RésuméNous introduisons la notion de structure algébrique dynamique, inspirée de l'évaluation dynamique et de la théorie des modèles. Nous montrons comment cette notion constructive permet une relecture de la théorie d'Artin-Schreier, avec la modification capitale que le résultat final est alors établi de manière constructive. Nous pensons que ce que nous avons réalisé ici sur un cas d'école peut être généralisé à des parties significatives de l'algèbre classique, et est donc une contribution à la réalisation du programme de Hilbert pour (...) l'algèbre classique.We introduce the notion of “Dynamic Algebraic Structure” inspired by Dynamic Evaluation and Model Theory. We show that this constructive notion allows a rereading of the Artin-Schreier-Robinson solution for the 17th Hilbert Problem. So, once we know how to reread the proofs, this kind of abstract theory contains an algorithm which computes the concrete result . Our method gives a constructive semantic for certain parts of abstract classical mathematics.The idea is the following: replace the classical algebraic structures “constructed” by Choice and Principle of Third Excluded Middle , by DAS and dynamic evaluations of these DAS. Then TEM is replaced by construction of branching in the trees of dynamic evaluation of the DAS. If Choice is used in the form of Godel completeness theorem, it is not really necessary to use it for obtaining concrete results: in DAS, Choice is simply replaced by … nothing!. This is because the classical proof is by contradiction: “if there were not a sum of squares then some formal theory would admit a pathological model”. The constructive reasoning is more direct: since the pathological theory proves 0 = 1 we know how to construct the sum of squares … and classical models have disappeared in the proof. They are replaced by dynamic evaluations of DAS. We think that we have given, for an academic example, a new method, realizing a kind of Hilbert Program for significant parts of classical algebra. (shrink)

A possible relevant meaning of Hilbert’s program is the following one: “give a constructive semantic for classical mathematics”. More precisely, give a systematic interpretation of classical abstract proofs about abstract objects, as constructive proofs about constructive versions of these objects.If this program is fulfilled we are able “at the end of the tale” to extract constructive proofs of concrete results from classical abstract proofs of these results.Dynamical algebraic structures or geometric theories seem to be a good tool for doing this (...) job. In this setting, classical abstract objects are interpreted through incomplete concrete specifications of these objects.The structure of axioms in geometric theories gives rise in a natural way to distributive lattices and pointfree topological spaces. Abstract objects correspond to classical points of these pointfree spaces.We shall insist on the Zariski spectrum of distributive lattices and commutative rings and give a constructive interpretation of the Krull dimension.We underline the fact that many abstract objects in classical mathematics can be viewed as points of spectral spaces corresponding to distributive lattices whose definition is concrete and natural.Two important facts are to be stressed.First, abstract proofs about points of these pointfree spaces can very often be reread as constructive proofs about constructible subsets of these spaces.Second, function spaces on these pointfree spaces are often explicitly used in elegant abstract theories. The structure of these function spaces is fully constructive: indeed by the compactness theorem, “all is finite”. The constructive rereading of the abstract proofs is in this setting is nothing but the simple constatation that abstract proofs use correctly axioms.RésuméUne manière pertinente de revisiter le Programme de Hilbert serait la suivante: « donner une sémantique constructive pour les mathématiques classiques ». Plus précisément donner une interprétation systématique des preuves classiques abstraites au sujet des objets abstraits, en terme de preuves constructives au sujet de contreparties constructives de ces objets abstraits.Si ce programme est rempli, nous sommes capables « à la fin de l’histoire » d’extraire des preuves constructives de résultats concrets à partir des preuves classiques abstraites de ces résultats.Les structures algébriques dynamiques, ou ce qui revient à peu près au même les théories géométriques, semblent être un bon outil pour réaliser ce travail. Dans cette optique, les objets abstraits des mathématiques classiques sont remplacés par des spécifications incomplètes mais concrètes de ces mêmes objets.La structure des théories géométriques donne naissance de manière naturelle à des treillis distributifs et à des espaces topologiques sans points. Les objets abstraits utilisés par les mathématiques classiques correspondent aux points classiques de ces espaces sans points.Dans cet article, nous illustrerons ce phénomène principalement avec le spectre de Zariski des treillis distributifs et celui des anneaux commutatifs, en indiquant notamment un équivalent constructif de la notion de dimension de Krull.Nous insistons sur le caractère extrêmement général de l’interpétation des objets abstraits idéaux des mathématiques classiques comme des points d’espaces spectraux associés à des treillis distributifs qui sont définis de façon naturelle et concrète.Souligons deux faits d’expérience importants.Tout d’abord, les preuves abstraites au sujet des points de ces espaces sans points peuvent en général être relues comme des preuves concernant les parties constructibles de ces espaces.Enfin, les espaces de fonctions continues sur ces espaces sans points sont souvent utilisés dans d’élégantes théories abstraites. Ces espaces de fonctions sont bien définis constructivement. Cela tient au « théorème de compacité » qui nous dit que dans le cadre en question « tout est fini ». La relecture constructive des preuves abstraites n’est alors rien d’autre que la constatation que les axiomes géométriques sont utilisés de manière correcte. (shrink)

