In this work we deal with a general class of spatially distributed periodic SIS epidemic models with two time scales. We let susceptible and infected individuals migrate between patches with periodic time dependent migration rates. The existence of two time scales in the system allows to describe certain features of the asymptotic behavior of its solutions with the help of a less dimensional, aggregated, system. We derive global reproduction numbers governing the general spatially distributed nonautonomous system through the aggregated system. (...) We apply this result when the mass action law and the frequency dependent transmission law are considered. Comparing these global reproductive numbers to their non spatially distributed counterparts yields the following: adequate periodic migration rates allow global persistence or eradication of epidemics where locally, in absence of migrations, the contrary is expected. (shrink)

Artikelen en lezingen uit de periode 1970-1982.

Uitgave ter gelegenheid van de vierhonderdste geboortedag van de Nederlandse jurist, diplomaat en schrijver Hugo de Groot (1583-1645).

Overzicht van de rationalistische traditie in de filosofie van de kunst sinds Kant door een hoogleraar aan de Leuvense universiteit.

Shaftesbury's Characteristics of Men, Manners, Opinions, Times was published in 1711. It ranges widely over ethics, aesthetics, religion, the arts (painting, literature, architecture, gardening), and ancient and modern history, and aims at nothing less than a new ideal of the gentleman. Together with Locke's Essay Concerning Human Understanding and Addison and Steele's Spectator, it is a text of fundamental importance for understanding the thought and culture of Enlightenment Europe. This volume presents a new edition of the text together with an (...) introduction, explanatory notes and a guide to further reading. (shrink)

In this 1974 book a practising scientist and gifted expositor sets forth an exciting point of view on the nature of science and how it works.

The paper deals with the "deuteros plous", literally ‘the second voyage’, proverbially ‘the next best way’, discussed in Plato’s "Phaedo", the key passage being Phd. 99e4–100a3. The second voyage refers to what Plato’s Socrates calls his “flight into the logoi”. Elaborating on the subject, the author first (I) provides a non-standard interpretation of the passage in question, and then (II) outlines the philosophical problem that it seems to imply, and, finally, (III) tries to apply this philosophical problem to the "ultimate (...) final proof" of immortality and to draw an analogy with the ontological argument for the existence of God, as proposed by Descartes in his 5th "Meditation". The main points are as follows: (a) the “flight into the logoi” can have two different interpretations, a common one and an astonishing one, and (b) there is a structural analogy between Descartes’s ontological argument for the existence of God in his 5th "Meditation" and the "ultimate final proof" for the immortality of the soul in the "Phaedo". (shrink)

This volume contains papers and abstracts of papers delivered at the colloquium at Tihany, Hungary in 1962. There were seven sections; mathematical logic, computers and automata theory, circuit theory, mathematical linguistics, computers and programming, applications of computers in economics, artificial intelligence. Among the more interesting—to the reviewer—were these papers: one by Church concerning an independence problem in recursive arithmetic; Muller—characterizing classes of recursive functions; a long and philosophically stimulating study by Watanabe on a formalization of inductive logic; Kiefer—applications of set (...) theoretic techniques in linguistics; Abraham and Salapina—recognition of synonymity by machine; Gelernter—problem-solving graphs and heuristic programming. A number of papers which were read are not included in this volume.—P. J. M. (shrink)

This is a collection of papers, all but one of which were previously published, by one of England's leading logicians. Goodstein has described his position in the philosophy of mathematics as that of a "constructive formalist": leaning toward the Hilbert school, but emphasizing the constructive nature of mathematical entities. The papers are more or less technical and symbolic; those most difficult are "The Nature of Mathematics," "The Decision Problem," and "The Definition of Number." Other titles are "Proof by Reductio ad (...) Absurdum," "Logic Paradoxes", "Language and Experience," "The Meaning of Counting," "Mathematical Systems," "The Axiomatic Method," "Pure and Applied Mathematics," and "The Significance of Incompleteness Theorems"; the last-mentioned paper is also quite difficult, but it constitutes not only one of the best semi-formal presentations of Gödel's theorems, but also helps make quite clear what their relevance is to considerations of the expressive power of formal languages in general. This collection constitutes a fine introduction to the philosophy of mathematics.—P. J. M. (shrink)

The author's central thesis is that a knowledge of set theory can be put to good use by the linguist interested in the syntax of natural languages. The author first points out the role of set theory in formal science, and then gives a short summary of some of the more important ideas. He then develops certain relations in set theory which are of special importance in the study of languages. A fair number of examples—admittedly in rather trivial form—which occur (...) in the study of language are exhibited to show some of the applications in mind. The last few pages are devoted to a review of how his thesis has fared. Although it may seem obvious to some that set theory is the means par excellence for the formal study of any discipline, many linguists apparently do not yet see this; this book will go some way toward demonstrating this.—P. J. M. (shrink)

