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)

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)

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)

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)

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)

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)

This paper deals with Popper's little-known work on deductive logic, published between 1947 and 1949. According to his theory of deductive inference, the meaning of logical signs is determined by certain rules derived from ?inferential definitions? of those signs. Although strong arguments have been presented against Popper's claims (e.g. by Curry, Kleene, Lejewski and McKinsey), his theory can be reconstructed when it is viewed primarily as an attempt to demarcate logical from non-logical constants rather than as a semantic foundation (...) for logic. A criterion of logicality is obtained which is based on conjunction, implication and universal quantification as fundamental logical operations. (shrink)

We classify two of Bertrand Russell's theories of events within the point-free ontology. The first of such approaches was presented informally by Russell in ‘The World of Physics and the World of Sense’ (Lecture IV in Our Knowledge of the External World of 1914). Based on this theory, Russell sketched ways to construct instants as collections of events. This paper formalizes Russell's approach from 1914. We will also show that in such a reconstructed theory, we obtain all axioms of Russell's (...) second theory from 1936 and all axioms of Thomason's theory of events from 1989. Russell's work certainly influenced the works of Stanisław Leśniewski, his student Alfred Tarski, and Czesław Lejewski – prominent members of the Lvov-Warsaw School (LWS). We see our work in the tradition of the research of Leśniewski and Tarski. Building on the technical tools developed in this environment and in the spirit of the traditional research of the LWS, we engage here, in particular, with two classic works by Russell on fundamental ontology. (shrink)

This paper discusses the philosophical background to the paper by lejewski in this issue. lejewski offers an ontologically neutral logic for the first two types (individuals and classes thereof). some peculiarities of the logic used are noted, in particular the distinction between empty individual terms, empty class terms, and non-empty class terms designating the empty class. lejewski ends by denying the truth of the formula meaning "there are classes," but we argue that the way in which truth-conditions (...) for formulae containing class terms are introduced absolves us from taking this as seriously committing us to the existence of classes. the main (inclining but not necessitating) reason for being a platonist lies in the sheer mass of mathematical results for which a non-platonist account has yet to be given. the theory of classes as fictions suggested by our modification of lejewski's view is insufficient to support frege-russell style logicism, but for a non-platonist the upper reaches of cantor's paradise must be regarded as fictitious anyway. (shrink)

The use of the primitive notion of mereological fusion (also known as composition and sum) has been considered by various philosophers and logicians, including Aristotle, G. Leibniz, S. Leśniewski, K. Fine, J. Ketland, T. Schindler, and S. Kleishmid. The problem of finding an axiomatization of Classical Mereology with primitive fusion, instead of the primitive notion of being a part, is quite old and was formally considered by C. Lejewski. Lejewski somehow axiomatized classical mereology using primitive fusion (1962, and (...) also later in 1984). However, his mereology is formulated in a very rich nonclassical language of Leśniewski’s ontology with the essential use of quantification over function symbols, including function symbols “part of” and “sum of.” Lejewski’s approach is not expressible in modern mereologies, and we do not use it in any way. We prove that classical mereology is axiomatizable using primitive mereological fusion within the framework of two-sorted logic. The theory presented here is the first contemporary axiomatization of classical mereology with primitive mereological fusion. (shrink)

The medieval version of the problem of universals centres around propositions such as ?man is a species? and ?animalis a genus?. One of C. Lejewski's analyses of such propositions shows the semantic status of their terms by means of Ajdukiewicz-style categorical indices having participial or infinitive forms as their natural-language counterparts. Some medievals certainly used such forms in their corresponding analyses, thus avoiding the alleged referential demands generated by nominally-termed propositions. Boethius the Consul exemplifies the confusion which may still (...) arise from the traditional definition of universal in terms of predication of many. Unnecessary adherence to nominally-termed analyses not only grounded a tendency towards nominalism and Platonism, but also towards the moderns? ?way of ideas? (shrink)

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)

Those who want to interpret the quantifier ? (3 x) (. . .x. . .)'as having no existence commitment often fail to distinguish between this objective and that of merely changing the values of the variables. The confusion vitiates solutions of the singular existence anomalies which purport to be based on a non?existential interpretation of the quantifier. An example of one who makes the distinction but still interprets the particular quantifier non?existentially is offered by Czeslaw Lejewski. Objection to the (...) classical interpretation of the quantifiers often runs hand in hand with aversion to extensional logic. However, it is at least arguable that such an aversion is the result of underestimating the resources of extensional logic. These points arc discussed in the wake of Professor Marcus's recent paper in this journal ?Interpreting Quantification? (shrink)

The Buddha’s final illness, brought on by his last meal prior to his death, was traditionally seen as one of a set of ailments suffered by him at various points during his lifetime. This paper looks at different Buddhist explications of the causes of these ailments and applies them to the episode of the Buddha’s final illness. In both instances, three explanatory strategies are detected: the first stresses the causative importance of the Buddha’s own negative karmic deeds in past lives; (...) the second looks to the negative deeds and karma of others than the Buddha; the third offers non-karmic explanations. The first two engendered two rather different kinds of j?taka stories; the last did not involve any j?takas but highlighted various kinds of ‘natural’ explanations. (shrink)