Quantifying in and Out of Quotes

Publisher Summary Logic is many things: a science, an art, a toy, and a joy. One thing the logician can do is provide useful systems—that is, systems that are both widely applicable and efficient. Set theory has been developed for the mathematician, modal logic for the metaphysician, boolean logic for the computer scientist, syllogistics for the rhetorician, and the first order functional calculus for all. The chapter discusses the combination of quotation with quantifiers bearing the substitutional interpretation, for use by the logicians themselves, or by any practicing metalinguist. There is some evidence that substitutional quantification into quotes is the formal analog of an intuitive idea that people naturally come to once variables and quotes have been made available. Quantifying into quotes might well prove useful in application to proof theory as well as to grammar and semantics. The chapter also discusses expressions and domain-and-values variables, propositional variables, lambda abstraction, predicate and operator variable, and convention T and infinite conjunctions.