Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, □ is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and □ can be understood as a topological modality. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Let a dynamic topological system (...) be a topological space X together with a continuous function f. f can be thought of in temporal terms, moving the points of the topological space from one moment to the next. Dynamic topological logics are the logics of dynamic topological systems, just as S4 is the logic of topological spaces. Dynamic topological logics are defined for a trimodal language with an S4-ish topological modality □ , and two temporal modalities, ○ and * , both interpreted using the continuous function f. In particular, ○ expresses f’s action on X from one moment to the next, and * expresses the asymptotic behaviour of f. (shrink)

Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, □ is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and □ can be understood as a topological modality. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Let a dynamic topological system (...) be a topological space X together with a continuous function f. f can be thought of in temporal terms, moving the points of the topological space from one moment to the next. Dynamic topological logics are the logics of dynamic topological systems, just as S4 is the logic of topological spaces. Dynamic topological logics are defined for a trimodal language with an S4-ish topological modality □, and two temporal modalities, ○ and *, both interpreted using the continuous function f. In particular, ○ expresses f’s action on X from one moment to the next, and * expresses the asymptotic behaviour of f. (shrink)

This note is a friendly amendment to Marti's analysis of the failure of Føllesdal's argument that modal distinctions collapse in Carnap's logic S2. Føllesdal's argument turns on the treatment of descriptions. Marti considers how modal descriptions, which Carnap banned, might be handled; she adopts an approach which blocks Føllesdal's argument, but requires a separate treatment of non-modal descriptions. I point out that a more general treatment of descriptions in S2 is possible, and indeed is implicit in Marti's informal discussion, and (...) that this treatment also blocks Føllesdal's argument. Further, I show by a semantic argument that no revised version of Føllesdal's argument could establish a collapse of modal distinctions. (shrink)

Let ${{\mathcal L}^{\square\circ}}$ be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality □ and a temporal modality ◦, understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language ${{\mathcal L}^{\square\circ}}$ by interpreting ${{\mathcal L}^{\square\circ}}$ in dynamic topological systems, i.e., ordered pairs 〈X, f〉, where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiomatized a logic S4C, and have shown (...) that S4C is sound and complete for this semantics. S4C is also complete for continuous functions on Cantor space (Mints and Zhang, Kremer), and on the real plane (Fernández Duque); but incomplete for continuous functions on the real line (Kremer and Mints, Slavnov). Here we show that S4C is complete for continuous functions on the rational numbers. (shrink)

Let $\mathcal{L}$ be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality $\square$ and a temporal modality $\bigcirc$ , understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language $\mathcal{L}$ by interpreting $\mathcal{L}$ in dynamic topological systems, i.e. ordered pairs $\langle X, f\rangle$ , where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiomatized a logic S4C, and have shown (...) that S4C is sound and complete for this semantics. Zhang and Mints have shown that S4C is complete relative to a particular topological space, Cantor space. The current paper produces an alternate proof of the Zhang-Mints result. (shrink)

§1. Introduction. When truth-theoretic paradoxes are generated, two factors seem to be at play: the behaviour that truth intuitively has; and the facts about which singular terms refer to which sentences, and so on. For example, paradoxicality might be partially attributed to the contingent fact that the singular term, "the italicized sentence on page one", refers to the sentence, The italicized sentence on page one is not true. Factors of this second kind might be represented by a ground model: an (...) interpretation of all the names, function symbols, and predicates in the potentially self-referential language under study, with the exception of the predicate "x is true". Formally, suppose that L is an uninterpreted first order language. M = 〈D, I〉 is a classical model for L if D is a nonempty set; and I is a function assigning to each name of L a member of D, to each n-place function symbol of L a function from Dn to D, and to each nonlogical n-place predicate of L a function from Dn to {t, f}. Suppose furthermore that L+ is obtained by adding a new one-place predicate T to L, and that L has a quote name ‘A’ for each sentence A of L+. We follow Gupta and Belnap [5] in defining S =df {A: A is a sentences of L+}. A classical model M = 〈D, I〉 for L is a ground model for L iff both S ⊆ D, and I(‘A’) = A for each A ∈ S. A classical ground model for L is a representation of the supposedly unproblematic fragment of L+: a representation of which terms refer to which objects, and of which objects have which nonsemantic properties. (shrink)

modality , understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language L by interpreting L in dynamic topological systems, i.e. ordered pairs X, f , where X is a topological space and f is a..

We investigate computational properties of propositional logics for dynamical systems. First, we consider logics for dynamic topological systems (W.f), fi, where W is a topological space and f a homeomorphism on W. The logics come with ‘modal’ operators interpreted by the topological closure and interior, and temporal operators interpreted along the orbits {w, f(w), f2 (w), ˙˙˙} of points w ε W. We show that for various classes of topological spaces the resulting logics are not recursively enumerable (and so not (...) recursively axiomatisable). This gives a ‘negative’ solution to a conjecture of Kremer and Mints. Second, we consider logics for dynamical systems (W, f), where W is a metric space and f and isometric function. The operators for topological interior/closure are replaced by distance operators of the form ‘everywhere/somewhere in the ball of radius a, ‘for a ε Q +. In contrast to the topological case, the resulting logic turns out to be decidable, but not in time bounded by any elementary function. (shrink)

The integration of standardized biomedical terminologies into a single, unified knowledge representation system has formed a key area of applied informatics research in recent years. The Unified Medical Language System (UMLS) is the most advanced and most prominent effort in this direction, bringing together within its Metathesaurus a large number of distinct source-terminologies. The UMLS Semantic Network, which is designed to support the integration of these source-terminologies, has proved to be a highly successful combination of formal coherence and broad scope. (...) We argue here, however, that its organization manifests certain structural problems, and we describe revisions which we believe are needed if the network is to be maximally successful in realizing its goals of supporting terminology integration. (shrink)

