This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is (...) of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures. (shrink)

_This tribute to Nathan Sivin (1931-2022), a pathbreaking scholar of Chinese science, medicine, and philosophy, highlights his distinctive contributions to historical understanding and his memorable wit. I offer a brief biographical sketch followed by an analysis of the main themes in Sivin’s voluminous publications and a personal note of appreciation. It is no exaggeration to say that Sivin transformed his field of study. His contrarian spirit, relentless curiosity, and humanistic insight helped make the history of East Asian science, technology, and (...) medicine the vibrant area of study that it is today._. (shrink)

Mind and Body in Early China: Beyond Orientalism and the Myth of Holism. By Edward Slingerland. New York: Oxford University Press, 2019. Pp. xiv + 385. $35.

Recipes from the Garden of Contentment. By Yuan Mei, translated and annotated by Sean J. S. Chen. Great Barrington, MA: Berkshire, 2019. Pp. xxxiii + 428. $125.

The techniques of natural duality theory are applied to certain finitely generated varieties of Heyting algebras to obtain optimal dualities for these varieties, and thereby to address algebraic questions about them. In particular, a complete characterisation is given of the endodualisable finite subdirectly irreducible Heyting algebras. The procedures involved rely heavily on Priestley duality for Heyting algebras.

The paper investigates completions in the context of finitely generated lattice-based varieties of algebras. In particular the structure of canonical extensions in such a variety $${\mathcal {A}}$$ is explored, and the role of the natural extension in providing a realisation of the canonical extension is discussed. The completions considered are Boolean topological algebras with respect to the interval topology, and consequences of this feature for their structure are revealed. In addition, we call on recent results from duality theory to show (...) that topological and discrete dualities for $${\mathcal {A}}$$ exist in partnership. (shrink)

Putnam's goal is to embed philosophy in social life. The first part of this book is dedicated to metaphysical questions.

A renewal of philosophy is precisely the point of this book, drawn from the 1989 Gifford Lectures by one of America's most distinguished philosophers.

Natural dualities are developed for varieties ofn-valued ukasiewicz algebras with and without negation. These dualities are based on hom-functors, and parallel Stone duality for Boolean algebras. A translation is described which relates the natural dualities to the corresponding restricted Priestley dualities. This enables a unified approach to free algebras to be presented, whence R. Cignoli's characterisations of the finitely generated free algebras are elucidated and new descriptions of arbitrary free algebras obtained. Finally it is shown how dualities for subvarieties (...) encode equational bases. An alternative approach is thereby provided to results of M.E. Adams and R. Cignoli. (shrink)

First published in 1978, this reissue presents a seminal philosophical work by professor Putnam, in which he puts forward a conception of knowledge which makes ethics, practical knowledge and non-mathematic parts of the social sciences just as much parts of 'knowledge' as the sciences themselves. He also rejects the idea that knowledge can be demarcated from non-knowledge by the fact that the former alone adheres to 'the scientific method'. The first part of the book consists of Professor Putnam's John Locke (...) lectures, delivered at the University of Oxford in 1976, offering a detailed examination of a 'physicalist' theory of reference against a background of the works of Tarski, Carnap, Popper, Hempel and Kant. The analysis then extends to notions of truth, the character of linguistic enquiry and social scientific enquiry in general, interconnecting with the great metaphysical problem of realism, the nature of language and reference, and the character of ourselves. (shrink)

The present paper is an attempt to give an account of the analytic-synthetic distinction both inside and outside of physical theory. It is hoped that the paper is sufficiently nontechnical to be followed by a reader whose background in science is not extensive; but it has been necessary to consider problems connected with physical science (particularly the definition of 'kinetic energy,' and the conceptual problems connected with geometry) in order to bring out features of the analytic-synthetic distinction that seem to (...) me to be the most important. (shrink)

Effective documentation is considered a core competency for clinical ethics consultation. Ethics consultants within the Cleveland Clinic in Cleveland, Ohio, observed variation in the formatting of ethics chart notes across consultants and realized that this formatting was based on their own views of effectiveness. To minimize variation and optimize the readability and understandability of ethics chart notes for end users, a team undertook a quality improvement project to assess the formatting preferences of healthcare professionals who rely on ethics consultation notes. (...) The team developed three sample templates and conducted interviews with stakeholders to understand their preferences. A single standardized template was developed based on the preferences that emerged, which all consultants on the ethics consultation service then utilized. In the first five months of implementation, the percentage of end user respondents marking the highest Likert scale option on a post-consultation survey regarding whether the ethics consultation service provided helpful documentation increased from 60 percent to 72 percent compared to the same five-month period in the year prior. (shrink)

Professor Hilary Putnam has been one of the most influential and sharply original of recent American philosophers in a whole range of fields. His most important published work is collected here, together with several new and substantial studies, in two volumes. The first deals with the philosophy of mathematics and of science and the nature of philosophical and scientific enquiry; the second deals with the philosophy of language and mind. Volume one is now issued in a new edition, including (...) an essay on the philosophy of logic first published in 1971. (shrink)

