In our paper “A general characterization of the variable-sharing property by means of logical matrices”, a general class of so-called “Relevant logical matrices”, RMLs, is defined. The aim of this paper is to define a class of simpler Relevant logical matrices RMLs′serving the same purpose that RMLs, to wit: any logic verified by an RML′has the variable-sharing property and related properties predicable of the logic of entailment E and of the logic of relevance R.

Taxometric analyses were applied to the construct of psychopathy (as measured by the Psychopathy Checklist) and to several variables reflecting antisocial childhood, adult criminality, and criminal recidivism. Subjects were 653 serious offenders assessed or treated in a maximum-security institution. Results supported the existence of a taxon underlying psychopathy. Childhood problem behaviors provided convergent evidence for the existence of the taxon. Adult criminal history variables were continuously distributed and were insufficient in themselves to detect the taxon.

We study for each computably bounded $\Pi ^0_1$ class P the set of degrees of c.e. paths in P. We show, amongst other results, that for every c.e. degree a there is a perfect $\Pi ^0_1$ class where all c.e. members have degree a. We also show that every $\Pi ^0_1$ set of c.e. indices is realized in some perfect $\Pi ^0_1$ class, and classify the sets of c.e. degrees which can be realized in some $\Pi ^0_1$ (...) class as exactly those with a computable representation. (shrink)

In the human sciences, experimental research is used to establish causal relationships. However, the extrapolation of these results to the target population can be problematic. To facilitate extrapolation, we propose to use the statistical technique Latent Class Regression Analysis in combination with the analogical reasoning theory for extrapolation. This statistical technique can identify latent classes that differ in the effect of X on Y. In order to extrapolate by means of analogical reasoning, one can characterize the latent classes by (...) a combination of features, and then compare these features to features of the target. (shrink)

In this article we show that it is possible to completely classify the degrees of r.e. bases of r.e. vector spaces in terms of weak truth table degrees. The ideas extend to classify the degrees of complements and splittings. Several ramifications of the classification are discussed, together with an analysis of the structure of the degrees of pairs of r.e. summands of r.e. spaces.

The partial ordering of Medvedev reducibility restricted to the family of Π0 1 classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a Π0 1 class, which we call a ``c.e. separating class''. We show that there are no non-trivial meets for c.e. separating classes, but that the density theorem holds in the sublattice generated by the c.e. separating classes.

Abstract.The partial ordering of Medvedev reducibility restricted to the family of Π01 classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a Π01 class, which we call a ``c.e. separating class''. We show that there are no non-trivial meets for c.e. separating classes, but that the density theorem holds in the sublattice generated by the c.e. separating classes.

MATERIALISTS claim that in principle mentality could be accounted for entirely by properties of matter. They must, of course, clarify, as far as possible, the precise scope of the concept "properties of matter." According to materialists there exists only one type of "substance" in the universe, namely matter. Sophisticated experimental and theoretical analyses have led contemporary physicists to interpret known material entities as being composed of two classes of elementary particles, namely quarks and leptons and constituents of interaction fields that (...) mediate interactions between some or all of the elementary particles and which comprise photons, gluons, intermediate bosons and gravitons. For instance, protons and neutrons are composed--by hypothesis--of quarks, while electrons are probably the most familiar leptons. Whether any analyzed and postulated elementary particles and constituents of interaction fields are "ultimate" components of matter can never be known. It remains always possible that more basic subcomponents of known components will be discovered. This has happened repeatedly throughout the history of physics. Hence, what physicists understand by the "physical properties" of the basic components of matter must always remain expressed in terms of usually intricate hypothetico-deductive theories which are tentative and fallible. Contemporary relativistic quantum mechanics of elementary particles and of interaction fields provide typical examples of such hypothetico-deductive theories relating to present known basic components of matter. (shrink)

Reaction-diffusion systems which have reaction term satisfying f(-q) = -f(q) tend strongly to form striped patterns. Haken’s slaving principle is used to derive differential equations for unstable mode amplitudes close to the Turing instability. This connects a dynamical symmetry to pattern selection, with possible relevance to biological and chemical pattern-forming phenomena.

