[FOM] The Lucas-Penrose Thesis

laureano luna laureanoluna at yahoo.es
Wed Oct 4 10:07:30 EDT 2006

Hartley Slater has been consistently arguing against
mechanism on the basis of the distinction between
syntax and semantics. He and Panu Raatikainen seem to
agree on the point that Goedel's theorems have not
much to say about this line of argumentation.

While I believe Slater's argumentation is essentially
well oriented I disagree on the point mentioned above.

I think anyone can see that pure syntactical objects
(as sentences and algorithms are) do not have per se
any semantical dimension and that this is a
potentially definitive difference berween mind and
machine. Nevertheless, given the structuralist bent of
modern mathematics, the argument would grow more
convincing if it could be shown that pure syntax
cannot represent semantics 'up to isomorphism', so to

I think that Goedel's and Tarski's theorems add
something of the like to the argument. Those results
prove that there is no syntactical representation of
the semantical concept of arithmetical truth. We could
say then that no purely syntactical device could
'possess' that concept. 

For a syntactical device 'possesing a concept' can
only mean being capable of behaving in a way that
accurately mirrors the correct and complete use of the
concept. In this sense no algorithmic device possesses
the concept of arithmetical truth.

It is evident that humans do not possess that concept
either in the above proposed sense, but it is no less
obvious that they possess the concept in other sense,
namely, in semantical sense i. e. in a way no purely
syntactical device could ever possess it.

I suggest that the semantical version of Goedel's
theorem as well as Tarski's theorem imply the
intelligent use of a concept machines have no way to

My contention is that if we could come to show that
semantics cannot be structurally reproduced by syntax,
then mechanism would become hardly tenable.


Laureano Luna Cabañero

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