New Scientist 21 Mar 92

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2 total messages Started by Thorsten Altenkirch Tue, 18 Aug 1992 14:03

#209

Author: Thorsten Altenkirch
Date: Tue, 18 Aug 1992 14:03

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Has anybody had a look at Paul Davies article "Is nature
mathematical?". I only browsed over it but I got the impression that
he confuses the questions of undecidability ("1st order logic is
undecidable" [Church]) and incompleteness ("Every consistent extension
of Peano arithmetic is incomplete"[G"odel]). Any comments?

T.

--
************************************************************
Thorsten Altenkirch		alti@dcs.ed.ac.uk
LFCS, Edinburgh
Scotland

Re: New Scientist 21 Mar 92

#211

Author: Charles R. Martin
Date: Tue, 18 Aug 1992 22:20

20 lines
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In article <ALTI.92Aug18150326@tanera.dcs.ed.ac.uk> alti@dcs.ed.ac.uk (Thorsten Altenkirch) writes:

   Has anybody had a look at Paul Davies article "Is nature
   mathematical?". I only browsed over it but I got the impression that
   he confuses the questions of undecidability ("1st order logic is
   undecidable" [Church]) and incompleteness ("Every consistent extension
   of Peano arithmetic is incomplete"[G"odel]). Any comments?

I believe they're very closely connected.  See e.g. Chaitin's
Algorithmic Information Theory (Cambridge Tract in Theoretical CS, I
think is the series.)
--
Charles R. Martin/(Charlie)/martinc@cs.unc.edu/(ne crm@cs.duke.edu) 
O/Dept. of Computer Science/CB #3175 UNC-CH/Chapel Hill, NC 27599-3175
H/3611 University Dr #13M/Durham, NC 27707/(919) 419 1754
----------------------------------------------------------------------
"I am he who walks the States with a barb'd tongue, questioning every
one I meet,/Who are you that wanted only to be told what you knew
before?/ Who are you that wanted only a book to join you in your
nonsense?"  _Leaves of Grass_ xxiii.4.

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