Predication in the logic terms.
Fred Sommers · Notre Dame Journal of Formal Logic · 1989
The paper contrasts modern predicate logic (MPL) and term/ functor logic (TFL) on predication.A predication in TFL consists of two terms and a "logical copula" that has formal properties such as symmetry or transitivity.The I-functor in 'PiS 9 (the old form of '(some) Sis P 9) is symmetrical, behaving like the plus sign of high school algebra; TFL transcribes 'PiS" as Ψ + S\ The transitive A-functor in 'PaS" (every S is P) is minuslike: Ψ -S = -((-P) + S) 9 represents the equivalence of 'PaS' to *not ((-P)iS)'.In propositional logic 'q + /?' transcribes 'p & q 9 and 'q -p 9 transcribes 'q if p 9 ; thus 'q -p = -((-q) + p) 9 is the algebraic form of 'p -> q = -(/?& (-q)) \ TFL applies to relational statements of any complexity.E.g., to show the inconsistency of 'every A is B and something R to an A is not R to a B 9 we add '-(R + B) + (R + A) 9 to Έ -A 9 to get the contradiction '-(R + B) + (R + B) 9 .The predicative functors are shown to give TFL a slight advantage over MPL in expressive and inference power when dealing with singular statements.The copula has no place in the language of modern logic.It will be shown that a significant price in the hard currency of inference power is being paid because of its absence.A properly formulated term logic, extended to handle relational inference, is both syntactically simpler and inferentially more powerful.But, historically, term logic took a wrong turn and we begin with that. /Traditional syllogistic logic with its A, E, I, and O classification of categorical staterjientsiias a distinctive syntax that was not properly understood by its practitioners.Confusion arose because most syllogists favored a parsing of *I am grateful to Michael Lockwood, Aris Noah, George Engebretsen, Jerry Samet, John Bacon, and David Kelley for much helpful discussion