The Birkhoff-Maltsev problem asks for a characterization of those lattices each of which is isomorphic to the lattice L(K) of all subquasivarieties for some quasivariety K of algebraic systems. The current status of this problem, which is still open, is discussed. Various unsolved questions that are related to the Birkhoff-Maltsev problem are also considered, including ones that stem from the theory of propositional logics.

We introduce a new interpretation of non-relativistic quantum mechanics (QM) called Relational Blockworld (RBW). We motivate the interpretation by outlining two results due to Kaiser, Bohr, Ulfeck, Mottelson, and Anandan, independently. First, the canonical commutation relations for position and momentum can be obtained from boost and translation operators,respectively, in a spacetime where the relativity of simultaneity holds. Second, the QM density operator can be obtained from the spacetime symmetry group of the experimental configuration exclusively. We show how QM, obtained from (...) relativistic quantum field theory per RBW, explains the twin-slit experiment and conclude by resolving the standard conceptual problems of QM, i.e., the measurement problem, entanglement and non-locality. (shrink)

Goethe and Wittgenstein -- Criticism without theory -- Wittgenstein's romantic inheritance -- Arnold and the socratic personality -- The dissolution of goodness : measure for measure and classical ethics -- Lamarque and Olsen on literature and truth -- The definition of 'art' -- Poetry and abstraction -- Larkin's 'Aubade'.

The task of the historian is not one of tracing a series of links in a temporal chain; rather, it is his task to analyze a complex pattern of change into the factors which served to make it precisely what it was. The relationship which I therefore take to be fundamental to historiography is ... a relationship of part to whole, not a relationship of antecedent to consequent.Mandelbaum's historian relates the part to the whole, leaving it for the sociologist to (...) relate the antecedent to the consequence.If that is so, then Maigret is first an historian ascertaining and accumulating the subjective meanings that individuals use to produce the facticity of their own lives. And in the course of so doing he discovers the nature of the reality in which the crime occurred. Once he finds his way into the realities of the crime there is time and need for the sociological analysis of antecedent and consequent. To suggest a comparison, Maigret practices in miniature the method of Norbert Elias in that he tries to understand his subjects as they understand themselves. Maigret's is an idiographic science and not a nomethetic one. For this reason Maigret, unlike Holmes, almost never refers to previous cases in the effort to understand the matter at hand.The temptation is to conclude that Maigret is a little like Fernand Braudel in combining history and sociology by turns. But I wonder if there is not a more profound sense in which Maigret, if not all sociologists, is an historian. If we have any knowledge it is of the past, not of the present or the future. Minerva's owl does indeed take wing only at dusk, as Hegel wrote. By the time we have understood the present, it is the past.If Maigret's aim is not the unvarnished truth, that is not because of the constraints of police work but because of the constraints of the world. The irony of Maigret's ethnomethodology is this. Simenon's style is rightly celebrated for its evocation of atmosphere. The apposite analogy occasionally offered is between Simenon's spare and laconic style and Impressionist painting. Simenon does not describe people and places in the Maigret stories but suggests them with a sentence or two. The style is not realism, whatever the effect. As Rafael Koskimies has written, Simenon selects and simplifies. Impressionism is the style of painting that accepts the surface as reality. The play of light and color on the surface of objects is suggested on the surface of the canvas with the texture and color of the paint. If Simenon is an impressionist in his art, Maigret cannot be in his. He does not settle for the surface, but goes inside of it. Once there he learns all he needs to know and all that he can know. The confessions that so frequently occur in the Maigret stories do not confirm his suppositions, but release the tensions of the drama in a catharsis. Finally, if Maigret's Maigret must admit in his Memoirs that he could not in fact go into the detail of every reality personally in the manner described above, it only proves how terribly taxing the method called Verstehen is.To conclude, Maigret has a method, but it is not a recipe that others can follow step-by-step. His method is an orientation to reality and a commitment to understanding in a certain way. To call Maigret's procedure a method requires the definition of “method” to include more than cook books, however brilliant the cook books are. Maigret's method is a part of the context of discovery. Naive realists like Méchin imagine that they live only in the context of justification.Of course, no one's understanding is perfect. Maigret makes mistakes. There are times when an explanation based on behavior would be more accurate and economical. If Simenon does not dwell on Maigret's failures it is clear that Maigret uses other methods, too. The triangulation of a variety of methods is what in fact most of us practice whatever we preach. (shrink)

