In this paper we first provide a new axiomatization of algebraically closed MV-algebras based on McNaughtonʼs Theorem. Then we turn to sheaves, and we represent algebraically closed MV-algebras as algebras of global sections of sheaves, where the stalks are divisible MV-chains and the base space is Stonean.

It is introduced a new algebra$$(A, \otimes, \oplus, *, \rightharpoonup, 0, 1)$$(A,⊗,⊕,∗,⇀,0,1)called$$L_PG$$LPG-algebra if$$(A, \otimes, \oplus, *, 0, 1)$$(A,⊗,⊕,∗,0,1)is$$L_P$$LP-algebra (i.e. an algebra from the variety generated by perfectMV-algebras) and$$(A,\rightharpoonup, 0, 1)$$(A,⇀,0,1)is a Gödel algebra (i.e. Heyting algebra satisfying the identity$$(x \rightharpoonup y ) \vee (y \rightharpoonup x ) =1)$$(x⇀y)∨(y⇀x)=1). The lattice of congruences of an$$L_PG$$LPG-algebra$$(A, \otimes, \oplus, *, \rightharpoonup, 0, 1)$$(A,⊗,⊕,∗,⇀,0,1)is isomorphic to the lattice of Skolem filters (i.e. special type ofMV-filters) of theMV-algebra$$(A, \otimes, \oplus, *, 0, 1)$$(A,⊗,⊕,∗,0,1). The variety$$\mathbf {L_PG}$$LPGof$$L_PG$$LPG-algebras (...) is generated by the algebras$$(C, \otimes, \oplus, *, \rightharpoonup, 0, 1)$$(C,⊗,⊕,∗,⇀,0,1)where$$(C, \otimes, \oplus, *, 0, 1)$$(C,⊗,⊕,∗,0,1)is ChangMV-algebra. Any$$L_PG$$LPG-algebra is bi-Heyting algebra. The set of theorems of the logic$$L_PG$$LPGis recursively enumerable. Moreover, we describe finitely generated free$$L_PG$$LPG-algebras. (shrink)

It is convenient to review these two books together because of the obvious indebtedness of the latter to the former. The book by Carnap is the first English translation of his classic Der Logische Aufbau der Welt initially published in Berlin in 1928. It also includes his short Scheinprobleme in der Philosophic published first in the same year. The translator has produced a very readable text of two complex works and Carnap has added a new preface outlining his present attitude (...) to his work of over thirty years ago together with a short bibliography of recent publications relevant to the Aufbau. (shrink)

These three volumes are amongst the first of a series of anthologies of philosophical writings under the title Oxford Readings in Philosophy, the series editor being G J Warnock. The blurb on the back of each says that ‘the aim of this series is to bring together important recent writings in major areas of philosophical inquiry, selected from a variety of sources, mostly periodicals, which may not be conveniently available to the university student or the general reader’. But all good (...) anthologists have at least this in mind. Hence the glut of anthologies and the reduplication of articles belying the aims of anthologists. (shrink)

The main aim of the paper is to solve a problem posed in Di Nola et al. (Multiple Val. Logic 8:715–750, 2002) whether every pseudo BL-algebra with two negations is good, i.e. whether the two negations commute. This property is intimately connected with possessing a state, which in turn is essential in quantum logical applications. We approach the solution by describing the structure of pseudo BL-algebras and pseudo hoops as important families of quantum structures. We show when a pseudo (...) hoop can be embedded into the negative cone of the reals. We give an equational base characterizing representable pseudo hoops. We also describe some subvarieties: normal-valued, and varieties where each maximal filter is normal. We produce some noncommutative covers and extend the area where each algebra is good. Finally, we show that there are uncountably many subvarieties of pseudo BL-algebras having members that are not good. (shrink)

