This paper sheds new light on the subtle relation between probability and logic by (i) providing a logical development of Bruno de Finetti's conception of events and (ii) suggesting that the subjective nature of de Finetti's interpretation of probability emerges in a clearer form against such a logical background. By making explicit the epistemic structure which underlies what we call Choice-based probability we show that whilst all rational degrees of belief must be probabilities, the converse doesn't hold: some probability values (...) don't represent decision-relevant quantifications of uncertainty. (shrink)

In the present paper we show that any at most countable linearly-ordered commutative residuated lattice can be embedded into a commutative residuated lattice on the real unit interval [0, 1]. We use this result to show that Esteva and Godo''s logic MTL is complete with respect to interpretations into commutative residuated lattices on [0, 1]. This solves an open problem raised in.

A simple complete axiomatic system is presented for the many-valued propositional logic based on the conjunction interpreted as product, the coresponding implication (Goguen's implication) and the corresponding negation (Gödel's negation). Algebraic proof methods are used. The meaning for fuzzy logic (in the narrow sense) is shortly discussed.

The present paper deals with the predicate version MTL of the logic MTL by Esteva and Godo. We introduce a Kripke semantics for it, along the lines of Ono''s Kripke semantics for the predicate version of FLew (cf. [O85]), and we prove a completeness theorem. Then we prove that every predicate logic between MTL and classical predicate logic is undecidable. Finally, we prove that MTL is complete with respect to the standard semantics, i.e., with respect to Kripke frames on (...) the real interval [0,1], or equivalently, with respect to MTL-algebras whose lattice reduct is [0,1] with the usual order. (shrink)

In his critique of Anselm’s ontological argument for God’s existence, William Rowe introduces the concepts of “magico” and “magican” — defining “magicos” as magicians that do not exist, and “magicans” as magicians that do exist — to help diagnose what may have gone wrong in Anselm’s argument. As I made my way through Rowe’s intriguing article, I found myself waiting for “Godo” — and for “Godan.” I expected Rowe to invoke these counterparts to his “magico” and “magican” — a (...) non-existing God to correspond to his non-existing magician, and an existing God to correspond to his existing magician — to complete his argument. Alas, like Vladimir and Estragon, I waited in vain: neither Godo — nor Godan — ever appeared. In what follows I shall argue that their inclusion in Rowe’s argument would have settled the matter against Anselm far more decisively than do Rowe’s forays into the murky waters of question-begging. (shrink)

The monoidal t-norm based logic MTL is obtained from Hájek''s Basic Fuzzy logic BL by dropping the divisibility condition for the strong (or monoidal) conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0,1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the issue of standard and rational completeness (...) (rational completeness meaning completeness with respect to a class of algebras in the rational unit interval [0,1]) of some important axiomatic extensions of MTL corresponding to well-known parallel extensions of BL. Moreover, we investigate varieties of MTL algebras whose linearly ordered countable algebras embed into algebras whose lattice reduct is the real and/or the rational interval [0,1]. These embedding properties are used to investigate finite strong standard and/or rational completeness of the corresponding logics. (shrink)

In this paper we provide a finite axiomatization (using two finitary rules only) for the propositional logic (called $L\Pi$ ) resulting from the combination of Lukasiewicz and Product Logics, together with the logic obtained by from $L \Pi$ by the adding of a constant symbol and of a defining axiom for $\frac{1}{2}$ , called $L \Pi\frac{1}{2}$ . We show that $L \Pi \frac{1}{2}$ contains all the most important propositional fuzzy logics: Lukasiewicz Logic, Product Logic, Gödel's Fuzzy Logic, Takeuti and Titani's (...) Propositional Logic, Pavelka's Rational Logic, Pavelka's Rational Product Logic, the Lukasiewicz Logic with $\Delta$ , and the Product and Gödel's Logics with $\Delta$ and involution. Standard completeness results are proved by means of investigating the algebras corresponding to $L \Pi$ and $L \Pi \frac{1}{2}$ . For these algebras, we prove a theorem of subdirect representation and we show that linearly ordered algebras can be represented as algebras on the unit interval of either a linearly ordered field, or of the ordered ring of integers, Z. (shrink)

The monoidal t-norm based logic MTL is obtained from Hájek's Basic Fuzzy logic BL by dropping the divisibility condition for the strong conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0, 1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the issue of standard and rational completeness of (...) some important axiomatic extensions of MTL corresponding to well-known parallel extensions of BL. Moreover, we investigate varieties of MTL algebras whose linearly ordered countable algebras embed into algebras whose lattice reduct is the real and/or the rational interval [0, 1]. These embedding properties are used to investigate finite strong standard and/or rational completeness of the corresponding logics. (shrink)