Ventricular Fibrillation is responsible for a majority of sudden cardiac death, but little is known about how ventricular tachycardia (VT) degenerates into ventricular fibrillation. Several clinical studies focused only on preventing VT with a class III antiarrhythmic drug resulted in many deaths. Our simulations investigate the interactions between an antiarrhythmic drug likely to suppress a VT and a Figure 8 reentry. A parameter AAR is introduced to increase the action potential duration and therefore simulate various Class III drugs. (...) Simulations are ran under several conditions (phases of the reentry, values of AAR, durations). They show that a VT can be suppressed whatever the phase of the reentry but it strongly depends on the duration of the effect. It confirms that a drug which can suppress a reentry can also worsen it. It also shows a great variety of activation patterns and thus the complexity of antiarrhythmic drugs effects. Simulations also demonstrate that suppressing VT is an increasing function of AAR. (shrink)

Important examples of $\Pi^0_1$ classes of functions $f \in {}^\omega\omega$ are the classes of sets (elements of ω 2) which separate a given pair of disjoint r.e. sets: ${\mathsf S}_2(A_0, A_1) := \{f \in{}^\omega2 : (\forall i < 2)(\forall x \in A_i)f(x) \neq i\}$ . A wider class consists of the classes of functions f ∈ ω k which in a generalized sense separate a k-tuple of r.e. sets (not necessarily pairwise disjoint) for each k ∈ ω: ${\mathsf S}_k(A_0,\ldots,A_k-1) (...) := \{f \in {}^\omega k : (\forall i < k) (\forall x \in A_i) f(x) \neq i\}$ . We study the structure of the Medvedev degrees of such classes and show that the set of degrees realized depends strongly on both k and the extent to which the r.e. sets intersect. Let ${\mathcal S}^m_k$ denote the Medvedev degrees of those ${\mathsf S}_k(A_0,\ldots,A_{k-1})$ such that no m + 1 sets among A 0,...,A k-1 have a nonempty intersection. It is shown that each ${\mathcal S}^m_k$ is an upper semi-lattice but not a lattice. The degree of the set of k-ary diagonally nonrecursive functions $\mathsf{DNR}_k$ is the greatest element of ${\mathcal S}^1_k$ . If 2 ≤ l < k, then 0 M is the only degree in ${\mathcal S}^1_l$ which is below a member of ${\mathcal S}^1_k$ . Each ${\mathcal S}^m_k$ is densely ordered and has the splitting property and the same holds for the lattice ${\mathcal L}^m_k$ it generates. The elements of ${\mathcal S}^m_k$ are exactly the joins of elements of ${\mathcal S}^1_i$ for $\lceil{k \over m}\rceil \leq i \leq k$. (shrink)

A general method for constructing a new class of topological Ramsey spaces is presented. Members of such spaces are infinite sequences of products of Fraïssé classes of finite relational structures satisfying the Ramsey property. The Product Ramsey Theorem of Sokič is extended to equivalence relations for finite products of structures from Fraïssé classes of finite relational structures satisfying the Ramsey property and the Order-Prescribed Free Amalgamation Property. This is essential to proving Ramsey-classification theorems for equivalence relations on fronts, generalizing (...) the Pudlák–Rödl Theorem to this class of topological Ramsey spaces. To each topological Ramsey space in this framework corresponds an associated ultrafilter satisfying some weak partition property. By using the correct Fraïssé classes, we construct topological Ramsey spaces which are dense in the partial orders of Baumgartner and Taylor generating p-points which are k-arrow but not \-arrow, and in a partial order of Blass producing a diamond shape in the Rudin-Keisler structure of p-points. Any space in our framework in which blocks are products of n many structures produces ultrafilters with initial Tukey structure exactly the Boolean algebra \\). If the number of Fraïssé classes on each block grows without bound, then the Tukey types of the p-points below the space’s associated ultrafilter have the structure exactly \. In contrast, the set of isomorphism types of any product of finitely many Fraïssé classes of finite relational structures satisfying the Ramsey property and the OPFAP, partially ordered by embedding, is realized as the initial Rudin-Keisler structure of some p-point generated by a space constructed from our template. (shrink)

Aristotle’s restriction of intellect to humans raised the problem of how animals are able to react to and learn from their environment if they lack the ability to recognize classes of objects, an ability supposedly conferred by intellect. Aristotle’s delineation of the internal senses into the common sense, imagination, and memory did not include a locus for the cleverness or prudence that he found animals to possess in varying degrees. Avicenna supplemented Aristotle’s internal senses by adding the estimative power, which (...) allowed animals to recognize the value of a perceived object in terms of its potential benefit or harm. Albert the Great, who showed more interest than most medieval philosophers in the problem of animal behavior, adopted the estimative power and began his inquiry by considering pygmies, which he judged to be the highest form of animal. This inquiry led Albert to weaken but in the end to retain the distinction based on intellectual abilities between animals and humans. (shrink)

Let w and M be the countable distributive lattices of Muchnik and Medvedev degrees of non-empty Π1 0 subsets of 2ω, under Muchnik and Medvedev reducibility, respectively. We show that all countable distributive lattices are lattice-embeddable below any non-zero element of w . We show that many countable distributive lattices are lattice-embeddable below any non-zero element of M.

