a UM
*i* is true, but that's all. For a LUM is is not just that *i* is
true, but *i*is believed by the machine. For a UM *i* is true but
B*i* is false. For a LUM we have both *i* is true, and B*i* is true.
Of course the induction here is basically the induction on
numbers(*). It can be related to learning, anticipating or doing
inductive inference, but the relation is not identity.
(*) The infinity of axioms: F(0) & for all n (P(n) -> P(s(n)) ->.
for all n P(n).
With F any arithmetical formula, that is a formula build with the
logical symbol, and the arithmetical symbols {0, s, +, *}.
So do you have a LISP program that will make my computer Lobian?
It would be easier to do it by hands:
1) develop a first order logic specification for your computer (that
is a first order axiomatic for its data structures, including the
elementary manipulations that your computer can do on them)
2) add a scheme of induction axioms on those data structure. For
example, for the combinators, it would be like this
"if P(K) and P(S) and if for all X and Y P(X) & P(Y) implies P((X,Y))
then for all X and Y P((X,Y))". And this for all "P" describable in
your language.
It will be automatically Löbian. And, yes, it should not be to
difficult to write a program in LISP, doing that. That is, starting
from a first order logical specification of an interpreter, extending
it into a Löbian machine.
Bruno
http://iridia.ulb.ac.be/~marchal/
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