The most difficult problem that Leniewski came across in constructing his system of the foundations of mathematics was the problem of defining definitions, as he used to put it. He solved it to his satisfaction only when he had completed the formalization of his protothetic and ontology. By formalization of a deductive system one ought to understand in this context the statement, as precise and unambiguous as possible, of the conditions an expression has to satisfy if it is added to (...) the system as a new thesis. Now, some protothetical theses, and some ontological ones, included in the respective systems, happen to be definitions. In the present essay I employ Leniewski's method of terminological explanations for the purpose of formalizing ukasiewicz's system of implicational calculus of propositions, which system, without having recourse to quantification, I first extended some time ago into a functionally complete system. This I achieved by allowing for a rule of implicational definitions, which enabled me to define any propositionforming functor for any finite number of propositional arguments. (shrink)
An attempt is made in the present essay to accommodate various senses of the notion of existence and ofthat of non-existence within the framework of logic. With this aim in view a system of Lesniewski's Ontology, referred to as System S, is outlined. Equipped with appropriate definitions and illustrated with a selection of theses it offers a logical theory of existence and non-existence. The usefulness of the theory is then tested by interpreting in its terms some of the principal notions (...) and assertions of Meinong's ontology. A few brief comments on the notion of 'possible object' and on 'semantics' of fiction conclude the essay. (shrink)
J. PELC (ed.) Semiotics in Poland 1894-1969. Translation from the Polish by 0. Wojtasiewicz. Dordrecht, Boston and London; D. Reidel Publishing Company; Warsaw: PWN?Polish Scientific Publishers; 1981. xxvi + 504 pp. Df. 105/ $49.50.
According to the author, no body of theories deserves to be called philosophy unless some of these theories and problems fall within the province of metphysics. No problems deserves the name of metaphysics unless some of them add up to constitute ontology. The author presents the reistic version of the science of being as the union of Protothetic, Ontology, Mereology and Chronology. The next possible step in the construction of the reistic ontology will be Stereology (a kind of reistic geometry).
As the author sees it, Tadeusz Kotarbiński's reism is an ontology with semantical ramifications. Contrary to Kazimierz Ajdukiewicz's view the reist is not commited to any particular categorially determined language; he has to use, and is at liberty to do so, the language of whoever happens to be his opponent always provide that it is a categorially determined language. Contrary to Ajdukiewicz's opinion, the positive ontological thesis of resim (i.e. the thesis that for all a and b, if a is (...) a b, then a is bulky and lasting) is not a tautology; it is a denial of the thesis held by unicategorial Platonism. Contrary to Ajdukiewicz's insistence, the negative ontological thesis of reism (i.e. the thesis that there are no properties, there are no relations, there are no events, etc.) consists of propositions which, in the light of multicategorial idealization of ordinary language, are meaningful and syntactically well constructed. They deny equally meaningful and syntactically well constructed assertions of multicategorial Platonism. (shrink)