published on February 11, 2016
Christopher S. Morrissey
A Logic Without Nominalism
Existential Assumptions on the Aristotelian Square of Opposition Revisited
The logical structure of the categories may be seen in the three fundamental oppositional relations assumed by the traditional formal logic of Aristotelian syllogistic. These fundamental oppositional relations are currently preserved in Term Functor Logic (TFL) but not in Modern Predicate Logic (MPL). Derivations of the immediate inferences traditionally permitted on the Aristotelian square of opposition are made using the rules of TFL in order to contrast TFL’s logical capabilities with those of MPL. It is argued that logic does not need any existential assumptions for a proper interpretation of the square; rather, all that is required are the three oppositional assumptions preserved in TFL but not in MPL. After considering TFL in relation to Peirce’s existential graphs, three suggestions are made: Firstness is most fundamentally understood in logical terms as the contrary opposition of terms; secondness is most fundamentally understood in logical terms as the predicative opposition of predicates affirmed or denied; and thirdness is most fundamentally understood in logical terms as the quantitative opposition of subjects. A famous example from Socrates in Plato’s Apology is used to illustrate these claims.