Research is crucial to advancing knowledge about dementia, yet the burden of the disease currently outpaces research activity. Research often excludes people with dementia and other cognitive impairments because researchers and ethics committees are concerned about issues related to capacity, consent, and substitute decision-making. In Australia, participation in research by people with cognitive impairment is governed by a national ethics statement and a patchwork of state and territorial laws that have widely varying rules. We contend that this legislative variation precludes (...) a consistent approach to research governance and participation and hinders research that seeks to include people with impaired capacity. In this paper, we present key ethical principles, provide a comprehensive review of applicable legal rules in Australian states and territories, and highlight significant differences and ambiguities. Our analysis includes recommendations for reform to improve clarity and consistency in the law and reduce barriers that may exclude persons with dementia from participating in ethically approved research. Our recommendations seek to advance the national decision-making principles recommended by the Australian Law Reform Commission, which emphasize the rights of all adults to make their own decisions and for those with impaired capacity to have access to appropriate supports to help them make decisions that affect their lives. (shrink)

The idea of family resemblance, when applied to science, can provide a powerful account of the nature of science (NOS). In this chapter we develop such an account by taking into consideration the consensus on NOS that emerged in the science education literature in the last decade or so. According to the family resemblance approach, the nature of science can be systematically and comprehensively characterised in terms of a number of science categories which exhibit strong similarities and overlaps amongst diverse (...) scientific disciplines. We then discuss the virtues of this approach and make some suggestions as to how one can go about teaching it in the classroom. (shrink)

People with dementia have commonly been excluded from research. The adverse impacts of this exclusion are now being recognized and research literature, position statements, and ethics guidelines increasingly call for inclusion of people with dementia in research. However, few published studies investigate the views of potential participants on taking part in research should they experience dementia-related cognitive impairment. This cross-sectional survey examined the views of people aged sixty and older attending hospital outpatient clinics about clinical research participation if they had (...) dementia and impaired decision-making ability. Over 90 percent of respondents were agreeable to participating in a wide range of research activities, such as cognitive testing, physical measurements, imaging procedures, and blood draws. For drug studies, however, agreement dropped to 60 percent. Altruism was a strong motivator for research participation. In regard to who should be involved in decisions about their participation in research during periods of incapacity, respondents mostly preferred the person they appoint as their substitute decision-maker for healthcare matters or a doctor or health professional on the research team. Over three-quarters expressed interest in making an advance research directive. The study findings are discussed in relation to law reforms in Australia that aim to strengthen respect and inclusion for people with impaired decision-making capacity, especially by providing frameworks for advance planning for research participation. (shrink)

This is a survey of theories of scientific method which opens the book "After Popper, Kuhn and Feyerabend: Recent Issues in Theories of Scientific Method".

Many philosophical naturalists eschew analysis in favor of discovering metaphysical truths from the a posteriori, contending that analysis does not lead to philosophical insight. A countercurrent to this approach seeks to reconcile a certain account of conceptual analysis with philosophical naturalism; prominent and influential proponents of this methodology include the late David Lewis, Frank Jackson, Michael Smith, Philip Pettit, and David Armstrong. Naturalistic analysis is a tool for locating in the scientifically given world objects and properties we quantify over in (...) everyday discourse. This collection gathers work from a range of prominent philosophers who are working within this tradition, offering important new work as well as critical evaluations of the methodology. Its centerpiece is an important posthumous paper by David Lewis, "Ramseyan Humility," published here for the first time. The contributors first address issues of philosophy of mind, semantics, and the new methodology's a priori character, then turn to matters of metaphysics, and finally consider problems regarding normativity. Conceptual Analysis and Philosophical Naturalism is one of the first efforts to apply this approach to such a wide range of philosophical issues. _Contributors: _David Braddon-Mitchell, Mark Colyvan, Frank Jackson, Justine Kingsbury, Fred Kroon, David Lewis, Dustin Locke, Kelby Mason, Jonathan McKeown-Green, Peter Menzies, Robert Nola, Daniel Nolan, Philip Pettit, Huw Price, Denis Robinson, Steve Stich, Daniel Stoljar The hardcover edition does not include a dust jacket. (shrink)

We define and study monadic MV-algebras as pairs of MV-algebras one of which is a special case of relatively complete subalgebra named m-relatively complete. An m-relatively complete subalgebra determines a unique monadic operator. A necessary and sufficient condition is given for a subalgebra to be m-relatively complete. A description of the free cyclic monadic MV-algebra is also given.

