We develop a Priestley-style duality theory for different classes of algebras having a bilattice reduct. A similar investigation has already been realized by B. Mobasher, D. Pigozzi, G. Slutzki and G. Voutsadakis, but only from an abstract category-theoretic point of view. In the present work we are instead interested in a concrete study of the topological spaces that correspond to bilattices and some related algebras that are obtained through expansions of the algebraic language.

The variety of N4? -lattices provides an algebraic semantics for the logic N4?, a version of Nelson 's logic combining paraconsistent strong negation and explosive intuitionistic negation. In this paper we construct the Priestley duality for the category of N4?-lattices and their homomorphisms. The obtained duality naturally extends the Priestley duality for Nelson algebras constructed by R. Cignoli and A. Sendlewski.

We generalize Priestley duality for distributive lattices to a duality for distributive meet-semilattices. On the one hand, our generalized Priestley spaces are easier to work with than Celani’s DS-spaces, and are similar to Hansoul’s Priestley structures. On the other hand, our generalized Priestley morphisms are similar to Celani’s meet-relations and are more general than Hansoul’s morphisms. As a result, our duality extends Hansoul’s duality and is an improvement of Celani’s duality.

The Priestley duality for Wajsberg algebras is developed. The Wajsberg space is a De Morgan space endowed with a family of functions that are obtained in rather natural way.As a first application of this duality, a theorem about unicity of the structure is given.

In this paper we describe the Priestley space of a quasi-Stone algebra and use it to show that the class of finite quasi-Stone algebras has the amalgamation property. We also describe the Priestley space of the free quasi-Stone algebra over a finite set.

Priestley duality can be used to study subalgebras of Heyting algebras and related structures. The dual concept is that of congruence on the dual space and the congruence lattice of a Heyting space is dually isomorphic to the subalgebra lattice of the dual algebra. In this paper we continue our investigation of the congruence lattice of a Heyting space that was undertaken in [10], [8] and [12]. Our main result is a characterization of the modularity of (...) this lattice (Theorem 2.12). Partial results about its complementedness are also given, and among other things a characterization of those finite Heyting algebras with a complemented subalgebra lattice (Theorem 3.5). (shrink)

A Priestley duality is developed for the variety j of all modal lattices. This is achieved by restricting to j a known Priestley duality for the variety of all bounded distributive lattices with a meet-homomorphism. The variety j was first studied by R. Beazer in 1986.The dual spaces of free modal lattices are constructed, paralleling P.R. Halmos'' construction of the dual spaces of free monadic Boolean algebras and its generalization, by R. Cignoli, to distributive lattices with a quantifier.

A Priestley duality is developed for the variety jω of all modal lattices. This is achieved by restricting to jω a known Priestley duality for the variety of all bounded distributive lattices with a meet-homomorphism. The variety jω was first studied by R. Beazer in 1986.The dual spaces of free modal lattices are constructed, paralleling P.R. Halmos' construction of the dual spaces of free monadic Boolean algebras and its generalization, by R. Cignoli, to distributive lattices with a quantifier.

In 1765, Joseph Priestley created what may be the world's first modern timeline, A Chart of Biography. This paper offers the first study of the philosophy underlying Priestley's timeline. It argues that Priestley was pushed towards representing times as lines by his views on abstract ideas and time, and there is no reason to believe that Newtonian absolutism grounds his uniform depiction of time. Further, the Chart confirms, and even advances, Priestley's views on human progress. Finally, (...) this study shows that Priestley's conception of time as a line comprises a landmark contribution to the history of space-time parallelism. (shrink)

Dialetheists believe some sentences are both true and false. Objectors have argued that this makes it unclear how people can disagree with each other because, given the dialetheist’s commitments, if I make a claim and you tell me my claim is false, we might both be correct. Graham Priest (2006a) thinks that people disagree by rejecting or denying what is said rather than ascribing falsehood to it. We build on the work of Julien Murzi and Massimiliano Carrara (2015) and show (...) that Priest’s approach cannot succeed: given the same dialetheist’s commitments you may be correct to reject a claim that I correctly believe. We argue further that any attempt to solve the problem by identifying a new attitude of disagreement will also fail. The culprit, we claim, is the attempt to find a pair of attitudes that satisfy ‘exclusivity’—that is, attitudes such that both cannot be simultaneously correct. Instead of identifying disagreement by the kinds of attitudes involved, we propose dialetheists focus on the normative landscape and identify it in part by whether parties have reasons to change their attitudes. We offer our own normative theory of disagreement to help dialetheists with this challenge. (shrink)

