We agree that supernatural beliefs are pervasive. However, we propose a more general account rooted in how people trace ordinary objects over time. Tracking identity involves attending to the causal history of an object, a process that may implicate hidden mechanisms. We discuss experiments in which participants exhibit the same “supernatural” beliefs when reasoning about the fates of cups and automobiles as those exhibited by Bering's participants when reasoning about spirits.
Pothos suggests dispensing with the distinction between rules and similarity, without defining what is meant by either term. We agree that there are problems with the distinction between rules and similarity, but believe these will be solved only by exploring the representations and processes underlying cases purported to involve rules and similarity.
This paper is based on Lectures 1, 2 and 4 in the series of ten lectures titled “Algebraic Structures for Logic” that Professor Blok and I presented at the Twenty Third Holiday Mathematics Symposium held at New Mexico State University in Las Cruces, New Mexico, January 8-12, 1999. These three lectures presented a new approach to the algebraization of deductive systems, and after the symposium we made plans to publish a joint paper, to be written by Blok, further (...) developing these ideas. That project was still incomplete when Blok died. In fact, there is no indication that he had prepared a draft of the paper, and we do not know what new material he intended to include. I am therefore not in a position to complete the project as he had envisioned it. So, I have settled for the more limited objective of presenting the material from the three lectures, leaving to others the task of adapting the techniques used there to more general situations. (shrink)
In the thirties, Martin Heidegger was heavily involved with the work of Ernst Jünger (1895-1998). He says that he is indebted to Jünger for the ‘enduring stimulus’ provided by his descriptions. The question is: what exactly could this enduring stimulus be? Several interpreters have examined this question, but the recent publication of lectures and annotations of the thirties allow us to follow Heidegger’s confrontation with Jünger more precisely. -/- According to Heidegger, the main theme of his philosophical thinking in the (...) thirties was the overcoming of the metaphysics of the will to power. But whereas he seems to be quite revolutionary in heralding ‘another beginning’ of philosophy in the beginning of the thirties, he later on realized that his own revolutionary vocabulary was itself influenced by the will to power. In his later work, one of the main issues is the releasement from the wilful way of philosophical thinking. My hypothesis is that Jünger has this importance for Heidegger in the thirties, because the confrontation with Jünger’s way of thinking showed him that the other beginning of philosophy presupposes the irrevocable releasement of willing and a gelassen or non-willing way of philosophical thinking. -/- In this article, we test this hypothesis in relation to the recently published lectures, annotations and unpublished notes from the thirties. After a brief explanation of Jünger’s diagnosis of modernity (§1), we consider Heidegger’s reception of the work of Jünger in the thirties (§2). He not only sees that Jünger belongs to Nietzsche’s metaphysics of the will to power, but also shows the modern-metaphysical character of Jünger’s way of thinking. In section three, we focus on Heidegger’s confrontation with Jünger in relation to the consummation of modernity. According to Heidegger, Jünger is not only the end of modern metaphysics, but also the perishing (Verendung) of this end, the oblivion of this end in the will to power of representation. In section four, we focus on the real controversy between Jünger and Heidegger: the releasement of willing and the necessity of a radical other beginning of philosophical thinking. -/- . (shrink)
The notion of an algebraic semantics of a deductive system was proposed in [3], and a preliminary study was begun. The focus of [3] was the definition and investigation of algebraizable deductive systems, i.e., the deductive systems that possess an equivalent algebraic semantics. The present paper explores the more general property of possessing an algebraic semantics. While a deductive system can have at most one equivalent algebraic semantics, it may have numerous different algebraic semantics. All of these give rise to (...) an algebraic completeness theorem for the deductive system, but their algebraic properties, unlike those of equivalent algebraic semantics, need not reflect the metalogical properties of the deductive system. Many deductive systems that don't have an equivalent algebraic semantics do possess an algebraic semantics; examples of these phenomena are provided. It is shown that all extensions of a deductive system that possesses an algebraic semantics themselves possess an algebraic semantics. Necessary conditions for the existence of an algebraic semantics are given, and an example of a protoalgebraic deductive system that does not have an algebraic semantics is provided. The mono-unary deductive systems possessing an algebraic semantics are characterized. Finally, weak conditions on a deductive system are formulated that guarantee the existence of an algebraic semantics. These conditions are used to show that various classes of non-algebraizable deductive systems of modal logic, relevance logic and linear logic do possess an algebraic semantics. (shrink)
There exist important deductive systems, such as the non-normal modal logics, that are not proper subjects of classical algebraic logic in the sense that their metatheory cannot be reduced to the equational metatheory of any particular class of algebras. Nevertheless, most of these systems are amenable to the methods of universal algebra when applied to the matrix models of the system. In the present paper we consider a wide class of deductive systems of this kind called protoalgebraic logics. These include (...) almost all (non-pathological) systems of prepositional logic that have occurred in the literature. The relationship between the metatheory of a protoalgebraic logic and its matrix models is studied. The following results are obtained for any finite matrix model U of a filter-distributive protoalgebraic logic : (I) The extension U of is finitely axiomatized (provided has only finitely many inference rules); (II) U has only finitely many extensions. (shrink)
Let S denote the variety of Sugihara algebras. We prove that the lattice (K) of subquasivarieties of a given quasivariety K S is finite if and only if K is generated by a finite set of finite algebras. This settles a conjecture by Tokarz [6]. We also show that the lattice (S) is not modular.
