[FOM] The Lucas Penrose Thesis
praatika at mappi.helsinki.fi
Mon Oct 2 03:17:38 EDT 2006
Hartley Slater <slaterbh at cyllene.uwa.edu.au>:
> Humans certainly can, like machines, utter sentences like '(x)Fx' -
> sentences which are then put in quotes - but they also do something a
> machine cannot, namely use sentences like '(x)Fx' to state things
> about models (in this case the standard model) - the sentences are
> then not in quotes. In terms of the operation of a machine it would
> have to not only utter a sentence, but *mean by it* one thing rather
> than another. But it lacks any capacity to mean anything.
I see... so the argument is really related to Searle's "Chinese room
(for those who don't know what it its; see
It is certainly true that a purely syntactic machine cannot mean anything.
However, it is less clear that a sophisticated machine (say, robot)
interacting causally with its environment could not in principle mean
something by some symbols.
How, on the other hand, even a human can refer to mathematical structures,
is very difficult question; no one seems to have a very good answer, and
the issue depends a lot on various choices in the philosphy of
mathematics. Therefore, before one has a clearer picture on that, it might
be wiser not to conclude too much on whether a machine could in principle
do the same or not.
But even if this line of argument worked, it is very different from the
Lucas-Penrose argument, and has really nothing to do with Gödel's theorem.
The latter is on the question whether a formal system, when intepreted
according to the standard intepretation, could prove anything that a human
mind can prove. The former is about the very possibility of giving
interpretations for symbols.
Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy
Department of Philosophy
University of Helsinki
E-mail: panu.raatikainen at helsinki.fi
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