We study some representations of real numbers. We compare these representations, on the one hand from the viewpoint of recursive functionals, and of complexity on the other hand.The impossibility of obtaining some functions as recursive functionals is, in general, easy. This impossibility may often be explicited in terms of complexity: - existence of a sequence of low complexity whose image is not a recursive sequence, - existence of objects of low complexity but whose images have arbitrarily high time- complexity .Moreover, (...) some representations of real numbers that are equivalent from the viewpoint of recursive functionals, are very distinct from the viewpoint of complexity.We make a particular study of representations via continued fractions . We precise exactly what part of information available in the x's dfc is equivalent to the information available in its Dedekinds cut. We show that the sum of two reals whose dfcs are polynomial-time computable may be a real whose dfc has time complexity arbitrarily high.This work confirms that the unique representation of real numbers suitable for the ordinary calculus is via explicit Cauchy sequences of rationals.RésuméNous étudions différentes manières de présenter les nombres réels. Nous comparons ces présentations du point de vue des fonctionnelles récursives d'une part, et de celui des classes de complexité d'autre part.L'impossibilité d'obtenir certaines fonctions sous forme de fonctionnelles récursives est en général facile à établir. Cette impossiblité peut souvent être explicitée en termes de complexité: - il existe une suite de faible complexité dont l'image est une suite non récursive, - il existe des objets de faible complexité mais dont les images sont des objets de complexité arbitrairement grande .En outre, certaines présentations des réels équivalentes du point de vue des fonctionnelles récursives se distinguent nettement du point de vue de la complexité.Nous faisons une étude particulière concernant les développements en fraction continue . Nous précisions exactement quelle est la partie de l'information disponible dans le dfc d'un réel x qui équivaut à l'information disponible dans sa coupure de Dedekind. Nous montrons également que la somme de deux réels dont le dfc est calculable en temps polynomial peut être un réel dont le dfc est de complexité arbitrairement grande.Ce travail confirme que seule une présentation des réels via des suites de rationnels explicitement de Cauchy est adaptée aux calculs avec les réels. (shrink)

A series of studies investigated the capacity of children between the ages of 7 and 12 to give free and informed consent to participation in psychological research. Children were reasonably accurate in describing the purpose of studies, but many did not understand the possible benefits or especially the possible risks of participating. In several studies children's consent was not affected by the knowledge that their parents had given their permission or by the parents saying that they would not be upset (...) if the children refused. In contrast, other studies found that children were much more likely to stop their participation if the experimenter said explicitly that she would not be upset if they stopped. We suggest that experimenters should pay more attention to describing the possible risks and benefits of participation in research, and that they should also make it clearer to children that they are free to stop once they have begun. (shrink)

