FOM: infinitesimals and AST
walter.felscher at uni-tuebingen.de
Wed Nov 26 09:30:02 EST 1997
Rick Sommer, on Nov. 11th, observed in connection with
infinitesimals, infeasible numbers etc. that
To me the best explanation for these objects is through
identifying infinite integers with something akin to the
"infeasible numbers" that have been discussed in recent
postings. Roughly, the idea is to finitize the
empirically relevant part of mathematical reality
(including infinitesimal and infinite numbers).
It may be of interest to some readers of FOM that Petr
Vopenka during the 1970ies (partly in collaboration with
A.Sochor) developed a possibly related foundational program
which distinguished between standard and non-standard
objects (in particular: numbers) already in the setup of
its underlying 'alternative' set theory (AST), cf.
Vopenka's short book
Mathematics in the Alternative Set Theory
Leipzig, Teubner 1979 , 120 pp .
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