LetEO be the elementary ontology of Leniewski formalized as in Iwanu [1], and letLS be the monadic second-order calculus of predicates. In this paper we give an example of a recursive function , defined on the formulas of the language ofEO with values in the set of formulas of the language of LS, such that EO A iff LS (A) for each formulaA.

SummaryLeśniewski presented his logical systems in a way which conformed to his nominalism, so the question arises whether Leśniewski's logic can be given a natural formal semantics which, unlike current versions, avoids commitment to abstract entities. Building on hints in Wittgenstein's Tractatus, I develop the idea of a way of meaning which is the basis for what I call combinatorial semantics. I then consider whether this commits us to abstract objects or an intensional metalogic.

This paper assesses those features of Lesniewski's Ontology which make it difficult to understand for logicians accustomed to more orthodox systems of logic. It is seen that certain general features of presentation and content can, by selective acceptance or modification, be accommodated with a fairly orthodox viewpoint. The chief difficulty lies in the interpretation of Le?niewski's names, and the constant ???. Four interpretations are suggested in turn: Le?niewski's names as monadic predicates; as class terms; as common nouns; and as empty, (...) singular or plural terms. This last and least orthodox interpretation is argued to be the most suitable, but it is shown how it can be made to live in harmony with either the common noun or the class interpretation. (shrink)