Animal welfare involves societal and human values, ethical concerns and moral considerations since it incorporates the belief of what is right or what is wrong in animal treatment and care. This paper aims to ascertain whether the different dimensions of individual attitudes toward animal welfare in food choices may be characterized by general human values, as identified by Schwartz. For this purpose, an EU-wide survey was carried out, covering almost 2500 nationally representative individuals from five European countries. Compared with the (...) previous literature this study shows a twofold novelty: it develops a general framework to link individual enduring beliefs and attitudes toward animal welfare attributes in food choices; the framework is analyzed within a broad-based cross-country study. Our empirical results prove that human values related to self-transcendence are strongly associated to overall animal welfare attitudes and especially to those explicitly related to food choices, while values related to the spheres of self-enhancement and conservatism are significantly associated to less sensitive attitudes to animal welfare. Moreover, our results appear to indicate that a determinant of animal welfarism in food choices is potentially associated to individual concerns regarding food safety issues. (shrink)

We give a general method for producing various effective Null and Positivstellensätze, and getting new Positivstellensätze in algebraically closed valued fields and ordered groups. These various effective Nullstellensätze produce algebraic identities certifying that some geometric conditions cannot be simultaneously satisfied. We produce also constructive versions of abstract classical results of algebra based on Zorn's lemma in several cases where such constructive version did not exist. For example, the fact that a real field can be totally ordered, or the fact that (...) a field can be embedded in an algebraically closed field. Our results are based on the concepts we develop of dynamical proofs and simultaneous collapse. (shrink)

We give an elementary theory of Henselian local rings and construct the Henselisation of a local ring. All our theorems have an algorithmic content.

We study in a constructive manner some problems of topology related to the set Irr of irrational reals. The constructive approach requires a strong notion of an irrational number; constructively, a real number is irrational if it is clearly different from any rational number. We show that the set Irr is one-to-one with the set Dfc of infinite developments in continued fraction . We define two extensions of Irr, one, called Dfc1, is the set of dfc of rationals and irrationals (...) preserving for each rational one dfc, the other, called Dfc2, is the set of dfc of rationals and irrationals preserving for each rational its two dfc. We introduce six natural distances over Irr wich we denote by dfc0, dfc1, dfc2, d, dmir and dcut. We show that only the four distances dfco, dfc1, d and dmir among the six make Irr a complete metric space. The last distances define in Irr the same topology in a constructive sens. We study further the set Dfc1 in which we show that the irrationals constitute a closed subset. Finally, we make a particular study of the completion Dfc2 of Dfc for the two equivalent metrics dfc2 and dcut. (shrink)

We compare two Picard groups in dimension 1. Our proofs are constructive and the results generalize a theorem of J. Sands [11].

cognitive, neuropsychological, and neurophysiological studies of both memory and consciousness. Before proceeding further, some discussion of terminology is necessary. It comes as no surprise to state that "consciousness" is one of the ...

We give a polynomial time controlled version of a theorem of M. Hall: every real number can be written as the sum of two irrational numbers whose developments into a continued fraction contain only 1, 2, 3 or 4.

George Herbert Mead, one of America’s most important and influential philosophers, a founder of pragmatism, social psychology, and symbolic interactionism, was also a keen observer of American culture and early modernism. In the period from the 1870s to 1895, Henry Northrup Castle maintained a correspondence with family members and with Mead—his best friend at Oberlin College and brother-in-law—that reveals many of the intellectual, economic, and cultural forces that shaped American thought in that complex era. Close friends of John Dewey, Jane (...) Addams, and other leading Chicago Progressives, the author of these often intimate letters comments frankly on pivotal events affecting higher education, developments at Oberlin College, Hawaii, progressivism, and the general angst that many young intellectuals were experiencing in early modern America. The letters, drawn from the Mead-Castle collection at the University of Chicago, were collected and edited by Mead after the tragic death of Henry Castle in a shipping accident in the North Sea. Working with his wife Helen Castle, he privately published fifty copies of the letters to record an important relationship and as an intellectual history of two progressive thinkers at the end of the nineteenth century. American historians, such as Robert Crunden and Gary Cook, have noted the importance of the letters to historians of the late nineteenth century. The letters are made available here using the basic Mead text of 1902. Additional insights into the connection between Mead, John Dewey, Henry and Harriet Castle, and Hawaii’s progressive kindergarten system are provided by the foundation’s executive director Alfred L. Castle. Marvin Krislov, president of Oberlin College, has added additional comments on the importance of the letters to understanding the intellectual relationship that flourished at Oberlin College. Published with the support of the Samuel N. and Mary Castle Foundation. (shrink)

