I note that the logics of the relevant group most closely tied to the research programme in paraconsistency are those without the contraction postulate(A.AB).AB and its close relatives. As a move towards gaining control of the contraction-free systems I show that they are prime (that wheneverA B is a theorem so is eitherA orB). The proof is an extension of the metavaluational techniques standardly used for analogous results about intuitionist logic or the relevant positive logics.

It is shown that there are exactly six normal DeMorgan monoids generated by the identity element alone. The free DeMorgan monoid with no generators but the identity is characterised and shown to have exactly three thousand and eighty-eight elements. This result solves the "Ackerman constant problem" of describing the structure of sentential constants in the logic R.

This paper presents F, substructural logic designed to treat vagueness. Weaker than Lukasiewicz’s infinitely valued logic, it is presented first in a natural deduction system, then given a Kripke semantics in the manner of Routley and Meyer's ternary relational semantics for R and related systems, but in this case, the points are motivated as degrees to which the truth could be stretched. Soundness and completeness are proved, not only for the propositional system, but also for its extension with first-order quantifiers. (...) The first-order models allow not only objects with vague properties, but also objects whose very existence is a matter of degree. (shrink)

We show that there are infinitely many pairwise non-equivalent formulae in one propositional variable p in the pure implication fragment of the logic T of “ticket entailment” proposed by Anderson and Belnap. This answers a question posed by R. K. Meyer.

An Ackermann constant is a formula of sentential logic built up from the sentential constant t by closing under connectives. It is known that there are only finitely many non-equivalent Ackermann constants in the relevant logic R. In this paper it is shown that the most natural systems close to R but weaker than it-in particular the non-distributive system LR and the modalised system NR-allow infinitely many Ackermann constants to be distinguished. The argument in each case proceeds by construction of (...) an algebraic model, infinite in the case of LR and of arbitrary finite size in the case of NR. The search for these models was aided by the computer program MaGIC (Matrix Generator for Implication Connectives) developed by the author at the Australian National University. (shrink)

In classical and intuitionistic arithmetics, any formula implies a true equation, and a false equation implies anything. In weaker logics fewer implications hold. In this paper we rehearse known results about the relevant arithmetic R, and we show that in linear arithmetic LL by contrast false equations never imply true ones. As a result, linear arithmetic is desecsed. A formula A which entails 0 = 0 is a secondary equation; one entailed by 0 6= 0 is a secondary unequation. A (...) system of formal arithmetic is secsed if every extensional formula is either a secondary equation or a secondary unequation. We are indebted to the program MaGIC for the simple countermodel SZ7, on which 0 = 1 is not a secondary formula. This is a small but signi cant success for automated reasoning. (shrink)

In this paper we consider the implications for belief revision of weakening the logic under which belief sets are taken to be closed. A widely held view is that the usual belief revision functions are highly classical, especially in being driven by consistency. We show that, on the contrary, the standard representation theorems still hold for paraconsistent belief revision. Then we give conditions under which consistency is preserved by revisions, and we show that this modelling allows for the gradual revision (...) of inconsistency. (shrink)

It is well known that the relevant arithmetic R# admits finite models whose domains are the integers modulo n rather than the expected natural numbers. Less well appreciated is the fact that the logic of these models is much more subtle than that of the three-valued structure in which they are usually presented. In this paper we consider the DeMorgan monoids in which R# can be modelled, deriving a fairly complete account of those modelling the stronger arithmetic RM# modulo n (...) and a partial account for the case of R# modulo a prime number. The more general case in which the modulus is arbitrary is shown to lead to infinite propositional structures even with the additional constraint that '0=1' implies everything. (shrink)

$LTL is a version of linear temporal logic in which eventualities are not expressible, but in which there is a sentential constant $ intended to be true just at the end of some behaviour of interest—that is, to mark the end of the accepted words of some language. There is an effectively recognisable class of $LTL formulae which express behaviours, but in a sense different from the standard one of temporal logics like LTL or CTL. This representation is useful for (...) solving a class of decision processes with temporally extended goals, which in turn are useful for representing an important class of AI planning problems. (shrink)

It is shown that the pure implication fragment of the modal logic [3], pp. 385--387) has finitely many non-equivalent formulae in one variable. The exact number of such formulae is not known. We show that this finiteness result is the best possible, since the analogous fragment of S4, and therefore of [3], in two variables has infinitely many non-equivalent formulae.

One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley-Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing (...) a general conception of conditionality that may unify the three given conceptions. (shrink)

The esteemed psychologist and thinker John Dewey headed for previously unexplored philosophical territory with this influential work. Written shortly after World War I, it embodies Dewey's system of pragmatic humanism and maintains that individuals can attain "a more ordered and intelligent happiness" by reconsidering the ultimate effects of their deepest beliefs and feelings. With its promise of achieving an understanding of the past and attaining a brighter future, Reconstruction in Philosophy remains ever relevant. "A modern classic." — Philosophy and (...) Phenomenological Research. (shrink)

The use of analogy and metaphor as descriptive and explanatory devices in neuroscientific research was examined. In particular, four analogies/metaphors common to research having to do with the brain and its function were illustrated. It is argued that the use of these and other similar literary devices in neuroscientific research sometimes leads to certain conceptual confusions and, thus, fails to aid in clarifying the nature of those phenomena they are intended to explain. 2012 APA, all rights reserved).