This contribution discusses the philosophical meaning of the Martin Heidegger’s Rectoral address. First of all, Heidegger’s philosophical basic experience is sketched as the background of his Rectoral address; the being-historical concept of “Anfang”. Then, the philosophical question of the Rectoral address is discussed. It is shown, that Die Selbstbehauptung der deutschen Universität is asking for the identity of human being there (Dasein) in connection with the question about dem Eigenen (the Germans) and dem Fremden (the Greeks). This opposition structuralizes the (...) confrontation with the beginning of philosophical thinking in the Rectoral address. When read against the philosophical background sustaining the Rectoral address, words appearing therein such as “Kampf”, “Macht”, “Volk” and “Marsch” have nothing in common with the same words as used by the Nazis. It is shown that the Rectoral address is an extremely ambiguous text, because it claims a transformation of human being there (Dasein). Although Heidegger’s view on National Socialism is distinguished from Nazis ideology, it is clear that he made a mistake about Hitler. This article makes clear how Heidegger later changed his mind and vocabulary, and in what way this kind of mistakes and changes of mind are inherent to philosophical empiricism. (shrink)
We study modal logics in the setting of varieties of modal algebras. Any variety of modal algebras generated by a finite algebra — such, a variety is called tabular — has only finitely many subvarieties, i.e. is of finite height. The converse does not hold in general. It is shown that the converse does hold in the lattice of varieties of K4-algebras. Hence the lower part of this lattice consists of tabular varieties only. We proceed to show that there is (...) a continuum of pretabular varieties of K4-algebras — those are the non-tabular varieties all of whose proper subvarieties are tabular — in contrast with Maksimova's result that there are only five pretabular varieties of S4-algebras. (shrink)
Different aspects of people's interactions with money are best conceptualized using the drug and tool theories. The key question is when these models of money are most likely to guide behavior. We suggest that the Drug Theory characterizes motivationally active uses of money and that the Tool Theory characterizes behavior in motivationally cool situations. (Published Online April 5 2006).
Modal logics are studied in their algebraic disguise of varieties of so-called modal algebras. This enables us to apply strong results of a universal algebraic nature, notably those obtained by B. Jonsson. It is shown that the degree of incompleteness with respect to Kripke semantics of any modal logic containing the axiom □ p → p or containing an axiom of the form $\square^mp \leftrightarrow\square^{m + 1}p$ for some natural number m is 2 ℵ 0 . Furthermore, we show that (...) there exists an immediate predecessor of classical logic (axiomatized by $p \leftrightarrow \square p$ ) which is not characterized by any finite algebra. The existence of modal logics having 2 ℵ 0 immediate predecessors is established. In contrast with these results we prove that the lattice of extensions of S4 behaves much better: a logic extending S4 is characterized by a finite algebra iff it has finitely many extensions and any such logic has only finitely many immediate predecessors, all of which are characterized by a finite algebra. (shrink)
The logic RM and its basic fragments (always with implication) are considered here as entire consequence relations, rather than as sets of theorems. A new observation made here is that the disjunction of RM is definable in terms of its other positive propositional connectives, unlike that of R. The basic fragments of RM therefore fall naturally into two classes, according to whether disjunction is or is not definable. In the equivalent quasivariety semantics of these fragments, which consist of subreducts of (...) Sugihara algebras, this corresponds to a distinction between strong and weak congruence properties. The distinction is explored here. A result of Avron is used to provide a local deduction-detachment theorem for the fragments without disjunction. Together with results of Sobociski, Parks and Meyer (which concern theorems only), this leads to axiomatizations of these entire fragments — not merely their theorems. These axiomatizations then form the basis of a proof that all of the basic fragments of RM with implication are finitely axiomatized consequence relations. (shrink)
The present paper is a study in abstract algebraic logic. We investigate the correspondence between the metalogical Beth property and the algebraic property of surjectivity of epimorphisms. It will be shown that this correspondence holds for the large class of equivalential logics. We apply our characterization theorem to relevance logics and many-valued logics.
