[FOM] FIRST-ORDER LOGIC WITH IDENTITY, INDIVIDUAL CONSTANTS AND FUNCTION CONSTANTS.
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.
University of Melbourne
>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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