Fundamental properties of N-valued logics are compared and eleven theorems are presented for their Logic Algebras, including Łukasiewicz–Moisil Logic Algebras represented in terms of categories and functors. For example, the Fundamental Logic Adjunction Theorem allows one to transfer certain universal, or global, properties of the Category of Boolean Algebras,, (which are well-understood) to the more general category \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal L}$$\end{document}Mn of Łukasiewicz–Moisil Algebras. Furthermore, the relationships of LMn-algebras to other many-valued logical structures, (...) such as the n-valued Post, MV and Heyting logic algebras, are investigated and several pertinent theorems are derived. Applications of Łukasiewicz–Moisil Algebras to biological problems, such as nonlinear dynamics of genetic networks – that were previously reported – are also briefly noted here, and finally, probabilities are precisely defined over LMn-algebras with an eye to immediate, possible applications in biostatistics. (shrink)

The lack of double negation and de Morgan properties makes fuzzy logic unsymmetrical. This is the reason why fuzzy versions of notions like closure operator or Galois connection deserve attention for both antiotone and isotone cases, these two cases not being dual. This paper offers them attention, comming to the following conclusions: – some kind of hardly describable ‘‘local preduality’’ still makes possible important parallel results; – interesting new concepts besides antitone and isotone ones (like, for instance, conjugated pair), that (...) were classically reducible to the first, gain independency in fuzzy setting. (shrink)

We introduce the notion of n-nuanced MV-algebra by performing a Łukasiewicz–Moisil nuancing construction on top of MV-algebras. These structures extend both MV-algebras and Łukasiewicz–Moisil algebras, thus unifying two important types of structures in the algebra of logic. On a logical level, n-nuanced MV-algebras amalgamate two distinct approaches to many valuedness: that of the infinitely valued Łukasiewicz logic, more related in spirit to the fuzzy approach, and that of Moisil n-nuanced logic, which is more concerned with nuances of truth rather than (...) truth degree. We study n-nuanced MV-algebras mainly from the algebraic and categorical points of view, and also consider some basic model-theoretic aspects. The relationship with a suitable notion of n-nuanced ordered group via an extension of the Γ construction is also analyzed. (shrink)

This paper is a contribution to the algebraic logic of probabilistic models of Łukasiewicz predicate logic. We study the MV-states defined on polyadic MV-algebras and prove an algebraic many-valued version of Gaifman’s completeness theorem.

In this paper we study the notion of forcing for Łukasiewicz predicate logic (Ł∀, for short), along the lines of Robinson’s forcing in classical model theory. We deal with both finite and infinite forcing. As regard to the former we prove a Generic Model Theorem for Ł∀, while for the latter, we study the generic and existentially complete standard models of Ł∀.

Chang algebras as algebraic models for Chang's modal logics [1] are defined. The main result of the paper is a representation theorem for these algebras.

In previous work, we have introduced and studied a lifting property in congruence–distributive universal algebras which we have defined based on the Boolean congruences of such algebras, and which we have called the Congruence Boolean Lifting Property. In a similar way, a lifting property based on factor congruences can be defined in congruence–distributive algebras; in this paper we introduce and study this property, which we have called the Factor Congruence Lifting Property. We also define the Boolean Lifting Property in varieties (...) with \ and \ having Boolean Factor Congruences and no skew congruences, and prove that it coincides to the Factor Congruence Lifting Property in the congruence–distributive case; we particularize this result to bounded distributive lattices and residuated lattices. (shrink)

We study the forcing operators on MTL-algebras, an algebraic notion inspired by the Kripke semantics of the monoidal t -norm based logic . At logical level, they provide the notion of the forcing value of an MTL-formula. We characterize the forcing operators in terms of some MTL-algebras morphisms. From this result we derive the equality of the forcing value and the truth value of an MTL-formula.

Power structures are obtained by lifting some mathematical structure (operations, relations, etc.) from an universe X to its power set ${\mathcal{P}(X)}$ . A similar construction provides fuzzy power structures: operations and fuzzy relations on X are extended to operations and fuzzy relations on the set ${\mathcal{F}(X)}$ of fuzzy subsets of X. In this paper we study how this construction preserves some properties of fuzzy sets and fuzzy relations (similarity, congruence, etc.). We define the notions of good, very good, Hoare good (...) and Smith good fuzzy relation and establish some connections between them, generalizing some results of Brink, Bošnjak and Madarász on power structures. (shrink)

In this paper we define the polyadic Pavelka algebras as algebraic structures for Rational Pavelka predicate calculus . We prove two representation theorems which are the algebraic counterpart of the completness theorem for RPL∀.

