Strict embedding of the elementary ontology into the monadic second-order calculus of predicates admitting the empty individual domain (Q1095133)

Recently [Stud. Logica 42, 197-207 (1983; Zbl 0596.03018)], the author disucssed the problem of embedding Leśniewski's Elementary Ontology (EO) into the monadic second-order predicate calculus (LS); his main theorem, however, has been shown to be false. In the paper under review, he considers, instead of LS, a certain system \(LS^-_ 1\) of universal monadic second-order predicate logic and improves the way of translating (into the language of EO) quantifiers binding individual variables in \(LS^-_ 1\)-formulas. After all, an embedding theorem of EO into \(LS^-_ 1\), as well as that of \(EO+\exists S(S\epsilon S)\) into \(LS^-_ 1+\forall...(\forall xA(x)\supset \exists xA(x))\) are obtained. Reviewers remarks. The new translation \(\psi: LS^-_ 1\to EO\) is not acceptable either: since \(LS^-_ 1\) has an additional run of variables, the \(\psi\)-translation of an \(LS^-_ 1\)-formula is not an EO-formula at all. The paper is not well-edited: there are a lot of misprints, inaccuracies and blunders in the text (e.g. the footnote 4 (p. 3) is wrongly indicated, since it concerns the definition of \(\psi\) on p. 11), and the quality of the English translation leaves much to be desired. In a number of cases, the reviewer would have been helpless without consulting the Russian version of the text [sect. 4.6 of the author's monograph ``Logical methods of analysis of scientific knowledge'', Nauka Publ., Moscow (1987)].