If ethical expressivism is true, then moral judgements are motivational desire-like states and do not robustly represent reality. This gives rise to the problem of how to understand moral error. How can we be mistaken if there is no moral reality to be mistaken about? The standard expressivist explanation of moral doubt is couched in terms of our fear that our judgements may not survive improvements to our epistemic situation. There is a debate between Egan :205–219, 2007), Blackburn :201–213, 2009), (...) Köhler :161–165, 2015) and Ridge :1–21, 2015) on the adequacy of this explanation when it comes to the phenomenon of fundamental moral error. This paper is my contribution to the debate. I argue, contrary to Blackburn and Ridge, that expressivism is committed to some first-order anti-realist sounding claims, and thus quasi-realism fails. If expressivism is true, none of us can coherently believe we might be fundamentally mistaken. However, contrary to Egan and Köhler, I do not think this is bad. Expressivists can still do what motivated the project of quasi-realism in the first place: they can interpret, make sense of, and vindicate ordinary moral discourse. I end by showing it yields some positive results for moral philosophers too – it effectively amounts to a transcendental argument against unhealthy moral scepticism. (shrink)

Many people believe that if you identify as a particular gender, then you are that gender. This paper is my attempt at making sense of this claim. I propose to conceive of genders as names: determined by the individual and not requiring any specific biological or psychological qualities, yet still important to the bearer.

Hybrid expressivists claim to solve the Frege-Geach problem by offloading the explanation of the logico-semantic properties of moral sentences onto beliefs that are components of hybrid states they express. We argue that this strategy is undermined by one of hybrid expressivism’s own commitments: that the truth of the belief-component is neither necessary nor sufficient for the truth of the hybrid state it composes. We articulate a new approach. Instead of explaining head-on what it is for, say, a pair of moral (...) sentences to be inconsistent, expressivists should “sidestep” and explain what it is _to think that_ a pair of moral sentences is inconsistent. To think so is to think they cannot both be true – a modal notion. Since expressivists have given accounts of such modals, we illustrate how sentences like ‘“lying is wrong” and “lying is not wrong” are inconsistent’ express sensible – and rationally compelling – states of mind. (shrink)

This paper compares and contrasts the main metaphysical and religious ideas of the eighteenth-century political theorist and chemist Joseph Priestley (1733–1804) with those of his correspondent Ruder Boscovic (1711–1787), astronomer, poet, mathematician, diplomat and Jesuit priest. It points out the theological differences between the two thinkers resulting from the divergent ontological and metaphysical implications of the theory of point atomism that they shared. This theory they placed in a wider context, considering both its limits and its value as a (...) contribution to ongoing speculations concerning the nature of space and time, theological conundrums such as free will and the mind-body problem. Where they differed, however, was that Priestley, a chemist rather than a mathematician, used point atomism mainly to support his campaign to further materialism and discredit Christianity. Boscovic, on the other hand, carefully distinguished the truths of faith and reason and was therefore indignant at Priestley's misuse of his speculations. Boscovic's protest was probably motivated in part by the materialism of atheists such as the Baron d’Holbach (1723–1789). Priestley was no atheist, however. Interestingly, François Arouet de Voltaire (1698–1778), unaware of the works of either Boscovic or Priestley, devised a theistic materialism in his last years that in many respects resembled Priestley's. I begin with brief biographies of the two thinkers, and outline their intermittent relationship. (shrink)

This Elibron Classics title is a reprint of the original edition published by J. Johnson in London, 1777.