With precision and profundity born of 30 years of devoted study, John Boyle offers an essential introduction to St. Thomas Aquinas on Scripture, shedding helpful light on the goals, methods, and commitments that animate the Angelic Doctor's engagement with the sacred page. Because the genius of St. Thomas's approach to the Bible lies not so much in its novelty but rather in the fidelity and clarity with which he recapitulates the riches of the preceding interpretive Tradition, this initiation into (...) St. Thomas's vision of Scripture is itself an orientation to the Church's vision of Scripture, from the Fathers through and beyond the Middle Ages. St. Thomas's embeddedness within the Church's Tradition and his own historical context is integral to his approach to Scripture, yet it sets him at some distance from modern readers, for whom his interpretive vision may seem perplexing or even impenetrable. In this Primer, Boyle first provides an acclimation to this medieval context through a survey and explanation of pertinent technical terminology used by St. Thomas and characteristic of the scholastic theology of the time. With an eye to the medieval practice of considering Scripture according to the fourfold division of causes, Boyle builds on this initial foundation by exploring in turn St. Thomas's accounts of the end or use of Scripture (final cause), its divine and human authorship (efficient cause), its order and division (material cause), and its literary styles or genres (formal cause). Drawing on writings from across St. Thomas's corpus, but especially his work On the Commendation and Division of Sacred Scripture and the prologues to his biblical commentaries, Boyle masterfully elucidates both the hermeneutical principles and deep wisdom of the Angelic Doctor's approach to Scripture, imparting invaluable guidance not only for reading and understanding St. Thomas and other great masters of the Tradition, but also-and ultimately-for understanding Scripture in light of this Tradition and reading it with greater benefit and joy. (shrink)

Despite recurring efforts, a gap exists across a variety of contexts between the protection of patients' safety in theory and in practice. This timely Research Handbook highlights these critical issues and suggests both legal and policy changes are necessary to better protect patients' safety. Multidisciplinary in nature, this Research Handbook features contributions from eminent academics, policy makers and medical practitioners from the Global North and South, discussing the essential facets concerning patient safety and the law. It highlights how the role (...) of legislation and case law has the potential to influence, both positively and negatively, medical practice and the quality of care. Chapters explore patient safety and the global health agenda; physiotherapy; 'non-therapeutic' clinical research with children; patient safety awareness in healthcare education; and the increasing use of robotics and artificial intelligence in healthcare. Outlining a wide range of international perspectives on patient safety and the law, this Research Handbook will appeal to academics and researchers specialising in health and medical law, human rights and healthcare regulation. It will also serve as a valuable resource for legal and medical practitioners alike, as well as clinicians and professionals working in healthcare governance. (shrink)

The notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master. In particular, undergraduate mathematics students often experience difficulties in understanding and constructing proofs. Understanding Mathematical Proof describes the nature of mathematical proof, explores the various techniques that mathematicians adopt to prove their results, and offers advice and strategies for constructing proofs. It will improve students’ ability to understand proofs and construct correct proofs of their own. The (...) first chapter of the text introduces the kind of reasoning that mathematicians use when writing their proofs and gives some example proofs to set the scene. The book then describes basic logic to enable an understanding of the structure of both individual mathematical statements and whole mathematical proofs. It also explains the notions of sets and functions and dissects several proofs with a view to exposing some of the underlying features common to most mathematical proofs. The remainder of the book delves further into different types of proof, including direct proof, proof using contrapositive, proof by contradiction, and mathematical induction. The authors also discuss existence and uniqueness proofs and the role of counter examples. (shrink)

Theories of discourse bring to realism new ideas about how knowledge develops and how representations of reality are influenced. We gain an understanding of the conceptual aspect of social life and the processes by which meaning is produced. This collection reflects the growing interest realist critics have shown towards forms of discourse theory and deconstruction. The diverse range of contributions address such issues as the work of Derrida and deconstruction, discourse theory, Eurocentrism and poststructuralism. What unites all of the contributions (...) is a sense that it is essential to provide a realist alternative to the hitherto dominance of social constructionism, hermeneutics and postmodernism, over many of the issues discussed. By developing a realist perspective the different authors attempt to embed discourse within the structured nature of the reality of the world. Realism can situate language, discourse and ideology within context specific, or 'causally efficacious' circumstances. Realism can help to uncover issues of power, representation, and subjectivity and how discursive and other social practices produce real effects. This can help us understand the manner in which social structures are reproduced through various forms of ideology and discourse. And by knowing this, we can start to address questions concerning human emancipation and how the world is to be transformed. (shrink)

This vital study offers a new interpretation of Hume's famous "Of Miracles," which notoriously argues against the possibility of miracles. By situating Hume's popular argument in the context of the 18th century debate on miracles, Earman shows Hume's argument to be largely unoriginal and chiefly without merit where it is original. Yet Earman constructively conceives how progress can be made on the issues that Hume's essay so provocatively posed about the ability of eyewitness testimony to establish the credibility of marvelous (...) and miraculous events. (shrink)

Though the revised edition of A Theory of Justice, published in 1999, is the definitive statement of Rawls's view, so much of the extensive literature on Rawls's theory refers to the first edition. This reissue makes the first edition once again available for scholars and serious students of Rawls's work.