ABSTRACT The term fuzzy logic has two different meanings -broad and narrow. In Zadeh's opinion, fuzzy logic is an extension of many- valued logic but having a different agenda—as generalized modus ponens, max-min inference, linguistic quantifiers etc. The question we address in this paper is whether there is something in Zadeh's specific agenda which cannot be grasped by “classiceli”, “traditional” mathematical logic. We show that much of fuzzy logic can be understood as classical deduction in a many-sorted many-valued Pavelka- Lukasiewicz (...) style rational quantification logic. This means that, besides the linguistic or approximation aspects, the logical aspect is present too and can be made explicit. (shrink)

Betting methods, of which de Finetti's Dutch Book is by far the most well-known, are uncertainty modelling devices which accomplish a twofold aim. Whilst providing an interpretation of the relevant measure of uncertainty, they also provide a formal definition of coherence. The main purpose of this paper is to put forward a betting method for belief functions on MV-algebras of many-valued events which allows us to isolate the corresponding coherence criterion, which we term coherence in the aggregate. Our framework generalises (...) the classical Dutch Book method. (shrink)

ABSTRACTIn this paper, we consider non-associative generalisations of Hájek's logics BL and psBL. As it was shown by Cignoli, Esteva, Godo, and Torrens, the former is the logic of continuous t-norms and their residua. Botur introduced logic naBL which is the logic of non-associative continuous t-norms and their residua. Thus, naBL can be viewed as a non-associative generalisation of BL. However, Botur has not presented axiomatization of naBL. We fill this gap by constructing an adequate Hilbert-style calculus for naBL. (...) Although, as was shown by Flondor, Georgescu, and Iorgulescu, there are no non-commutative continuous t-norms, Hájek's psBL can be viewed as BL's non-commutative generalisation. We present the logic psnaBL of psnaBL-algebras which can be viewed as naBL's non-commutative generalisation as well as psBL's non-associative generalisation and BL's both non-commutative and non-associative generalisation. (shrink)

The ŁΠ and logics were introduced by Godo, Esteva and Montagna. These logics extend many other known propositional and predicate logics, including the three mainly investigated ones (Gödel, product and Łukasiewicz logic). The aim of this paper is to show some advances in this field. We will see further reduction of the axiomatic systems for both logics. Then we will see many other logics contained in the ŁΠ family of logics (namely logics induced by the continuous finitely constructed t-norms (...) and Takeuti and Titani's fuzzy predicate logic). (shrink)

Drawing on the Agency-Stewardship approach, which suggests that manager profile may range from the agent model to the steward model, this article aims to examine how important CEOs are to corporate social responsibility (CSR). Specifically, this exploratory study proposes the existence of a relationship between manager profile and CSR practices and that this relation is mediated by the perceived role of ethics and social responsibility. After applying a mediated regression analysis using survey information collected from 149 CEOs in Spain, results (...) show that those closer to the steward model are more inclined to attach great importance to ethics and social responsibility, and to implement CSR practices in their companies. Results also provide support for the suggested mediating effect. Thus, this article extends research in understanding top managers as drivers for CSR and suggests new ways to deal with this issue empirically. (shrink)

This paper examines the relationships between the many-valued logics G~ and Gn~ of Esteva, Godo, Hajek, and Navara, i.e., Godel logic G enriched with Łukasiewicz negation, and neighbors of intuitionistic logic. The popular fragments of Rauszer's Heyting-Brouwer logic HB admit many-valued extensions similar to G which may likewise be enriched with Łukasiewicz negation; the fuzzy extensions of these logics, including HB, are equivalent to G ~, as are their n-valued extensions equivalent to Gn~ for any n ≥ 2. These (...) enriched systems extend Wansing's logic I4C4, showing that Łukasiewicz negation is a species of Nelson's negation of constructible falsity and yielding a Kripke-style semantics for G~ and Gn~ to complement the many-valued semantics. (shrink)

This paper based on the distinction between the instrumental and normative views of stakeholder management explores how business education and personal moral philosophies may influence the orientation adopted by an individual. A mediated regression analysis using survey information collected from 206 Spanish university students showed that those exposed to management theories were less willing to consider stakeholders when making business decisions if the consequent economic impacts on the firm were omitted. The results also provided support for a negative effect of (...) business education on idealism and a mediating effect of the latter on the relationship between education and stakeholder management orientation. This study thus raises awareness on the influence of business education on individuals’ ethical decision-making processes and suggests some possible changes for business education. (shrink)

