What is Quantification Theory?

Quantification, in logic, the attachment of signs of quantity to the predicate or subject of a proposition. The universal quantifier, symbolized by (∀-) or (-), where the blank is filled by a variable, is used to express that the formula following holds for all values of the particular variable quantified.According to Peirce, conditional propositions can be regarded as modal propositions, and he accepted the scholastic view that modal propositions are quantified propositions of a special kind: “the necessary proposition is a sort of universal proposition; the possible contingent, in the sense of  proposition, a sort of particular proposition” . As was observed earlier in the discussion of the pragmatic interpretation of quantifiers, modalities function as quantifiers over possible circumstances or courses of events; thus Peirce accepted a version of the possible worlds analysis of modalities. In the system of existential graphs this semantical view is expressed by the assumption that the analysis of modal propositions requires a “book” of sheets of assertion, not just a single sheet. In one of his unpublished manuscripts Peirce explains the semantics of counterfactual conditionals by means of the following example:

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