Theodor W. Adorno is best known for his contributions to aesthetics and social theory. Critics have always complained about the lack of a practical, political or ethical dimension to Adorno's philosophy. In this highly original contribution to the literature on Adorno, J. M. Bernstein offers the first attempt in any language to provide an account of the ethical theory latent in Adorno's writings. Bernstein relates Adorno's ethics to major trends in contemporary moral philosophy. He analyses the full range of Adorno's (...) major works, with a special focus on Dialectic of Enlightenment, Minima Moralia and Negative Dialectics. In developing his account Bernstein lays particular stress on Adorno's contention that the event of Auschwitz demands a new categorical imperative. This book will be widely acknowledged as the standard work on Adorno's ethics and as such will interest professionals and students of philosophy, political theory, sociology, history of ideas, art history and music. (shrink)

This study described the relationships between academic class and student moral sensitivity and reasoning and between curriculum design components for ethics education and student moral sensitivity and reasoning. The data were collected from freshman (n = 506) and senior students (n = 440) in eight baccalaureate nursing programs in South Korea by survey; the survey consisted of the Korean Moral Sensitivity Questionnaire and the Korean Defining Issues Test. The results showed that moral sensitivity scores in patient-oriented care and conflict were (...) higher in senior students than in freshman students. Furthermore, more hours of ethics content were associated with higher principled thinking scores of senior students. Nursing education in South Korea may have an impact on developing student moral sensitivity. Planned ethics content in nursing curricula is necessary to improve moral sensitivity and moral reasoning of students. (shrink)

Malthus did not leave us with a systematic treatment of colonization, but from remarks scattered throughout his publications and correspondence it is possible to assemble a fairly coherent account of his views on the advantages and disadvantages of colonies, and on the reasons why some have failed and others succeeded. Included in these scattered remarks are some comparisons between his own views on colonies and those of Adam Smith. The question of the relationship between Malthus and Adam Smith is a (...) rather complex and subtle one, and cannot be given the full consideration it deserves in one short paper. But, as a general summary, it can be said that Malthus had a high regard for Smith and considered himself a follower and disciple of Smith, by contrast with Ricardo, James Mill, and McCulloch etc., whom he considered as exponents of a ‘New System of Political Economy”. His own Principles of Political Economy was conceived as a collection of ‘tracts or essays”, not as a new systematic treatise replacing the Wealth of Nations, Joseph Gamier in his article ‘Malthus” in the Dictionnaire de l'Economie Politique, 1852, saw that the title of the Principles was in fact a misnomer: ‘Malgré son titre, le livre sur les Principes n'est point un traité complet, mais seulement une collection de dissertations.” In what was probably intended as a criticism of Ricardo's Principles of Political Economy and Taxation, 1817, Malthus stated that the ‘present period … seems to be unpropitious to the publication of a new systematic treatise on political economy”, and, referring to Smith's work, stated that ‘the treatise which we already possess is still of the very highest value”. Nevertheless, despite professing his affiliation, Malthus did not hesitate to criticize Smith when he disagreed with him. He recognized that the Wealth of Nations contained ‘controverted points” and that it would require some ‘additions … which the more advanced stage of the science has rendered necessary”. (shrink)

In this unflinching look at the experience of suffering and one of its greatest manifestations—torture—J.M. Bernstein critiques the repressions of traditional moral theory, showing that our morals are not immutable ideals but fragile constructions that depend on our experience of suffering itself. Morals, Bernstein argues, not only guide our conduct but also express the depth of mutual dependence that we share as vulnerable and injurable individuals. Beginning with the attempts to abolish torture in the eighteenth century, and then sensitively examining (...) what is suffered in torture and related transgressions, such as rape, Bernstein elaborates a powerful new conception of moral injury. Crucially, he shows, moral injury always involves an injury to the status of an individual as a person—it is a violent assault against his or her dignity. Elaborating on this critical element of moral injury, he demonstrates that the mutual recognitions of trust form the invisible substance of our moral lives, that dignity is a fragile social possession, and that the perspective of ourselves as potential victims is an ineliminable feature of everyday moral experience. (shrink)

John and Mary have fully consensual sex, but they do not want to have a child, so they use contraception with the intention of avoiding pregnancy. Unfortunately, although they used the contraception in the way in which it is supposed to be used, Mary has become pregnant. The couple decides to have the baby, whom they name ‘Ernie’. Now we fill in the story a bit. The universe is causally deterministic, and 30 years later Ernie performs some action A and (...) thereby brings about event E. We also stipulate that Ernie meets plausible compatibilist conditions for acting freely . That is, we suppose that there are no uncontroversially freedom- and responsibility-undermining conditions present in the context in which Ernie performs A, and, further, that Ernie meets plausible compatibilist conditions for acting freely. Let us say, for example, that one adopts the theory according to which the freedom-relevant condition on moral responsibility is that the agent exhibits ‘guidance control’ of his action and . On this approach, one acts freely in so far as one acts from one's own, suitably reasons-responsive mechanism. We can then simply stipulate that, in the relevant context, Ernie acts from his own, suitably reasons-responsive mechanism . If one prefers a different set of compatiblist-friendly conditions for acting freely, one can simply stipulate that Ernie meets them; indeed, the plausible compatibilist-friendly conditions seem to be compatible with each other, and thus Ernie could presumably meet all of them in the relevant context. In such a case, and given that the epistemic condition on acting freely and moral responsibility is met, I am inclined to say that Ernie …. (shrink)