This edition of G. E. Moore's notes taken at Wittgenstein's seminal Cambridge lectures in the early 1930s provides, for the first time, an almost verbatim record of those classes. The presentation of the notes is both accessible and faithful to their original manuscripts, and a comprehensive introduction and synoptic table of contents provide the reader with essential contextual information and summaries of the topics in each lecture. The lectures form an excellent introduction to Wittgenstein's middle-period thought, covering a broad range (...) of philosophical topics, ranging from core questions in the philosophy of language, mind, logic, and mathematics, to illuminating discussions of subjects on which Wittgenstein says very little elsewhere, including ethics, religion, aesthetics, psychoanalysis, and anthropology. The volume also includes a 1932 essay by Moore critiquing Wittgenstein's conception of grammar, together with Wittgenstein's response. A companion website offers access to images of the entire set of source manuscripts. (shrink)

Modules in ethics have become astonishingly popular at the University of the Western Cape. This could reflect students’ concern about morality, but the saying by Lafargue in Tao te ching in the title suggests that moral discourse flourishes when moral behaviour is languishing. This article reflects on some 15 years of teaching ethical theory to third-year students. Three trends are identified: Students’ responses to the theories are unpredictable and surprising. Nietzsche and Kant are very popular, although some modern ‘contextual’ theories (...) draw less support. Students who can be extremely moralistic in class are sometimes amoral in their practices and offhand pronouncements. Students are hampered by their poor conceptual skills and rely excessively on memorising. The last two trends raise questions about our teaching of ethics and the ethics of our teaching. Although many students embrace character-based theories, to some ‘a good character’ apparently means ‘what makes me feel good about myself’ and to others ‘what makes me look good to my group’. Thus, they effectively embrace either individual relativism or group relativism, which is understandable when theories are presented without the backing of at least a rudimentary philosophical anthropology. Questions of indoctrination become acute in the teaching of ethics. Are we, in the name of moral formation, teaching students to parrot current dogmas presented without arguments? If so, our practice may be both morally dubious and counterproductive. The best students rebel against such manipulation. The article calls for more reflection on how and to what ends we teach ethics. (shrink)

Some statements couched in the present tense have no reference to time. They are, if you like, grammatically tensed but logically tenseless. Mathematical statements such as ‘twice two is four’ or ‘there is a prime number between 125 and 128’ are of this sort. So is the statement I have just made. To ask in good faith whether there is still the prime number there used to be between 125 and 128 would be to show that one did not understand (...) the use of such statements, and so would any attempt to answer the question. It is tempting to take another step and talk of such timeless statements as statements about timeless entities. If the number 4 neither continues nor ceases to be twice two this is, surely, because the number 4 has no history of any kind, not even the being a day older today than yesterday. Other timeless statements might shake our confidence in this inference: ‘clocks are devices for measuring time’ is a timeless statement, but it is not about a class of timeless clocks. But, given a preoccupation with a favoured set of examples and a stage of thought at which men did not distinguish the properties of statements from the properties of the things they are about, we can expect timeless entities to appear as the natural proxies of timeless statements. (shrink)

In this paper we consider an intuitionistic variant of the modal logic S4 (which we call IS4). The novelty of this paper is that we place particular importance on the natural deduction formulation of IS4— our formulation has several important metatheoretic properties. In addition, we study models of IS4— not in the framework of Kirpke semantics, but in the more general framework of category theory. This allows not only a more abstract definition of a whole class of models but (...) also a means of modelling proofs as well as provability. (shrink)

Let be the class of frames satisfying the condition.

Rising social, political and economic inequality in many countries, and rising protest against it, has seen the restoration of the concept of 'class' to a prominent place in contemporary anthropological debates. A timely intervention in these discussions, this book explores the concept of class and its importance for understanding the key sources of that inequality and of people's attempts to deal with it. Highly topical, it situates class within the context of the current economic crisis, integrating elements (...) from today into the discussion of an earlier agenda. Using cases from North and South America, Western Europe and South Asia, it shows the - sometimes surprising - forms that class can take, as well as the various effects it has on people's lives and societies. (shrink)

In _Violence and Civility_, Étienne Balibar boldly confronts the insidious causes of violence, racism, nationalism, and ethnic cleansing worldwide, as well as mass poverty and dispossession. Through a novel synthesis of theory and empirical studies of contemporary violence, the acclaimed thinker pushes past the limits of political philosophy to reconceive war, revolution, sovereignty, and class. Through the pathbreaking thought of Derrida, Balibar builds a topography of cruelty converted into extremism by ideology, juxtaposing its subjective forms and its objective manifestations. (...) Engaging with Marx, Hegel, Hobbes, Clausewitz, Schmitt, and Luxemburg, Balibar introduces a new, productive understanding of politics as antiviolence and a fresh approach to achieving and sustaining civility. Rooted in the principles of transformation and empowerment, this theory brings hope to a world increasingly divided even as it draws closer together. (shrink)