In this paper we study the notion of forcing for Łukasiewicz predicate logic (Ł∀, for short), along the lines of Robinson’s forcing in classical model theory. We deal with both finite and infinite forcing. As regard to the former we prove a Generic Model Theorem for Ł∀, while for the latter, we study the generic and existentially complete standard models of Ł∀.

Fundamental properties of N-valued logics are compared and eleven theorems are presented for their Logic Algebras, including Łukasiewicz–Moisil Logic Algebras represented in terms of categories and functors. For example, the Fundamental Logic Adjunction Theorem allows one to transfer certain universal, or global, properties of the Category of Boolean Algebras,, (which are well-understood) to the more general category \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal L}$$\end{document}Mn of Łukasiewicz–Moisil Algebras. Furthermore, the relationships of LMn-algebras to other many-valued logical structures, (...) such as the n-valued Post, MV and Heyting logic algebras, are investigated and several pertinent theorems are derived. Applications of Łukasiewicz–Moisil Algebras to biological problems, such as nonlinear dynamics of genetic networks – that were previously reported – are also briefly noted here, and finally, probabilities are precisely defined over LMn-algebras with an eye to immediate, possible applications in biostatistics. (shrink)

States have been introduced on commutative and non-commutative algebras of fuzzy logics as functions defined on these algebras with values in [0,1]. Starting from the observation that in the definition of Bosbach states there intervenes the standard MV-algebra structure of [0,1], in this paper we introduce Bosbach states defined on residuated lattices with values in residuated lattices. We are led to two types of generalized Bosbach states, with distinct behaviours. Properties of generalized states are useful for the development of an (...) algebraic theory of probabilistic models for non-commutative fuzzy logics. (shrink)

We continue the investigation of generalized Bosbach states that we began in Part I, restricting our research to the commutative case and treating further aspects related to these states. Part II is concerned with similarity convergences, continuity of states and the construction of the s-completion of a commutative residuated lattice, where s is a generalized Bosbach state.

ABSTRACT In this paper we shall prove that l-rings are categorally equivalent to the MV*-algebras, a subcategory of perfect MV-algebras. We shall use this equivalence in order to characterize l-rings as quotients of certain semirings of matrices over MV*-algebras. We shall establish a relation between l-ideals in l-rings and some ideals in MV*-algebras. This edlows us to study the MV* f-algebras, a subclass of the MV*-algebras corresponding to the f-rings.

George Molnar came to see that the solution to a number of the problems of contemporary philosophy lay in the development of an alternative to Hume's metaphysics. This alternative would have real causal powers at its centre. Molnar set about developing a thorough account of powers that might persuade those who remained, perhaps unknowingly, in the grip of Humean assumptions. He succeeded in producing something both highly focused and at the same time wide-ranging. He showed both that the notion (...) of a power was central and that it could serve to dispel a number of long-standing philosophical problems.Molnar's account of powers is as realist as any that has so far appeared. He shows that dispositions are as real as any other properties. Specifically, they do not depend for their existence on their manifestations. Nevertheless, they are directed towards such manifestations. Molnar thus appropriates the notion of intentionality, from Brentano, and argues that it is the essential characteristic of powers. He offers a persuasive case for there being some basic and ungrounded powers, thus ruling out the reducibility of the dispositional to the non-dispositional. However, he does allow that there are non-power properties as well as power properties. In this respect, his final position is dualistic.This is contemporary metaphysics of the highest quality. It is a work that was almost complete when its author died. It has been edited for publication by another specialist in the subject, Stephen Mumford, who has also provided an introduction that will allow non-specialists to become acquainted with the issues. David Armstrong, one of the greatest living metaphysicians and personal friend of George Molnar, has provided a Foreword. (shrink)

A revision of George Kennedy's translation of, introdution to, and commentary on Aristotle's On Rhetoric. His translation is most accurate, his general introduction is the most thorough and insightful, and his brief introductions to sections of the work, along with his explanatory footnotes, are the most useful available.

<Hylas> It is indeed something unusual; but my thoughts were so taken up with a subject I was discoursing of last night, that finding I could not sleep, ...

