Contemporary formalisations of Meinong's theory of objects prove that Russell's accusation of inconsistency of the theory is not valid. However, in the same formalisations there has appeared a new source of potential inconsistency. Theories of objects inspired by Meinong's ontology usually include, in addition to basic principles of the ontology, abstraction-axioms for defining objects and properties (relations). Although these axioms seem to be perfectly acceptable, they lead to paradoxes when adopted without any restrictions. These paradoxes may be understood as paradoxes (...) of size (not of self-referentiality): too many objects or too many properfies are defined by the axioms. We can avoid them at the cost of counterintuifive stipulations, some of them similar to those applied in set theory or in higher-order logics (like a stratificafion of formulas). We need however to look for phenomenologically well grounded protecfions against paradoxes. This search can deepen our understanding of the nature of Meinongian objects. (shrink)

A. Meinong’s views are usually associated with an highly inflated ontology including various kinds of nonexistent objects, incomplete and impossible ones among others. Around the turn of the century B. Russell strongly criticised this ontology accusing it of inconsistency. And perhaps because of this criticism Meinong’s views have been forgotten for a long time. Only recently some philosophers have created theories of objects which are formalisations of Meinong’s ontology or which are directly inspired by the ontology 1 . However there (...) still remains a need to discuss the problem of ways of reference to Meinongian objects regarding their specific structure of predication, and the interrelated problem of ontological commitment of those theories. Meinong’s ontological theory seems to be not so bizzare if we interpret it as a theory of possible intentional objects, i.e. possible objects of consciousness. And this interpretation perfectly agrees with phenomenological tradition from Brentano to Husserl and with the contemporary philosophy of mind. Needless to say reference is a special form of intentional relation so semantical investigations into these objects are of great relevance for general theory of intentionality. (shrink)

Contemporary formalisations of Meinong's theory of objects prove that Russell's accusation of inconsistency of the theory is not valid. However, in the same formalisations there has appeared a new source of potential inconsistency. Theories of objects inspired by Meinong's ontology usually include, in addition to basic principles of the ontology, abstraction-axioms for defining objects and properties (relations). Although these axioms seem to be perfectly acceptable, they lead to paradoxes when adopted without any restrictions. These paradoxes may be understood as paradoxes (...) of size (not of self-referentiality): too many objects or too many properfies are defined by the axioms. We can avoid them at the cost of counterintuifive stipulations, some of them similar to those applied in set theory or in higher-order logics (like a stratificafion of formulas). We need however to look for phenomenologically well grounded protecfions against paradoxes. This search can deepen our understanding of the nature of Meinongian objects. (shrink)

Intentionality is one of the most frequently discussed topics in contemporary phenomenology and analytic philosophy. This book investigates intentionality from the point of view of intentional objects. According to the classical approach to this concept, whatever can be consciously experienced is regarded as an intentional object. Thus, not only ordinary existing individuals but also various kinds of non-existents and non-individuals are considered as intentional. Alexius Meinong, an Austrian philosopher, is particularly well-known as the `inventor' of an abundant ontology of objects (...) among which even incomplete and impossible ones, like `the round square', find their place. Drawing inspirations from Meinong's ideas, the author develops a simple logic of intentional objects, M-logic. M-logic closely resembles classical first-order logic and, as opposed to the formally complicated contemporary theories of non-existent objects, it is much more friendly in apprehending and applications. However, despite this resemblance, the ontological content of M-logic far exceeds that of classical logic. In this book formal investigations are intertwined with philosophical analyses. On the one hand, M-logic is used as a tool for investigating formal features of intentional objects. On the other hand, the study of intentionality phenomena suggests further ways of extending and modifying M-logic. Audience: The book is addressed to logicians, cognitive scientists, philosophers of language and metaphysics with either a phenomenological or an analytic background. (shrink)

Putting individual constants and quantifiers into the same syntactic category within first-order language promises to have far-reaching consequences: a syntax of this kind can reveal the potential of any such language, allowing us to realize that a vast class of noun phrases, including non-denoting terms, can be accommodated in the new syntax as expressions suited to being subjects of sentences. In the light of this, a formal system that is an extension of classical first-order logic is developed here, and is (...) equipped with an appropriate semantics. An ontological interpretation of the new logic is then also provided, with several categories of object and notions of existence being distinguished. Last but not least, a modal version of the logic, with some interesting formal features, is proposed. (shrink)

ABSTRACT Leśniewskian Ontology (LO) is a system in which the basic subject-predicate formula takes the form of a b and express one-argument predication, e.g. John is a student. In LO’s language, there is no many-argument form of predication given that would allow for the structural expression of, for example, the sentence John is Anne’s son. In this article, a simple and natural extension of LO is suggested to encompass many-argument predication. The system thus obtained corresponds to polyadic second-order logic.

Contemporary formalisations of Meinong's theory of objects prove that Russell's accusation of inconsistency of the theory is not valid. However, in the same formalisations there has appeared a new source of potential inconsistency. Theories of objects inspired by Meinong's ontology usually include, in addition to basic principles of the ontology, abstraction-axioms for defining objects and properties . Although these axioms seem to be perfectly acceptable, they lead to paradoxes when adopted without any restrictions. These paradoxes may be understood as paradoxes (...) of size : too many objects or too many properfies are defined by the axioms. We can avoid them at the cost of counterintuifive stipulations, some of them similar to those applied in set theory or in higher-order logics . We need however to look for phenomenologically well grounded protecfions against paradoxes. This search can deepen our understanding of the nature of Meinongian objects. (shrink)

The paper discusses main issues concerning truthmakers: (1) what is the ontological status of truthmakers (are they ordinary objects, situations, tropes etc?), (2) what are deduvtive properties of truthmakers. A simple logic of truthmakers is developed. The logic consists of an axiomatic system and a possible world semantics.