Hoop residuation algebras are the {, 1}-subreducts of hoops; they include Hilbert algebras and the {, 1}-reducts of MV-algebras (also known as Wajsberg algebras). The paper investigates the structure and cardinality of finitely generated free algebras in varieties of k-potent hoop residuation algebras. The assumption of k-potency guarantees local finiteness of the varieties considered. It is shown that the free algebra on n generators in any of these varieties can be represented as a union of n subalgebras, each of which (...) is a copy of the {, 1}-reduct of the same finite MV-algebra, i.e., of the same finite product of linearly ordered (simple) algebras. The cardinality of the product can be determined in principle, and an inclusion-exclusion type argument yields the cardinality of the free algebra. The methods are illustrated by applying them to various cases, both known (varieties generated by a finite linearly ordered Hilbert algebra) and new (residuation reducts of MV-algebras and of hoops). (shrink)
The veiled recession frame has served several times in the literature to provide examples of modal logics failing to have certain desirable properties. Makinson [4] was the first to use it in his presentation of a modal logic without the finite model property. Thomason [5] constructed a (rather complicated) logic whose Kripke frames have an accessibility relation which is reflexive and transitive, but which is satisfied by the (non-transitive) veiled recession frame, and hence incomplete. In Van Benthem [2] the frame (...) was an essential tool to find simple examples of incomplete logics, axiomatized by a formula in two proposition letters of degree 2, or by a formula in one proposition letter of degree 4 (the degree of a modal formula is the maximal number of nested occurrences of the necessity operator in ). In [3] we showed that the modal logic determined by the veiled recession frame is incomplete, and besides that, is an immediate predecessor of classical logic (or, more precisely, the modal logic axiomatized by the formula pp), and hence is a logic, maximal among the incomplete ones. Considering the importance of the modal logic determined by the veiled recession frame, it seems worthwhile to ask for an axiomatization, and in particular, to answer the question if it is finitely axiomatizable. In the present paper we find a finite axiomatization of the logic, and in fact, a rather simple one consisting of formulas in at most two proposition letters and of degree at most three. (shrink)
This contribution discusses the philosophical meaning of Martin Heidegger’s Rectoral address. Firstly, Heidegger’s philosophical basic experience (Grunderfahrung) is sketched as providing the background of his Rectoral address: the being-historical concept of beginning (Anfang). Next, the philosophical question of the Rectoral address is discussed. It is shown that Die Selbstbehauptung der deutschen Universität is inquiring into the identity of human being (Dasein) in connection with the question about das Eigene (the Germans) and das Fremde (the Greeks). This opposition structures the confrontation (...) with the beginning of philosophical thinking in the Rectoral address. When read against the philosophical background sustaining the Rectoral address, words that appear in it, such as “Kampf,” “Macht,” “Volk,” and “Marsch” have nothing in common with the same words as used by the Nazis. It is shown that the Rectoral address is an extremely ambiguous text, because it claims a transformation of human Dasein. Although Heidegger’s view on National Socialism is distinguished from Nazi ideology, it is clear that he made a mistake about Hitler. The article explores how Heidegger later changed his mind and vocabulary, and in what way this kind of mistakes and changes of mind are inherent to philosophical empiricism. (shrink)
Tests of economic theory often focus on choice outcomes and find significant individual differences in these outcomes. This variability may mask universal psychological processes that lead to different choices because of differences across cultures in the information people have available when making decisions. On this view, decision making research within and across cultures must focus on the processes underlying choice.
The question addressed in this article is to what extent a destructed concept of religion can be said to characterize the philosophical method of Martin Heidegger. In order to approach this question, we first characterize his method as “Vollzug der Fraglichkeit”: philosophy in its deepest sense does not mean to give answers to questions but to ask questions. According to Heidegger, the execution of questioning consists in the “transforming repetition” of the leading question (Leitfrage) of philosophy in order to ask (...) the basic question of philosophy (Grundfrage). In the second part of the article, we reflect on the “religious” character of Heidegger’s method of questioning. The reflection makes use of different etymological derivations of the word ‘Religion’: relegere (to observe carefully), re-eligere (to choose again), religare (to bind back), relinquere (to leave behind). In the third part of the article, we discuss what Heidegger’s “religious” method of philosophy means for present questions concerning religion. To that end, we finish with a confrontation between Heidegger and Derrida with respect to the “religious” method of philosophy. (shrink)
In the work of the Russian symbolist Andrej Belyj (1880-1934) the question concerning the essence of personality [ličnost'] plays an important role throughout his life and is developed in both his literary and philosophical-theoretical writings. Although Belyj wrote no text specifically devoted to this notion, it is nonetheless possible to reconstruct genetically a more or less cohesive theory of personality. In the case of Aleksandr Blok (1880-1921), who left behind relatively few works of a theoretical nature, the situation is (...) different. In these works, moreover, the problems involved in the notion of personality are hardly touched upon and are not philosophically deepened. Nevertheless, a few disparate elements of a notion of personality can be pointed out for Blok. /// Im Schaffen des russischen Symbolisten Andrej Belyj (1880-1934) nimmt die Frage nach dem Wesen von Persönlichkeit [ličnost'] zeit seines Lebens einen wichtigen Raum ein und ist sowohl in seinen literarischen wie philosophisch-theoretischen Schriften entwickelt. Wenngleich Belyj keinen Text verfasst hat, der sich diesem Begriff eigens widmet, können dennoch aus seinem Werk Grundzüge einer Theorie der Persönlichkeit genetisch rekonstruiert werden. Anders sieht dies im Fall von Aleksandr Blok (1880-1921) aus, der verhältnismäßig wenige Arbeiten mit theoretischem Charakter hinterlassen hat. Auch wird in ihnen die Problematik des Persönlichkeitsbegriffs kaum berührt und nicht philosophisch vertieft. Dennoch können vereinzelte Elemente eines Persönlichkeitsbegriffs für Blok aufgezeigt werden. (shrink)
