The Alan Sondheim Mail Archive

August 6, 2016

~/ homedirectory

./homedirectory performative

w | grep sondheim sondheim pts/20 pool-96-253-57-46.prvdri.f
5:09PM 0 grep sondheim
pwd /net/u/6/s/sondheim
who | grep sondheim sondheim pts/20 Aug 6 17:09 (

"I see no reason why a similar phenomenon could not happen in
mathematics; in extrapolating a formal mechanism to the limit of
its generative capacities, it does not take long to assemble
formulas that are so long and complex that all possibility of
intuitive interpretation disappears. The 'theorems' thus
obtained will probably be formally correct but semantically
insignificant. Thus for a given intuitive theory T one must
expect to have to use not one but several 'local' axiomatiza-
tions; each local axiomatization S has a contact zone Z(sub)S in
the morphology for which S is valid; but as soon as one
constructs formulas in S which are too long or involved, the
intelligibility disappears. At the boundary of the zone Z(sub)S,
the semantic link between S and Z(sub)S breaks down; this
prohibits the extension beyond Z(sub)S of the isomorphisms
S --> T, defined by the meaning. The idea that a theory T could
be generated by just one formal system S is, a priori, just as
unlikely as the idea that the earth should be flat or that one
could cover a surface by a single system of coordinates."

- from Rene Thom, "Modern Mathematics: An Educational and
Philosophic Error?," p. 73, in New Directions in the Philosophy
of Mathematics, An Anthology, ed. Thomas Tymoczko, Birkhauser,
Boston, 1986. (some changes in notation)

gamespace(edgespace) <--> edgespace(gamespace); ~/.entangled ;
blankspace jectivity <--> (edgespace, gamespace); here, there's
a change in ontology.

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