[FOM] Falsify Platonism?

Vaughan Pratt pratt at cs.stanford.edu
Thu Apr 29 17:50:32 EDT 2010

I had the following thoughts in response to Andrej's nice point about 
incompleteness in the natural universe.

1.  There is some overlap between the search for an ideal spouse and 
Diogenes' search for an honest man: both raise the question of 
admissibility of white lies, for example.

2.  Assuming one can draw a line between the natural universe and the 
mathematical universe, on which side of that line does so-called strong 
AI fall?  Is a robot whose source code we have full access to an entity 
of the natural universe or the mathematical universe?

3.  The literature on the connection between Heisenberg uncertainty (the 
unknowability of e.g. position and momentum together) and incompleteness 
in mathematics is so extensive today as to be itself unknowable.  The 
actual connection however should in principle be more knowable than 
between mathematical incompleteness and human inscrutability, because we 
understand both quantum mechanics and metamathematics in much greater 
technical depth than human relationships and thought processes.  (I 
would go further and say that Heisenberg uncertainty and mathematical 
incompleteness are essentially the same phenomenon, both being traceable 
to row-column interference in matrices, namely those representing 
respectively inner product and satisfiability.)


On 4/29/2010 12:27 PM, Andrej Bauer wrote:
> I colleague of mine whose area of expertise is discrete mathematics
> and algorithms for symbolic computation once told me he was a
> Platonist. He gave a very good response to my asking him how he dealt
> with incompleteness phenomena: "My wife is real and I know her but I
> do not know everything about her, nor do I presume that everything
> about her is knowable. The situation with the natural numbers is much
> the same." Naturally, my follow-up question was about the ideal status
> of natural numbers, but I could not induce him to state that his wife
> was ideal.
> Anyhow, I thought his was a very reasonable and defensible position.
> With kind regards,
> Andrej
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