This paper describes an attempt to develop a pedagogy for teaching philosophy in science rather than a philosophy of science to be taught in the Bulgarian educational system.

Unter dem Begriff der „Verwissenschaftlichung der Methodologie der Wissenschaft“ verstehen wir den Einfluß wissenschaftlicher Erkenntnis auf die eine oder andere Art und Weise auf die Methodologie der Wissenschaft, insbesondere den Gebrauch von wissenschaftlichen Ideen und Methoden für die Formulierung und Lösung von methodologischen Problemen der Wissenschaft und Problemen der Methodologie selbst. Es werden vier Haupttendenzen im Prozeß der Verwissenschaftlichung der Methodologie vorgestellt: (a) der Übergang vom „statement view“ zum mathematischen Holismus; (b) die Verwissenschaftlichung auf system-theoretischer Basis; (c) der Einzug soziologischer (...) Methoden in die methodologische Analyse der Wissenschaft und (d) die methodologischen Anwendungen von Forschungsresultaten im Bereich der Künstlichen Intelligenz. Darüberhinaus werden einige besondere Formen der Implementierung wissenschaftlicher Konstruktionen in der Methodologie ins Auge gefaßt. (shrink)

It is the purpose of this paper to represent an analysis of four variants of critical philosophy of science: the constructivistic methodology, the reflexion upon science from the viewpoint of the critical theory of society, the ‘social natural science’ as a further development of the finalization conception, and the projective philosophy of science. Special attention is paid to the comparison of these variants. Some points of convergence as well as of divergence among them are revealed. A common shortcoming is indicated.

The following paper discusses from the point of view of the translator the obstacles, both institutional and linguistic, encountered during the introduction of Heidegger’s book Being and Time in the Bulgarian socio-cultural context. In particular some basic terms, which compose the core of Heidegger’s book, have been thoroughly analyzed. These include terms and categories such as: Dasein, Geschichte / Historie, Zeitigkeit / Zeitlichkeit, Gegenwart / Gegen-wart, Zukunft / Zukommen, Gewärtigen, Vergangenheit, Man / Manselbst, Bewandtnis and others. Concrete arguments have been (...) given in order to prove that direct borrowing of some of those terms, existing in translations from Russian and other languages, is not feasible. (shrink)

Given a class ℱ oft otal functions in the set oft he natural numbers, one could study the real numbers that have arbitrarily close rational approximations explicitly expressible by means of functions from ℱ. We do this for classes ℱsatisfying certain closedness conditions. The conditions in question are satisfied for example by the class of all recursive functions, by the class of the primitive recursive ones, by any of the Grzegorczyk classes ℰnwith n ≥ 2, by the class of all (...) functions recursive in a given function and by the class of the functions primitive recursive in it, as well as by the class of all total functions in the set of the natural numbers. (shrink)

The following paper discusses from the point of view of the translator the obstacles, both institutional and linguistic, encountered during the introduction of Heidegger’s book Being and Time in the Bulgarian socio-cultural context. In particular some basic terms, which compose the core of Heidegger’s book, have been thoroughly analyzed. These include terms and categories such as: Dasein, Geschichte / Historie, Zeitigkeit / Zeitlichkeit, Gegenwart / Gegen-wart, Zukunft / Zukommen, Gewärtigen, Vergangenheit, Man / Manselbst, Bewandtnis and others. Concrete arguments have been (...) given in order to prove that direct borrowing of some of those terms, existing in translations from Russian and other languages, is not feasible. (shrink)

In this paper I try to underline both the positive and negative circumstances in which I began translating Heidegger's "Sein und Zeit" in Greek. In 1971 I started, as a young student of philosophy, to study and translate this book, although I misunderstood it and considered it as a paradigm of "existentiell", not existential philosophy. I benefited essentially from both the English and the French translations and I've also received great help from my Greek mentor, E. N. Platis. I published (...) my translation in two volumes, one in 1978 and the other in 1985 and the critics have been very positive. At the beginning, I gave extended explanations about the translation problems and my solutions in a paper published in 1974. In the following years, I wrote articles about the Heideggerian concepts, in order to facilitate a better understanding of his philosophy.. (shrink)

