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)

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)

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)

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)

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

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 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 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)

Purpose. The dynamics and pace of social and economic transformations that are characteristic of modern society, lead to an increase in tension and the destruction of habitual stereotypes – ideals, values, norms, patterns of behaviour that unite people. These moments encourage us to rethink the understanding of "security" essence, in particular, psychological, which emphasizes the urgency of its study in the philosophical and sociocultural coordinates. Theoretical basis of the research is based on the philosophical methodology of K. Jaspers, E. Fromm (...) and the A. Maslow’s psychological approach to understanding of a person. Originality. Psychological security is considered at different levels: first and foremost, society is a characteristic of social security, that is an analysis of how today’s social technologies, social changes affect the quality of life of the country’s population; secondly, the social environment – the family, the immediate environment, reference groups, training teams; thirdly, a person is an experience of his own security-insecurity, when it is possible to talk about the manifestations of psychological violence, when certain behavioral acts contribute to the violation of the security of the other or to self-destruction. It is found out that the knowledge of psychological security is closely connected with the socio-historical conditions of being, with the level of development of material and spiritual culture, with the interests and values prevailing in society, which determines its ontological, epistemological and axiological features. The presented issue is considered in the correlation of psychological security with types of scientific rationality – classical, nonclassical and post-nonclassical approaches, within the framework of which various perspectives, aspects, forms and types of psychological security are studied. Conclusions. The concept of security requires a systematic description of its manifestations, types, levels, concepts: security as the absence of dangers ; security as a certain activity to ensure or to prevent any threats or dangers ; security as a conscious necessity, the value of the individual. The study systematizes various ideas about psychological security in accordance with the logic of scientific knowledge: in the mainstream of classical, non-classical and post-nonclassical approaches. (shrink)

COVID-19 often manifests with different outcomes in different patients, highlighting the complexity of the host-pathogen interactions involved in manifestations of the disease at the molecular and cellular levels. In this paper, we propose a set of postulates and a framework for systematically understanding complex molecular host-pathogen interaction networks. Specifically, we first propose four host-pathogen interaction (HPI) postulates as the basis for understanding molecular and cellular host-pathogen interactions and their relations to disease outcomes. These four postulates cover the evolutionary dispositions involved (...) in HPIs, the dynamic nature of HPI outcomes, roles that HPI components may occupy leading to such outcomes, and HPI checkpoints that are critical for specific disease outcomes. Based on these postulates, an HPI Postulate and Ontology (HPIPO) framework is proposed to apply interoperable ontologies to systematically model and represent various granular details and knowledge within the scope of the HPI postulates, in a way that will support AI-ready data standardization, sharing, integration, and analysis. As a demonstration, the HPI postulates and the HPIPO framework were applied to study COVID-19 with the Coronavirus Infectious Disease Ontology (CIDO), leading to a novel approach to rational design of drug/vaccine cocktails aimed at interrupting processes occurring at critical host-coronavirus interaction checkpoints. Furthermore, the host-coronavirus protein-protein interactions (PPIs) relevant to COVID-19 were predicted and evaluated based on prior knowledge of curated PPIs and domain-domain interactions, and how such studies can be further explored with the HPI postulates and the HPIPO framework is discussed. (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)

Here we present what we believe is a novel account of what languages are, along with an axiomatically rich representation of languages and language-related data that is based on this account. We propose an account of languages as aggregates of dispositions distributed across aggregates of persons, and in doing so we address linguistic competences and the processes that realize them. This paves the way for representing additional types of language-related entities. Like demographic data of other sorts, data about languages may (...) be of use to researchers in a number of areas, including biomedical research. Data on the languages used in clinical encounters are typically included in medical records, and capture an important factor in patient-provider interactions. Like many types of patient and demographic data, data on a person’s preferred and primary languages are organized in different ways by different systems. This can be a barrier to data integration. We believe that a robust framework for representing language in general and preferred and primary language in particular – which has been lacking in ontologies thus far – can promote more successful integration of language-related data from disparate data sources. (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)

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)

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)