Jurgen Habermas' construction of a critical social theory of society grounded in communicative reason is one of the very few real philosophical inventions of recent times that demands and repays extended engagement. In this elaborate and sympathetic study which places Habermas' project in the context of critical theory as a whole past and future, J. M. Bernstein argues that despite its undoubted achievements, it contributes to the very problems of ethical dislocation and meaninglessness it aims to diagnose and remedy. Bernstein (...) further argues that the precise character of the failures of Habermas' program demonstrate the necessity for a return to the first generation critical theory of Adorno. Reading across nearly the whole range of Habermas' corpus, Recovering Ethical Life traces the development of the theory of communicative reason from its inception in Knowledge and Human Interests through its elaboration in The Theory of Communicative Action and into its defense against postmodernism in The Philosophical Discourse of Modernity . In separate chapters Habermas' readings of Freud, Durkheim amd Mead, Adorno and Foucault, Castoriadis and Taylor are critically examined. The focus of Bernstein's analyses, however, is always problem centered and thematic rather than textual psychoanalytic theory as an account of self knowledge, the competing claims of ethical identity and moral reason, the place of judgment in practical reason, and the debate between philosophies of language based communities versus those oriented towards world-disclosure. Critical theory is unique among current philosophies in engaging with the problems of social injustice and nihilism by siding with an abstract moral reason that forfeits the processes of intersubjective recognition it intended to salvage. Even in the fine grain of Habermas' account of performative contradictions and the theory of discourses of application, Bernstein perceives a squandering of the resources of an ethical life in need of transfiguration. (shrink)

Aesthetic alienation may be described as the paradoxical relationship whereby art and truth have come to be divorced from one another while nonetheless remaining entwined. J. M. Bernstein not only finds the separation of art and truth problematic, but also contends that we continue to experience art as sensuous and particular, thus complicating and challenging the cultural self-understanding of modernity. Bernstein focuses on the work of four key philosophers—Kant, Heidegger, Derrida, and Adorno—and provides powerful new interpretations of their views. Bernstein (...) shows how each of the three post-Kantian aesthetics to construct a philosophical language that can criticize and displace the categorical assumption of modernity. He also examines in detail their responses to questions concerning the relations among art, philosophy, and politics in modern societies. (shrink)

Despite optimistic reports about the results of amputation for advanced vascular disease, the patient’s assessment of advantages and disadvantages is seldom acknowledged. A detailed social study of 67 amputees has revealed considerable disparity between the patient’s views and those of the medical staff. About a third of the patients are forced to retire from active work by the amputation; about three-quarters report a serious decline in their social activities; only about half are really independent with prostheses in the long term; (...) a quarter report severe and intractable symptoms related to their amputation stumps; only about a quarter feel that the amputation was definitely beneficial; and only about one in five feel that the medical staff have provided adequate support during their hospital stay. Amputees face physical and financial disability, isolation, and discomfort. Every effort must be made to explain the implications of amputation honestly and realistically and to ensure continuing patient assessment and support. (shrink)

This paper suggests that medically the term a 'human being' should be defined by the presence of an active human brain. The brain is the only unique and irreplaceable organ in the human body, as the orchestrator of all organ systems and the seat of personality. Thus, the presence or absence of brain life truly defines the presence or absence of human life in the medical sense. When viewed in this way, human life may be seen as a continuous spectrum (...) between the onset of brain life in utero (eight weeks gestation), until the occurrence of brain death. At any point human tissue or organ systems may be present, but without the presence of a functional human brain, these do not constitute a 'human being', at least in a medical sense. The implications of this theory for various ethical concerns such as in vitro fertilisation and abortion are discussed. This theory is the most consistent possible for the definition of a human being with no contradictions inherent. However, having a good theory of definition of a 'human being' does not necessarily solve the ethical problems discussed herein. (shrink)

In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent calculus. (...) When applied to a certain natural calculus for L, the resulting models are equivalent to a class of abstract logics (in the sense of Brown and Suszko) which we call distributive. Among other results, we prove that D is exactly the class of the algebraic reducts of the reduced models of L, that there is an embedding of the theories of L into the theories of the equational consequence (in the sense of Blok and Pigozzi) relative to D, and that for any algebra A of type (2,2) there is an isomorphism between the D-congruences of A and the models of L over A. In the second part of this paper (which will be published separately) we will also apply some results to give proofs with a logical flavour for several new or well-known lattice-theoretical properties. (shrink)