What is the relationship between our perceptions and reality? What is the relationship between the mind and the body? These are questions with which philosophers have grappled for centuries, and they are topics of considerable contemporary debate as well. Hilary Putnam has approached the divisions between perception and reality and between mind and body with great creativity throughout his career. Now, in _The Threefold Cord: Mind, Body, and World,_ he expounds upon these issues, elucidating both the strengths and weaknesses (...) of current schools of thought. With his characteristic wit and acuity, Putnam offers refreshing solutions to some of philosophy's most vexing problems. Putnam first examines the problem of realism: is objective truth possible? He acknowledges the deep impasse between empirical and idealist approaches to this question, critiquing them both, however, by highlighting the false assumption they share, that we cannot perceive the world directly. Drawing on the work of J. L. Austin and William James, Putnam develops a subtle and creative alternative, which he calls "natural realism." The second part of the book explores the mind-body question: is the mind independent of our interactions with the physical world? Again, Putnam critically assesses two sharply antithetical contemporary approaches and finds them both lacking. _The Threefold Cord_ shows the entire mind-body debate to be miscast and draws on the later work of Wittgenstein, once more advancing original views on perception and thought and their relationship with both the body and the external world. Finally, Putnam takes up two related problems--the role of causality in human behavior and whether or not thoughts and sensations have an "existence" all their own. With Putnam's lucid prose and insightful examples, _The Threefold Cord_ loosens the Gordian knots into which philosophy has bound itself over the issue of epistemology. (shrink)

Both syntactic and semantic solutions are given for the entailment problem of duality theory. The test algebra theorem provides both a syntactic solution to the entailment problem in terms of primitive positive formulae and a new derivation of the corresponding result in clone theory, viz. the syntactic description of $\operatorname{Inv(Pol}(R))$ for a given set R of finitary relations on a finite set. The semantic solution to the entailment problem follows from the syntactic one, or can be given in the form (...) of an algorithm. It shows, in the special case of a purely relational type, that duality-theoretic entailment is describable in terms of five constructs, namely trivial relations, intersection, repetition removal, product, and retractive projection. All except the last are concrete, in the sense that they are described by a quantifier-free formula. It is proved that if the finite algebra $\underline{M}$ generates a congruence-distributive variety and all subalgebras of $\underline{M}$ are subdirectly irreducible, then concrete constructs suffice to describe entailment. The concept of entailment appropriate to strong dualities is also introduced, and described in terms of coordinate projections, restriction of domains, and composition of partial functions. (shrink)

This paper focuses on natural dualities for varieties of bilattice-based algebras. Such varieties have been widely studied as semantic models in situations where information is incomplete or inconsistent. The most popular tool for studying bilattices-based algebras is product representation. The authors recently set up a widely applicable algebraic framework which enabled product representations over a base variety to be derived in a uniform and categorical manner. By combining this methodology with that of natural duality theory, we demonstrate how to build (...) a natural duality for any bilattice-based variety which has a suitable product representation over a dualisable base variety. This procedure allows us systematically to present economical natural dualities for many bilattice-based varieties, for most of which no dual representation has previously been given. Among our results we highlight that for bilattices with a generalised conflation operation. Here both the associated product representation and the duality are new. Finally we outline analogous procedures for pre-bilattice-based algebras. (shrink)

This paper is a study of duality in the absence of canonicity. Specifically it concerns double quasioperator algebras, a class of distributive lattice expansions in which, coordinatewise, each operation either preserves both join and meet or reverses them. A variety of DQAs need not be canonical, but as has been shown in a companion paper, it is canonical in a generalized sense and an algebraic correspondence theorem is available. For very many varieties, canonicity (as traditionally defined) and correspondence lead on (...) to topological dualities in which the topological and correspondence components are quite separate. It is shown that, for DQAs, generalized canonicity is sufficient to yield, in a uniform way, topological dualities in the same style as those for canonical varieties. However topology and correspondence are no longer separable in the same way. (shrink)

SummaryI discuss a simple case in which theories with different ontologies appear equally adequate in every way. . I contend that the appearance of equal adequacy is correct, and that what this shows is that the notion of “existence” has a variety of different but legitimate uses. I also argue that this provides a counterexample to the claim advanced by Davidson, that conceptual relativity is incoherent.RésuméJe discute un cas simple où des théories comportant des ontologies différentes apparaissent également adéquates à (...) tout point de vue. . Je prétends que ľapparence ?on;égale adéquation est correcte et ceci montre que la notion ?on;existence a plusieurs sens différents, mais également légitimes. Je montre aussi que cela constitue un contre‐exemple à la thèse avancée par Davidson, selon laquelle la relativité con‐ceptuelle est incoherénte.ZusammenfassungIch diskutiere einen einfachen Fall, wo Theorien mit verschiedenen Ontologien in jeder Beziehung als gleich adäquat erscheinen. . Ich behaupte, dass die Ansicht, wonach gleiche Adäquatheit bestehen soil, korrekt ist und dass entsprechend der Begriff der Existenz mehrere verschiedene Verwendungs‐weisen hat, die alle legitim sind. Ich argumentiere, dass damit ein Gegenbeispiel zu Davidsons Auffassung vorliegt, wonach die These der begrifflichen Relativität inkohärent sein soil. (shrink)

As George Boole saw it, the laws of logic are the laws of thought, and by this he meant, not that human thought is actually governed by the laws of logic, but, rather, that it should be. Boole’s view that the laws of logic have normative implications for how we ought to think is anything but an outlier. The idea that violating the laws of logic involves epistemic impropriety has seemed to many to be just obvious. It has seemed especially (...) obvious to those who see propositional justification as more fundamental than doxastic justification. Whatever other principles are required for defining propositional justification, the laws of logic seem indispensable. The idea that violation of the laws of logic involves some sort of epistemic impropriety—whatever the peculiarities of our psychology may be—has served as a fixed point around which defenders of the fundamentality of propositional justification are united, whatever their other differences. This paper challenges that common thread in defenses of the fundamentality of propositional justification. It is argued that the laws of logic have no bearing whatever on epistemic justification. Once we see why this should be so, the way is paved for seeing why it is that doxastic justification is more fundamental than propositional justification. (shrink)