In order to avoid the use of individual variables in predicate calculus, several authors proposed language whose expressions can be interpreted, in general, as denotations of predicates . The present author also proposed a language of this kind [5]. The absence of individual variables makes all these languages rather different from the traditional language of predicate calculus and from the usual language of mathematics. The translation procedures from the ordinary predicate languages into the predicate languages without individual variables and vice (...) versa have a technical character. It is desirable to make possible carrying out such procedures by performing some transformations in a suitable new language which comprises both a sublanguage similar to the ordinary predicate languages and another one not using individual variables. We shall propose now a language of the desired kind. The expressions of this language could be interpreted, in general, as denoting predicates which depend on parameters on a given object domain – this predicate has one argument and depends on one parameter). The proposed language will have the modal features noted in [3] and [5]. It is worthy of mention that the language proposed at the end of [4] although containing expressions interpreted as predicates and expressions with parameters does not allow simultaneous availability of argument places and parameters. (shrink)

A theorem published by A. Grzegorczyk in 1955 states a certain kind of effective uniform continuity of computable functionals whose values are natural numbers and whose arguments range over the total functions in the set of the natural numbers and over the natural numbers. Namely, for any such functional a computable functional with one function-argument and the same number-arguments exists such that the values of the first of the functionals at functions dominated by a given one are completely determined by (...) their restrictions to numbers not exceeding the corresponding values of the second functional at the given function. We prove versions of this theorem for the class of the primitive recursive functionals and for the class of the elementary recursive ones. Analogous results can be proved for many other subrecursive classes of functionals. (shrink)

We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: $$\begin{array}{ll}\mathbf{Some}\, a \,{\rm are} \,R-{\rm related}\, {\rm to}\, \mathbf{some} \,b;\\ \mathbf{Some}\, a \,{\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{all}\, b;\\ \mathbf{All}\, a\, {\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{some}\, b;\\ \mathbf{All}\, a\, {\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{all} \,b.\end{array}$$ Such primitives formalize sentences from natural language like ‘ All students read some textbooks’. Here a, b denote arbitrary sets (of objects), and R denotes an (...) arbitrary binary relation between objects. The language of the logic contains only variables denoting sets, determining the class of set terms, and variables denoting binary relations between objects, determining the class of relational terms. Both classes of terms are closed under the standard Boolean operations. The set of relational terms is also closed under taking the converse of a relation. The results of the paper are the completeness theorem with respect to the intended semantics and the computational complexity of the satisfiability problem. (shrink)

At stake in the classical realism-debate is the clash between realist and anti-realist positions. In recent years, the classical form of this debate has undergone a double transformation. On the one hand, the champions of realism began to pay more attention to the interpretative dimensions of scientific research. On the other hand, anti-realists of various sorts realized that the rejection of the hypostatization of a “reality out there” does not imply the denial of working out a philosophically adequate concept of (...) reality. Against the background of this double transformation, new arguments in the realism-debate emerged. The present Introduction is an attempt at systematizing these arguments within the spectrum of doctrines between the poles of scientific realism (exposed and defended by Howard Sankey) and hermeneutic realism (advocated by Dimitri Ginev). The authors try also to demonstrate that after the classical debates the issue of scientism has to be addressed in new ways. (shrink)

This paper is a continuation of [VAK 01]. The notion of local connection algebra, based on the primitive notions of connection and boundedness, is introduced. It is slightly different but equivalent to Roeper's notion of region-based topology [ROE 97]. The similarity between the local proximity spaces of Leader [LEA 67] and local connection algebras is emphasized. Machinery, analogous to that introduced by Efremovi?c [EFR 51],[EFR 52], Smirnov [SMI 52] and Leader [LEA 67] for proximity and local proximity spaces, is developed. (...) This permits us to give new proximity-type models of local connection algebras, to obtain a representation theorem for such algebras and to give a new shorter proof of the main theorem of Roeper's paper [ROE 97]. Finally, the notion of MVD-algebra is introduced. It is similar to Mormann's notion of enriched Boolean algebra [MOR 98], based on a single mereological relation of interior parthood. It is shown that MVD-algebras are equivalent to local connection algebras. This means that the connection relation and boundedness can be incorporated into one, mereological in nature relation. In this way a formalization of the Whiteheadian theory of space based on a single mereological relation is obtained. (shrink)

Four known three-valued logics are formulated axiomatically and several completeness theorems with respect to nonstandard intuitive semantics, connected with the notions of information, contrariety and subcontrariety is given.

