The paper aims to reconstruct Heidegger’s historical-intentional assumptions in his ontological interpretation of Kant’s Critique of Pure Reason. The paper presents young Heidegger’s project of the “metaphysical-teleological interpretation of consciousness.” The project indicates the direction of his further ontological interpretation of transcendentalism: Heidegger stands up to the traditional, well known neo-Kantian interpretation of the Critique, and offers a new conception of ontological knowledge and cognition. According to this conception, cognition is grounded in transcendental imagination where a threefold synthesis takes place. (...) Heidegger’s original temporal interpretation of transcendental schematism is also recalled to stress the significance of his new ontological approach to Kant’s theoretical philosophy. (shrink)

The point of departure in the paper is the problem of Heidegger’s interpretation of Nietzsche’s thought in the light of the problematic term “Perspektivismus”. The author explicates the methodological position taken by Heidegger in his interpretation to give an answer to the question of epistemical, ontological or methodological domain of perspectivism.

A first-order formulation of Leśniewski's ontology is formulated and shown to be interpretable within a free first-order logic of identity extended to include nominal quantification over proper and common-name concepts. The latter theory is then shown to be interpretable in monadic second-order predicate logic, which shows that the first-order part of Leśniewski's ontology is decidable.

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 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)

"Lesniewski defined ontology, one of his three foundational systems, as 'a certain kind of modernized 'traditional logic' [On the foundations of mathematics (FM), p. 176]. In this respect it is worth bearing in mind that in the 1937-38 academic year Lesniewski taught a course called "Traditional 'formal logic' and traditional 'set theory' on the ground of ontology"; cf. Srzednicki and Stachniak, S. Lesniewski's Systems. Protothetic, 1988, p. 180. On this see Kotarbinski Gnosiology. The scientific approach to the theory (...) of knowledge, 1966, pp. 253-54 [the Polish original was published in 1929], which Lesniewski praised in [FM]: see in particular pp. 373 ff. Kotarbinski noted that Lesniewski "calls his system 'ontology' in harmony with certain terms used earlier (as in.. (shrink)

In this paper, we shall give another proof of the faithfulness of Blass translation of the propositional fragment \ of Leśniewski’s ontology in the modal logic \ by means of Hintikka formula. And we extend the result to von Wright-type deontic logics, i.e., ten Smiley-Hanson systems of monadic deontic logic. As a result of observing the proofs we shall give general theorems on the faithfulness of B-translation with respect to normal modal logics complete to certain sets of well-known accessibility (...) relations with a restriction that transitivity and symmetry are not set at the same time. As an application of the theorems, for example, B-translation is faithful for the provability logic \ ), that is, \ \ \ \supset \Box \phi \). The faithfulness also holds for normal modal logics, e.g., \, \, \, \. We shall conclude this paper with the section of some open problems and conjectures. (shrink)

We formulate a certain subtheory of Ishimoto’s [1] quantifier-free fragment of Leśniewski’s ontology, and show that Ishimoto’s theory can be reconstructed in it. Using an epimorphism theorem we prove that our theory is complete with respect to a suitable set-theoretic interpretation. Furthermore, we introduce the name constant 1 and we prove its adequacy with respect to the set-theoretic interpretation. Ishimoto’s theory enriched by the constant 1 is also reconstructed in our formalism with into which 1 has been introduced. Finally (...) we examine for both our theories their quantifier extensions and their connections with Leśniewski’s classical quantified ontology. (shrink)

A structure A for the language L, which is the first-order language (without equality) whose only nonlogical symbol is the binary predicate symbol , is called a quasi -struoture iff (a) the universe A of A consists of sets and (b) a b is true in A ([p) a = {p } & p b] for every a and b in A, where a(b) is the name of a (b). A quasi -structure A is called an -structure iff (c) {p (...) } A whenever p a A. Then a closed formula in L is derivable from Leniewski's axiom x, y[x y u (u x) u; v(u, v x u v) u(u x u y)] (from the axiom x, y(x y x x) x, y, z(x y z y x z)) iff is true in every -structure (in every quasi -structure). (shrink)

Stanislaw Lesniewski’s interests were, for the most part, more philosophical than mathematical. Prior to taking his doctorate at Jan Kazimierz University in Lvov, Lesniewski had spent time at several continental universities, apparently becoming relatively attached to the philosophy of one of his teachers, Hans Comelius, to the chapters of John Stuart Mill’s System of Logic that dealt specifically with semantics, and, in general, to studies of general grammar and philosophy of language. In these several early interests are already to be (...) found the roots of the work that was to occupy Lesniewski’s life: a search for a definitive doctrine of what sorts of things there are in the world, or better, of what language must be like if it is adequately and efficiently to represent the world. (shrink)

The volume collects many of the most significant commentaries on, and contributions to, Protothetic. A Protothetic Bibliography is included.