Speciation is an aspect of evolutionary biology that has received little philosophical attention apart from articles mainly by biologists such as Mayr (1988). The role of speciation as a terminus a quo for the individuality of species or in the context of punctuated equilibrium theory has been discussed, but not the nature of speciation events themselves. It is the task of this paper to attempt to bring speciation events into some kind of general scheme, based primarily upon the work of (...)Sergey Gavrilets on adaptive landscapes, using migration rate, or gene flow, as the primary scale, and concluding that adaptive and drift explanations are complementary rather than competing. I propose a distinction between intrinsic and extrinsic selection, and the notion of reproductive reach and argue that speciation modes should be discriminated in terms of gene flow, the nature of selection maintaining reproductive reach, and whether the predominant cause is selective or stochastic. I also suggest that the notion of an adaptive “quasispecies” for asexual species is the primitive notion of species, and that members of reproductively coherent sexual species are additionally coadapted to their mating partners. (shrink)
In 1988, David Hull presented an evolutionary account of science. This was a direct analogy to evolutionary accounts of biological adaptation, and part of a generalized view of Darwinian selection accounts that he based upon the Universal Darwinism of Richard Dawkins. Criticisms of this view were made by, among others, Kim Sterelny, which led to it gaining only limited acceptance. Some of these criticisms are, I will argue, no longer valid in the light of developments in the formal modeling of (...) evolution, in particular that of Sergey Gavrilets’ work on adaptive landscapes. If we can usefully recast the Hullian view of science as being driven by selection in terms of Gavrilets’ and Kaufmann’s view of there being “giant components” of high-fitness networks through any realistic adaptive landscape, we may now find it useful to ask what the adaptive pressures on science are, and to extend the metaphor into a full analogy. This is in effect to reconcile the Fisherianism of the Dawkins–Hull approach to selection and replicators, with a Wrightean drift account of social constructionist views of science, preserving, it is to be hoped, the valuable aspects of both. (shrink)
Machine generated contents note: List of contributors; Acknowledgments; Introduction: the humanist tradition in Russian philosophy G. M. Hamburg and Randall A. Poole; Part I. The Nineteenth Century: 1. Slavophiles, Westernizers, and the birth of Russian philosophical humanism Sergey Horujy; 2. Alexander Herzen Derek Offord; 3. Materialism and the radical intelligentsia: the 1860s Victoria S. Frede; 4. Russian ethical humanism: from populism to neo-idealism Thomas Nemeth; Part II. Russian Metaphysical Idealism in Defense of Human Dignity: 5. Boris Chicherin and human (...) dignity in history G. M. Hamburg; 6. Vladimir Solov'iev's philosophical anthropology: autonomy, dignity, perfectibility Randall A. Poole; 7. Russian panpsychism: Kozlov, Lopatin, Losskii James P. Scanlan; Part III. Humanity and Divinity in Russian Religious Philosophy after Solov'iev: 8. A Russian cosmodicy: Sergei Bulgakov's religious philosophy Paul Valliere; 9. Pavel Florenskii's trinitarian humanism Steven Cassedy; 10. Semën Frank's expressivist humanism Philip J. Swoboda; Part IV. Freedom and Human Perfectibility in the Silver Age: 11. Religious humanism in the Russian silver age Bernice Glatzer Rosenthal; 12. Russian liberalism and the philosophy of law Frances Nethercott; 13. Imagination and ideology in the new religious consciousness Robert Bird; 14. Eschatology and hope in silver age thought Judith Deutsch Kornblatt; Part V. Russian Philosophy in Revolution and Exile: 15. Russian Marxism Andrzej Walicki; 16. Adventures in dialectic and intuition: Shpet, Il'in, Losev Philip T. Grier; 17. Nikolai Berdiaev and the philosophical tasks of the emigration Stuart Finkel; 18. Eurasianism: affirming the person in an 'Era of Faith' Martin Beisswenger; Afterword: on persons as open-ended ends-in-themselves (the view from two novelists and two critics) Caryl Emerson; Bibliography. (shrink)
The paper attempts to establish a methodological complementarity between Foucault’s and Deleuze’s accounts of the body on the basis of Nietzsche’s theory of active and reactive forces systematically elaborated in Deleuze’s Nietzsche et la philosophie. Deleuze’s reading of Nietzsche’s physics of forces opens up two prospective developments of Nietzsche’s legacy: the genealogical critique of the historical body produced by reactive forces on the one hand and the invention of a new unknown body produced by active forces on the other. The (...) paper shows how throughout their careers both Foucault and Deleuze pursue these two divergent yet mutually complementary scenarios respectively. Given the shared background of both thinkers, neither is complete without the other, especially when the question of resistance is at stake. Just as active force is necessarily presupposed by the existence of reactive force in the Nietzschean calculus, Foucault’s reactive body cannot exist without its own inverse, Deleuze’s active ‘body-without-organs’. (shrink)
The article presents a verbal and mathematical model of medium-term business cycles (with a characteristic period of 7–11 years) known as Juglar cycles. The model takes into account a number of approaches to the analysis of such cycles; in the meantime it also takes into account some of the authors' own generalizations and additions that are important for understanding the internal logic of the cycle, its variability and its peculiarities in the present-time conditions. The authors argue that the most important (...) cause of cyclical crises stems from strong structural disproportions that develop during economic booms. These are not only disproportions between different economic sectors, but also disproportions between different societal subsystems; at present these are also disproportions within the World System as a whole. The proposed model of business cycle is based on its subdivision into four phases: – recovery phase (which could be subdivided into the start sub-phase and the acceleration sub-phase); – upswing/prosperity/expansion phase (which could be subdivided into the growth sub-phase and the boom/overheating sub-phase); – recession phase (within which one may single out the crash/bust/acute crisis subphase and the downswing sub-phase); – depression/stagnation phase (which we could subdivide into the stabilization subphase and the breakthrough sub-phase). The article provides a detailed qualitative description of macroeconomic dynamics at all the phases; it specifies driving forces of cyclical dynamics and the causes of transition from one phase to another (including psychological causes); a special attention is paid to the turning point from the peak of overheating to the acute crisis, as well as to the turning point from the downswing to recovery. The proposed mathematical model of Juglar cycle takes into account the following effects that are typical for the market economy: • positive feedbacks between various economic processes; • presence of a certain inertia, time lags in reactions of the economic subsystem to the change in conditions; • amplification by the financial subsystem of positive feedbacks and time lags in the economic subsystem; • excessive reaction to changing conditions during the acute crisis sub-phase. The authors suggest that the current crisis turns out to be rather similar to classical Juglar crises; however, there is also a significant difference, as the current crisis occurs at a truly global scale. Yet, due to this truly global scale of the current crisis, the possibilities of regulation with the national state's measures have turned out to be ineffective,whereas the suprastate regulation of financial processes hardly exists. It is shown that all these have led to the reproduction of the current crisis according to a classical Juglar scenario. (shrink)
