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)

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 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 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)

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)

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)

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)

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)

Patrick McGrath has argued that my defence of papal infallibility does not succeed. His basic strategy is to establish that, contrary to my arguments, infallible papal utterances are statements and not merely declarations. He wants this result in order to go on to show that the Pope, in possession of no priviliged epistemic access to the world, is not infallible. I agree that the Pope has no priviliged epistemic access; so that is not in dispute. What is in dispute is (...) the fundamental question of whether infallible papal utterances are statements or declarations. I want to show that McGrath's arguments against my position do not work. If I am successful, then the Pope's infallibility is secure. (shrink)

This article defends my claim, first presented in "identity and trinity," "journal of religion" (1978), that the doctrine of the trinity is consistent. drawing upon tertullian's defense of the doctrine in "adversus praxean", i argue that the logic of the trinity is similar to the logic of emperorship. at various times, two persons, for example, diocletian and maximian, were the same emperor of the roman empire, just as three persons are the same god.

THE MAJOR PREMISE OF DUNS SCOTUS'S IMPRESSIVE PROOF FOR THE EXISTENCE OF GOD HAS BEEN NEGLECTED. THAT PREMISE, "THE MOST PERFECT BEING IS INFINITE," IS ESTABLISHED IN TWO WAYS. THE KEY PREMISE IN EACH WAY IS THE PROPOSITION, "POSSIBLY, SOME BEING IS INFINITE." THIS PROPOSITION CANNOT BE PROVEN TO BE TRUE, NOT BECAUSE IT IS IN ANY WAY DUBIOUS OR LACKING IN EVIDENCE, BUT BECAUSE ITS TERMS ARE SIMPLE AND NOT SUBJECT TO PROOF OR FURTHER ANALYSIS. BEING IS THE SIMPLEST (...) AND MOST IMMEDIATE OF CONCEPTS; AND BEING INFINITE IS SIMPLY THE NEGATION OF BEING FINITE. INSTEAD OF PROOF, SCOTUS PRESENTS "PERSUASIONES", SKETCHES OF LANGUAGE-GAMES TO SHOW THAT THE PROPOSITION IS TRUE. (shrink)

The criminal law presently distinguishes between actions and omissions, and only rarely proscribes failures to avert consequences that it would be an offense to bring about. Why? In recent years it has been persuasively argued by both Glover and Bennett that, celeris paribus, omissions to prevent a harm are just as culpable as are actions which bring that harm about. On the other hand, and acknowledging that hitherto “lawyers have not been very successful in finding a rationale for it,” Tony (...) Honoré has sought to defend the law's differential treatment. He proposes a “distinct-duties theory” that in addition to the general duties we owe to everyone, we also owe distinct duties to a more limited collection of people and associations, specified by features of our relationship with them. Where a distinct duty holds, breach by omission may well be no better than breach by positive action. But absent a distinct duty, omissions, per Honoré, are less culpable. They are mere failures to intervene and improve or rectify things, whereas actions are positive interventions which make things worse. And, thus, the law has good reason to differentiate between them. (shrink)

It has often been charged that the doctrine of papal infallibility is either false or incoherent. These charges stem, I believe, from a misunderstanding of the logical character of infallible papal utterances, a misunderstanding shared alike by friends and foes of the doctrine. In this paper, I shall argue that the doctrine is both coherent and correct. I devote section I to uncovering some of the sources of this misunderstanding and thereby defending what might be called my negative thesis, namely, (...) that infallible papal utterances are not statements. In section II, I continue defending my negative thesis, not now as an end in itself, but rather as a means of advancing my positive thesis that infallible papal utterances are declarations and have the same logic as other declarations. The latter thesis requires a discussion of the difference between statements and declarations. Section III contains a formal speech act analysis of successful and non-defective statements and declarations with some additional explanatory notes. In section IV, I speak rather generally about the task of philosophical theology in the light of the results and procedures of sections I–III. (shrink)

In 1956, a few writings of Wittgenstein that he didn't publish in his lifetime were revealed to the public. These writings were gathered in the book Remarks on the Foundations of Mathematics (1956). There, we can see that Wittgenstein had some discontentment with the way philosophers, logicians, and mathematicians were thinking about paradoxes, and he even registered a few polemic reasons to not accept Gödel’s incompleteness theorems.