Here I discuss the basic elements, major stages, and completion of progressive evolution. The cosmic world of self-realization is based on extensive self-development within a closed contour: temporal counter-transitions of spatial counter-elements (energy bonds and media and, basically, substance structures) form of local worlds within it through evolution of informational structures. The organic world of reproduction develops through the open informational path: the initial substance, through energy exchange and metabolism, reproduces similar substance; the latter interacts with the environment and, subsequently, (...) reproduces its like, and so on. The animal world of self-regulation builds up a closed informational contour in the environment through the informational input and command output. The human world of self-cognition forms the intensive type of development within the internal closed informational contour of cognition. Counter-transitions of ideal images and signs relate to their real prototypes. In the course of cognition, abstractive thinking develops and brings man to the possibility of reflection of the initial world in its integrity (thus, elevates man to the infinite, by Hegel). (shrink)

While denying that God has moral obligations, William Alston defends divine moral goodness based on God’s performance of supererogatory acts. The present article argues that an agent without obligations cannot perform supererogatory acts. Hence, divine moral goodness cannot be established on that basis. Defenses of divine moral obligation by Eleonore Stump and Nicholas Wolterstorff are also questioned. Against Stump, it is argued (among other things) that the temptations of Jesus do not establish the existence of a tendency to sin in (...) a divine being. Hence, Stump’s Christological objection to Alston’s denial of divine moral obligation fails. Some counterexamples to that denial offered by Wolterstorff also fail. It is concluded that claims of divine moral goodness remain problematic. (shrink)

Young children's early understanding of emotion was investigated by examining their use of emotion terms such as happy, sad, mud, and cry. Five children's emotion language was examined longitudinally from the age of 2 to 5 years, and as a comparison their reference to pains via such terms as burn, sting, and hurt was also examined. In Phase 1 we confirmed and extended prior findings demonstrating that by 2 years of age terms for the basic emotions of happiness, sadness, anger, (...) and fear are commonly used by children as are terms for such related states as crying and hurting. At this early age children produce such terms to refer to self and to others, and to past and future as well as to present states. Over the years from 2 to 5 children's emotion vocabulary expands, their discussion of hypothetical emotions gets underway, and the complexity of their emotion utterances increases. In Phase 2 our analyses go beyond children's production of emotion terms to analyses of their conception of emotion. We focus especially on when children use emotion terms to refer to subjective experiential states of persons. From their earliest uses of these terms in our data children. (shrink)

Alvin Plantinga’s solution to J. L. Mackie’s logical problem of evil invokes possible-worlds metaphysics. There are reasons for thinking that the solution is, at least, problematic. Difficulties emerge in the attempts to answer four related questions. Can God’s necessary existence, understood in terms of possible-world metaphysics, make God’s actual existence impossible to explain? Can an omniscient being with knowledge of the contents of every possible world prove ignorant of the consequences of his creative acts? Can an immoral action performed by (...) an agent suffering from “transworld depravity” also be free in the libertarian sense? Does the possible-worlds interpretation of libertarian freedom generate a vicious infinite regress? Special focus is on the possibility, advanced by Plantinga, that there are possible worlds that even an omnipotent being cannot create. Plantinga’s views are contrasted with those of Thomas Aquinas. (shrink)

