Re: Foundations Of Mathematics Absconditus

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

FOMA.  Note 6 : The QED Manifesto Today

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Re: http://www.cs.nyu.edu/pipermail/fom/2009-January/013340.html

Catarina Dutilh wrote:
|
| I am very interested in surprising, counterintuitive results
| (in logic or mathematics) attained largely or exclusively by
| means of the ‘blind’ manipulation of formalisms, so I would
| be grateful if people could mention examples of such cases.

Catarina,

Somewhere in the middle of my first course in Lisp, 1977 I think,
I started work on a propositional calculus theorem prover, using
some ideas from C.S. Peirce's logical graphs.  Those first dozen
increments taught me a lot about the problem domain that I don't
think I could have learned any other way but through the work of
express formulation that it took to teach a machine how to think,
even at that most primitive level.  Most of what I learned would
fall more into the realm of pragmatic meta-maxims than brand new
theorems, but there were a few surprises of the theorematic type.
In particular, the utilities of "minimal negation operators" led
to theorems about their properties that were somewhat surprising.
See http://www.mywikibiz.com/Minimal_negation_operator for a few
hints of how this begins.

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
inquiry e-lab: http://stderr.org/pipermail/inquiry/
mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey
knol: http://knol.google.com/k/-/-/3fkwvf69kridz/1
mathweb: http://www.mathweb.org/wiki/User:Jon_Awbrey
planet math: http://planetmath.org/?op=userobjs;id=15246
proof wiki: http://www.proofwiki.org/wiki/User:Jon_Awbrey
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o