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.

The paper discusses regularisation of dualities. A given duality between (concrete) categories, e.g. a variety of algebras and a category of representation spaces, is lifted to a duality between the respective categories of semilattice representations in the category of algebras and the category of spaces. In particular, this gives duality for the regularisation of an irregular variety that has a duality. If the type of the variety includes constants, then the regularisation depends critically on the location or absence of constants (...) within the defining identities. The role of schizophrenic objects is discussed, and a number of applications are given. Among these applications are different forms of regularisation of Priestley, Stone and Pontryagin dualities. (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.

We discuss some recent work by Tim Maudlin concerning Black Hole Information Loss. We argue, contra Maudlin, that there is a paradox, in the straightforward sense that there are propositions that appear true, but which are incompatible with one another. We discuss the significance of the paradox and Maudlin's response to it.

We show a sense in which the spacetime property of effective completeness—a type of “local hole-freeness” or “local inextendibility”—is not stable.

We consider various curious features of general relativity, and relativistic field theory, in two spacetime dimensions. In particular, we discuss: the vanishing of the Einstein tensor; the failure of an initial-value formulation for vacuum spacetimes; the status of singularity theorems; the non-existence of a Newtonian limit; the status of the cosmological constant; and the character of matter fields, including perfect fluids and electromagnetic fields. We conclude with a discussion of what constrains our understanding of physics in different dimensions.

This introduction to one of the liveliest and most popular fields in philosophy is written specifically for a beginning readership with no background in philosophy or science. Step-by-step analyses of the key arguments are provided and the philosophical heart of the issues is revealed without recourse to jargon, maths, or logical formulas. The book introduces Einstein's revolutionary ideas in a clear and simple way, along with the concepts and arguments of philosophers, both ancient and modern that have proved of lasting (...) value. Specifically, the theories of the ancient Greek philosophers, Zeno, Euclid and Parmenides are considered alongside the ideas of Newton, Leibniz and Kant as well as the giants of twentieth-century physics, Einstein and Lorentz. The problems at the heart of the philosophy of space and time, such as change, motion, infinity, shape, and inflation, are examined and the seismic impact made by relativity theory and quantum theory is assessed in the light of the latest research. The writing is lucid and entertaining, allowing a beginning readership to grasp some difficult concepts while offering the more experienced reader a succinct and illuminating presentation of the state of the debate. "Space, Time and Einstein" shows the reader the excitement of scientific discovery and the beauty of theory in the search for answers to these fundamental questions. (shrink)

This study investigates specific behavioral perceptual differences of ethics between practitioners and students enrolled in sales classes. Respondents were asked to indicate their beliefs to issues related to ethics in sales. A highly significant difference was found between mean responses of students and sales personnel. Managers indicated a greater concern for ethical behavior and less attention to sales than did the students. Students indicated a strong desire for success regardless of ethical constraints violated.

This chapter explores the opportunities and limitations of the ideal of transparency in responsible innovation, by consulting the virtual case of "The Circle", a company which appears in Dave Eggers' novel The Circle. The Circle is a high-tech company with the main purpose of being responsive to societal needs. They want to eradicate unethical behaviour in society, enhance public health and make a positive impact on the environment. The ultimate goal of The Circle is to reach 100% full transparency in (...) the world, which is impossible without any societal desirability. In first instance, it is free choice of people to accept and embrace the products and services of The Circle, who invest resources in keeping customers happy and in raising awareness about the dangers of privacy. The chapter concludes that The Circle meets the requirements regarding the outcomes of responsible innovation, at least to a certain extent, while at the same time, one feels unease about certain activities they undertake. (shrink)

**A newly revised edition of two seminal works on Imperial Rome** Undeniably one of Rome’s most important historians, Tacitus was also one of its most gifted. *The Agricola* is both a portrait of Julius Agricola-the most famous governor of Roman Britain and Tacitus’s respected father-in-law-and the first known detailed portrayal of the British Isles. In the *Germania*, Tacitus focuses on the warlike German tribes beyond the Rhine, often comparing the behavior of "barbarian" peoples favorably with the decadence and corruption of (...) Imperial Rome. (shrink)

Practitioners in the vanguard of new economic thinking will also find plenty of useful information in this path-breaking book.

Here we discuss the challenge posed by self-organization to the Darwinian conception of evolution. As we point out, natural selection can only be the major creative agency in evolution if all or most of the adaptive complexity manifest in living organisms is built up over many generations by the cumulative selection of naturally occurring small, random mutations or variants, i.e., additive, incremental steps over an extended period of time. Biological self-organization—witnessed classically in the folding of a protein, or in the (...) formation of the cell membrane—is a fundamentally different means of generating complexity. We agree that self-organizing systems may be fine-tuned by selection and that self-organization may be therefore considered a complementary mechanism to natural selection as a causal agency in the evolution of life. But we argue that if self-organization proves to be a common mechanism for the generation of adaptive order from the molecular to the organismic level, then this will greatly undermine the Darwinian claim that natural selection is the major creative agency in evolution. We also point out that although complex self-organizing systems are easy to create in the electronic realm of cellular automata, to date translating in silico simulations into real material structures that self-organize into complex forms from local interactions between their constituents has not proved easy. This suggests that self-organizing systems analogous to those utilized by biological systems are at least rare and may indeed represent, as pre-Darwinists believed, a unique ascending hierarchy of natural forms. Such a unique adaptive hierarchy would pose another major challenge to the current Darwinian view of evolution, as it would mean the basic forms of life are necessary features of the order of nature and that the major pathways of evolution are determined by physical law, or more specifically by the self-organizing properties of biomatter, rather than natural selection. (shrink)

Woodger's substitution of the "allegedly more precise term 'an environmentally insensitive set of lives'" for the term 'an inborn character' is discussed by haldane. He proposes that "woodger's definitions do not appear to have reached precision." (staff).