A logical calculus of analogy involving functions of order $2$.

Abstract

A LOGICAL CALCULUS OF ANALOGY INVOLVING FUNCTIONS OF ORDER 2 DOUGLAS C. DORROUGH 7 2. NOTATION Our logic will be called A.S.j, i.e., proposal of an analogical system for individuals. In stating and developing A.S.j, we make the following assumptions: (1) there exists a standard elementary logic of the sort developed by Quine 8 and Copi 9 included in which is a consistent and deductively complete propositional calculus 10 ; (2) the rules governing the quantification and substitution of predicate variables are formally identical to those for individual variables 11 ; and (3) Post's criterion of consistency is