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)

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 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 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)

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)

Integrated information theory (IIT) is a candidate theory of consciousness that highlights the role of complex interactions between parts of a system as the basis of consciousness – and, due to its general information-theoretic formulation, is capable of making statements about consciousness in neural and non-neural systems alike. Here, we argue that a system radically different to a human brain, host to complex physiological and functional structures capable of integrating information, can be found in the meristems and vascular system of (...) higher plants. Following a pragmatic and ontologically innocent approach, neither taking for granted that plants are conscious nor dismissing the possibility that they are, we argue that the time is ripe to apply analysis tools inspired by IIT to plants, taking advantage of recent developments in both plant imaging and information theory. We introduce and discuss the relevant literature, and pro information and integration in plant behaviour, assessing the plausibility of plant sentience. If successful, these experiments could position plants as the next frontier in consciousness science, and urge us to rethink our perspectives on consciousness, how to measure it, and its prevalence amongst living beings. (shrink)

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)

I argue that four-dimensionalism and the desire satisfaction account of well-being are incompatible. For every person whose desires are satisfied, there will be many shorter-lived individuals (‘person-stages’ or ‘subpersons’) who share the person’s desires but who do not exist long enough to see those desires satisfied; not only this, but in many cases their desires are frustrated so that the desires of the beings in whom they are embedded as proper temporal parts may be fulfilled. I call this the frustrating (...) problem for four-dimensionalism. In the first half of the paper I lay the groundwork for understanding the frustrating problem, and then in the second half, I will examine six possible responses to the frustrating problem on behalf of the four-dimensionalist, (i) the Parfit (1984) inspired claim that identity is not what matters, (ii) the personal pronoun revisionism of Noonan (2010), (iii) the indirect concern account of Hudson (2001), (iv) the sensible stages account of Lewis (1986), (v) a multiple-concepts account of desire satisfaction, and (vi) a No Desire View according to which subpersons have no mental states and thus no desires to frustrate. I argue that none of these solutions will help the four-dimensionalist; she does better to reject the desire satisfaction theory, while the defender of the desire satisfaction theory does better to reject four-dimensionalism. (shrink)

We describe and analyse how large herbivores strongly diminished a woody vegetation, dominated by the unpalatable shrub Sambucus nigra L. and changed it into grassland. Density of woody species and cover of vegetation were measured in 1996, 2002 and 2012 in the grazed Oostvaardersplassen. In 2002 and 2012 we also measured density and cover in an ungrazed control site. In 2002 we measured intensity of browsing and bark loss of Sambucus shrubs in the grazed and control sites. In the grazed (...) site the density of Sambucus and Salix spp. declined significantly between 1996 and 2012, and large areas changed into grassland. In the control site the density of Sambucus increased significantly during this period, the density of Salix spp. did not change, and the vegetation consisted of a mixture of woody species and a field layer dominated by tall herbs. In 2002 and 2012 the percentages of dead Sambucus shrubs were significantly higher in the grazed site than in the control site. In 2002 the percentages of twigs browsed and ring barked stems of Sambucus shrubs were significantly higher in the grazed site than in the control site. Our results show that debarking caused mature Sambucus shrubs to die, but that heavy browsing may have helped this process. Our results also point to a significant neighbour effect on the break down of Sambucus, suggesting that Aggregational Resistance and Associational Palatability were both active. Essential conditions for the break down of this woody vegetation were the presence of large herbivores, the low ratio between the areas of summer and winter feeding habitats and the competition amongst herbivores. Browsing may have been responsible for seedling death, as seedlings were found only in the control site and not on the old and newly established grasslands in the grazed site. (shrink)

