Abstract
Alternatives to standard semantics are legion, some even antedating standard semantics. I shall study several here, among them: substitutional semantics, truth-value semantics, and probabilistic semantics. All three interpret the quantifiers substitutionally, i.e. all three rate a universal (an existential) quantification true if, and only if, every one (at least one) of its substitution instances is true.2 As a result, the first, which retains models, retains only those which are to be called Henkin models. The other two dispense with models entirely, truth-value semantics using instead truth-value assignments (or equivalents thereof to be called truth-value functions) and probabilistic semantics using probability functions. So reference, central to standard semantics, is no concern at all of truth-value and probabilistic semantics; and truth, also central to standard semantics, is but a marginal concern of probabilistic semantics.
The essay was written while I held a research grant (SES 8007179) from the National Science Foundation and was on a partial research leave from Temple University. Some of the material was used in lectures delivered at City College of CUNY in 1980–1981 and to be published by D. Reidel Publishing Company under the title Probabilistic Semantics
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Leblanc, H. (1983). Alternatives to Standard First-Order Semantics. In: Gabbay, D., Guenthner, F. (eds) Handbook of Philosophical Logic. Synthese Library, vol 164. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7066-3_3
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