In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. A gripping combination of science and accessibility, Godel’s Proof by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy (...) the chance to satisfy their intellectual curiosity. (shrink)

The first major work in the history of philosophy to bear the title "Metaphysics" was the treatise by Aristotle that we have come to know by that name. But Aristotle himself did not use that title or even describe his field of study as 'metaphysics'; the name was evidently coined by the first century C.E. editor who assembled the treatise we know as Aristotle's Metaphysics out of various smaller selections of Aristotle's works. The title 'metaphysics' -- literally, 'after the Physics' (...) -- very likely indicated the place the topics discussed therein were intended to occupy in the philosophical curriculum. They were to be studied after the treatises dealing with nature (ta phusika). In this entry, we discuss the ideas that are developed in Aristotle's treatise. (shrink)

In this highly original account of Bishop George Berkeley's epistemological and metaphysical theories, George S. Pappas seeks to determine precisely what doctrines the philosopher held and what arguments he put forward to support them. Specifically, Pappas overturns accepted opinions about Berkeley's famous attack on the Lockean doctrine of abstract ideas. Berkeley's criticism of these ideas had been thought relevant only to his views on language and to his nominalism; Pappas persuasively argues that Berkeley's ideas about abstraction are crucial to nearly (...) all of the fundamental principles that he defends. Pappas demonstrates how an adequate appreciation of Berkeley's views on abstraction can lead to an improved understanding of his important principle of esse is percipi, and of the arguments Berkeley proposes in support of this principle. Pappas also takes up Berkeley's widely rejected claim to be a philosopher of common sense. He assesses the validity of this self-description and considers why Berkeley might have chosen to align himself with a commonsense position. Pappas shows how three core concepts—abstraction, perception, and common sense—are central to and interdependent in the work of one of the major figures of early modern Western thought. (shrink)

Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and their residua as truth functions for implication. In these logics, a negation is also definable from the implication and the truth constant $\overline{0}$ , namely $\neg \varphi$ is $\varphi \to \overline{0}$. However, this negation behaves quite differently depending on the t-norm. For a nilpotent t-norm (a t-norm which is isomorphic to Łukasiewicz t-norm), it turns out that $\neg$ is an involutive negation. However, (...) for t-norms without non-trivial zero divisors, $\neg$ is Gödel negation. In this paper we investigate the residuated fuzzy logics arising from continuous t-norms without non-trivial zero divisors and extended with an involutive negation. (shrink)

The aim of this article is to discuss the role that victim groups and organizations may have in framing and supporting an accountability agenda, as well as their potential for endorsing a distributive justice agenda. The article explores two empirical cases where victims' rights have been introduced and applied by victim organizations to promote accountability—Colombia and Peru. It will be argued that if transitional justice in general and victim reparations in particular are to embark in a quest for distributive justice, (...) it cannot do so without considering victims as political actors, and putting forward demands in terms of victims’ rights. (shrink)

In Carnap’s autobiography, he tells the story how one night in January 1931, “the whole theory of language structure” in all its ramifications “came to [him] like a vision”. The shorthand manuscript he produced immediately thereafter, he says, “was the first version” of Logical Syntax of Language. This document, which has never been examined since Carnap’s death, turns out not to resemble Logical Syntax at all, at least on the surface. Wherein, then, did the momentous insight of 21 January 1931 (...) consist? We seek to answer this question by placing Carnap’s shorthand manuscript in the context of his previous efforts to accommodate scientific theories and metalinguistic claims within Wittgenstein’s Tractatus theory of meaning. The breakthrough of January 1931 consists, from this viewpoint, in the rejection of the Tractatus theory in favor of the meta-mathematical perspective of Hilbert, Gödel, and Tarski. This was not yet the standpoint of the published Logical Syntax, as we show, but led naturally to the “principle of tolerance” and thus to Carnap’s mature philosophy, in which the inconsistencies between this first view and the principle of tolerance, which survived into the published Syntax, were overcome. (shrink)

This text provides a unique and compelling account of Wittgenstein's impact upon twentieth century analytic philosophy, from its inception at the turn of the ...

G. E. Moore observed that to assert, 'I went to the pictures last Tuesday but I don't believe that I did' would be 'absurd'. Over half a century later, such sayings continue to perplex philosophers. In the definitive treatment of the famous paradox, Green and Williams explain its history and relevance and present new essays by leading thinkers in the area.