The purpose of this study is to examine the relationship between the corporate social performance of an organization and three variables: the size of the organization, the financial performance of the organization, and the environmental performance of the organization. By empirically testing data from 1987 to 1992, the results of the study show that a firm's corporate social performance is indeed impacted by the size of the firm, the level of profitability of the firm, and the amount of pollution emissions (...) released by the firm. (shrink)

It is often alleged that an agent is morally responsible in a liability sense for a transgression just in case s/he deserves a negative interpersonal response for that transgression, blaming responses such as resentment and indignation being paradigms. Aside from a few exceptions, guilt is cited in recent discussions of moral responsibility, if at all, as merely an effect of being blamed, or as a reliable indicator of moral responsibility, but not itself an explanation of moral responsibility. In this paper, (...) I argue that an agent is morally responsible in a liability sense for a transgression just in case s/he deserves to feel moral guilt for that transgression. I argue that this alternative view offers all that the predominant blame-focused view offers, while also solving some puzzling features of moral responsibility. Specifically, it offers a compelling way to reconcile conflicting intuitions about the suberogatory, and allows those who do not understand what Darwall calls ‘second-personal’ reasons to be morally responsible for their immoral acts. (shrink)

Aristotle's definition of the soul should be interpreted as: 'the soul is the entelechy of a natural body that serves as its instrument'.

BackgroundAs moral case deliberations (MCDs) have increasingly been implemented in health care institutions as a form of ethics support, it is relevant to know whether and how MCDs actually contribute to positive changes in care. Insight is needed on what actually happens in daily care practice following MCD sessions. This study aimed at investigating the impact of MCD and exploring how ‘impact of MCD’ should be conceptualized for future research.MethodsA multiple-case study was conducted in a care organization for people with (...) intellectual disabilities and/or acquired brain injury, by observing MCD sessions as ‘cases’, followed by interviews with health care professionals concerning the follow-up to these cases, and a focus group with involved MCD facilitators. A conceptual scheme concerning the possible impact formed the basis for analysis: (1) individual moral awareness; (2) the actions of health care professionals; (3) collaboration among health care professionals; (4) the concrete situation of the client; (5) the client’s quality of care and life; (6) the organizational and policy level.ResultsAccording to interviewees, their moral awareness and their collaboration, both among colleagues and with clients’ relatives, improved after MCD. Perceived impact on client situation, quality of care/life and the organizational level varied among interviewees or was difficult to define or link to MCD. Three aspects were added to the conceptual scheme concerning the impact of MCD: (a) preparations and expectations prior to the MCD session; (b) a translational step between the conclusions of the MCD session and practical events in the following period, and (c) collaboration with clients’ relatives. A negative impact of MCD was also found on misunderstandings among participants and disappointment about lack of follow-up.ConclusionsConcretizing and conceptualizing the ‘impact’ of MCD is complicated as many factors play a role either before or during the transition from MCD to practice. It is important to consider ‘impact’ in a broad sense and to relate it to the goals and context of the MCD in question. Future studies in this field should pay additional attention to the preparations, content and process involved in ethics support, including clients’ and relatives’ experiences. (shrink)

A continuoxis t- norm is a continuous map * from [0, 1]² into [0,1] such that is a commutative totally ordered monoid. Since the natural ordering on [0,1] is a complete lattice ordering, each continuous t-norm induces naturally a residuation → and becomes a commutative naturally ordered residuated monoid, also called a hoop. The variety of basic hoops is precisely the variety generated by all algebras, where * is a continuous t-norm. In this paper we investigate the structure of the (...) variety of basic hoops and some of its subvarieties. In particular we provide a complete description of the finite subdirectly irreducible basic hoops, and we show that the variety of basic hoops is generated as a quasivariety by its finite algebras. We extend these results to Hájek's BL-algebras, and we give an alternative proof of the fact that the variety of BL-algebras is generated by all algebras arising from continuous t-norms on [ 0,1] and their residua. The last part of the paper is devoted to the investigation of the subreducts of BL- algebras, of Gödel algebras and of product algebras. (shrink)

In a quantum mechanical two-slit experiment one can observe a single photon simultaneously as particle (measuring the path) and as wave (measuring the interference pattern) if the path and the interference pattern are measured in the sense of unsharp observables. These theoretical predictions are confirmed experimentally by a photon split-beam experiment using a modified Mach—Zehnder interferometer.