While denying that God has moral obligations, William Alston defends divine moral goodness based on God’s performance of supererogatory acts. The present article argues that an agent without obligations cannot perform supererogatory acts. Hence, divine moral goodness cannot be established on that basis. Defenses of divine moral obligation by Eleonore Stump and Nicholas Wolterstorff are also questioned. Against Stump, it is argued (among other things) that the temptations of Jesus do not establish the existence of a tendency to sin in (...) a divine being. Hence, Stump’s Christological objection to Alston’s denial of divine moral obligation fails. Some counterexamples to that denial offered by Wolterstorff also fail. It is concluded that claims of divine moral goodness remain problematic. (shrink)

In a recent paper, Prugovečki offered a theory of simultaneous measurements based upon an axiomatic description of the measurement act which excludes certain illustrations of simultaneous measurement previously discussed by the present writers. In this article, the fundamental conceptions of state preparation, state determination, and measurement which underlie our research are compared to Prugovečki's interpretations of the analogous constructs in his theory of measurement.

"L'oeuvre d'art est une tentative vers l'unique, elle s'affirme comme un tout, comme un absolu et, en même temps, elle appartient à un système de relations complexes [...]. Elle est matière et elle est esprit, elle est forme et elle est contenu [...]. Elle est créatrice de l'homme, créatrice du monde et elle installe dans l'histoire un ordre qui ne se réduit à rien d'autre." Un Eloge de la main complète ce texte. "La main arrache le toucher à sa passivité (...) réceptive, elle l'organise pour l'expérience et pour l'action [...]. Elle se mesure avec la matière qu'elle métamorphose, avec la forme qu'elle transfigure. Educatrice de l'homme, elle le multiplie dans l'espace et dans le temps." [Source : 4e de couv.]. (shrink)

Pursuing a suggestion made by Christopher Stead in his book Divine Substance and employing distinctions made by Gottlob Frege in his article “Concept and Object,” it becomes possible to answer a common charge against Trinitarian Theism: its alleged inconsistency in claiming that, while there is only one God, there are also three “persons,” each rightly named “God.” The argument advanced, while supporting the logical coherence of traditional Trinitarian Theism, also defends the orthodoxy of the controversial “Social Trinitarianism” associated with Richard (...) of Saint Victor. (shrink)

Alvin Plantinga’s solution to J. L. Mackie’s logical problem of evil invokes possible-worlds metaphysics. There are reasons for thinking that the solution is, at least, problematic. Difficulties emerge in the attempts to answer four related questions. (1) Can God’s necessary existence, understood in terms of possible-world metaphysics, make God’s actual existence impossible to explain? (2) Can an omniscient being with knowledge of the contents of every possible world (a being endowed with “middle knowledge”) prove ignorant of the consequences of his (...) creative acts? (3) Can an immoral action performed by an agent suffering from “transworld depravity” also be free in the libertarian sense? (4) Does the possible-worlds interpretation of libertarian freedom generate a vicious infinite regress? Special focus is on the possibility, advanced by Plantinga, that there are possible worlds that even an omnipotent being cannot create. Plantinga’s views are contrasted with those of Thomas Aquinas. (shrink)

In a magisterial book-length study, Professor E. Christian Brugger concludes that the canons of the Council of Trent, given the beliefs and intentions of its participants, provide “a dogmatic definition of the absolute indissolubility of marriage as a truth of divine revelation” (original italics). The present concern is whether Brugger’s arguments support this conclusion. Also subject to scrutiny are the relevance, plausibility, and consistency of the conciliar thinking on which his arguments are premised. It will be argued that Brugger’s conclusion (...) is unwarranted, leaving the question of divorce and remarriage an open one. (shrink)

Defenders of theistic morality sometimes insist that God's will can impose moral obligation only if God has a right to command. The right is compared to that which parents have over their children and which is thought to derive from a filial debt of gratitude. This essay examines arguments for divine authority based on gratitude which employ the parental analogy. It is argued that neither parental nor divine authority is based on gratitude. An alternative derivation of parental authority is suggested (...) but shown to be unavailable to those who would compare divine to parental rights. (shrink)