[FOM] historical question about the axiomatisation of identity

Muller F.A. F.A.Muller at phys.uu.nl
Mon Sep 19 18:43:26 EDT 2005

 Dear all,

 In *Grundzuge der theoretischen Logik* (1928),
 Hilbert & Ackermann axiomatised identity as
 an equivalence-relation that obeys substitutivity
 (page 86).

 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
     Utrecht University 
     Erasmus University Rotterdam

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