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 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)
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)
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)
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 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)
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)
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.
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)
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.
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)
_Philosophical Writing: An Introduction_, _4th Edition_, features numerous updates and revisions to A. P. Martinich’s best-selling text that instructs beginning philosophy students on how to craft a well-written philosophical essay. Features an entirely new chapter on how to read a philosophical essay, new sections on quantification and modality, and rhetoric in philosophical writing, as well as more updated essay examples Includes many new essay examples and an accompanying website with further topics and examples Traces the evolution of a good philosophical (...) essay from draft stage to completion Emphasizes what a student _should_ do in crafting an essay, rather than on what not to do Written with clarity and humor by a leading philosopher. (shrink)
_Philosophical Writing: An Introduction_, _4th Edition_, features numerous updates and revisions to A. P. Martinich’s best-selling text that instructs beginning philosophy students on how to craft a well-written philosophical essay. Features an entirely new chapter on how to read a philosophical essay, new sections on quantification and modality, and rhetoric in philosophical writing, as well as more updated essay examples Includes many new essay examples and an accompanying website with further topics and examples Traces the evolution of a good philosophical (...) essay from draft stage to completion Emphasizes what a student _should_ do in crafting an essay, rather than on what not to do Written with clarity and humor by a leading philosopher. (shrink)
Substantially updated and revised, the third edition of Philosophical Writing is designed to help those with little or no experience in philosophy to think and write successfully. Traces the evolution of a good philosophical essay from draft stage to completion Now includes new examples of the structures of a philosophical essay, new examples of rough drafts, tips on how to study for a test and a new section on how to utilize the internet effectively Written with clarity and wit by (...) a bestselling author. (shrink)
Divided into eight sections, each with introductory essays, the selections offer rich and detailed insights into a diverse multinational philosophical landscape. Revealed in this pathbreaking work is the way in which traditional philosophical issues related to ethics, metaphysics, and epistemology, for instance, take on specific forms in Africa's postcolonial struggles. Much of its moral, political, and social philosophy is concerned with the turbulent processes of embracing modern identities while protecting ancient cultures.
Substantially updated and revised, the third edition of _Philosophical Writing_ is designed to help those with little or no experience in philosophy to think and write successfully. Traces the evolution of a good philosophical essay from draft stage to completion Now includes new examples of the structures of a philosophical essay, new examples of rough drafts, tips on how to study for a test and a new section on how to utilize the internet effectively Written with clarity and wit by (...) a bestselling author. (shrink)
Hobbes' classic work has set the tone for the course of political philosophy through to our own day. This new Broadview edition includes the full text of the 1651 edition, together with a wide variety of background documents that help set the work in context. Also included are an introduction, explanatory notes, and a chronology.
Substantially updated and revised, the third edition of Philosophical Writing is designed to help those with little or no experience in philosophy to think and write successfully.
This Broadview edition of Hobbes's classic work of political philosophy includes the full text of Part I, Part II, and the Review and Conclusion. The appendices, which set the work in its historical context, include a rich selection of contemporary responses to Leviathan. Also included are an introduction, explanatory notes, and a chronology of Hobbes's life. Please note that the Broadview Edition of the complete Leviathan also remains available.
