Bertrand Russell introduced several novel ideas in his 1903 Principles of Mathematics that he later gave up and never went back to in his subsequent work. Two of these are the related notions of denoting concepts and classes as many. In this paper we reconstruct each of these notions in the framework of conceptual realism and connect them through a logic of names that encompasses both proper and common names, and among the latter, complex as well as simple common names. (...) Names, proper or common, and simple or complex, occur as parts of quantifier phrases, which in conceptual realism stand for referential concepts, i.e., cognitive capacities that inform our speech and mental acts with a referential nature and account for the intentionality, or directedness, of those acts. In Russell’s theory, quantifier phrases express denoting concepts (which do not include proper names). In conceptual realism, names, as well as predicates, can be nominalized and allowed to occur as "singular terms", i.e., as arguments of predicates. Occurring as a singular term, a name denotes, if it denotes at all, a class as many, where, as in Russell’s theory, a class as many of one object is identical with that one object, and a class as many of more than one object is a plurality, i.e., a plural object that we call a group. Also, as in Russell’s theory, there is no empty class as many. When nominalized, proper names function as "singular terms" just the way they do in so-called free logic. Leśniewski’s ontology, which is also called a logic of names can be completely interpreted within this conceptualist framework, and the well-known oddities of Leśniewski’s system are shown not to be odd at all when his system is so interpreted. Finally, we show how the pluralities, or groups, of the logic of classes as many can be used as the semantic basis of plural reference and predication. We explain in this way Russell’s "fundamental doctrine upon which all rests", i.e., "the doctrine that the subject of a proposition may be plural, and that such plural subjects are what is meant by classes [as many] which have more than one term" (Russell 1938, p. 517). (shrink)

This article is an attempt to recreate the intuitions which accompanied Leśniewski when he was creating his calculus of names called Ontology. Although every reconstruction is to some extent an interpretation, and as such may be defective, still, there are reasons justifying such reconstruction. The most important justification is the fact that both Leśniewski and his commentators stressed that ontology originated from reflections about ordinary language, in which sentences such as A is B appear in one of the meanings associated (...) with them in Ontology, and that the users of the Polish language use such sentences accordingly and properly identify them. Assumed it is so, let us try, based on Leśniewski’s guidelines as well as comments and elaborations on Ontology, to evaluate the accuracy of this approach, referring also to certain knowledge of the Polish language. To make it clear, this article is not about Ontology as a formal theory of language. It is solely an attempt to assess whether some syntactical constructs of the Polish language and this language’s properties are significant conditions of a proper understanding of Ontology, and whether Ontology is, in fact, in a relationship with the ethnic language of its author. (shrink)

Sobocinski in his paper on Leśniewski's solution to Russell's paradox (1949b) argued that Leśniewski has succeeded in explaining it away. The general strategy of this alleged explanation is presented. The key element of this attempt is the distinction between the collective (mereological) and the distributive (set-theoretic) understanding of the set. The mereological part of the solution, although correct, is likely to fall short of providing foundations of mathematics. I argue that the remaining part of the solution which suggests a specific (...) reading of the distributive interpretation is unacceptable. It follows from it that every individual is an element of every individual. Finally, another Leśniewskian-style approach which uses so-called higher-order epsilon connectives is used and its weakness is indicated. (shrink)

RésuméCet article offre une introduction aux théories déductives si peu connues de S. Leniewski. Sont exposées les raisons qui ont conduit ce savant polonais à davelopper une théorie des classes collectives ainsi que les théories logiques qui la fondent. Les trois systèmes de Leniewski méréologie, protothétique et ontologie – sont présentés sous ľaspect de leurs caractéristiques essentielles. Cette étude s'accompagne de quelques réflexions épistémologiques.

When Russell argued for his ontological convictions, for instance that there are negative facts or that there are universals, he expressed himself in English. But Wittgenstein must have noticed that from the point of view of Russell's ideal language these ontological statements appear to be pseudo-propositions. He believed therefore that what these statements pretend to say, could not really be said but only shown. Carnap discovered a way out of this mutism: what in the material mode of speech of the (...) object language looks like a pseudo-proposition can be translated into a perfectly meaningful proposition in the formal mode of speech (in the metalinguistic mode of speech of the logical syntax of language). But is this ascent into the metalanguage necessary? Taking advantage of Lésniewski's logical system there exists another way outwe can expand the number of categories of our ideal language. But Leniewski's formulas raise another profound problem, the problem of semantical muteness (cf. W. G. Lycan Semantic Competence and Funny Functors Monist 64 (1979), 209–222). (shrink)