[FOM] historical question about the axiomatisation of identity
F.A.Muller at phys.uu.nl
Mon Sep 19 18:43:26 EDT 2005
In *Grundzuge der theoretischen Logik* (1928),
Hilbert & Ackermann axiomatised identity as
an equivalence-relation that obeys substitutivity
In his completeness paper of 1930, Godel axiomatised
identity as a reflexive relation that obeys substitutivity
(Van Heijenoort's source book, page 589) --- symmetry
and transitivity can be deduced.
Two historical questions.
Q1: Were Hilbert & Ackermann the first to do what
they did (see first paragraph)?
Q2: Was Godel the first to see that reflexivity
and substitutivity suffice?
--> F.A. Muller
Erasmus University Rotterdam
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