Thomas Hobbes’s _Leviathan_ is the greatest work of political philosophy in English and the first great work of philosophy in English. Beginning with premises that were sometimes controversial, such as that every human action is caused by the agent’s desire for his own good, Hobbes derived shocking conclusions, such as that the civil government enjoys absolute control over its citizens and that the sovereign has the right to determine which religion is to be practiced in a commonwealth. Hobbes’s contemporaries recognized (...) the power of arguments in _Leviathan_ and many of them wrote responses to it; selections by John Bramhall, Robert Filmer, Edward Hyde, George Lawson, William Lucy, Samuel Pufendorf, and Thomas Tenison are included in this edition. This revised Broadview Edition of Hobbes’s classic work of political philosophy includes the full text of Part I, Part II, and the Review and Conclusion. The appendices, which set the work in its historical context, include a rich selection of contemporary responses to _Leviathan_. Also included are an introduction, explanatory notes, and a chronology of Hobbes’s life. (shrink)
Thomas Hobbes’s _Leviathan_ is the greatest work of political philosophy in English and the first great work of philosophy in English. Beginning with premises that were sometimes controversial, such as that every human action is caused by the agent’s desire for his own good, Hobbes derived shocking conclusions, such as that the civil government enjoys absolute control over its citizens and that the sovereign has the right to determine which religion is to be practiced in a commonwealth. Hobbes’s contemporaries recognized (...) the power of arguments in _Leviathan_ and many of them wrote responses to it; selections by John Bramhall, Robert Filmer, Edward Hyde, George Lawson, William Lucy, Samuel Pufendorf, and Thomas Tenison are included in this edition. _Leviathan _is divided into four parts: In the first part, Of Man, Hobbes presents a view of human beings and of the natural world in general that is materialistic and mechanistic. In the second part, Of Commonwealth, he defends the theory of absolute sovereignty, the view that the government has all the political power and has the right to control any aspect of life. In the third part, Of a Christian Commonwealth, he critiques concepts like revelation, prophets, and miracles in such a way that it becomes doubtful whether they can be rationally justified. In the fourth part, Of the Kingdom of Darkness, he explains various ways in which priestly religion has corrupted religion and transgressed the rights of the sovereign. (shrink)
When should we make use of the criminal law? Crimes, Harms, and Wrongs offers a philosophical analysis of the nature and ethical limits of criminalisation. The authors explore the scope of harm-based prohibitions, proscriptions of offensive behaviour, and 'paternalistic' prohibitions aimed at preventing self-harm, developing guiding principles for these various grounds of state prohibition. Both authors have written extensively in the field. They have produced an integrated, accessible, philosophically-sophisticated account that will be of great interest to legal academics, philosophers, and (...) advanced students alike. 'this elegant, closely argued and convincing book is of great value and can be expected to be of lasting influence.' James Chalmers 'Crimes, Harms, and Wrongs . . . is a welcome addition to this field, and should clarify the reader's thinking on a breathtakingly broad range of issues. . . . This is an important book, and [its] consideration of not only Anglo-American theory and law, but also German legal doctrines and writings on criminalisation, should ensure that this debate reaches new heights in the future.' Findlay Stark 'the result of [the authors'] many decades of thought and writing on this fundamental subject is an integrated, accessible, philosophically sophisticated discussion of this subject.' Justice Gilles Renaud 'A.P. Simester and Andreas von Hirsch present an informed and systematic account of the principles that, in their view, should structure decisions about what to criminalize, and when.' Vincent Chiao 'an outstanding work, original in many respects and meticulous in its arguments. It represents the greatest advance on this subject since Feinberg's four volumes . . . an outstanding contribution to the re-invigorated criminalization debate.' Andrew Ashworth 'important, original, interesting, and often ingenious. Unlike some recent competitive books it has the virtue of making sound arguments. And like everything else the authors have written, it is a joy to read ...This is an absolutely wonderful book.' Douglas Husak. (shrink)
First published in 1913, this collection of essays was created with the intention of promoting Christianity as a valid system in the face of scientific rationalism. Specifically written for young men experiencing a crisis of belief between childhood and adulthood, the 'Interregnum' of the title, the book avoids dogmatic assertions in favour of a sympathetic approach towards the potential reader, one that emphasises openness within religious faith. The text is divided into two parts: part one argues for the ethical and (...) practical benefits of Christianity; part two constitutes an argument for the truth value of the Christian system in the face of scepticism from rival modes of thought. This volume will be of value to anyone with an interest in theology and the crisis of faith caused by scientific development. (shrink)
Substantially updated and revised, the third edition of _Philosophical Writing_ is designed to help those with little or no experience in philosophy to think and write successfully. Traces the evolution of a good philosophical essay from draft stage to completion Now includes new examples of the structures of a philosophical essay, new examples of rough drafts, tips on how to study for a test and a new section on how to utilize the internet effectively Written with clarity and wit by (...) a bestselling author. (shrink)
From early sage philosophers to Leopold Senghor of Senegal and Steve Biko of South Africa, African thinking has challenged the way we think. As we enter a new millenium, the perspectives provided in this volume offer wise and refreshing alternatives to problems of self and society, culture, aesthetics, metaphysics and religion. Out of Africa always something new, and in these pages contemporary problems of cross-cultural cognition and post-coloniality are not only addressed, but also enacted. The reader witnesses the collision and (...) the coalescence of cultures in the writings of philosophers from Africa. (shrink)
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)