For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect to this class. These two computability notions are natural generalizations of certain notions introduced in a previous paper co-authored by Andreas Weiermann and in another previous paper by the same authors, respectively. Under certain weak assumptions about the class in question, (...) we show that conditional computability is preserved by substitution, that all conditionally computable real functions are locally uniformly computable, and that the ones with compact domains are uniformly computable. The introduced notions have some similarity with the uniform computability and its non-uniform extension considered by Katrin Tent and Martin Ziegler, however, there are also essential differences between the conditional computability and the non-uniform computability in question. (shrink)

Constructive logic with Nelson negation is an extension of the intuitionistic logic with a special type of negation expressing some features of constructive falsity and refutation by counterexample. In this paper we generalize this logic weakening maximally the underlying intuitionistic negation. The resulting system, called subminimal logic with Nelson negation, is studied by means of a kind of algebras called generalized N-lattices. We show that generalized N-lattices admit representation formalizing the intuitive idea of refutation by means of counterexamples giving in (...) this way a counterexample semantics of the logic in question and some of its natural extensions. Among the extensions which are near to the intuitionistic logic are the minimal logic with Nelson negation which is an extension of the Johansson's minimal logic with Nelson negation and its in a sense dual version — the co-minimal logic with Nelson negation. Among the extensions near to the classical logic are the well known 3-valued logic of Lukasiewicz, two 12-valued logics and one 48-valued logic. Standard questions for all these logics — decidability, Kripke-style semantics, complete axiomatizability, conservativeness are studied. At the end of the paper extensions based on a new connective of self-dual conjunction and an analog of the Lukasiewicz middle value ½ have also been considered. (shrink)

The paper is devoted to the contributions of Helena Rasiowa to the theory of non-classical negation. The main results of Rasiowa in this area concerns–constructive logic with strong (Nelson) negation.

Mereotopology is an extension of mereology with some relations of topological nature like contact. An algebraic counterpart of mereotopology is the notion of contact algebra which is a Boolean algebra whose elements are considered to denote spatial regions, extended with a binary relation of contact between regions. Although the language of contact algebra is quite expressive to define many useful mereological relations and mereotopological relations, there are, however, some interesting mereotopological relations which are not definable in it. Such are, for (...) instance, the relation of n-ary contact, internal connectedness and some others. To overcome this disadvantage, we introduce a generalisation of contact algebra, replacing the contact with a binary relation between finite sets of regions and a region, satisfying some formal properties of Tarski consequence relation. The obtained system is called sequent algebra, considered as an algebraic counterpart of a new mereotopology. We develop the topological representation theory for sequent algebras showing in this way certain correspondence between point-free and point-based models of space. As a by-product, we show how one logical relation in nature notion, Tarski consequence relation, may have also certain spatial meaning. (shrink)

In this paper, intuitionistic modal logics which do not admit the law of the excluded middle are studied. The main result is that there exista a continuum of such logics.

lecting statistics about missing bindings and macros, and other errors. This guides debugging and development efforts, leading to iterative improvements in both the tools and the quality of the converted corpus. The build system thus serves as both a production conversion engine and software test harness. We have now processed the complete arχiv collection through 2006 consisting of more than 400,000 documents (a complete run is a processor-yearsize undertaking), continuously improving our success rate. We are now able to convert more (...) than 90% of these documents to XHTML+MathML. We consider over 60% to be successes, converted with no or minor warnings. While the remaining 30% can also be converted, their quality is doubtful, due to unsupported macros or conversion errors. (shrink)

In this paper we show how modal logic can be applied in the axiomatizations of some dynamic ontologies. As an example we consider the case of mereotopology, which is an extension of mereology with some relations of topological nature like contact relation. We show that in the modal extension of mereotopology we may define some new mereological and mereotopological relations with dynamic nature like stable part-of and stable contact. In some sense such “stable” relations can be considered as approximations of (...) the “essential relations” in the domain of mereotopology. (shrink)

The main results of the paper are the following: For each monadic prepositional formula which is classically true but not intuitionistically so, there is a continuum of intuitionistic monotone modal logics L such that L+ is inconsistent.There exists a consistent intuitionistic monotone modal logic L such that for any formula of the kind mentioned above the logic L+ is inconsistent.