The dynamic approach to understanding of the human consciousness, its cognitive activities and cognitive architecture is one of the most promising approaches in the modern epistemology and cognitive science. The conception of embodied mind is under discussion in the light of nonlinear dynamics and of the idea co-evolution of complex systems developed by the Moscow scientific school. The cognitive architecture of the embodied mind is rather complex: data from senses and products of rational thinking, the verbal and the pictorial, logic (...) and intuition, the analytical and synthetic abilities of perception and of thinking, the local and the global, the analogue and the digital, the archaic and the post-modern are intertwined in it. In the process of cognition, co-evolution of embodied mind as an autopoietic system and its surroundings takes place. The perceptual and mental processes are bound up with the structure of human body. Nonlinear and circular connecting links between the subject of cognition and the world constructed by him can be metaphorically called a nonlinear cobweb of cognition. Cognition is an autopoietic activity because it is directed to the search of elements that are missed; it serves to completing integral structures. According to the theory of blow-up regimes in complex systems elaborated by Sergey P.Kudyumov and his followers, the idea of co-evolution is connected with the concept of tempoworlds. To co-evolve means to start to develop in one and the same tempoworld and to use the possibility – in case of a proper intergation into a whole structure – to accelerate the tempo of evolution. The cognitive activities of the human being can be considered as a movement (active walk) in landscapes of co-evolution when he cognizes and changes environment and is changed himself by the very activities. The similar conclusion can be drawn from Francisco Varela’s conception of enactive cognition. (shrink)
This paper investigates (modal) extensions of Heyting–Brouwer logic, i.e., the logic which results when the dual of implication (alias coimplication) is added to the language of intuitionistic logic. We first develop matrix as well as Kripke style semantics for those logics. Then, by extending the Gödel-embedding of intuitionistic logic into S4 , it is shown that all (modal) extensions of Heyting–Brouwer logic can be embedded into tense logics (with additional modal operators). An extension of the Blok–Esakia-Theorem is proved for (...) this embedding. (shrink)
An extensions by new axioms and rules of an algebraizable logic in the sense of Blok and Pigozzi is not necessarily algebraizable if it involves new connective symbols, or it may be algebraizable in an essentially different way than the original logic. However, extension whose axioms and rules define implicitly the new connectives are algebraizable, via the same equivalence formulas and defining equations of the original logic, by enriched algebras of its equivalente quasivariety semantics. For certain strongly algebraizable logics, (...) all connectives defined implicitly by axiomatic extensions of the logic are explicitly definable. (shrink)
Abstract This article traces a historical shift, and in particular its erasure from memory on the intellectual map of the West, in concepts of subjectivity across practices of rabbinic thinking in late antiquity, medieval interpretations of the Talmud, and modern talmudic scholarship. I first introduce a comparative perspective that relies on a mutual hermeneutics of philosophical and talmudic traditions. I consequently engage with Alain de Libera's archaeological analysis of the birth of the thinking subject in medieval philosophy and theology. In (...) this light, I analyze the role of the notion of the thinking subject in construing the Talmud from Maimonides to contemporary Talmud criticism. Finally, I explore the implications of de Libera's program of a philosophical archaeology of the thinking subject for mapping the complex relationship of mutual presupposition and exclusion between philosophical, rhetorical, and talmudic traditions of thinking in antiquity, as manifested in the larger scope of these traditions. (shrink)
Philosophy of science is the object of metaphilosophical investigations. Metaphilosophy is the philosophy of philosophy. Philosophy is an archetypical thinking of being or an experience-of-being. History of Greek-European tradition of philosophy has three archetypes of thinking: objectivity, subjectivity, and inter-subjectivity. They are three archetypical contexts of interpretations of the concept of a philosophy of science too. Is philosophy of science part of philosophy? Is philosophy ofscience part of epistemology? What are methods of philosophy of science? These questions are the topics (...) of metaphilosophy. The topic of a scientific fact is a focal point of contemporary epistemology and philosophy of science. Is a scientific fact a fallible knowledge? The nature of a scientific fact is discussed in keeping with to the opposition of fallibilism and infallibilism. If fallibilism is universal quality of knowledge then there is a problem: is a scientific fact a fallible knowledge too? We are understanding and make clear the nature of a scientific fact by correlation of facts with: (1) data and evidence; (2) languages and theories; (3) methods of empirical investigations; (4) values, norms, and conventions of scientific investigations. Philosophy of science communicates with philosophy ofeconomics as the contemporary branch of philosophy. Its problems arise from the relationship of philosophy and philosophy of science with economics and practice. (shrink)
In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent (...) calculus. When applied to a certain natural calculus for L, the resulting models are equivalent to a class of abstract logics (in the sense of Brown and Suszko) which we call distributive. Among other results, we prove that D is exactly the class of the algebraic reducts of the reduced models of L, that there is an embedding of the theories of L into the theories of the equational consequence (in the sense of Blok and Pigozzi) relative to D, and that for any algebra A of type (2,2) there is an isomorphism between the D-congruences of A and the models of L over A. In the second part of this paper (which will be published separately) we will also apply some results to give proofs with a logical flavour for several new or well-known lattice-theoretical properties. (shrink)
In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent (...) calculus. When applied to a certain natural calculus for L, the resulting models are equivalent to a class of abstract logics (in the sense of Brown and Suszko) which we call distributive. Among other results, we prove that D is exactly the class of the algebraic reducts of the reduced models of L, that there is an embedding of the theories of L into the theories of the equational consequence (in the sense of Blok and Pigozzi) relative to D, and that for any algebra A of type (2,2) there is an isomorphism between the D-congruences of A and the models of L over A. In the second part of this paper (which will be published separately) we will also apply some results to give proofs with a logical flavour for several new or well-known lattice-theoretical properties. (shrink)
We give an example of a variety of Heyting algebras and of a splitting algebra in this variety that is not finitely presentable. Moreover, we show that the corresponding splitting pair cannot be defined by any finitely presentable algebra. Also, using the Gödel-McKinsey-Tarski translation and the Blok-Esakia theorem, we construct a variety of Grzegorczyk algebras with similar properties.
