In the present paper we prove that the poset of all extensions of the logic defined by a class of matrices whose sets of distinguished values are equationally definable by their algebra reducts is the retract, under a Galois connection, of the poset of all subprevarieties of the prevariety generated by the class of the algebra reducts of the matrices involved. We apply this general result to the problem of finding and studying all extensions of the logic of paradox. In (...) order to solve this problem, we first study the structure of prevarieties of Kleene lattices. Then, we show that the poset of extensions of the logic of paradox forms a four-element chain, all the extensions being finitely many-valued and finitely-axiomatizable logics. There are just two proper consistent extensions of the logic of paradox. The first is the classical logic that is relatively axiomatized by the Modus ponens rule for the material implication. The second extension, being intermediate between the logic of paradox and the classical logic, is the one relatively axiomatized by the Ex Contradictione Quodlibet rule. (shrink)

In this paper we study 12 four-valued logics arisen from Belnap's truth and/or knowledge four-valued lattices, with or without constants, by adding one or both or none of two new non-regular operations—classical negation and natural implication. We prove that the secondary connectives of the bilattice four-valued logic with bilattice constants are exactly the regular four-valued operations. Moreover, we prove that its expansion by any non-regular connective (such as, e.g., classical negation or natural implication) is strictly functionally complete. Further, finding axiomatizations (...) of the quasi varieties generated by the 12 logics involved (that prove to be varieties), we find naturell equational axiomatizations of these logics. Finally, applying Pynko's general theory of algebraizable sequential consequence operations, we also find equivalent natural sequentiell axiomatizations of the logics under consideration that expand either of two Pynko's sequential calculi for the constant-free truth-lattice four-valued logic. (shrink)

In this paper we define and study a generalized notion of a logical system that covers on an equal formal basis sentential, equational and sequential systems. We develop a general theory of equivalence between generalized logics that provides, first, a conception of algebraizable logic , second, a formal concept of equivalence between sequential systems and, third, a notion of equivalence between sentential and sequential systems. We also use our theory of equivalence for developing a general algebraic approach to conjunctive non-pseudo-axiomatic (...) self-extensional sentential logics. Finally, we consider within the framework of the mentioned approach various sequential formulations for some well-known sentential logics. (shrink)

The aim of this paper is technically to study Belnap's four-valued sentential logic . First, we obtain a Gentzen-style axiomatization of this logic that contains no structural rules while all they are still admissible in the Gentzen system what is proved with using some algebraic tools. Further, the mentioned logic is proved to be the least closure operator on the set of {Λ, V, ⌝}-formulas satisfying Tarski's conditions for classical conjunction and disjunction together with De Morgan's laws for negation. It (...) is also proved that Belnap's logic is the only sentential logic satisfying the above-mentioned conditions together with Anderson-Belnap's Variable-Sharing Property. Finally, we obtain a finite Hilbert-style axiomatization of this logic. As a consequence, we obtain a finite Hilbert-style axiomatization of Priest's logic of paradox. (shrink)

The present paper concerns a technical study of PRIEST'S logic of paradox [Pri 79], We prove that this logic has no proper paraconsistent strengthening. It is also proved that the mentioned logic is the largest paraconsistent one satisfaying TARSKI'S conditions for the classical conjunction and disjunction together with DE MORGAN'S laws for negation. Finally, we obtain for the logic of paradox an algebraic completeness result related to Kleene lattices.

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)

In this paper we deal with infinitary universal Horn logic both with and without equality. First, we obtain a relative Lyndon-style interpolation theorem. Using this result, we prove a non-standard preservation theorem which contains, as a particular case, a Lyndon-style theorem on surjective homomorphisms in its Makkai-style formulation. Another consequence of the preservation theorem is a theorem on bimorphisms, which, in particular, provides a tool for immediate obtaining characterizations of infinitary universal Horn classes without equality from those with equality. From (...) the theorem on surjective homomorphisms we also derive a non-standard Beth-style preservation theorem that yields a non-standard Beth-style definability theorem, according to which implicit definability of a relation symbol in an infinitary universal Horn theory implies its explicit definability by a conjunction of atomic formulas. We also apply our theorem on surjective homomorphisms, theorem on bimorphisms and definability theorem to algebraic logic for general propositional logic. (shrink)