In this paper, we shall show that the following translation \(I^M\) from the propositional fragment \(\bf L_1\) of Leśniewski's ontology to modal logic \(\bf KTB\) is sound: for any formula \(\phi\) and \(\psi\) of \(\bf L_1\), it is defined as (M1) \(I^M(\phi \vee \psi) = I^M(\phi) \vee I^M(\psi)\), (M2) \(I^M(\neg \phi) = \neg I^M(\phi)\), (M3) \(I^M(\epsilon ab) = \Diamond p_a \supset p_a. \wedge. \Box p_a \supset \Box p_b.\wedge. \Diamond p_b \supset p_a\), where \(p_a\) and \(p_b\) are propositional variables (...) corresponding to the name variables \(a\) and \(b\), respectively. In the last, we shall give some comments including some open problems and my conjectures. (shrink)

In the paper we build up the ontology of Leśniewski’s type for formalizing synthetic propositions. We claim that for these propositions an unconventional square of opposition holds, where a, i are contrary, a, o (resp. e, i) are contradictory, e, o are subcontrary, a, e (resp. i, o) are said to stand in the subalternation. Further, we construct a non-Archimedean extension of Boolean algebra and show that in this algebra just two squares of opposition are formalized: conventional and the (...) square that we invented. As a result, we can claim that there are only two basic squares of opposition. All basic constructions of the paper (the new square of opposition, the formalization of synthetic propositions within ontology of Leśniewski’s type, the non-Archimedean explanation of square of opposition) are introduced for the first time. (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)

This paper assesses those features of Lesniewski's Ontology which make it difficult to understand for logicians accustomed to more orthodox systems of logic. It is seen that certain general features of presentation and content can, by selective acceptance or modification, be accommodated with a fairly orthodox viewpoint. The chief difficulty lies in the interpretation of Le?niewski's names, and the constant ???. Four interpretations are suggested in turn: Le?niewski's names as monadic predicates; as class terms; as common nouns; and as (...) empty, singular or plural terms. This last and least orthodox interpretation is argued to be the most suitable, but it is shown how it can be made to live in harmony with either the common noun or the class interpretation. (shrink)

This is an examination of Aristotle's notion of an "accidental being" -- something intermediate between a substance and a property. An accidental being (sometimes called "accidental compound" or "kooky object") is an ephemeral object, typically the compound of a substance and a property, that exists for only as long as its components are united. I set out the role that accidental beings play in Aristotle's solutions to several philosophical problems. I also investigate the similarity between these beings and the individual (...) non-substances of Aristotle's Categories. Finally, I propose that accidental beings can be assimilated into a more contemporary conceptual scheme as events -- the states or conditions that substances are in or undergo. (shrink)

The aim of this inquiry is to investigate Heidegger's ontology of technology. We will show that this ontology is aporetic. In Heidegger's key technical essays, ?The question concerning technology? and its earlier versions ?Enframing? and ?The danger?, enframing is described as the ontological basis of modern life. But the account of enframing is ambiguous. Sometimes it is described as totally binding and at other times it appears to allow for exceptions. This oscillation between, what we will call total (...) enframing and partial enframing, is underscored in the work of two influential scholars of Heidegger's later thought, Hubert Dreyfus and Iain Thomson. We will show that like Heidegger, Dreyfus and Thomson unwittingly perpetuate this dilemma that ultimately covers up the aporetic structure of enframing. (shrink)

This is an investigation of Aristotle's conception of accidental compounds (or "kooky objects," as Gareth Matthews has called them)—entities such as the pale man and the musical man. I begin with Matthews's pioneering work into kooky objects, and argue that they are not so far removed from our ordinary thinking as is commonly supposed. I go on to assess their utility in solving some familiar puzzles involving substitutivity in epistemic contexts, and compare the kooky object approach to more modern approaches (...) involving the notion of referential opacity. I conclude by proposing that Aristotle provides an implicit role for kooky objects in such metaphysical contexts as the Categories and Metaphysics. (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 book reinvigorates the philosophical treatment of the nature, purpose, and meaning of thought in today’s universities. The wider discussion about higher education has moved from a philosophical discourse to a discourse on social welfare and service, economics, and political agendas. This book reconnects philosophy with the central academic concepts of thought, reason, and critique and their associated academic practices of thinking and reasoning. Thought in this context should not be considered as a merely mental or cognitive construction, still less (...) a cloistered college, but a fully developed individual and social engagement of critical reflection and discussion with the current pressing disciplinary, political, and philosophical issues. The editors hold that the element of thought, and the ability to think in a deep and groundbreaking way is, still, the essence of the university. But what does it mean to think in the university today? And in what ways is thought related not only to the epistemological and ontological issues of philosophical debate, but also to the social and political dimensions of our globalised age? In many countries, the state is imposing limitations on universities, dismissing or threatening academics who speak out critically. With this volume, the editors ask questions such as: What is the value of thought? What is the university’s proper relationship to thought? To give the notion of thought a thorough philosophical treatment, the book is divided into in three parts. The focus moves from an epistemological perspective in Part I, to a focus on existence and values in higher education in Part II, and then to a societal-oriented focus on the university in Part III. All three parts, in their own ways, debate the notion of thought in higher education and the university as a thinking form of being. (shrink)

