[FOM] The Lucas Penrose Thesis

Hartley Slater slaterbh at cyllene.uwa.edu.au
Tue Oct 3 01:49:30 EDT 2006

Panu Raatikainen with respect to my line of argument:

>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.

If, as I maintain, truth is not a property of sentences, then it is 
not to be expected that a generator of sentences, like a Turing 
machine, will generate truths.  Goedel demonstrated a particular case 
of this, and the lesson is also available from a study of the Liar 
Paradox, as I have shwon.  But the conclusion comes much more 
generally and directly from a study of the differences between syntax 
and semantics.  Goedel's Theorems are only especially significant to 
a tradition that thought Hilbert's Meta-mathematics at least proved 
*some* truths about numbers (for instance).  In fact it did not prove 
any, as I have also shown.  The title of my paper at Monash 
University this Friday is 'Proving that 2 + 3 = 5', and it is about a 
process that has been forgotten, or ignored for most of the last 100 
years (by the Logical Positivists it was even explicitly supressed). 
The process in question is what the Foundations of Mathematics 
consists in.
Barry Hartley Slater
Honorary Senior Research Fellow
Philosophy, M207 School of Humanities
University of Western Australia
35 Stirling Highway
Crawley WA 6009, Australia
Ph: (08) 6488 1246 (W), 9386 4812 (H)
Fax: (08) 6488 1057
Url: http://www.philosophy.uwa.edu.au/staff/slater

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