The goal of the paper is to develop a universal semantic approach to derivable rules of propositional multiple-conclusion sequent calculi with structural rules, which explicitly involve not only atomic formulas, treated as metavariables for formulas, but also formula set variables, upon the basis of the conception of model introduced in :27–37, 2001). One of the main results of the paper is that any regular sequent calculus with structural rules has such class of sequent models that a rule is derivable in (...) the calculus iff it is sound with respect to each model of the semantics. We then show how semantics of admissible rules of such calculi can be found with using a method of free models. Next, our universal approach is applied to sequent calculi for many-valued logics with equality determinant. Finally, we exemplify this application by studying sequent calculi for some of such logics. (shrink)

As it was proved in [4, Sect. 3], the poset of extensions of the propositional logic defined by a class of logical matrices with equationally-definable set of distinguished values is a retract, under a Galois connection, of the poset of subprevarieties of the prevariety generated by the class of the underlying algebras of the defining matrices. In the present paper we apply this general result to the three-valued paraconsistent logic proposed by Hałkowska–Zajac [2]. Studying corresponding prevarieties, we prove that extensions (...) of the logic involved form a four-element chain, the only proper consistent extensions being the least non-paraconsistent extension of it and the classical logic. RID=""ID="" Mathematics Subject Classification (2000): 03B50, 03B53, 03G10 RID=""ID="" Key words or phrases: Many-valued logic – Paraconsistent logic – Extension – Prevariety – Distributive lattice. (shrink)

ABSTRACT A bilattice is said to be regular provided its truth conjunction and disjunction are monotonic with respect to its knowledge ordering. The principal result of this paper is that the following properties of a bilattice B are equivalent: 1. B is regular; 2. the truth conjunction and disjunction of B are definable through the rest of the operations and constants of B; 3. B is isomorphic to a bilattice of the form L 1 · L 2 where L 1 (...) and L 2 are bounded lattices. We also derive from this metaequivalence a number of corollaries concerning distributive bilattices, degenerated bilattices and bilattices with negation. (shrink)

In this paper, we study multiplicative extensions of propositional many-place sequent calculi for finitely-valued logics arising from those introduced in Sect. 5 of Pynko (J Multiple-Valued Logic Soft Comput 10:339–362, 2004) through their translation by means of singularity determinants for logics and restriction of the original many-place sequent language. Our generalized approach, first of all, covers, on a uniform formal basis, both the one developed in Sect. 5 of Pynko (J Multiple-Valued Logic Soft Comput 10:339–362, 2004) for singular (...) finitely-valued logics (when singularity determinants consist of a variable alone) and conventional Gentzen-style (i.e., two-place sequent) calculi suggested in Pynko (Bull Sect Logic 33(1):23–32, 2004) for finitely-valued logics with equality determinant. In addition, it provides a universal method of constructing Tait-style (i.e., one-place sequent) calculi for finitely-valued logics with singularity determinant (in particular, for Łukasiewicz finitely-valued logics) that fits the well-known Tait calculus (Lecture Notes in Mathematics, Springer, Berlin, 1968) for the classical logic. We properly extend main results of Pynko (J Multiple-Valued Logic Soft Comput 10:339–362, 2004) and explore calculi under consideration within the framework of Sect. 7 of Pynko (Arch Math Logic 45:267–305, 2006), generalizing the results obtained in Sect. 7.5 of Pynko (Arch Math Logic 45:267–305 2006) for two-place sequent calculi associated with finitely-valued logics with equality determinant according to Pynko (Bull Sect Logic 33(1):23–32, 2004). We also exemplify our universal elaboration by applying it to some denumerable families of well-known finitely-valued logics. (shrink)

Basic results of the paper are that any four-valued expansion L4 of Dunn-Belnap's logic DB4 is de_ned by a unique conjunctive matrix ℳ4 with exactly two distinguished values over an expansion.

