Herbrand semantics, the potential infinite, and ontology-free logic
Theodore Hailperin · History and Philosophy of Logic · 1992
This paper investigates the ontological presuppositions of quantifier logic. It is seen that the actual infinite, although present in the usual completeness proofs, is not needed for a proper semantic foundation. Additionally, quantifier logic can be given an adequate formulation in which neither the notion of individual nor that of a predicate appears