Berkeley's idealism started a revolution in philosophy. As one of the great empiricist thinkers he not only influenced British philosophers from Hume to Russell and the logical positivists in the twentieth century, he also set the scene for the continental idealism of Hegel and even the philosophy of Marx. There has never been such a radical critique of common sense and perception as that given in Berkeley's Principles of Human Knowledge (1710). His views were met with disfavour, and his response (...) to his critics was the Three Dialogues between Hylas and Philonous. This edition of Berkeley's two key works has an introduction which examines and in part defends his arguments for idealism, as well as offering a detailed analytical contents list, extensive philosophical notes, and an index. (shrink)

G.E. Moore, more than either Bertrand Russell or Ludwig Wittgenstein, was chiefly responsible for the rise of the analytic method in twentieth-century philosophy. This selection of his writings shows Moore at his very best. The classic essays are crucial to major philosophical debates that still resonate today. Amongst those included are: * A Defense of Common Sense * Certainty * Sense-Data * External and Internal Relations * Hume's Theory Explained * Is Existence a Predicate? * Proof of an External World (...) In addition, this collection also contains the key early papers in which Moore signals his break with idealism, and three important previously unpublished papers from his later work which illustrate his relationship with Wittgenstein. (shrink)

Berkeley's idealism started a revolution in philosophy. As one of the great empiricist thinkers he not only influenced British philosophers from Hume to Russell and the logical positivists in the twentieth century, he also set the scene for the continental idealism of Hegel and even the philosophy of Marx. -/- There has never been such a radical critique of common sense and perception as that given in Berkeley's Principles of Human Knowledge (1710). His views were met with disfavour, and his (...) response to his critics was the Three Dialogues between Hylas and Philonous. -/- This edition of Berkeley's two key works has an introduction which examines and in part defends his arguments for idealism, as well as offering a detailed analytical contents list, extensive philosophical notes and an index. (shrink)

Berkeley's idealism started a revolution in philosophy. As one of the great empiricist thinkers he not only influenced British philosphers from Hume to Russell and the logical positivists in the twentieth-century, he also set the scene for the continental idealism of Hegel and even the philsophy of Marx.

In works of literary fiction, it is a part of the fiction that the words of the text are being recounted by some work-internal 'voice': the literary narrator. One can ask similarly whether the story in movies is told in sights and sounds by a work-internal subjectivity that orchestrates them: a cinematic narrator. George M. Wilson argues that movies do involve a fictional recounting (an audio-visual narration ) in terms of the movie's sound and image track. Viewers are usually (...) prompted to imagine seeing the items and events in the movie's fictional world and to imagine hearing the associated fictional sounds. However, it is much less clear that the cinematic narration must be imagined as the product of some kind of 'narrator' - of a work-internal agent of the narration. Wilson goes on to examine the further question whether viewers imagine seeing the fictional world face-to-face or whether they imagine seeing it through some kind of work-internal mediation . It is a key contention of this book that only the second of these alternatives allows one to give a coherent account of what we do and do not imagine about what we are seeing on the screen. Having provided a partial account of the foundations of film narration, the final chapters explore the ways in which certain complex strategies of cinematic narration are executed in three exemplary films: David Fincher's Fight Club , von Sternberg's The Scarlet Empress , and the Coen brothers' The Man Who Wasn't There. (shrink)

Reproduction of the original: Mental Evolution in Man by George John Romanes.

Best known for his influential History of Greece, the historian and politician George Grote wrote this account of Plato's dialogues as a philosophical supplement to the History. First published in 1865 and written in dialogic form, Grote's account of Plato's works includes substantial footnotes and marginalia. This first volume focuses on Plato's early and transitional dialogues, all of which feature Socrates. It also includes a preface to the whole project which discusses the meaning and importance of philosophy itself, and (...) extensive introductory material on pre-Socratic philosophy, the life of Plato and history of the Platonic canon. With three volumes each running to over six hundred pages, Grote's scholarship is formidably comprehensive. The publication of Plato and the Other Companions of Sokrates confirmed him as one of the greatest authorities on Plato in the nineteenth century. (shrink)