The primary objective of this paper, which is an addendum to the author’s [8], is to apply the general study of the latter to Łukasiewicz’s n-valued logics [4]. The paper provides an analytical expression of a 2(n−1)-place sequent calculus (in the sense of [10, 9]) with the cut-elimination property and a strong completeness with respect to the logic involved which is most compact among similar calculi in the sense of a complexity of systems of premises of introduction rules. This together (...) with a quite effective procedure of construction of an equality determinant (in the sense of [5]) for the logics involved to be extracted from the constructive proof of Proposition 6.10 of [6] yields an equally effective procedure of construction of both Gentzen-style [2] (i.e., 2-place) and Tait-style [11] (i.e., 1-place) minimal sequent calculi following the method of translations described in Subsection 4.2 of [7]. (shrink)

The incredible achievements of modern scientific theories lead most of us to embrace scientific realism: the view that our best theories offer us at least roughly accurate descriptions of otherwise inaccessible parts of the world like genes, atoms, and the big bang. In Exceeding Our Grasp, Stanford argues that careful attention to the history of scientific investigation invites a challenge to this view that is not well represented in contemporary debates about the nature of the scientific enterprise. The historical record (...) of scientific inquiry, Stanford suggests, is characterized by what he calls the problem of unconceived alternatives. Past scientists have routinely failed even to conceive of alternatives to their own theories and lines of theoretical investigation, alternatives that were both well-confirmed by the evidence available at the time and sufficiently serious as to be ultimately accepted by later scientific communities. Stanford supports this claim with a detailed investigation of the mid-to-late 19th century theories of inheritance and generation proposed in turn by Charles Darwin, Francis Galton, and August Weismann. He goes on to argue that this historical pattern strongly suggests that there are equally well-confirmed and scientifically serious alternatives to our own best theories that remain currently unconceived. Moreover, this challenge is more serious than those rooted in either the so-called pessimistic induction or the underdetermination of theories by evidence, in part because existing realist responses to these latter challenges offer no relief from the problem of unconceived alternatives itself. Stanford concludes by investigating what positive account of the spectacularly successful edifice of modern theoretical science remains open to us if we accept that our best scientific theories are powerful conceptual tools for accomplishing our practical goals, but abandon the view that the descriptions of the world around us that they offer are therefore even probably or approximately true. (shrink)

The place of the emotions among the passions -- The analytic of the emotions I -- The analytic of the emotions II -- The dialectic of the emotions -- Pride, arrogance, and humility -- Shame, embarrassment, and guilt -- Envy -- Jealousy -- Anger -- Love -- Friendship -- Sympathy and empathy.

The concept of normal is so familiar that it can be hard to imagine contemporary life without it. Yet the term entered everyday speech only in the mid-twentieth century. Before that, it was solely a scientific term used primarily in medicine to refer to a general state of health and the orderly function of organs. But beginning in the middle of the twentieth century, normal broke out of scientific usage, becoming less precise and coming to mean a balanced condition to (...) be maintained and an ideal to be achieved. In Normality, Peter Cryle and Elizabeth Stephens offer an intellectual and cultural history of what it means to be normal. They explore the history of how communities settle on any one definition of the norm, along the way analyzing a fascinating series of case studies in fields as remote as anatomy, statistics, criminal anthropology, sociology, and eugenics. Cryle and Stephens argue that since the idea of normality is so central to contemporary disability, gender, race, and sexuality studies, scholars in these fields must first have a better understanding of the context for normality. This pioneering book moves beyond binaries to explore for the first time what it does—and doesn’t—mean to be normal. (shrink)

An Interdisciplinary Approach to Cognitive Modelling presents a new approach to cognition that challenges long-held views. It systematically develops a broad-based framework to model cognition, which is mathematically equivalent to the emerging 'quantum-like modelling' of the human mind. The book argues that a satisfactory physical and philosophical basis of such an approach is missing, a particular issue being the application of quantization to the mind for which there is no empirical evidence as yet. In response to this issue, the book (...) adopts a COM (classical optical modelling) approach, broad-based but mathematically equivalent to quantum-like modelling while avoiding its problematic features. It presents a philosophically informed and empirically motivated mathematical model of cognition, mainly concerning decision making processes. It also deals with applications to different areas of the social sciences. It will be of interest to scholars and research students interested in the mathematical modelling of cognition and decision making, and also interdisciplinary researchers interested in broader issues of cognition. (shrink)