In this book, Sara Monoson challenges the longstanding and widely held view that Plato is a virulent opponent of all things democratic. She does not, however, offer in its place the equally mistaken idea that he is somehow a partisan of democracy. Instead, she argues that we should attend more closely to Plato's suggestion that democracy is horrifying and exciting, and she seeks to explain why he found it morally and politically intriguing.Monoson focuses on Plato's engagement with democracy as he (...) knew it: a cluster of cultural practices that reach into private and public life, as well as a set of governing institutions. She proposes that while Plato charts tensions between the claims of democratic legitimacy and philosophical truth, he also exhibits a striking attraction to four practices central to Athenian democratic politics: intense antityrantism, frank speaking, public funeral oratory, and theater-going. By juxtaposing detailed examination of these aspects of Athenian democracy with analysis of the figurative language, dramatic structure, and arguments of the dialogues, she shows that Plato systematically links democratic ideals and activities to philosophic labor. Monoson finds that Plato's political thought exposes intimate connections between Athenian democratic politics and the practice of philosophy.Situating Plato's political thought in the context of the Athenian democratic imaginary, Monoson develops a new, textured way of thinking of the relationship between Plato's thought and the politics of his city. (shrink)

Our study presents an overview of the issues that were brought forward by participants of a moral case deliberation (MCD) project in two elderly care organizations. The overview was inductively derived from all case descriptions (N = 202) provided by participants of seven mixed MCD groups, consisting of care providers from various professional backgrounds, from nursing assistant to physician. The MCD groups were part of a larger MCD project within two care institutions (residential homes and nursing homes). Care providers are (...) confronted with a wide variety of largely everyday ethical issues. We distinguished three main categories: ‘resident’s behavior’, ‘divergent perspectives on good care’ and ‘organizational context’. The overview can be used for agendasetting when institutions wish to stimulate reflection and deliberation. It is important that an agenda is constructed from the bottom-up and open to a variety of issues. In addition, organizing reflection and deliberation requires effort to identify moral questions in practice whilst at the same time maintaining the connection with the organizational context and existing communication structures. Once care providers are used to dealing with divergent perspectives, inviting different perspectives (e.g. family members) to take part in the deliberation, might help to identify and address ethical ‘blind spots’. (shrink)

In his book Shadows of the Mind: A search for the missing science of con- sciousness [SM below], Roger Penrose has turned in another bravura perfor- mance, the kind we have come to expect ever since The Emperor’s New Mind [ENM ] appeared. In the service of advancing his deep convictions and daring conjectures about the nature of human thought and consciousness, Penrose has once more drawn a wide swath through such topics as logic, computa- tion, artificial intelligence, quantum physics (...) and the neuro-physiology of the brain, and has produced along the way many gems of exposition of difficult mathematical and scientific ideas, without condescension, yet which should be broadly appealing.¹ While the aims and a number of the topics in SM are the same as in ENM , the focus now is much more on the two axes that Pen- rose grinds in earnest. Namely, in the first part of SM he argues anew and at great length against computational models of the mind and more specifi- cally against any account of mathematical thought in computational terms. Then in the second part, he argues that there must be a scientific account of consciousness but that will require a (still to be found) non-computational extension or modification of present-day quantum physics. (shrink)

Stages on Life's Way, the sequel to Either/Or, is an intensely poetic example of Kierkegaard's vision of the three stages, or spheres, of existence: the esthetic, the ethical, and the religious. With characteristic love for mystification, he presents the work as a bundle of documents fallen by chance into the hands of "Hilarius Bookbinder," who prepared them for printing. The book begins with a banquet scene patterned on Plato's Symposium. (George Brandes maintained that "one must recognize with amazement that it (...) holds its own in this comparison.") Next is a discourse by "Judge William" in praise of marriage "in answer to objections." The remainder of the volume, almost two-thirds of the whole, is the diary of a young man, discovered by "Frater Taciturnus," who was deeply in love but felt compelled to break his engagement. The work closes with a letter to the reader from Taciturnus on the three "existence-spheres" represented by the three parts of the book. Stages on Life's Way not only repeats themes, characters, and pseudonymous authors of the earlier works but also goes beyond them and points to further development of central ideas in Concluding Unscientific Postscript. (shrink)

Our study presents an overview of the issues that were brought forward by participants of a moral case deliberation (MCD) project in two elderly care organizations. The overview was inductively derived from all case descriptions (N = 202) provided by participants of seven mixed MCD groups, consisting of care providers from various professional backgrounds, from nursing assistant to physician. The MCD groups were part of a larger MCD project within two care institutions (residential homes and nursing homes). Care providers are (...) confronted with a wide variety of largely everyday ethical issues. We distinguished three main categories: ‘resident’s behavior’, ‘divergent perspectives on good care’ and ‘organizational context’. The overview can be used for agendasetting when institutions wish to stimulate reflection and deliberation. It is important that an agenda is constructed from the bottom-up and open to a variety of issues. In addition, organizing reflection and deliberation requires effort to identify moral questions in practice whilst at the same time maintaining the connection with the organizational context and existing communication structures. Once care providers are used to dealing with divergent perspectives, inviting different perspectives (e.g. family members) to take part in the deliberation, might help to identify and address ethical ‘blind spots’. (shrink)

Sebastian Gardner competently tackles one of Sartre's more complex and challenging works in this new addition to the Reader's Guides series.