Thomas Hobbes was the first great English philosopher and one of the most important theorists of human nature and politics in the history of Western thought. This superlative introduction presents Hobbes' main doctrines and arguments, covering all of Hobbes' philosophy. A.P. Martinich begins with a helpful overview of Hobbes' life and work, setting his ideas against the political and scientific background of seventeenth-century England. He then introduces and assesses, in clear chapters, Hobbes' contributions to fundamental areas of philosophy: epistemology and (...) metaphysics, in particular Hobbes' materialism and determinism and his relation to Descartes ethics and political philosophy, concentrating on Hobbes' most famous work, _Leviathan,_ and the theory of the social contract it advances philosophy of science, logic and language, considering Hobbes' theory of nominalism and his writing on rhetoric and the uses of language; religion, examining Hobbes' analyses of revelation, prophets and miracles. The final chapter considers the legacy of Hobbes' thought and his influence on contemporary philosophy. (shrink)

The work _De spiritu_ is an important but neglected work by Aristotle. It clearly shows for the first time that Aristotle assumed a special body as the ‘instrument’ of the soul. By means of this soul/body the soul forms the visible body of plants, animals and human beings.

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

Amazing as it may be, to this day few commentaries on the treatises of Plotinus' Enneads are written. The classic ninth treatise, for example, has hardly been studied. This treatise, however, is of vital importance, because it is in this work that for the first time in the Enneads, the One in its superform emerges and Plotinus dwells on the remarkable phenomenon of a 'mystical union' of the soul with the One. A thorough analysis of the argument and its development (...) next to philosophical and philo-logical support will be welcome to any reader of this in-triguing but difficult treatise. These aims are pursued in the main part of Meijer's work, the commentary. The first part of the book, preceding the commentary, examines the philosophical history of the concept of the One and its status in the first eight treatises. This new approach to the problem of the One leads to striking conclusions. It appears that while Plotinus was writing these first eight treatises, the concept of the One developed from that of a Supreme Entity of a Mesoplatonian character, viz. the upper part of the mind, to One of a Superone above mind. This casts an entirely new light on the position of the One in Plotinus and that of the ninth treatise itself. The third part not only examines the mystical union as pictured in the ninth treatise, but also provides a full scale discussion of Plotinus' descriptions of this union in his en-tire work. The degree of unification, viz. the question whether a part of the mystic self remains intact during the unification, is a matter of vigorous scholarly debate. Meijer shows that, in spite of some inconsistencies in his doctrine about the union, one must accept that Plotinus basically considered the union as a complete absorption of the soul into the Supreme Entity. (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)

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.

This volume brings together a number of important studies by leading scholars on ritual and law, philosophy and religion, literature and entertainments in Qin and Han China. A few contributions deal with the Han legacy to later Chinese culture.

Analysis of sportsmen behavior enabled the authors to conduct simultaneous analysis of emotional expression of people from many distinct countries and cultures. In the study, participants from Nigeria and Poland watched all the goals scored in group matches of the 1998, 2002 and 2006 World Cups and assessed the emotions players expressed after scoring each goal on three scales. Based on the assessment of the participants, emotional expression of football players from 51 countries was analyzed. Basing on “Montesquieu hypothesis”, it (...) was shown that players born in warmer climates express more excitement and happiness after scoring a goal. Further cross-cultural differences were also found. The results are discussed in context of previous cross-cultural studies regarding emotional expression. (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.

Husserl came over to philosophy from mathematics and he devoted many years to the formulation of a firm foundation for Philosophy that could even secure the status of "science" for it. But unlike some of his contemporaries (like Frege and Russell), he did not seek salvation for philosophy in the mathematical method. He argued philosophy (like any other field of study) should pay attention to uninterpreted basic experience and this would lead the way to understanding the essence of things. Essence, (...) then, would become conscious and this process was addressed by him as “phenomenological reduction.”. (shrink)

Let’s suppose all the rules of physics will change, but, before the change, we finally figured out everything there was to be figured out about physics. This means that we achieved pragmatic completeness at that point. It’s not a universal Platonic completeness, but everything there was to be expressed about the physics at that moment was expressed.