When should we make use of the criminal law? Suppose that a responsible legislature seeks to enact a morally justifiable range of criminal prohibitions. What criteria should it apply when deciding whether to proscribe conduct? Crimes, Harms, and Wrongs is a philosophical analysis of the nature, significance, and ethical limits of criminalisation. The authors explore the scope and moral boundaries of harm-based prohibitions, proscriptions of offensive behaviour, and 'paternalistic' prohibitions aimed at preventing self-harm. Their aim is to develop guiding principles (...) for these various grounds of state prohibition, including an analysis of the constraints and mediating factors that weigh for and against criminalisation. Both authors have written extensively in the field. In Crimes, Harms, and Wrongs they have reworked a number of well-known essays and added several important new essays to produce an integrated, accessible, philosophically-sophisticated account that will be of great interest to legal academics, philosophers, and advanced students alike"--Provided by publisher. (shrink)

A continuoxis t- norm is a continuous map * from [0, 1]² into [0,1] such that ([ 0,1], *, 1) is a commutative totally ordered monoid. Since the natural ordering on [0,1] is a complete lattice ordering, each continuous t-norm induces naturally a residuation → and ([ 0,1], *, →, 1) becomes a commutative naturally ordered residuated monoid, also called a hoop. The variety of basic hoops is precisely the variety generated by all algebras ([ 0,1], *, →, 1), where (...) * is a continuous t-norm. In this paper we investigate the structure of the variety of basic hoops and some of its subvarieties. In particular we provide a complete description of the finite subdirectly irreducible basic hoops, and we show that the variety of basic hoops is generated as a quasivariety by its finite algebras. We extend these results to Hájek's BL-algebras, and we give an alternative proof of the fact that the variety of BL-algebras is generated by all algebras arising from continuous t-norms on [ 0,1] and their residua. The last part of the paper is devoted to the investigation of the subreducts of BL- algebras, of Gödel algebras and of product algebras. (shrink)

Altered state theories of hypnosis posit that a qualitatively distinct state of mental processing, which emerges in those with high hypnotic susceptibility following a hypnotic induction, enables the generation of anomalous experiences in response to specific hypnotic suggestions. If so then such a state should be observable as a discrete pattern of changes to functional connectivity (shared information) between brain regions following a hypnotic induction in high but not low hypnotically susceptible participants. Twenty-eight channel EEG was recorded from 12 high (...) susceptible (highs) and 11 low susceptible (lows) participants with their eyes closed prior to and following a standard hypnotic induction. The EEG was used to provide a measure of functional connectivity using both coherence (COH) and the imaginary component of coherence (iCOH), which is insensitive to the effects of volume conduction. COH and iCOH were calculated between all electrode pairs for the frequency bands: delta (0.1–3.9Hz), theta (4–7.9Hz) alpha (8–12.9Hz), beta1 (13–19.9Hz), beta2 (20–29.9Hz) and gamma (30–45Hz). The results showed that there was an increase in theta iCOH from the pre-hypnosis to hypnosis condition in highs but not lows with a large proportion of significant links being focused on a central-parietal hub. There was also a decrease in beta1 iCOH from the pre-hypnosis to hypnosis condition with a focus on a fronto-central and an occipital hub that was greater in high compared to low susceptibles. There were no significant differences for COH or for spectral band amplitude in any frequency band. The results are interpreted as indicating that the hypnotic induction elicited a qualitative change in the organization of specific control systems within the brain for high as compared to low susceptible participants. This change in the functional organization of neural networks is a plausible indicator of the much theorized “hypnotic-state”. (shrink)

A Companion to Analytic Philosophy is a comprehensive guide to many significant analytic philosophers and concepts of the last hundred years. Provides a comprehensive guide to many of the most significant analytic philosophers of the last one hundred years. Offers clear and extensive analysis of profound concepts such as truth, goodness, knowledge, and beauty. Written by some of the most distinguished philosophers alive, some of whom have entries in the book devoted to them.

A Companion to Analytic Philosophy is a comprehensive guide to many significant analytic philosophers and concepts of the last hundred years. Provides a comprehensive guide to many of the most significant analytic philosophers of the last one hundred years. Offers clear and extensive analysis of profound concepts such as truth, goodness, knowledge, and beauty. Written by some of the most distinguished philosophers alive, some of whom have entries in the book devoted to them.

The book opens with a description of the smooth transition from Newtonian to Einsteinian behaviour from electrons as their energy is progressively increased, ...

Thomas Hobbes is recognized as one of the fathers of modern philosophy and political theory. In his own time he was as famous for his work in physics, geometry, and religion. He associated with some of the greatest writers, scientists, and politicians of his age. Martinich has written a complete and accessible biography of Hobbes. The book takes full account of the historical and cultural context in which Hobbes lived, drawing on both published and unpublished sources. It will be a (...) great resource for philosophers, political theorists and historians of ideas. The clear, crisp prose style will also ensure that the book appeals to general readers with an interest in the history of philosophy, the rise of modern science and the English Civil War. (shrink)