Hempel's paradox of the ravens has to do with the question of what constitutes confirmation from a logical point of view; Wason 's selection task has been used extensively to investigate how people go about attempting to confirm or disconfirm conditional claims. This paper presents an argument that the paradox is resolved, and that people's typical performance in the selection task can be explained, by consideration of what constitutes an effective strategy for seeking evidence of the tenability of universal or (...) conditional claims in everyday life. (shrink)

In this paper we show that the subvarieties of BL, the variety of BL-algebras, generated by single BL-chains on [0, 1], determined by continous t-norms, are finitely axiomatizable. An algorithm to check the subsethood relation between these subvarieties is provided, as well as another procedure to effectively find the equations of each subvariety. From a logical point of view, the latter corresponds to find the axiomatization of every residuated many-valued calculus defined by a continuous t-norm and its residuum. Actually, the (...) paper proves the results for a more general class than t-norm BL-chains, the so-called regular BL-chains. (shrink)

This article explores the characteristics of research sites that scientists have called “natural experiments” to understand and develop usable distinctions for the social sciences between “Nature’s or Society’s experiments” and “natural experiments.” In this analysis, natural experiments emerge as the retro-fitting by social scientists of events that have happened in the social world into the traditional forms of field or randomized trial experiments. By contrast, “Society’s experiments” figure as events in the world that happen in circumstances that are already sufficiently (...) “controlled” to be open for direct analysis without reconstruction work. (shrink)

Plato’s dialogue Cratylus focuses on being and human dependence on words, or the essential truths about the human condition. Arguing that comedy is an essential part of Plato's concept of language, S. Montgomery Ewegen asserts that understanding the comedic is key to an understanding of Plato's deeper philosophical intentions. Ewegen shows how Plato’s view of language is bound to comedy through words and how, for Plato, philosophy has much in common with playfulness and the ridiculous. By tying words, language, and (...) our often uneasy relationship with them to comedy, Ewegen frames a new reading of this notable Platonic dialogue. (shrink)

Hintikka has criticized psychologists for "hasty epistemologizing," which he takes to be an unwarranted transfer of ideas from psychology (a discipline dealing with questions of fact) into epistemology (a discipline dealing with questions of method and theory). Hamlyn argues, following Hintikka, that Gibson's theory of perception is an example of such an inappropriate transfer, especially insofar as Hamlyn feels Gibson does not answer several important questions. However, Gibson's theory does answer the relevant questions, albeit in a new and radical way, (...) which suggests that the alleged distinction between psychology and epistemology is suspect. In fact, contrary to Hintikka and Hamlyn's claims, Gibson's theory of perception appears to be a valuable source of epistemological as well as psychological ideas. (shrink)

Nearly as famous as his denial of the existence of matter is Berkeley's insistence that his philosophy is somehow a defense of commonsense. This is most often taken to mean that Berkeley thinks of his philosophy as supporting commonsense beliefs. However, the inadequacies of such views have persuaded some to disregard entirely Berkeley's claims about commonsense. Both readings are undesirable. Extant interpretations misunderstand the relationship between Berkeley's philosophy and commonsense. In this paper, I present a new account of how to (...) understand Berkeley's so-called defense of commonsense; it is not a defense-cum­-apology for commonsense beliefs, but a defensive attack against a skeptical threat. I then examine two rival accounts of the defense of commonsense and show how each fails to satisfy the criteria for a successful account. Finally, I briefly address the implications this view has for future scholarship. (shrink)

Various claims have been made, recently, that Darwin's argumentation in the Origin instantiates and so supports some general philosophical proposal about scientific theorizing, for example, the "semantic view". But these claims are grounded in various incorrect analyses of that argumentation. A summary is given here of an analysis defended at greater length in several papers by the present author. The historical and philosophical advantages of this analysis are explained briefly. Darwin's argument comprises three distinct evidential cases on behalf of natural (...) selection, cases, that is, for its existence, its adequacy and its responsibility. Theorizing, today, about evolution by natural selection involves a similar structure of evidential and explanatory concerns. (shrink)

A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.