Roman Jakobson, who had left Russia in 1920 and in 1941 took refuge in the USA from the Nazis, was one of the main figures in post war linguistics and structuralism. Two aspects of his work are examined in this article. Firstly, Jakobson purifies his linguistic theory of pragmatic references. Secondly, he develops his own diplomatic mission of mediating between East and West. In this article, I argue that these two aspects did not develop independently from one another. Instead I (...) claim that his theory is designed to slip through the Iron Curtain, while at the same time providing the means to analyse ways of acting politically by using language. This argument is unfolded in two steps, each consisting of two parts. First, I compare the theory of pronominal expressions as developed by Emil Benveniste to Jakobson’s theory of shifters. While Benveniste focuses on the relation of language and its subject using language, Jakobson introduces a model of communication to allow maximal formalisation of language. According to this even the category of person can be freed from its reference to a subject which would be understood as having a place in space and time. Then, Jakobson’s theory of shifters is studied in relation to his analyses of poetry. For this, two examples are chosen: Jakobson’s text on two poems by Russian poet Alexandr Blok, and his text on a poem by Bertold Brecht. In both texts, the theory of shifters—and the alleged purification from pragmatic aspects of language use ensuing from this theory—is challenged by the simple fact that they focus on the pronoun of the first person plural. According to Jakobson, the category of number does not belong to the shifters. Rather, number quantifies participants of the related event. The pronoun ‘we’ is at the same time a shifter and a non-shifter, as it refers to the speech event and the related event. Thus the pronoun ‘we’ opens up the possibility to include or exclude the participants of a communicative situation, and thereby enables the speaker to act socially or even politically by using language. The article concludes by coming back to the historical situation in which Jakobson developed his analyses of poetry. Analysing poetry seems to have been a passe-partout for him, a seemingly harmless subject that allowed him to get a foot in the door of remote and secluded lecture halls. (shrink)
A category theoretic generalization of the theory of algebraizable deductive systems of Blok and Pigozzi is developed. The theory of institutions of Goguen and Burstall is used to provide the underlying framework which replaces and generalizes the universal algebraic framework based on the notion of a deductive system. The notion of a term -institution is introduced first. Then the notions of quasi-equivalence, strong quasi-equivalence and deductive equivalence are defined for -institutions. Necessary and sufficient conditions are given for the quasi-equivalence (...) and the deductive equivalence of two term -institutions, based on the relationship between their categories of theories. The results carry over without any complications to institutions, via their associated -institutions. The -institution associated with a deductive system and the institution of equational logic are examined in some detail and serve to illustrate the general theory. (shrink)
The belief in the Darwinian theory of evolution appeared to be shaken when one tried to interpret statements of molecular biology in it. As a consequence there arose a theory of non-Darwinian neutral evolution. The supporters of this theory believe that under natural conditions no factors exist which can distinguish and select organisms on their internal (molecular) structure. In the opinion of these neutralists natural selection cannot in principle control the molecular constitution of organisms. Contrary to the viewpoint of the (...) critics of neutralism it is impossible to admit that nucleic acids, proteins and other biomolecules can evolve without the participation of natural selection. This controversy in contemporary theoretical biology can be solved by integrating the conceptions of molecular ecology with Darwinian theory. Molecular ecology acknowledges the interactions of organisms by means of chemical substances synthesized by them. Such chemical ecological factors play a leading part in the selective stages of biomolecular evolution. These diverse chemical ecological interrelations take place intensively when living beings interact with parasitic microbes. (shrink)
This paper gives a characterization of those quasi-normal extensions of the modal system S4 into which intuitionistic propositional logic Int is embeddable by the Gödel translation. It is shown that, as in the normal case, the set of quasi-normal modal companions of Int contains the greatest logic, M*, for which, however, the analog of the Blok-Esakia theorem does not hold. M* is proved to be decidable and Halldén-complete; it has the disjunction property but does not have the finite model (...) property. (shrink)
Relatively congruence regular quasivarieties and quasivarieties of logic have noticeable similarities. The paper provides a unifying framework for them which extends the Blok-Pigozzi theory of elementarily algebraizable (and protoalgebraic) deductive systems. In this extension there are two parameters: a set of terms and a variable. When the former is empty or consists of theorems, the Blok-Pigozzi theory is recovered, and the variable is redundant. On the other hand, a class of membership logics is obtained when the variable is (...) the only element of the set of terms. For these systems the appropriate variant of equivalent algebraic semantics encompasses the relatively congruence regular quasivarieties. (shrink)
