[FOM] More on first-order logic with operation constants

John Corcoran corcoran at buffalo.edu
Sat Dec 4 07:42:49 EST 2004

In Hilbert-Ackermann 1938 and in Church 1956, addition is is treated as
a 3-place relation. Kleene 1952 and Mendelson 1956, on the other hand,
treat addition as a 2-place operation.
Q1.When did the logic community, as opposed to the algebra community,
come to recognize the "legitimacy" of taking operation symbols as
primitive symbols?
Q2.What was the motivation, philosophical or otherwise, of treating
operations as if they were "really" relations?
Q3.Was there ever any discussion in the mathematical or philosophical
literature of whether the operation had the same ontological or logical
status and legitimacy as the relation, or whether operations are
"really" relations or are in some other way inferior or improper?
Q4.Do the above issues relate to the issue of whether it is more
"proper" to call first-order logic a "predicate calculus" or "functional
Q5.Has anyone of note expressed in print reasons for prefering one of
the six expressions'logic'[unmodified], 'predicate logic', 'predicate
calculus', 'functional logic', 'functional calculus', 'quantification
theory'to be modified by 'first-order'as opposed to the others?
Q6.Do you have opinions on these issues or do you regard them as
subjective matters of taste? If the later, what would good taste

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