For the performer, a career in the circus often brings with it a nomadic, lonely life. These photographs capture beautiful and unusual images of circus girls, photographs which evoke this sense of darkness and resignation that underlies the otherworldly feats they perform under the big top.

ABSTRACTElder abuse is a serious and under-detected problem. Law reform agencies and legal profession regulatory authorities have called for action to ensure that lawyers meet their ethical obligations to older clients, including identifying and acting on risk factors for abuse. Screening tools to detect situations of elder abuse exist, but they are targeted mainly at health and social care practitioners. Drawing on international literature, this article identifies and discusses screening tools that could be adapted for use by legal professionals. Three (...) general categories of screening are relevant for lawyers who serve older clients: elder abuse screening tools that cover all domains of abuse or target specific behaviours, such as financial exploitation; screening for decision-making capacity, especially taking account of the impact of abuse or neglect on capacity; and screening to probe the suitability of a person to act in a formal decision-making role for an older person. The article emphas... (shrink)

In this paper we prove that the category of abelianl-groups is equivalent to the category of perfect MV-algebras. Furthermore, we give a finite equational axiomatization of the variety generated by perfect MV-algebras.

What is it to be scientific? Is there such a thing as scientific method? And if so, how might such methods be justified? Robert Nola and Howard Sankey seek to provide answers to these fundamental questions in their exploration of the major recent theories of scientific method. Although for many scientists their understanding of method is something they just pick up in the course of being trained, Nola and Sankey argue that it is possible to be explicit about (...) what this tacit understanding of method is, rather than leave it as some unfathomable mystery. They robustly defend the idea that there is such a thing as scientific method and show how this might be legitimated. This book begins with the question of what methodology might mean and explores the notions of values, rules and principles, before investigating how methodologists have sought to show that our scientific methods are rational. Part 2 of this book sets out some principles of inductive method and examines its alternatives including abduction, IBE, and hypothetico-deductivism. Part 3 introduces probabilistic modes of reasoning, particularly Bayesianism in its various guises, and shows how it is able to give an account of many of the values and rules of method. Part 4 considers the ideas of philosophers who have proposed distinctive theories of method such as Popper, Lakatos, Kuhn and Feyerabend and Part 5 continues this theme by considering philosophers who have proposed naturalised theories of method such as Quine, Laudan and Rescher. This book offers readers a comprehensive introduction to the idea of scientific method and a wide-ranging discussion of how historians of science, philosophers of science and scientists have grappled with the question over the last fifty years. (shrink)

We present a stronger variation of state MV-algebras, recently presented by T. Flaminio and F. Montagna, which we call state-morphism MV-algebras. Such structures are MV-algebras with an internal notion, a state-morphism operator. We describe the categorical equivalences of such state MV-algebras with the category of unital Abelian ℓ-groups with a fixed state operator and present their basic properties. In addition, in contrast to state MV-algebras, we are able to describe all subdirectly irreducible state-morphism MV-algebras.

The MV-algebra S m w is obtained from the (m+1)-valued ukasiewicz chain by adding infinitesimals, in the same way as Chang's algebra is obtained from the two-valued chain. These algebras were introduced by Komori in his study of varieties of MV-algebras. In this paper we describe the finitely generated totally ordered algebras in the variety MV m w generated by S m w . This yields an easy description of the free MV m w -algebras over one generator. We characterize (...) the automorphism groups of the free MV-algebras over finitely many generators. (shrink)

In this paper we define sheaf spaces of BL-algebras (or BL-sheaf spaces), we study completely regular and compact BL-sheaf spaces and compact representations of BL-algebras and, finally, we prove that the category of non-trivial BL-algebras is equivalent with the category of compact local BL-sheaf spaces.

In this paper we prove that the category of abelian l-groups is equivalent to the category of perfect MV-algebras. Furthermore, we give a finite equational axiomatization of the variety generated by perfect MV-algebras.