This is the Spanish translation, by María Gabriela Fulugonio, of Arend Heyting’s classical text “Die logizistische Grundlegung der Mathematik”, which was originally presented at the Königsberg’s Symposium on Philosophy of Mathematics in 1930, and finally published in Erkenntnis in 1931.

La littérature témoigne d’une tendance croissante à soutenir l’intuitionisme par la phénoménologie. Le disciple de Brouwer Arend Heyting est considéré comme un précurseur de cette tendance, parce qu’il usait d’une terminologie phénoménologique en vue de définir la négation intuitioniste, en élaborant la première logique intuitioniste. Dans cet article, l’auteur tente d’explorer — en référence aux matériaux inédits conservés aux Archives Heyting — ce qui, dans la pensée de Heyting, est compatible avec la phénoménologie. Dans la conclusion, (...) l’auteur suggère que Heyting et Husserl, pour autant qu’ils pensent tous deux que la conscience doit être le véritable commencement de la connaissance, partagent une même attitude antipsychologiste coexistant avec une tentative de dépassement du solipsisme. Toutefois, le concept phénoménologique de degré d’évidence ne peut être appliqué à l’échelle de l’évidence de Heyting (incluant les petits nombres naturels, les grands nombres naturels, les suites infinies, le quantificateur universel), d’un côté parce qu’on ne voit pas clairement si la seconde est partagée par tous les intuitionistes, et de l’autre parce que le premier présuppose une évidence révisable qui ne cadre pas avec le point de vue de Heyting. En outre, les conceptions de la nature de la mathématique et de la logique et de leurs relations mutuelles défendues par Husserl et Heyting sont essentiellement différentes. D’un point de vue intuitioniste, la mathématique est le domaine de l’évidence, alors que la logique transcrit ses régularités. D’un point de vue phénoménologique, la mathématique demeure en dehors du domaine de l’évidence. La logique apophantique coïncide avec la mathématique (sans que l’une absorbe l’autre), mais la logique transcendantale se situe à un niveau plus élevé. (shrink)

At the beginning of the twentieth century, among the foundational schools of mathematics appeared ‘intuitionism’ by Dutchman L. E. J. Brouwer, who based arithmetic on the intuition of time and all mental constructions that could be made out of it. His pupil Arend Heyting was the first populariser of intuitionism, and he repeatedly emphasised that no philosophy was required to practise intuitionism so that such mathematics could be shared by anyone. Still, stimulated by invitations to humanistic conferences, he (...) wrote a series of notes, preserved in the State Archives, Haarlem, about solipsism. In them, he operated a series of theoretical reflections consisting of the stripping away of the patterns that are part of our consciousness and their subsequent progressive re-introduction, in order to understand the formation of our Self as distinct from the natural world and other humans. In 1996, following a stroke, neuroscientist Jill Bolte Taylor experienced the deprivation of certain abilities in her brain and their successive regaining. In her experience there are remarkable similarities with what Heyting had hypothesised about the formation of the self. The purpose of this article is to highlight them and point out how Heyting's theoretical construct was found to be embodied in the brain. (shrink)

Brouwer’s intuitionism was a far-reaching attempt to reform the foundations of mathematics. While the mathematical community was reluctant to accept Brouwer’s work, its response to later-developed brands of intuitionism, such as those presented by Hermann Weyl and Arend Heyting, was different. The paper accounts for this difference by analyzing the intuitionistic versions of Brouwer, Weyl, and Heyting in light of a two-tiered model of the body and image of mathematical knowledge. Such a perspective provides a richer account (...) of each story and points to a possible connection between the community’s reaction and the changes each mathematician had proposed. (shrink)

This paper presents the content of the unpublished notes that the Dutch mathematician Arend Heyting wrote in different periods of his life on solipsism and that are preserved in Heyting's archive at the University of Amsterdam. Most of the notes are quoted here and translated into English. Their study shows the originality of Heyting's reflections on a subject that was typical of his master, L. E. J. Brouwer, the father of intuitionism.

