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)

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.

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)

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)

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.

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)

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)

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)

This article tells the empirical story of women from seven villages of Kwale, the most southeastern county in the Coast Province of Kenya that borders with Tanzania—Lunga Lunga, Godo, Perani, Umoja, Maasailand, Mpakani and Jirani—as they searched for community health, equity, gender equality and peace on their own terms. This article shows that creative health initiatives can be successfully used as mechanisms for peace building. Since 2010, the Nikumbuke-Health by All Means projects from the University of Madison-Wisconsin in the (...) United States, have trained 57 health promoters and 32 female actors on disease prevention and health promotion that have outreached approximately 120,000 inhabitants around the county enhancing unity in diversity, and breaking down the walls of ethnic hostilities and prejudice. Because of its low cost and high effectivity, the United Nations awarded N-HbAM[1] the 2013 Public Service Award as a model of best practice in gender, community development and sustainable wellbeing. [1] In 2013, at the time of the UNPS Award the projects were still called Nikumbuke-Health by Motorbike. The name was changed in 2018 as the projects broadened in scope and geographical location. (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)

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)

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 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)

This comprehensive, critical account of Buber's life and work incorporates extensive research and draws on the author's experiences as Buber's coworker and friend.

Traces the development of the famous theologian's philosophy as he faced the challenges of the Weimar Republic, Nazi Germany, and prewar Palestine.

Possibilistic logic and modal logic are knowledge representation frameworks sharing some common features, such as the duality between possibility and necessity, and the decomposability of necessity for conjunctions, as well as some obvious differences since possibility theory is graded. At the semantic level, possibilistic logic relies on possibility distributions and modal logic on accessibility relations. In the last 30 years, there have been a series of attempts for bridging the two frameworks in one way or another. In this paper, we (...) compare the relational semantics of epistemic logics with simpler possibilistic semantics of a fragment of such logics that only uses modal formulas of depth 1. This minimal epistemic logic handles both all-or-nothing beliefs and explicitly ignored facts. We also contrast epistemic logic with the S5-based rough set logic. Finally, this paper presents extensions of generalized possibilistic logic with objective and non-nested multimodal formulas, in the style of modal logics KD45 and S5. (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)

Telegraphy, the distant ancestor of Internet and GSM, was invented by Samuel Morse in 1838. One year later, William Grove invented the fuel cell. Although numerous highly successful innovations stemming from telegraphy may be observed, the development of fuel cells has been insignificant, slow, and erratic and has not yet resulted in notable positive socioeconomic effects. By comparing the modern development of fuel cells and hydrogen technology, that is, a potential radical innovation in energy generation, with some aspects related to (...) the evolution of two highly successful radical innovations, Internet and GSM, the author focuses on the role of innovation regimes and policy in a sectorial system of innovations perspective. In the slow pace in fuel cells and hydrogen technology development, two factors seem to interact negatively: weak and fragmented innovation regimes in the energy sector and the current hegemony of market-oriented R&D policies. (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)

As a spiritual autobiography, Kierkegaard's The Point of View for My Work as an Author stands among such great works as Augustine's Confessions and Newman's Apologia pro Vita Sua. Yet Point of View is neither a confession nor a defense; it is an author's story of a lifetime of writing, his understanding of the maze of greatly varied works that make up his oeuvre. Upon the imminent publication of the second edition of Either/Or, Kierkegaard again intended to cease writing. Now (...) was the time for a direct "report to history" on the authorship as a whole. In addition to Point of View, which was published posthumously, the present volume also contains On My Work as an Author, a contemporary substitute, and the companion piece Armed Neutrality. (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)

Einstein, in his “Zur Elektrodynamik bewegter Körper”, gave a physical (operational) meaning to “time” of a remote event in describing “motion” by introducing the concept of “synchronous stationary clocks located at different places”. But with regard to “place” in describing motion, he assumed without analysis the concept of a system of co-ordinates.In the present paper, we propose a way of giving physical (operational) meaning to the concepts of “place” and “co-ordinate system”, and show how the observer can define both the (...) place and time of a remote event. Following Einstein, we consider another system “in uniform motion of translation relatively to the former”. Without assuming “the properties of homogeneity which we attribute to space and time”, we show that the definitions of space and time in the two systems are linearly related. We deduce some novel consequences of our approach regarding faster-than-light observers and particles, “one-way” and “two-way” velocities of light, symmetry, the “group property” of inertial reference frames, length contraction and time dilatation, and the “twin paradox”. Finally, we point out a flaw in Einstein’s argument in the “Electrodynamical Part” of his paper and show that the Lorentz force formula and Einstein’s formula for transformation of field quantities are mutually consistent. We show that for faster-than-light bodies, a simple modification of Planck’s formula for mass suffices. (Except for the reference to Planck’s formula, we restrict ourselves to Physics of 1905.). (shrink)

Newton's Philosophiae Naturalis Principia Mathematica provides a coherent and deductive presentation of his discovery of the universal law of gravitation. It is very much more than a demonstration that 'to us it is enough that gravity really does exist and act according to the laws which we have explained and abundantly serves to account for all the motions of the celestial bodies and the sea'. It is important to us as a model of all mathematical physics.Representing a decade's work from (...) a distinguished physicist, this is the first comprehensive analysis of Newton's Principia without recourse to secondary sources. Professor Chandrasekhar analyses some 150 propositions which form a direct chain leading to Newton's formulation of his universal law of gravitation. In each case, Newton's proofs are arranged in a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's connected prose. In almost every case, a modern version of the proofs is given to bring into sharp focus the beauty, clarity, and breath-taking economy of Newton's methods.Subrahmanyan Chandrasekhar is one of the most reknowned scientists of the twentieth century, whose career spanned over 60 years. Born in India, educated at the University of Cambridge in England, he served as Emeritus Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics at the University of Chicago, where he has was based from 1937 until his death in 1996. His early research into the evolution of stars is now a cornerstone of modern astrophysics, and earned him the Nobel Prize for Physics in 1983. Later work into gravitational interactions between stars, the properties of fluids, magnetic fields, equilibrium ellipsoids, and black holes has earned him awards throughout the world, including the Gold Medal from the Royal Astronomical Society in London, the National Medal of Science in the United States, and the Copley Medal from the Royal Society. His many publications include Radiative transfer, Hydrodynamic and hydromagnetic stability, and The mathematical theory of black holes, each being praised for its breadth and clarity. Newton's Principia for the common reader is the result of Professor Chandrasekhar's profound admiration for a scientist whose work he believed is unsurpassed, and unsurpassable. (shrink)

An able and clear defense of Bradley's principal theses and the underlying conception of metaphysical enterprise. "This is a book about a metaphysician, about metaphysics, and, most importantly, it attempts to develop elements of a metaphysical position long the lines of what is called Absolute Idealism." The Introduction takes up the Verificationists [[sic]] argument and two recent accounts of metaphysics. Part I devotes ten Chapters to the elucidation and defense of Bradley's conception of reality. It culminates in examining three alternative (...) accounts of "Real". Part II considers "the major philosophical theories of the self in order to defend Bradley's Theory of the self within his metaphysical scheme."--A. S. C. (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)

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)

A biography of the noted philosopher and Jewish theologian focuses on the years in which Buber became internationally acclaimed for his work as an author, philosopher, and peacemaker.

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

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)