The article on my theory of descriptions by Mr. Lejewski raises two points. One is as to the copula. I do not quite understand why it is thought that an ambiguity in the meaning of the word “is” is relevant in regard to my theory of descriptions. There are many problems in regard to which it is relevant. I have mentioned one of these in criticizing Hegel in Our Knowledge of the External World on p. 39 n of the original (...) edition . But, although I have read Mr. Lejewski's argument several times, it still seems to me quite clear that in “Scott is the author of Waverley” the “is” is that of identity. Nor have I been able to understand why he considers his theory of descriptions preferable to mine. I am, however, quite willing to believe that there is some point that I have missed in his discussion. (shrink)

We propose an intuitive understanding of the statement: ‘an axiom (or: an axiomatic basis) determines the meaning of the only specific constant occurring in it.’ We introduce some basic semantics for functors of the category s/n,n of Lesniewski’s Ontology. Using these results we prove that the popular claim that the axioms of Ontology determine the meaning of the primitive constants is false.

George Boolos's employment of plurals to give an ontologically innocent interpretation of monadic higher‐order quantification continues and extends a minority tradition in thinking about quantification and ontological commitment. An especially prominent member of that tradition is Stanislaw Leśniewski, and shall first draw attention to this work and its relation to that of Boolos. Secondly I shall stand up briefly for plurals as logically respectable expressions, while noting their limitations in offering ontologically deflationary accounts of higher‐order quantification. Thirdly I shall focus (...) on the key idea of ontological commitment and investigate its connection with the idea of truth‐making. Fourthly I shall consider how different interpretations of quantification may sideline Boolos's work, but finally I shall largely support his analysis of quantification involving nominal expressions, while arguing, in the spirit of Arthur Prior, that non‐nominal quantification is non‐committing. (shrink)

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.

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.

The article on my theory of descriptions by Mr. Lejewski raises two points. One is as to the copula. I do not quite understand why it is thought that an ambiguity in the meaning of the word “is” is relevant in regard to my theory of descriptions. There are many problems in regard to which it is relevant. I have mentioned one of these in criticizing Hegel in Our Knowledge of the External World on p. 39 n of the original (...) edition. But, although I have read Mr. Lejewski's argument several times, it still seems to me quite clear that in “Scott is the author of Waverley” the “is” is that of identity. Nor have I been able to understand why he considers his theory of descriptions preferable to mine. I am, however, quite willing to believe that there is some point that I have missed in his discussion. (shrink)

SummaryThis article proposes to clarify the problem of interpreting Lesniewski's ontology. A distinction is made between two kinds of interpretation: substitutional and “natural”. Substitutional interpretation is shown to involve difficulties and limitations. A “natural” ontology, the major principles of which are presented here, is shown to be of considerable interest.