The first part of the paper deals with some subclasses of B-algebras and their applications to the semantics of SCI B , the Boolean strengthening of the sentential calculus with identity (SCI). In the second part a generalization of the McKinsey-Tarski construction of well-connected topological Boolean, algebras to the class of B-algebras is given.

This paper deals with Boolean algebras supplied with an additional binary operation, calledB-algebras for short.The aim of the paper is to generalize some theorems concerning topological Boolean algebras to more comprehensive classes ofB-algebras, to formulate fundamental properties ofB-algebras, and to find more important relationships of these algebras to other known algebras.

The starting point for the investigation in this paper is the following McKinsey-Tarski's Theorem: if f and g are algebraic functions (of the same number of variables) in a topological Boolean algebra (TBA) and if C(f)C(g) vanishes identically, then either f or g vanishes identically. The present paper generalizes this theorem to B-algebras and shows that validity of that theorem in a variety of B-algebras (B-variety) generated by SCI B -equations implies that its free Lindenbaum-Tarski's algebra is normal. This is (...) important in the semantical analysis of SCI B (the Boolean strengthening of the sentential calculus with identity, SCI) since normal B-algebras are just models of this logic. The rest part of the paper is concerned with relationships between some closure systems of filters, SCI B -theories, B-varieties and closed sets of SCI B -equations that have been derived both from the semantics of SCI B and from the semantics of the usual equational logic. (shrink)

Działanie Boga a prawa przyrody: odpowiedź Łukasiewiczowi W odpowiedzi Łukasiewiczowi na Opatrzność Boża a przypadek w świecie bronię trzech wniosków. Po pierwsze, stanowisko nazwane przez niego „deizmem epistemicznym” staje przed wyzwaniami ze strony fizyki, których często się nie zauważa. Po drugie, jeśli teiści opowiadający się za argumentem celowościowym opartym na tzw. delikatnym dostrojeniu nie mają racji, to nie ma jej również większość fizyków, która uważa, że delikatne dostrojenie wymaga wyjaśnienia. Po trzecie, nie wszystkie prawa przyrody są warunkowe w takim sensie, (...) jaki przyjmuje Łukasiewicz. Na szczęście rozróżnienie między prawami a nienomologiczną informacją pozwala na rozszerzenie jego modelu działania Boga. (shrink)

The question of whether there are laws in ecology is important for a number of reasons. If, as some have suggested, there are no ecological laws, this would seem to distinguish ecology from other branches of science, such as physics. It could also make a difference to the methodology of ecology. If there are no laws to be discovered, ecologists would seem to be in the business of merely supplying a suite of useful models. These models would need to be (...) assessed for their empirical adequacy but not for their ability to capture fundamental truths, or the like. If, on the other hand, ecology does have laws, this prompts further questions about what these laws are and why even the best candidates for ecological laws fall short of what might be expected of laws. (shrink)

Thinking Tools is a regular feature that introduces pointers on thinking clearly and rigorously.

Thinking tools is a regular feature that offers tips and pointers on thinking clearly and rigorously.

A dialogue investigating whether the usual religious defences of belief in God are really up to the job.

Thinking Tools is a regular feature that introduces pointers on thinking clearly and rigorously. Here we get to grips with an everyday reasoning error: the gambler's fallacy.

Thinking Tools is a regular feature that introduces tips and pointers on thinking clearly and rigorously. Here we get to grips with two everyday reasoning errors.

Thinking Tools is a regular feature that introduces pointers on thinking clearly and rigorously. Here I tell a cautionary tale about flying saucers and take a brief look at the virtues of ‘open-mindedness’.

Thinking Tools is a regular feature that introduces pointers on thinking clearly and rigorously. Here l explain some of the techniques commonly used by ‘gurus’ to dupe people into thinking they have something profound to say.

Thinking Tools is a regular feature that introduces pointers on thinking clearly and rigorously. Here we get to grips with two everyday reasoning errors.

Thinking tools is a regular feature that offers tips and pointers on thinking clearly and rigorously.

Thinking Tools is a regular feature that introduces pointers on thinking clearly and rigorously.

Thinking tools is a regular feature that offers tips and pointers on thinking clearly and rigorously.

Thinking Tools is a regular feature that introduces tips and pointers on thinking clearly and rigorously.

The year is 2100. Geena is the proud new owner of Emit, a state-of-the-art robot. She has just unwrapped him, the packaging strewn across the dining room floor. Emit is designed to replicate the outward behaviour of a human being down to the last detail . Emit responds to questions in much the same way humans do. Ask him how he feels and he will say he has had a tough day, has a slight headache, is sorry he broke that (...) vase, and so on. Geena flips the switch at the back of Emit's neck to ‘on’. Emit springs to life. (shrink)

Journal Name: Semiotica Issue: Ahead of print.

Thinking Tools is a regular feature that introduces pointers on thinking clearly and rigorously. In this installment, we focus, not on faulty reasoning per se, but on an example of how we can be led astray or manipulated without our even realizing what is going on. Our critical faculties are entirely sidestepped!

