A.P. Hazen a.hazen at philosophy.unimelb.edu.au
Thu Dec 2 02:43:06 EST 2004

John Corcoran asks various questions  about the history of the logic 
mentinoned in the title.  I'm not sure who would have formulated the 
theory of individual constants and function-symbols  explicitly 
(their theoretical dispensability is a consequence of Russell's 
theory of descriptions and would have been familiar to foundational 
workers of the 1920s), but Gödel DOES discuss identity in his 1930 
completeness theorem paper: theorems VII and VIII state weak 
completeness (= valid formulas provable) for FOL-with-identity, and 
after giving theorems IX (strong completeness (a contradiction is 
derivable from any denumerable set of formulas which is not 
satisfiable)) and X (Compactness) for FOL, Gödel remarks that they 
also generalize to FOL-with-I.

Allen Hazen
Philosophy Department
University of Melbourne

Corcoran's questions:
>1 Who discusses the history of this logic?
>2 Who were the early logicians to specifically mention this logic as an
>extension of Gödel 1930 logic?
>3 Who were the early logicians to notice that the Gödel 1930
>completeness results extend to this logic?
>43 Who were the early logicians to formulate the semantics and actually
>carry out a completeness proof?

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