Part One reviews some recent history of epistemology, focusing on ways in which the intellectual virtues have been invoked to solve specific epistemological problems. This part gives a sense of the contemporary landscape that has emerged and clarifies some of the disagreements among those who invoke the virtues in epistemology. Part Two explores some problems about knowledge in greater detail, and defends a externalist approach in virtue epistemology.

This book continues and revises the ideas of justice as fairness that John Rawls presented in _A Theory of Justice_ but changes its philosophical interpretation in a fundamental way. That previous work assumed what Rawls calls a "well-ordered society," one that is stable and relatively homogenous in its basic moral beliefs and in which there is broad agreement about what constitutes the good life. Yet in modern democratic society a plurality of incompatible and irreconcilable doctrines--religious, philosophical, and moral--coexist within (...) the framework of democratic institutions. Recognizing this as a permanent condition of democracy, Rawls asks how a stable and just society of free and equal citizens can live in concord when divided by reasonable but incompatible doctrines? This edition includes the essay "The Idea of Public Reason Revisited," which outlines Rawls ' plans to revise _Political Liberalism,_ which were cut short by his death. "An extraordinary well-reasoned commentary on _A Theory of Justice_...a decisive turn towards political philosophy." --_Times Literary Supplement_. (shrink)

A Norton Library edition of Locke's Second Treatise of Government, edited by A. John Simmons.

Much as we would like to conceive empirical thought as rationally grounded in experience, pitfalls await anyone who tries to articulate this position, and ...

For this second edition, the editors have returned to Austin's original lecture notes, amending the printed text where it seemed necessary.

John Dupre warns that our understanding of human nature is being distorted by two faulty and harmful forms of pseudo-scientific thinking. Not just in the academic world but in everyday life, we find one set of experts who seek to explain the ends at which humans aim in terms of evolutionary theory, while the other set uses economic models to give rules of how we act to achieve those ends. Dupre demonstrates that these theorists' explanations do not work and (...) that, if taken seriously, their theories tend to have dangerous social and political consequences. For these reasons, it is important to resist scientism: an exaggerated conception of what science can be expected to do for us. Dupre restores sanity to the study of human nature by pointing the way to a proper understanding of humans in the societies that are our natural and necessary environments. Anyone interested in science and human life will enjoy this book--unless they are its targets. (shrink)

The so-called "problem of theoretical terms" rests on the notion that the signifiers of theoretical concepts cannot be completely defined for the reason that their referents are beyond the boundaries of human perception and/or cognition. Empirical realism is a scientific tradition that was born, in part, out of a dissatisfaction with the positivist treatment of theoretical terms. Empirical realists generally conceive of theoretical terms as playing an essential role in scientific activity, giving it its explanatory force, as it is such (...) terms which denote the real, but unobservable, hypothetical entities which are thought to underlie those observable phenomena that the scientist seeks to explain. Despite certain consistencies that run throughout realist thought, there also exist a number of points of divergence among empirical realists. These are examined along with 2 different and contrasting traditions of empirical realism within psychological science. 2012 APA, all rights reserved). (shrink)

John Searle's Speech Acts (1969) and Expression and Meaning (1979) developed a highly original and influential approach to the study of language. But behind both works lay the assumption that the philosophy of language is in the end a branch of the philosophy of the mind: speech acts are forms of human action and represent just one example of the mind's capacity to relate the human organism to the world. The present book is concerned with these biologically fundamental capacities, (...) and, though third in the sequence, in effect it provides the philosophical foundations for the other two. Intentionality is taken to be the crucial mental phenomenon, and its analysis involves wide-ranging discussions of perception, action, causation, meaning, and reference. In all these areas John Searle has original and stimulating views. He ends with a resolution of the 'mind-body' problem. (shrink)

"What is a military aircraft? John Law shows in his beautiful analysis that it is a constant oscillation between multiplicity and singularity.

Though the revised edition of A Theory of Justice, published in 1999, is the definitive statement of Rawls's view, so much of the extensive literature on Rawls's theory refers to the first edition.

John Searle's Speech Acts (1969) and Expression and Meaning (1979) developed a highly original and influential approach to the study of language. But behind both works lay the assumption that the philosophy of language is in the end a branch of the philosophy of the mind: speech acts are forms of human action and represent just one example of the mind's capacity to relate the human organism to the world. The present book is concerned with these biologically fundamental capacities, (...) and, though third in the sequence, in effect it provides the philosophical foundations for the other two. Intentionality is taken to be the crucial mental phenomenon, and its analysis involves wide-ranging discussions of perception, action, causation, meaning, and reference. In all these areas John Searle has original and stimulating views. He ends with a resolution of the 'mind-body' problem. (shrink)