[FOM] The Lucas Penrose Thesis

praatika@mappi.helsinki.fi 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. 

Best, Panu

Panu Raatikainen
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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