This study concerns the ideas of one particular philosopher, Henri Bergson, whose views of time, intuition, and creativity have had a significant impact on art, literature, and the humanities, both in his time and in our own. Although it is generally recognized that Bergson's ideas have significantly impacted the arts and the humanities, it has not been recognized how they have also had a creative influence on the sciences as well. Nor has it been realized that this was one of (...) his most basic contentions. Bergson's conception of intuition--his fundamental insight into reality--was not limited to fugitive insights into human existence. By realizing previously unsuspected possibilities for research and discovery, his endeavors were also meant to make possible new advances in the sciences. If it enabled his cousin by marriage, Marcel Proust, to explore human memory in depth, it also inspired psychologists like Daniel Schachter to use Bergson's ideas to make real contributions to contemporary memory science. If his notion of creative evolution brought many thinkers to a belief in human creative freedom, it brought others (notably Alexis Carrel and Pierre Lecomte de Noüy) to a scientific study of biological time. Among his successful speculations was the theory of the Big Bang cosmology. 'Getting Bergson Straight' shows many points at which Bergson's ideas anticipated future developments in the sciences. This was seen clearly by the Nobel Prize-winning physicist Luis de Broglie who viewed Bergson's physics as presaging quantum physics. Thus, the text is well situated for arts, humanities, social science, and natural science classrooms studying creative thinking and/or intellectual history. (shrink)

Profoundly important ethical and political controversies turn on the question of whether biological life is an essential aspect of a human person, or only an extrinsic instrument. Lee and George argue that human beings are physical, animal organisms - albeit essentially rational and free - and examine the implications of this understanding of human beings for some of the most controversial issues in contemporary ethics and politics. The authors argue that human beings are animal organisms and that their personal identity (...) across time consists in the persistence of the animal organisms they are; they also argue that human beings are essentially rational and free and that there is a radical difference between human beings and other animals; criticize hedonism and hedonistic drug-taking; present detailed defenses of the prolife positions on abortion and euthanasia; and defend the traditional moral position on marriage and sexual acts. (shrink)

Do the ethical features of an artwork bear on its aesthetic value? This movie endorses misogyny, that song is a civil rights anthem, the clay constituting this statue was extracted with underpaid labor—are facts like these the proper bases for aesthetic evaluation? I argue that this debate has suffered from a false presupposition: that if the answer is yes (for at least some such ethical features), such considerations feature as pro tanto contributions to an artwork's overall aesthetic value, i.e., as (...) merits or flaws which make something have more or less overall aesthetic value. As the case of ethically laden, aesthetic evaluation makes clear, however, good aesthetic judgement is irreducibly multi-dimensional, e.g., "the movie has an engaging soundtrack, tasteful camera work, and takes a misogynistically prurient perspective on its female lead.'' Such a "non-summative" judgement refuses to reduce those various dimensions of aesthetic value to a single aggregate aesthetic evaluation, like "it's a 6/10" or "it's a pretty good movie!" I defend both the modest claim that such non-summative evaluations are not mistaken and the extremist claim that summative (i.e., unidimensional) aesthetic evaluation is defective by considering other domains of normative assessment in which summing seems inappropriate, notably including evaluations of people's character. (shrink)

This practical and essential text, co-authored by an engineer and an ethicist, covers ethical dilemmas that any engineer might encounter on the job, emphasizing the responsibility of a practicing engineer to act in an ethical manner. To illustrate the complexities involved, the authors present characters who encounter situations that test the engineering code of ethics. The dialogue between the characters highlights different perspectives of each dilemma. As they proceed through the book, students see how the code of ethics can help (...) in decision making, as well as the implications of various decisions. The philosophical theory that supports the ethical situations encountered is presented as boxed material following each section. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. (shrink)

In worlds that lack life, there is no value. For all that, there is no mystery about 'the existence of values in a world of facts'. The world does not consist of facts, rather true descriptions of the world consist of statements of fact. It is as much a fact concerning the world that there are things that are of value to living things, that human beings value things and possess valuable characteristics, perform valuable deeds, stand in valuable relationships to (...) others, as it is a fact that there is life on earth. (shrink)