In [14] we used the term finitely algebraizable for algebraizable logics in the sense of Blok and Pigozzi [2] and we introduced possibly infinitely algebraizable, for short, p.i.-algebraizable logics. In the present paper, we characterize the hierarchy of protoalgebraic, equivalential, finitely equivalential, p.i.-algebraizable, and finitely algebraizable logics by properties of the Leibniz operator. A Beth-style definability result yields that finitely equivalential and finitely algebraizable as well as equivalential and p.i.-algebraizable logics can be distinguished by injectivity of the Leibniz operator. (...) Thus, from a characterization of equivalential logics we obtain a new short proof of the main result of [2] that a finitary logic is finitely algebraizable iff the Leibniz operator is injective and preserves unions of directed systems. It is generalized to nonfinitary logics. We characterize equivalential and, by adding injectivity, p.i.-algebraizable logics. (shrink)
The notion of an algebraizable logic in the sense of Blok and Pigozzi [3] is generalized to that of a possibly infinitely algebraizable, for short, p.i.-algebraizable logic by admitting infinite sets of equivalence formulas and defining equations. An example of the new class is given. Many ideas of this paper have been present in [3] and [4]. By a consequent matrix semantics approach the theory of algebraizable and p.i.-algebraizable logics is developed in a different way. It is related to (...) the theory of equivalential logics in the sense of Prucnal and Wroski [18], and it is extended to nonfinitary logics. The main result states that a logic is algebraizable (p.i.-algebraizable) iff it is finitely equivalential (equivalential) and the truth predicate in the reduced matrix models is equationally definable. (shrink)
The notion of a pseudo-interior algebra was introduced by Blok and Pigozzi in [BPIV]. We continue here our studies begun in [BK]. As a consequence of the representation theorem for pseudo-interior algebras given in [BK] we prove that the variety of all pseudo-interior algebras is generated by its finite members. This result together with Jónsson's Theorem for congruence distributive varieties provides a useful technique in the study of the lattice of varieties of pseudo-interior algebras.
We describe in detail the first experimental test that distinguishes between an event-based corpuscular model of the interaction of photons with matter and quantum mechanics. The test looks at the interference that results as a single photon passes through a Mach-Zehnder interferometer. The experimental results, obtained with a low-noise single-photon source, agree with the predictions of standard quantum mechanics.
Two classes of π are studied whose properties are similar to those of the protoalgebraic deductive systems of Blok and Pigozzi. The first is the class of N-protoalgebraic π-institutions and the second is the wider class of N-prealgebraic π-institutions. Several characterizations are provided. For instance, N-prealgebraic π-institutions are exactly those π-institutions that satisfy monotonicity of the N-Leibniz operator on theory systems and N-protoalgebraic π-institutions those that satisfy monotonicity of the N-Leibniz operator on theory families. Analogs of the correspondence property (...) of Blok and Pigozzi for π-institutions are also introduced and their connections with preand protoalgebraicity are explored. Finally, relations of these two classes with the (, N)-algebraic systems, introduced previously by the author as an analog of the -algebras of Font and Jansana, and with an analog of the Suszko operator of Czelakowski for π-institutions are also investigated. (shrink)
Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the steady influx of new classes. According to the model, the distribution changes from a pure exponential form for zero influx of new classes to a power law with an exponential cut-off form when the influx of new classes is (...) substantial. Predictions of the model are tested through the analysis of a unique industrial database, which covers both elementary units (products) and classes (markets, firms) in a given industry (pharmaceuticals), covering the entire size distribution. The model's predictions are in good agreement with the data. The paper sheds light on the emergence of the exponent tau approximately 2 observed as a universal feature of many biological, social and economic problems. (shrink)
Given a normal (multi-)modal logic a characterization is given of the finitely presentable algebras A whose logics L A split the lattice of normal extensions of . This is a substantial generalization of Rautenberg [10] and [11] in which is assumed to be weakly transitive and A to be finite. We also obtain as a direct consequence a result by Blok [2] that for all cycle-free and finite A L A splits the lattice of normal extensions of K. Although (...) we firmly believe it to be true, we have not been able to prove that if a logic splits the lattice of extensions of then is the logic of an algebra finitely presentable over ; in this respect our result remains partial. (shrink)
This paper investigates man's feeling of law, i . e. the perception of law, the comprehension of law and its influence on human activity, in the countries that have historically belonged to the Orthodox tradition. Consciousness of law is based, firstly, upon a concept of law, and, secondly upon a certain attitude to law, i.e. the place of this concept in everyday life and human activity. The paper treats those elements of the Orthodox outlook that constituted certain inherent mechanisms of (...) culture, and thus greatly influenced the process of formation of the feeling of law in the countries of the Orthodox culture. These elements include interaction of the Orthodox Church and the State, then the problem of the meaning of life according to the Orthodox doctrine, and finally the way personality is perceived and treated in the Orthodox outlook. The paper also considers particular features of the Orthodox outlook as they were exposed in the course of the cultural history of Orthodox countries. (shrink)
