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.

The theory of descriptions occupies a very prominent place in Russell's system of logic and indeed in his system of philosophy. Since the publication of the now classical paper “On Denoting” in Mind for 1905 the theory had been incorporated into Principia Mathematica , the first volume of which appeared in 1910. In 1918 Russell discussed descriptions in his lectures on the Philosophy of Logical Atomism, which subsequently were published in The Monist for 1919. A very lucid exposition of the (...) main tenets of the doctrine is to be found in the Introduction to Mathematical Philosophy dating from the same year. Epistemological aspects of the theory of descriptions are examined in “Knowledge by Acquaintance and Knowledge by Description“, in the Proceedings of the Aristotelian Society for 1910–11, and also in Chapter V of The Problems of Philosophy, first published in 1912. (shrink)

SummaryInterpreted distributively the sentence‘Indiana is a member of the class of American federal states’means the same as‘Indiana is an American federal state’. In accordance with the collective sense of class expressions the sentence can be understood as implying that Indiana is a part of the country whose capital city is Washington. Neither interpretation appears to accommodate all the intuitions connected with the informal notion of class. A closer accommodation can be achieved, it seems, if class expressions are interpreted as verb‐like (...) expressions of a certain kind available within the framework of Lesniewski's Ontology. (shrink)

The propositional fragment L 1 of Leniewski's ontology is the smallest class (of formulas) containing besides all the instances of tautology the formulas of the forms: (a, b) (a, a), (a, b) (b,). (a, c) and (a, b) (b, c). (b, a) being closed under detachment. The purpose of this paper is to furnish another more constructive proof than that given earlier by one of us for: Theorem A is provable in L 1 iff TA is a thesis of first-order (...) predicate logic with equality, where T is a translation of the formulas of L 1 into those of first-order predicate logic with equality such that T(a, b) = FblxFax (Russeltian-type definite description), TA B = TA TB, T A = TA, etc. (shrink)

This paper is a reaction to G. Küng's and J. T. Canty's Substitutional Quantification and Leniewskian quantifiers'Theoria 36 (1970), 165–182. I reject their arguments that quantifiers in Ontology cannot be referentially interpreted but I grant that there is what can be called objectual — referential interpretation of quantifiers and that because of the unrestricted quantification in Ontology the quantifiers in Ontology should not be given a so-called objectual-referential interpretation. I explain why I am in agreement with Küng and Canty's recommendation (...) that Ontology's quantifiers not be substitutionally interpreted even if Leniewski intended them to be so interpreted. A notion of an interpretation which is referential but yet which does not interpret as an assertor of existence of objects in a domain is developed. It is then shown that a first order version of Ontology is satisfied by those special kind of referential interpretations which read as Something as epposed to Something existing. (shrink)