Frege’s distinction between sense (Sinn) and meaning (Bedeutung) is his most influential contribution to philosophy, however central it was to his own projects, and however he may have conceived its importance. Philosophers of language influenced by, or reacting against the distinction, and historians of philosophy commenting on it, have all contributed to the voluminous literature surrounding it.1 Nonetheless in this essay I hope to shed new light on the distinction by considering it in the context of the development of Frege’s (...) thought, and connecting it more intimately than is usually done with Frege’s interests in logic, especially his views on judgment, truth and inference, which were central to his own projects as he conceived them. (shrink)

Rorty claimed that politics is more important than science and philosphy, even his own philosophy. From pragmatist point of view science is also problemsolving and belongs to practice in broader sense.

Rorty claims that humans do not have absolute moral norms in metaphysical sense. There are important values and principles for him, but from his idea of contingency followes that he prefers the actual redescription and evaluation of every particular situation.

Fine and Kripke extended S5, S4, S4.2 and such to produce propositionally quantified systems , , : given a Kripke frame, the quantifiers range over all the sets of possible worlds. is decidable and, as Fine and Kripke showed, many of the other systems are recursively isomorphic to second-order logic. In the present paper I consider the propositionally quantified system that arises from the topological semantics for S4, rather than from the Kripke semantics. The topological system, which I dub , (...) is strictly weaker than its Kripkean counterpart. I prove here that second-order arithmetic can be recursively embedded in . In the course of the investigation, I also sketch a proof of Fine's and Kripke's results that the Kripkean system is recursively isomorphic to second-order logic. (shrink)

Dans la double perspective d'une épistémologie et d'une histoire des idées, cet ouvrage explicite le sens et la portée du concept de science positive, à l'époque de sa prise de conscience en Europe et dans les travaux auxquels Auguste Comte est mêlé de près ou de loin.

Where humans can manipulate and integrate the information they receive in subtle and ever-changing ways from context to context, computers need structured and context-free background information of a sort which ontologies can help to provide. A domain ontology captures the stable, highly general and commonly accepted core knowledge for an application domain. The domain at issue here is that of the life sciences, in particular molecular biology and bioinformatics. Contemporary life science research includes components drawn from physics, chemistry, mathematics, medicine (...) and many other areas, and all of these dimensions, as well as fundamental philosophical issues, must be taken into account in the construction of a domain ontology. Here we describe the basic features of domain ontologies in the life sciences and show how they can be used. (shrink)

This book is the fourth volume of selected papers from the Central European Pragmatist Forum (CEPF). It deals with the general question of self and society, and the papers are organized into sections on Self and History, Self and Society, Self and Politics, Self and Neopragmatism, and an Interview with Richard Rorty. The authors are among the leading specialists in American philosophy from universities across the US and in Central and Eastern Europe.

Appearing in English for the first time, Schelling’s 1842 lectures develop the idea that many philosophical concepts are born of religious-mythological notions.

This paper starts with one of Chalmers’ basic points: first-hand experience is an irreducible field of phenomena. I claim there is no ‘theoretical fix’ or ‘extra ingredient’ in nature that can possibly bridge this gap. Instead, the field of conscious phenomena requires a rigorous method and an explicit pragmatics for its exploration and analysis. My proposed approach, inspired by the style of inquiry of phenomenology, I have called neurophenomenology. It seeks articulations by mutual constraints between phenomena present in experience and (...) the correlative field of phenomena established by the cognitive sciences. It needs to expand into a widening research community in which the method is cultivated further. (shrink)

With fascinating historical anecdotes and incisive scientific analysis, this important work combines ancient thought with modern theory to reveal a new way of viewing our universe that can expand our awareness, our lives, and may well point the way to a new science for the twenty-first century.

Moral Case Deliberation is an up and coming form of ethics support wherein clinical professionals deliberate about moral questions they face in their work. So far, it has been unclear what quality of deliberation in MCD is entailed and how to evaluate this quality. This article proposes a coding scheme that fits the theoretical background of MCD and allows researchers to evaluate the quality of the deliberation in MCDs. We consider deliberation in MCD to be of good quality when participants (...) enrich their own understanding of a case by being exposed to the viewpoints of others. In order to have such an enriching effect, the deliberation in an MCD ought to involve different kinds of arguments from the perspectives of different stakeholders and in favour of different resolutions to the case; and the process of deliberation ought to be critical but constructive. (shrink)

The article considers approaches in order to study large municipal entities and their economic potential. The authors specify that large municipal entities in modern conditions have a multifunctional structure, so they propose an interdisciplinary approach to their study. The article discusses such approaches to analyzing large municipalities as: philosophical; research from the perspective of social sciences and the humanities (political science, sociological, psychological, historiographic and ethnographic approaches). The authors analyze large municipalities from the perspective of the geographical approach; urban theory; (...) urban planning and architecture. The problem of studying large municipalities in the legal sciences is separately investigated. With the help of the economic approach the authors show that at the core of urbanization and the emergence of large municipalities there are three effects: comparative advantage, concentration effect, and localization effect. The authors give classification of large municipalities. The authors propose a systematic approach to analyzing large cities, representing the unity of the functional approach, open systems methodology and the factor approach. Under the latter, it is proposed to understand the economic potential of the city, which presupposes the possibility of efficient use of available resources and their maximum inclusion in social reproduction in order to meet the needs of the municipality population. The authors substantiate the classification of the economic potential of a large municipal formation, which consists of: the resource (basic and used), innovative and infrastructural potentials. (shrink)