From descriptive interpretation of "understanding" to abstract-gnosiological understanding of mentality. The historical deconstruction of the existential understanding introduced as ontologic property of constantly becoming stable "Being-in-the-World" allows us to interpret this concept as mentality. Through theprism of existential philosophy in general and its interpreters such as Jacque Le Goff it allows us to make a conclusion that mentality is one of complete formations of public consciousness. But in the course of such interpretation of mentality it is important to avoid the (...) methodological situation in which Plato deadlocked, when he had decided to find out, what was beautiful itself. For the way out from this situation he had to introduce independently existing ideas and special space of ideas which define all the things and even gods. We, unfortunately, do not have such an opportunity which the history gave to Plato. Somehow to define structural and historical conditions for breaking out of mentality we shall be limited to the instruction that it is more complex, compound, but in the same time integrally complete formation historically actualized, unlike traditionally allocated kinds and forms of consciousness. Another important question is whether the concept "mentality" is acceptable for analysis of the current modern processes or it can only be used for the reconstruction of the completed formations. The mentality cannot be analyzed from inside. And we are inclined to consider that to operate the concept "mentality" in relation to a modern representative of civilization is inappropriate. (shrink)
The notion of a pseudo-interior algebra was introduced by Blok and Pigozzi in [3]. We continue here our studies begun in [6]. As a consequence of the representation theorem for pseudo-interior algebras given in [6] we prove that the variety of all pseudo-interior algebras has the amalgamation property. Using algebraic methods of Bergman [1] we find infinitely many varieties of pseudo-interior algebras with this property.
According to Popper, democracy, and the one of the western type at that, is the best form of the state system which makes open society possible. At the same time, democratic traditions and institutions have been historically developing not only in the West but also in the East. A number of crucial principles of Buddhistcivilization forming throughout the millennium appear to be quite corresponding to the model of open society. The principles of universal humanism and compassion as the staple of (...) the world; the principle of universal responsibility for forming social institutes and organizations aimed to solve problems common to all people; the principle of tolerance and common ethical direction of all world religions can be attributed to such principles. The humanistic ideal of Buddhism is an individual satisfied with life in society and living in harmony with nature. Buddhism encourages self-restriction and social solidarity, justice and equality, pure thoughts and deeds. Buddhist civilization lies “in between” since in most cases it acts a close-to-perfect mediator among other cultures and civilizations, various ethnic groups and peoples. (shrink)
The modification of Frege's semantics that consists in using only one reference (Bedeutung, denotate) truth instead of two references truth and falsity is proposed. According to Frege 1) every true sentence stands for truth, 2) every false sentence stands for falsity. We modify the second statement: 2*) every false sentence doesn't stand for truth. The modification of sentential logic interpretation will consist in change of semantic rules: a) every formula A stands either for truth or falsity, b.1) the formula A (...) has value T iff the formula A stands for truth, b.2) the formula A has value F iff the formula A stands for falsity. Let’s change rules a) and b.2) on: a*) every formula A either stands or doesn't stand for truth, b.2*) the formula A has value F iff the formula A doesn't stand for truth. So, we have only one reference but still two values. The proposed approach can be extended to non-classical cases, for which the bivalence principle doesn't take place. An ordered pair of the sentences A, ~A is put in correspondence to the sentence A. Each sentence of ordered pair can either stands or doesn't stand for truthindependently from the other. Thus for each pair of sentences we have four possible variants of reference which are generate four functional values. (shrink)
The aim of this paper is to study the paraconsistent deductive systemP 1 within the context of Algebraic Logic. It is well known due to Lewin, Mikenberg and Schwarse thatP 1 is algebraizable in the sense of Blok and Pigozzi, the quasivariety generated by Sette's three-element algebraS being the unique quasivariety semantics forP 1. In the present paper we prove that the mentioned quasivariety is not a variety by showing that the variety generated byS is not equivalent to any (...) algebraizable deductive system. We also show thatP 1 has no algebraic semantics in the sense of Czelakowski. Among other results, we study the variety generated by the algebraS. This enables us to prove in a purely algebraic way that the only proper non-trivial axiomatic extension ofP 1 is the classical deductive systemPC. Throughout the paper we also study those abstract logics which are in a way similar toP 1, and are called hereabstract Sette logics. We obtain for them results similar to those obtained for distributive abstract logics by Font, Verdú and the author. (shrink)
From the end of the XX century academic community has been extensively discussing globalization issues affecting economy, politics and culture. First and foremost there grew anticipations of an ecological disaster on a global scale associated with environmental pollution. Solution of these problems on a global scale is based on a sustainable development strategy. The sustainable development is a balance between natural environment (biosphere) and artificial environment (technosphere). Russian thinkers of the early XX century introduced a notion of noosphere. One of (...) the landmarks of sustainable developmentmust become ecosophy. Asian civilization has been developing in the spirit of ecosophy. It shows that one can live in equilibrium with natural surroundings and scientific progress, preserving spiritual culture and maintaining high spiritual standard. Extending of culture dialogue became more essential in XXI century. (shrink)