A critical note on Christopher Bartel and Jack M. C. Kwong, ‘Pluralism, Eliminativism, and the Definition of Art’, Estetika 58 (2021): 100–113. Art pluralism is the view that there is no single, correct account of what art is. Instead, art is understood through a plurality of art concepts and with considerations that are different for particular arts. Although avowed pluralists have retained the word ‘art’ in their discussions, it is natural to ask whether the considerations that motivate pluralism should lead (...) us to abandon art talk altogether; that is, should pluralism lead to eliminativism? This paper addresses arguments both for and against this move. We ultimately argue that pluralism allows one to retain the word ‘art’, if one wants it, but only in a loose, conversational sense. The upshot of pluralism is that talk of art in general cannot be asked to do theoretical and philosophical work. (shrink)

Some scientific categories seem to correspond to genuine features of the world and are indispensable for successful science in some domain; in short, they are natural kinds. This book gives a general account of what it is to be a natural kind and puts the account to work illuminating numerous specific examples.

" In a book that seeks to shift the ground of debate within theory of knowledge, William P. Alston finds that the century-lo.

In lieu of an abstract, here is a brief excerpt of the content:Burma’s Healthcare Under Fire: My Experience as an Exiled Medical ProfessionalP. P. KyawI used to work as a medical doctor in a less developed state than many big cities in Burma1 that experienced prolonged civil wars and current similar atrocities decades before the urban areas of the country experienced them. Before everything started, I was responsible for the medical management of the most vulnerable communities and had been struggling (...) with pandemic-related medical activities. Those were the happiest years of my life. I was with one of the best international organizations, where every effort I made was directly delivered to the patients with no unnecessary paperwork. The system was efficient, my colleagues were supportive, and I had a good work-life balance. I supported my family and whoever needed temporary financial support, played music weekly, met good friends who I hung out with every weekend, and [End Page 164] found hobbies like gardening and crocheting. I was content and happy. I even postponed my plans to get registered as a doctor in the Western world.Before moving to this beautiful ethnic state in 2019, I previously worked as a government medical doctor in Yangon, the capital. As much as I loved working in those civilian hospitals, I could not support myself with a monthly pay of $100-$150 USD. It was a hard decision to leave the service because it meant I could not pursue the medical specialty that I had always longed for and had to leave like-minded supportive colleagues. In Myanmar, unless you are a civil servant, you cannot pursue further clinical specialties. However, after leaving the government’s service to work in humanitarian medical assistance in hard-to-reach areas of Burma, I learned that life is still beautiful outside my comfort zone, until February 2021 when the coup began. Democratically elected members of the country’s ruling party were overthrown by the military, which then bestowed power in a military junta.I expected the election prior to the coup in November 2020 to be an uphill battle for Burma, but nothing more. I was still in denial when I first heard the news from one of the town’s NGO staff. The person had to travel on a motorbike to inform everyone that the junta had staged the coup. No telephone or internet was working at that time. My colleagues and I cried in our office, saying, “We are so young, and the future is still ahead. I don’t think this is going to last long. Maybe it will be over in a few days or, at most, a few weeks.” Once the peaceful protests started nationwide, my friends and I provided medical cover for the protesters, initially for minor medical problems such as low sugar, low blood pressure, injuries from accidental minor slips and falls, etc. Never in my life had I imagined that I would be taking care of bullet wounds and people injured by live rounds. While learning about gunshot wounds in forensic medicine, I thought, “Oh, this is not going to be very useful because Burma is not America, and I am not going there.” Then suddenly, it became too real and more useful than I would’ve liked it to be.I always think back to one especially bloody day when many people in the town were shot with live rounds. We assisted many patients. Usually, we would go around with the protest groups until they were over in the late afternoon. The protesters were always peaceful. There were no riots, no harmful acts, or vandalism. Only when the protesters were cruelly dispersed with tear gas, high-pressure pumps, rubber bullets, and live rounds (to the head) did they decide to defend themselves while still making their voices heard. The only defenses people had to counteract the live rounds were things like metal covers, firecrackers, and slingshots.One afternoon in March 2021, my team and I took an early break for lunch—unaware that some people would lose their lives that afternoon. We followed the local protests through Facebook Live while having lunch and started to hear firecracker sounds. A few seconds later, we knew... (shrink)

This book examines the relationship between law and scientific advancement, with a particular focus on the theory of evolution and medical innovation. Historically, the law has struggled to keep pace with modern medical advances. The authors demonstrate that the laws that govern human behaviour must evolve in response to such advances."--Provided by publisher.