A duality between Pawlak's knowledge representation systems and certain information systems of logical type, called bi-consequence systems is established. As an application a first-order characterization of some informational relations is given and a completeness theorem for the corresponding modal logic INF is proved. It is shown that INF possesses finite model property and hence is decidable.

A new modal logic containing four dynamic modalities with the following informal reading is introduced: $${\square^\forall}$$ – always necessary , $${\square^\exists}$$ – sometimes necessary , and their duals – $${\diamondsuit^\forall}$$ – always possibly , and $${\diamondsuit^\exists}$$ – sometimes possibly . We present a complete axiomatization with respect to the intended formal semantics and prove decidability via fmp.

ABSTRACT The notion of n-dimensional arrow structure is introduced, which for n = 2 coincides with the notion of directed multi-graph. In part I of the paper several first-order and modal languages connected with arrow structures are studied and their expressive power is compared. Part II is devoted to the axiomatization of some arrow logics. At the end some further perspectives of ?arrow approach? are discussed.

We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all inductive formulae (...) are elementary canonical and thus extend Sahlqvist’s theorem over them. In particular, we give a simple example of an inductive formula which is not frame-equivalent to any Sahlqvist formula. Then, after a deeper analysis of the inductive formulae as set-theoretic operators in descriptive and Kripke frames, we establish a somewhat stronger model-theoretic characterization of these formulae in terms of a suitable equivalence to syntactically simpler formulae in the extension of the language with reversive modalities. Lastly, we study and characterize the elementary canonical formulae in reversive languages with nominals, where the relevant notion of persistence is with respect to discrete frames. (shrink)

One of the important extensions of PDL is PDL with intersection of programs. We devote this paper to its complete axiomatization.

This paper is devoted to the complete axiomatization of dynamic extensions of arrow logic based on a restriction of propositional dynamic logic with intersection. Our deductive systems contain an unorthodox inference rule: the inference rule of intersection. The proof of the completeness of our deductive systems uses the technique of the canonical model.

_ _In __The Tenets of Cognitive Existentialism__, Dimitri Ginev draws on devel-opments in hermeneutic phenomenology and other programs in hermeneutic philosophy to inform an interpretative approach to scientific practices. At stake is the question of whether it is possible to integrate forms of reflection upon the ontological difference in the cognitive structure of scientific research. A positive answer would have implied a proof that “science is able to think.” This book is an extended version of such a proof. Against (...) those who claim that modern science is doomed to be exclusively committed to the nexus of objectivism and instrumental rationality, the interpretative theory of scientific practices reveals science’s potentiality of hermeneutic self-reflection. Scientific research that takes into consideration the ontological difference has resources to enter into a dialogue with Nature. Ginev offers a critique of postmodern tendencies in the philosophy of science, and sets out arguments for a feminist hermeneutics of scientific research. (shrink)

Ginev works out a conception of the constitution of scientific objects in terms of hermeneutic phenomenology. Recently there has been a revival of interest in hermeneutic theories of scientific inquiry. The present study is furthering this interest by shifting the focus from interpretive methods and procedures to the kinds of reflexivity operating in scientific conceptualization. According to the book's central thesis, a reflexive conceptualization enables one to take into consideartion the role which the ontic-ontological difference plays in the constitution (...) of scientific objects. The book argues for this thesis by analyzing the formation of objects of inquiry in a range of scientific domains stretching from highly formalized domains where the quest for objects' identities is carried out in terms of objects' emancipation from structures to linguistic and historiographic programs that avoid procedural objectification in their modes of conceptualization. The book sets up a new strategy for the dialogue between scientifc inquiry and hermeneutic phenomenology. (shrink)

We propose a generalization of Sahlqvist formulas to polyadic modal languages by representing such languages in a combinatorial PDL style and thus, in particular, developing what we believe to be the right syntactic approach to Sahlqvist formulas at all. The class of polyadic Sahlqvist formulas PSF defined here expands essentially the so far known one. We prove first-order definability and canonicity for the class PSF.

