Quantification And Predication In Modal Predicative Propositional Logic

Daniel Vanderveken

Abstract


The main objective of this paper is to enrich first order propositional predicative logic by dealing all together with intensional attributes, quantification, logical and historic modalities and ramified time. Predicative propositional logic advocates a finer analysis in terms of predication of the logical form of propositions. Like Church’s logic of sense and denotation (Church 1951), my new predicative approach of quantification is based on Frege’s theory of indirect reference (Frege 1892). However in my approach, like in algebraic intensional logic, generalized propositions predicate first order generalizations of attributes. In the first section, I will analyze in terms of predication the logical form of elementary propositions with all kinds of attributes (whether intensional or extensional) and of generalized, modal and temporal propositions. Next I will define the ideographic object-language of my logic. Its formulas can express different propositions in different contexts of utterance. In the third section, I will define the structure of a standard model for my ideography. In the last section, I will enumerate new valid laws of my logic.


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