Predicate-Functor Logics(*)

Abstract

Bound variable, so characteristic of analysis rather than of algebra, has became central to logic. This new logic has come to constitute even a basic theory of the bound variable; for, all the other desired uses of bound variables can be so paraphrased as to cause the bound variables to figure solely as variables of quantification. For, the logic of quantification excels the old algebras of classes and relations not only in flexibility, but in scope; and so it seems worthwhile to see what it would add up to when couched in just the block like sort of constants and connectives and free variables that are the stock in trade of elementary algebra. Such a translation need have no practical advantages, but it would be an algebraic explanation of the bound variable––an algebraic analysis of analysis. Predicate-functor logic is just adequate to the ordinary logic of quantification and identity. It is shown how to translate closed formulas of ordinary logic into predicate-functor logic; it is convenient to adopt three abbreviations.