Tragedy and Citizenship provides a wide-ranging exploration of attitudes toward tragedy and their implications for politics. Derek W. M. Barker reads the history of political thought as a contest between the tragic view of politics that accepts conflict and uncertainty, and an optimistic perspective that sees conflict as self-dissolving. Drawing on Aristotle's political thought, alongside a novel reading of the Antigone that centers on Haemon, its most neglected character, Barker provides contemporary democratic theory with a theory of tragedy. He sees (...) Hegel's philosophy of reconciliation as a critical turning point that results in the elimination of citizenship. By linking Hegel's failure to address the tragic dimensions of politics to Richard Rorty, John Rawls, and Judith Butler, Barkeroffers a major reassessment of contemporary political theory and a fresh perspective on the most urgent challenges facing democratic politics. Derek W. M. Barker is a program officer at the Kettering Foundation. (shrink)

The formulas-as-types isomorphism tells us that every proof and theorem, in the intuitionistic implicational logic $H_\rightarrow$, corresponds to a lambda term or combinator and its type. The algorithms of Bunder very efficiently find a lambda term inhabitant, if any, of any given type of $H_\rightarrow$ and of many of its subsystems. In most cases the search procedure has a simple bound based roughly on the length of the formula involved. Computer implementations of some of these procedures were done in Dekker. (...) In this paper we extend these methods to full classical propositional logic as well as to its various subsystems. This extension has partly been implemented by Oostdijk. (shrink)

Written in a relaxed, readable style, A Concise Introduction to Pure Mathematics leads students gently but firmly into the world of higher mathematics. It provides beginning undergraduates with a rigourous grounding in the basic tools and techniques of the discipline and prepares them for further more advanced studies in analysis, differential equations, and algebra. This edition contains additional material on secret codes, permutations, and prime numbers. It features more than 200 exercises, with many completely new. The text is organized into (...) relatively independent chapters, allowing instructors to tailor the book to meet their individual course needs. · Contains extra material concerning prime numbers, forming the basis for data encryption · Explores "Secret Codes" - one of today's most spectacular applications of pure mathematics Discusses Permutations and their importance in many topics in discrete mathematics. (shrink)

Realities are structured categorially, and comprehension of our internal and external conditions do not appear to be global or unitary. Rather, both human and non human animals function within their worlds and understand these by categorizing their experiences. Drawing upon many areas of life, the authors consider the ontological, mereological and multi-faceted structure of experience to explore how an understanding of categories can further knowledge.

Philosophers have hitherto only interpreted the world in various ways; the point is to change it.Karl marx’s distinction between interpreting the world and changing it points by extension to the state of contemporary philosophy and psychiatry. The 1990s resurgence of interdisciplinary work in this area was driven equally by phenomenological scholarship and by initiatives in analytic philosophy. The former reflected the focus in phenomenology on ‘what it is like’ to experience a given mental symptom with the aim of reconstructing the (...) life-worlds of people experiencing mental disorders, while the latter reflected directly or indirectly the influence of J. L. Austin and others from... (shrink)

The passing on of information to GPs by genito-urinary doctors is to be encouraged but is not always possible and ultimately the patient's wishes and confidentiality must be respected if sexually transmitted diseases and HIV infection are to be controlled. Infected health-care workers should seek counselling and medical support and clear guidelines from professional organisations which are in existence. However, they will only do so if strict confidentiality is maintained and assurance about future employment can be given.