Ramsey questions the distinction between subject and predicate in sentences. Since the distinction mirrors the ontological distinction object/property (particular/universal) he questions the latter distinction as well. There is a symmetry between the category of objects and the category of properties: an object can possess a number of properties and a property can be exemplified by a number of objects. Consequently, it may be claimed that the two categories are formally indiscernible. The paper develops Ramsey's thesis on the ground of logic. (...) Different senses of indiscernibility are discussed and various systems of logic are examined with respect to these senses. Most systems do not distinguish objects from properties in at least one sense. (shrink)

Let J be any proper ideal of subsets of the real line R which contains all finite subsets of R. We define an ideal J * ∣B as follows: X ∈ J * ∣B if there exists a Borel set $B \subset R \times R$ such that $X \subset B$ and for any x ∈ R we have $\{y \in R: \langle x,y\rangle \in B\} \in \mathscr{J}$ . We show that there exists a family $\mathscr{A} \subset \mathscr{J}^\ast\mid\mathscr{B}$ of power ω (...) 1 such that $\bigcup\mathscr{A} \not\in \mathscr{J}^\ast\mid\mathscr{B}$ . In the last section we investigate properties of ideals of Lebesgue measure zero sets and meager sets in Cohen extensions of models of set theory. (shrink)

Jacek Urbaniec: Platonism in the philosophy of mathematics does not necessarily imply that there are links between the temporal physical world and the eternal world of mathematics..

In this paper we present a characterization of hyper-connexivity by means of a relating semantics for Boolean connexive logics. We also show that the minimal Boolean connexive logic is Abelardian, strongly consistent, Kapsner strong and antiparadox. We give an example showing that the minimal Boolean connexive logic is not simplificative. This shows that the minimal Boolean connexive logic is not totally connexive.

The author presents Leszek Kołakowski from the perspective of his private acquaintanceship, lasting for about 47 years, as a witty man and a workaholic. L. Kołakowski never formed a classic “school”, but there is something all his disciples share: a thesis, key to understanding his ideas, which holds that “THERE IS MORE THAN ONE CORRECT OPINION IN THE HUMANITIES”, i.e. we will ALWAYS have opinions for and against, which goes against any dogmatism, wherever it may appear; this also bears consequences (...) in diagnosing the socio-political reality past and present. (shrink)

In the present article I explain the role of the figure of “the last god” in Heidegger’s thought after the so-called Heideggerian “turn.” Drawing on Heidegger’s Contributions to Philosophy (From Enowning), it is argued that the figure of “the last god” demonstrates Heidegger’s path to “being itself,” which I distinguish from the path to being presented by him in his earlier thought, mainly laid out in Being and Time. The figure of the last god is not to be understood as (...) a god in a religious framework, but rather as an explication of metaphysical radical thinking, rendered as Heidegger’s view of “divinity of the other beginning.” The notion of the last god is presented against the background of several of Heidegger’s ideas (as specifications) discussed in Contributions namely: disclosure of being itself, the renewal of metaphysics, the understanding of nothing/nothingness in relation to being, the problem of the “sign” (Wink) or the ontic and ontological differences. In a metaphorical form, Heidegger leads us – by means of the specifications given – towards the experience of the “last god,” whose “passage” is for Dasein the experience of being itself, is the event of being. In the text presented here, I will “lead” the reader along such “path.” At the same time, I will engage Heidegger’s language without neglecting its semantic “depth,” showing how Heidegger extracts hidden meanings from words. (shrink)

In this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ℝ2 and ℝ. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly nonmeasurable subset of the real line, which has different properties than classical non-measurable subsets of reals. We shall also consider the question whether all images of bounded measurable subsets of the plane via a such mapping are non-measurable.

In this paper the notion of unifier is extended to the infinite set case. The proof of existence of the most general unifier of any infinite, unifiable set of types (terms) is presented. Learning procedure, based on infinite set unification, is described.

We prove that no logic (i.e. consequence operation) determined by any class of orthomodular lattices admits the deduction theorem (Theorem 2.7). We extend those results to some broader class of logics determined by ortholattices (Corollary 2.6).

We assess Cartwright's models for probabilistic causality and, in particular, her models for EPR-like experiments of quantum mechanics. Our first objection is that, contrary to econometric linear models, her quasi-linear models do not allow for the unique estimation of parameters. We next argue that although, as Cartwright proves, Reichenbach's screening-off condition has only limited validity, her generalized condition is not empirically applicable. Finally, we show that her models for the EPR are mathematically incorrect and physically implausible.

We assess Cartwright's models for probabilistic causality, and in particular, her models for EPR-like experiments of quantum mechanics. We show that her models for the EPR are mathematically incorrect and physically implausible. Finally, we argue that her models are not adequate for EPR-phenomena, since they ignore modal and spatiotemporal aspects inherent in their setup.