The dream of a community of philosophers engaged in inquiry with shared standards of evidence and justification has long been with us. It has led some thinkers puzzled by our mathematical experience to look to mathematics for adjudication between competing views. I am skeptical of this approach and consider Skolem's philosophical uses of the Löwenheim-Skolem Theorem to exemplify it. I argue that these uses invariably beg the questions at issue. I say ?uses?, because I claim further that Skolem shifted his (...) position on the philosophical significance of the theorem as a result of a shift in his background beliefs. The nature of this shift and possible explanations for it are investigated. Ironically, Skolem's own case provides a historical example of the philosophical flexibility of his theorem. Our suspicion ought always to be aroused when a proof proves more than its means allow it. Something of this sort might be called ?a puffed-up proof?. Ludwig Wittgenstein, Remarks on the foundations of mathematics (revised edition), vol. 2, 21. (shrink)

In this festschrift for the eminent philosopher Hilary Putnam, a team of distinguished philosophers write on a broad range of topics and thus reflect the remarkably fertile and provocative research of Putnam himself. The volume is not merely a celebration of a man, but also a report on the state of philosophy in a number of significant areas. The essays fall naturally into three groups: a central core on the theme of conventionality and content in the philosophy of mind, language, (...) and science, and two smaller sections on the relationship of ethics and language, and on the philosophy of logic and aesthetics. (shrink)

"Those who think they know George Dickie's views should be sure to read this book. They are in for some interesting surprises. Of course, those unfamiliar with Dickie's views will also learn a lot." --Anita Silvers, San Francisco State University In this book George Dickie presents a theory about how to judge a work of art--as opposed to a theory that explains why a particular work is defined as art. Focusing mainly on the writings of Monroe Beardsley and (...) critically examining the views of seven other philosophers and art critics--Paul Ziff, Frank Sibley, Nelson Goodman, Nicholas Wolterstorff, David Hume, Bruce Vermazen, and J. O. Urmson--Dickie synthesizes their insights to discover what can be derived from their theories. On this basis, he attempts to work out a theory of art evaluation--the first such book on this topic by a contemporary philosopher. Initially, the author outlines all possible theories of art evaluation, assuming that traditional evaluative notions are used. He identifies seven theory-types that fall under four general headings: imitation value theory, objective intrinsic value theories, subjective intrinsic value theory, and instrumental value theories. Dickie then discusses the historical development of the theory of art evaluation, examining the ways in which eighteenth- and nineteenth-century philosophers treated representation and other cognitive dimensions of art as artistic values. His thorough analysis of the work of other contemporary theorists argues for a theory of art evaluation derived from various strands of thought. (shrink)

Religious pluralism model holds the belief that there is virtue in every religion, just as all religions are good and are of equal value. It does not consider religion’s particularity but is interested in the ideas that have not favoured any religion. The issue with this concept is not its assertion of the validity of all religions. It is rather with its denial of the finality of any religion as the way by which people could come to God. Hence, it (...) allows the existence of multiple religions in a given society and encourages religious tolerance. The beauty of pluralism is its flexibility which makes religious practicing a wilful act and religious conversion a choice and not a force, although it has the tendency to encourage syncretism. This research examines critically the implications of pluralism using historical approach on the development of Christian church. Data for the research were basically obtained from secondary sources. The findings reveal that although religious pluralism has its negative sides, it gives the much needed boost to development of church if its tenets are followed. Accordingly, the article recommends that Christian churches in pluralist societies such as Nigeria should imbibe the virtues of religious tolerance, and dialogue, if they want to remain alive and continue to be relevant.Contribution: Religious pluralism is a panacea to inordinate and incessant religious conflict, if given its proper place in Nigeria, will breed religious tolerance, peace and progress. This work would be of immense of benefit to government, missionaries and students across all strata of discipline. (shrink)

"I do solemnly swear" -- Economics in practice : what do economists do? -- Ethical challenges confronting the applied economist -- Historical perspective : "don't predict the interest rate!" -- Interpreting the silence : the economic case against professional economic ethics -- The economic case against professional economic ethics : a rebuttal -- The positive case for professional economic ethics -- Learning from others : ethical thought across the professions -- Economists as social engineers : an ethical evaluation of market (...) liberalization in the south and transition economies -- Global economic crisis and the crisis in economics -- On sleeping too well : in search of professional economic ethics -- Training the "ethical economist" -- The economist's oath. (shrink)

George Wilson; Transparency and Twist in Narrative Fiction Film, The Journal of Aesthetics and Art Criticism, Volume 64, Issue 1, 8 March 2005, Pages 81–95, htt.