On how best to make sense of Leśniewski's ontology.
Paul Thomas Sagal · Notre Dame Journal of Formal Logic · 1973
Familiarity breeds contempt; on the other hand it can be very comforting.Philosophers find familiar logical systems very comforting.On the whole they prefer the logic they learned on their mother's knee or in graduate school.When confronted with an unfamiliar system they either resist it or twist and turn to put the unfamiliar in a familiar frame.A. N. Prior, in his essay Existence in Lesnίewskί and in Russell 1 does a lot of twisting and turning.Prior centers his discussion upon Theorem 24.52 of Russell and Whiteheads's Principia Mathematica.This theorem asserts that there exists at least one individual.But where does a logical system come off telling us that something exists ?Lesniewski's ontology contains no such thesis.Prior's essay investigates how ontology could get away with this when Russell considered 24.52 a necessary evil.This investigation leads Prior to make some general claims about Lesniewski's ontology, and to present its basic ideas in what Prior considers a less puzzling way than is customary.Prior's thesis is "that ontology is just a broadly Russellian theory of classes deprived of any variables of Russell's lowest logical type."(150) If we consider lowest type variables to range over individuals then we are left with a no individual theory.The only logical truths which remain would be those not involving individuals.According to Prior, the above characterization captures the essence of ontology.To give the reader who is completely unfamiliar with ontology enough information to appreciate the following discussion, I will make a few observations about ontology.Ontology is constructed upon a basis provided by the propositional calculus (P.C.), Lesniewski's own version of the P.C. (called protothetic) was an extended version of familiar systems.For example, quantification (of the substitutional variety)2 was already introduced at that 1. A. N. Prior, "Existence in Lesniewski and Russell," in Formal Systems and Recursive Functions, ed. by Crosley and Dummett, North Holland (1963).(Page references in paper will be to Prior's essay.)2. For substitutional quantification see W. V. Quine, 'Existence and Quantification' in [5].