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)

Joseph Priestley (1733-1804) was arguably the most important English theorist to focus on the issue of political liberty during the English Enlightenment. His concept of freedom is of crucial importance to two of the major issues of his day: the right of dissenters to religious toleration, and the right of the American colonists to self-government. Priestley's writings lack a modern edition and this new collection will be the first to render accessible his Essay on First Principles, The Present (...) State of Liberty and the Letter of Advice. An introduction and notes, and guides to further reading and key figures in the text provide the student with all the material necessary for approaching Priestley. (shrink)

The English polymath Joseph Priestley wrote on a wide range of scientific, theological and pedagogical subjects. After the appearance of his influential Rudiments of English Grammar and A Course of Lectures on the Theory of Language and Universal Grammar, both of which are reissued in this series, Priestley produced in 1765 his Essay on a Course of Liberal Education, which is included and expanded on in this 1778 publication. Here he explains the reasons behind his decision to guide (...) the curriculum at Warrington Academy towards a greater focus on subjects with a more direct application to 'civil and active life'. He offers more general instruction on the cultivation of young men in various spheres, notably through foreign travel and developing 'knowledge of the world'. Priestley ends by outlining a suggested course of lectures on the history and laws of England. (shrink)

It is often assumed that disagreement only occurs when there is a clash (e.g., inconsistency) between beliefs. In the philosophical literature, this “narrow” view has sometimes been considered the obvious, intuitively correct view. In this paper, we argue that it should not be. We have conducted two preregistered studies gauging English speakers’ intuitions about whether there is disagreement in a case where the parties have non-clashing beliefs and clashing intentions. Our results suggest that common intuitions tell against the default view. (...) Ordinary speakers describe clashes of intentions as disagreements, suggesting that the ordinary concept of disagreement is “wide” in that it extends beyond beliefs. (shrink)

When theorising about disagreement, it is tempting to begin with a person's belief that p and ask what mental state one must have in order to disagree with it. This is the wrong way to go; the paper argues that people may also disagree with attitudes that are not beliefs. It then examines whether several existing theories of disagreement can account for this phenomenon. It argues that its own normative theory of disagreement gives the best account, and so, given that (...) there is good reason to believe disagreement without belief is possible, there is good reason to think that disagreement itself is normative. (shrink)

The Lisp programming language is often described as the first functional programming language and also as an important early AI language. In the history of functional programming, however, it occupies a rather anomalous position, as the circumstances of its development do not fit well with the widely accepted view that functional languages have been developed through a theoretically-inspired project of deriving practical programming languages from the lambda calculus. This paper examines the origins of Lisp in the early AI programming work (...) of the mid-to-late 1950s, and in particular in the work of Allen Newell, Cliff Shaw and Herbert Simon. Their 1956 program, the Logic Theory Machine, introduced new ideas about data and program structures that were articulated in response to perceived limitations in existing programming technique. Later writers, notably John Backus, have described these features as constituting a “programming language style” distinct from the traditional style that preceded it. The paper examines the origins of the earlier style in practices of manual computation, analyses the key technical differences between it and the style first manifested in the Logic Theory Machine, and concludes that programming practice and experience play a large and underappreciated role in the development of programming styles and languages. (shrink)

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)

The Free Discussion between Richard Price and Joseph Priestley (1778) originated as a correspondence between the two after the publication of Priestley's Disquisitions on Matter and Spirit, his most important philosophical work (1777). At the time it was thought remarkable that a controversey such as this could be conducted so amicably, but then the two were close friends. Nevertheless their philosophical, as opposed to their oft mentioned political views, were at opposite ends of a spectrum.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in (...) the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This paper describes several emotion expressions in Koromu, a language of Papua New Guinea. As in other languages, emotions can be expressed by reference to body events and processes. Bodily images are used for common and pertinent emotion expressions in Koromu and the alternative grammatical constructions in which some of these expressions occur enable speakers to express varying emotions while still indicating that there are shared semantic components between the expressions. In addition, as the emotion expressions are examined and their (...) meanings explicated, a number of universal concepts and components of meaning can be observed. A study of these language specific expressions therefore contributes to a cross-linguistic understanding of the relationship between emotion and the body. (shrink)