Stephen Law follows THE PHILOSOPHY FILES with a second book of philosophical conundrums for teenagers. This time he asks such questions as Do Miracles Happen? Why Do These Words Mean Something? and Do I Know the Sun will Rise Tomorrow? You can dip into the arguments that interest you, in eight chapters where the themes are set up in witty scenarios and then debated. There are wacky thought experiments to work out and a variety of characters appear - some of (...) them Martians. As in THE PHILOSOPHY FILES, there are hundreds of lively cartoons running through the book. Stephen Law is a brilliant communicator with a passion to make young people think for themselves. As the GUARDIAN said: 'It's philosophy in action rather than philosophy in aspic... a real philosophy book for kids - which students and adults could enjoy too - finally exists'. (shrink)

In a secular society, does Christmas mean anything anymore? As we stuff ourselves with plumped-up turkeys, unwrap the latest useless gadget, and gather round the family tree, what real relevance does the festive season have and why do we perpetuate it? The Philosophy of Christmas is designed to be a fun book but one underpinned by an exploration of serious philosophical issues. The way we celebrate Christmas says a lot about the way we relate to each other, our society and (...) values. For instance, did you know that Santa's outfit is only red and white because those are the colours of the Coca Cola company? Already a bestselling author, Stephen Law takes a look at such things as the virgin birth (David Hume's theories on miracles), Bertrand Russell's turkey, the existential angst of Santa, and peace on earth to produce a humourous, varied and thought-provoking collection. (shrink)

This article argues that it is a mistake to assume that atheism entails naturalism, that naturalism is what leads someone to embrace atheism, and that atheists must sign up to a ‘naturalistic world-view’.

The theological energies released by Martin Luther in 1517 created a set of theological insights and problems that eventually led to the development of kenotic Christology. This article traces how kenotic Christology originated in the Eucharistic Controversy between Luther and Zwingli, before receiving its first extensive treatment in the debate between the Lutheran theologians of Tübingen and Giessen in,the early seventeenth century. Attention then turns to the nine-teenth century, when doctrinal tensions resulting from the enforced union of the Prussian Lutheran (...) and Reformed churches created the conditions for a new flowering of kenotic Christology in the theologies of Ernst Sartorius and, subsequently, Gottfried Thomasius. Kenotic Christology ultimately originates with Luther, however, for it owes its existence to the creative theological energies he unleashed and which remain his lasting legacy. (shrink)

Human rights discourse has been likened to a global lingua franca, and in more ways than one, the analogy seems apt. Human rights discourse is a language that is used by all yet belongs uniquely to no particular place. It crosses not only the borders between nation-states, but also the divide between national law and international law: it appears in national constitutions and international treaties alike. But is it possible to conceive of human rights as a global language or lingua (...) franca not just in a figurative or metaphorical sense, but in a literal or linguistic sense as a legal dialect defined by distinctive patterns of word choice and usage? Does there exist a global language of human rights that transcends not only national borders, but also the divide between domestic and international law? Empirical analysis suggests that the answer is yes, but this global language comes in at least two variants or dialects. New techniques for performing automated content analysis enable us to analyze the bulk of all national constitutions over the last two centuries, together with the world’s leading regional and international human rights instruments, for patterns of linguistic similarity and to evaluate how much language, if any, they share in common. Specifically, we employ a technique known as topic modeling that disassembles texts into recurring verbal patterns. The results highlight the existence of two species or dialects of rights talk—the universalist dialect and the positive-rights dialect—both of which are global in reach and rising in popularity. The universalist dialect is generic in content and draws heavily on the type of language found in international and regional human rights instruments. It appears in particularly large doses in the constitutions of transitional states, developing states, and states that have been heavily exposed to the influence of the international community. The positive-rights dialect, by contrast, is characterized by its substantive emphasis on positive rights of a social or economic variety, and by its prevalence in lengthier constitutions and constitutions from outside the common law world, especially those of the Spanish-speaking world. Both dialects of rights talk are truly transnational, in the sense that they appear simultaneously in national, regional, and international legal instruments and transcend the distinction between domestic and international law. Their existence attests to the blurring of the boundary between constitutional law and international law. (shrink)

David Law's new book deals with Kierkegaard's `apophaticism' - or those elements of Kierkegaard's thought which emphasize the incapacity of human reason and the hiddenness of God.

Law's article begins by restating the classical ANT position that objects do not exist `in themselves' but are the effect of a performative stabilization of relational networks. In addition, these material enactments inevitably have a spatial dimension; they simultaneously establish spatial conditions for objectual identity, continuity, and difference. Space must not be reified as a natural, pre-existing container of the social and the material, but is itself a performance. Moreover, there are multiple forms of spatiality beyond the Euclidean space of (...) regions (e.g. networks and fluids), and objects may exist and achieve homeomorphism within several different spatial systems. Technologies such as the Zimbabwe Bush Pump present a fluid object which is able to exist and cohere without the presence of fixed boundaries or the permanence of a particular functional definition. The network logic, however, which gravitates towards stability and functionality, tends to exclude and silence this spatial Other. An alternative political ontology is needed which goes beyond the reification of network space in order to give voice to the fluid objects which escape its unidimensional functionality. (shrink)

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