We propose a generalization of Sahlqvist formulae to polyadic modal languages by representing modal polyadic languages in a combinatorial style and thus, in particular, developing what we believe to be the right approach to Sahlqvist formulae at all. The class of polyadic Sahlqvist formulae PSF defined here expands essentially the so far known one. We prove first-order definability and canonicity for the class PSF.

Recently there has been a revival of interest in hermeneutic theories of scientific inquiry. Ginev is furthering this interest by shifting the focus from interpretive methods and procedures to the kinds of reflexivity operating in scientific concept.

Hyperboolean algebras are Boolean algebras with operators, constructed as algebras of complexes (or, power structures) of Boolean algebras. They provide an algebraic semantics for a modal logic (called here a {\em hyperboolean modal logic}) with a Kripke semantics accordingly based on frames in which the worlds are elements of Boolean algebras and the relations correspond to the Boolean operations. We introduce the hyperboolean modal logic, give a complete axiomatization of it, and show that it lacks the finite model property. The (...) method of axiomatization hinges upon the fact that a "difference" operator is definable in hyperboolean algebras, and makes use of additional non-Hilbert-style rules. Finally, we discuss a number of open questions and directions for further research. (shrink)

The paper provides an overview of the hermeneutic and phenomenological context from which the idea of a “constitutional analysis” of science originated. It analyzes why the approach to “hermeneutic fore-structure of scientific research” requires to transcend the distinction between the context of justification and the context of discovery. By incorporating this approach into an integral “postmetaphysical philosophy of science”, I argue that one can avoid the radical empiricism of recent science studies, while also preventing the analysis of science's discursive practices (...) from collapsing into the frames of radical anti-epistemological critique mandated by some hermeneutic philosophers. (shrink)

In this article, I examine various aspects of the application of Heidegger's motif of interpretative articulation (the core phenomenological motif of existential analytic) to the constitutional analysis of meaningful objects in scientific research that are contextually ready-to-hand. It is my contention that not only the concepts of the ‘fore-structure of understanding’ and the ‘as-structure of interpretation’, but also the extended concepts of the ‘hermeneutic fore-structure of meaning constitution’ and ‘characteristic hermeneutic situation’ are the keys to understanding the interpretative nature of (...) scientific research. The paper applies the constitutional analysis of hermeneutic phenomenology to several phenomena of scientific research—constitution of meaningful objects, situational fulfilment of a domain's general project, production of a domain's thematically given objects, implementation of readable technologies to what is contextually ready-to-hand, reading hypothetical theoretical objects, and exegetical textualizing within interrelated practices. The study is supplied with exemplary illustrations from enzymology and biochemistry. The correlation between a domain's interpretative articulation and the appropriation of research possibilities within the research everydayness is addressed. Special attention is paid to the belief in and reading of intracellular enzymes as hypothetical theoretical objects. (shrink)

Much of Ludwik Fleck’s work on the social constitution of knowledge, scientific facts, and objects of inquiry is informed by a specific use of transcendental arguments. This paper analyzes the ways in which Fleck looks for “conditions of possibilities” for the stylization and circulation of cognition. Following a brief discussion of his political agenda regarding science’s “cultural mission,” the paper offers a reconstruction of Fleck’s implicit concept of the transcendental. It is argued that Fleck addresses scientific truth as an ongoing (...) revealing and concealing of possibilities for doing research. By implication, the truth about a scientific fact is at once situated in scientific practices and transcended by a horizon of possibilities. The transcendental takes shape in Fleck’s social epistemology as a result of the reflection upon knowledge production’s “situated transcendence.”. (shrink)