Professor Bergmann is an original thinker who has for many years wrestled with some of the most important and difficult problems of philosophy. Although at first mainly interested in epistemology, he has gradually come to the conclusion that the fundamental questions of philosophy are ontological and that even epistemology is in the last analysis “the ontology of the knowing process.” He holds that by neglecting the explicit formulation of his ontology, a philosopher courts intellectual disaster because the inadequacies (...) of the ontological foundation are likely to affect all philosophical superstructures built on it. In his last book [1], Bergmann explains some of the main features of his ontology in systematic form and criticizes competing systems, especially those of Brentano and Meinong, by comparing them with his own. In the critical parts of his work he tries to show that the competing ontologies are not adequate to the tasks for which they are intended and why this is so. The constructive and the critical parts supplement each other very well, since Brentano's and Meinong's questions and emphases are similar to Bergmann's. Broadly speaking, he regards his own ontology as a phase in a development of ontological insight which consists, at least negatively, in the gradual elimination of three major errors: nominalism, reism, and representationalism. (shrink)

It is Frege's third contribution that makes the point of departure for the present paper. Not merely did Frege show how to manipulate symbols more exactly; he also gave a searching account of what these symbols mean. Consider a philosophical problem that arises out of the simplest arithmetic. When we say that 5 = 2 + 3, what do we mean? Do we mean that 5 is identical with 2 + 3? But in some ways 5 and 2 + 3 (...) are obviously different. Or do we mean that 5 and 2 + 3 are equal but not identical, equality being a relation that falls short of complete identity? But in that case, some ordinary ways of speaking in mathematics must be false. Suppose a pupil is asked for the positive square root of 25. The phrasing of the question implies that there is one and only one. No doubt he may answer, '5'. But then it follows that the answer '2 + 3' is not allowable, since ex hypothesi 5 and 2 + 3, though equal, are not identical. Yet ordinarily the answer '2 + 3' would be regarded as strange but not as wrong. (shrink)

I understand Sartre's ontology to develop in three stages: first, through Being and Nothingness and Saint Genet: Actor and Martyr; second, through the Critique of Dialectical Reason; and, finally, as it unfolds in The Family Idiot. Each stage depends upon the former and deepens the original ontology, while still introducing novel elements. For example, in Being and Nothingness, the in-itself, which is the source of our world-making, develops in the Critique into the practico-inert, which is the world made (...) artifact, and in The Family Idiot, both the in-itself and the practico-inert unite to become the Spirit of the Age, joining our adventure with nature to that of our adventure with our family and our history. My reflection will be developed in four stages: first, a general overview; second, a more extended study of what Sartre calls the problematic of human reality; third, a brief reflection on Sartre's methodology; and finally, a concluding survey. (shrink)

Lesniewski’s ontology was one of the most inspiring aspects of Polish philosophy in the 20th century. I would like to reveal two original ways of thinking about names present in Polish pre-war philosophy and inspired by Lesniewski’s ideas, i.e. Kotarbinski’s reism and Ajdukiewicz’s criticism of the latter. It seems obvious, at least in texts of the philosophers quoted above, that the question of names was hiding much deeper quarrels. Although Kotarbinski’s and Ajdukiewicz’s positions were not in radical opposition, several (...) disagreements between them were very fruitful regarding their respective works. This paper gives an overview of their respective contributions to logic presented against the background of their philosophical positions. (shrink)

In this short, dense essay, Jean Cavaillès evaluates philosophical efforts to determine the origin - logical or ontological - of scientific thought, arguing that, rather than seeking to found science in original intentional acts, a priori meanings, or foundational logical relations, any adequate theory must involve a history of the concept. Cavaillès insists on a historical epistemology that is conceptual rather than phenomenological, and a logic that is dialectical rather than transcendental. His famous call (cited by Foucault) to abandon "a (...) philosophy of consciousness" for "a philosophy of the concept" was crucial in displacing the focus of philosophical enquiry from aprioristic foundations toward structural historical shifts in the conceptual fabric. This new translation of Cavaillès's final work, written in 1942 during his imprisonment for Resistance activities, presents an opportunity to reencounter an original and lucid thinker. Cavaillès's subtle adjudication between positivistic claims that science has no need of philosophy, and philosophers' obstinate disregard for actual scientific events, speaks to a dilemma that remains pertinent for us today. His affirmation of the authority of scientific thinking combined with his commitment to conceptual creation yields a radical defense of the freedom of thought and the possibility of the new. (shrink)