As public research organisations are increasingly driven by their national and regional governments to engage in knowledge transfer, they have started to support the creation of companies. These research based spin-off companies (RBSOs) often keep contacts with the research institutes they originate from. In this paper we present the results of a study of four research institutes within two universities and two non-university public research organisations (PROs) in the Netherlands. We show that research organisations have distinct motivations to support the (...) creation of spin-off companies. In terms of resources RBSOs contribute, mostly in a modest way, to research activities by providing information, equipment and monetary resources. In particular, RBSOs are helpful for researchers competing for research grants that demand participation of industry. Furthermore, RBSOs may be seen as a proactive response by Dutch public research organisations to demands of economic relevance from their institutional environment. RBSOs enhance the prestige of their parent organisations and create legitimacy for public funds invested in PROs. At the same time, most RBSOs do not have a significant impact on the direction of the research conducted at the PROs. (shrink)

This book provides an interdisciplinary examination of international law by addressing four critical questions: How are international legal rules distinctive? How does an investigator determine the existence of a rule of international law? Does international law really matter in international politics? and What effect could the changing nature of international relations have on international law? Using Constructivist theory, Arend argues that international law can alter the identity of states, and, consequently, have a profound impact on state behavior.

The purpose of this paper is the clarification of some methodological problems concerning Rawls’ theory of justice. The first part seeks to make more precise Tugendhat’s distinction between 1st-person-theory and 3rd-person-theory. Rawls’ theory fulfills all criteria for 1st-person-theories. In the second part Rawl’s coherence model for the justification of norms („reflective equilibrium“) is critically analyzed and opposed to the hypothetical decision which individuals are to make in the original position (contract model). It is shown that the conception of reflective equilibrium (...) is in various aspects mistaken. In conclusion a problem is indicated which Rawls has not satisfactorily resolved: The veil of ignorance is supposed to guarantee that the decision for the basic principles of social justice is unanimous. Nevertheless it would appear that the individuals in the original position either have too little empirical knowledge in order to make a rational decision, or they have too much knowledge in order to come to an unanimous decision. The veil of ignorance is either too fine or not fine enough. (shrink)

We report to which extent elementary particles and the nucleons can be described by an Ansatz that is alternative to the established standard model, and can still yield predicted results that reproduce the observed ones, without using the formalism of quantum mechanics. The different Ansatz is motivated by the attempt to explain known properties of elementary particles as a consequence of an inner structure, in contrast to the approach of the standard model, where the properties are ascribed to point-like particles. (...) Based on the assumption of the existence of photons, the possibility of the creation of fermion and anti-fermion in an interaction of two photons of equal energy is shown. The properties of these created elementary material particles are found to agree with the ones observed. Also the possibility of the creation of a neutron by interaction of two photons of equal energy is shown. In this case, the newly formed neutron rests in the center of the collision system as a combined system of the localized two photons. The created neutron is shown to have the known properties of the neutron, and in addition, to have a definite shape of definite size. The proton is described as the particle formed by decay of the neutron, also owning the observed properties, and in addition a definite shape. For all particles described by the Ansatz, their properties are consequences of an inner structure. The merits of the alternative description as compared to the standard model and the application of quantum mechanics are discussed. (shrink)

Several theoretical publications on the Dirac equation published during the last decades have shown that, an interpretation is possible, which ascribes the origin of electron spin and magnetic moment to an autonomous circular motion of the point-like charged particle around a fixed centre. In more recent publications an extension of the original so called “Zitterbewegung Interpretation” of quantum mechanics was suggested, in which the spin results from an average of instantaneous spin vectors over a Zitterbewegung period. We argue that, the (...) corresponding autonomous motion of the electron should, if it is real, determine non-relativistic spin measurements. Such a direct connection with the established formal quantum mechanical description of spin measurements, into which spin is introduced as a “non-classical” quantity has, to our knowledge, not been reported. In the present work we show that, under certain “model assumptions” concerning the proposed autonomous motion, results of spin measurements, including measurements of angular correlations in singlet systems, can indeed be correctly described using classical probabilities. The success of the model is evidence for the “reality” of the assumed autonomous motion. The resulting model violates the Bell—inequalities to the same extent as quantum mechanics. (shrink)

In this paper the thesis is argued that there is no need for a special legal logic to deal with the defeasibility of legal arguments. An important argument for this thesis is that legal judgements ask for a complete justification and that such a complete justification requires a deductively valid argument.

In this contribution I argue that Brouwer’s legal positivism suffers from an internal tension that is not easily solved. This tension stems from the combination of two strands in Brouwer’s thought. The first is that Brouwer wants to stick to the legal positivist view that the law is fixed by convention. The second is that there can be exceptions to the application of legal rules, based on legal principles. The combination of these two strands is, I argue, problematic, because the (...) conventional basis for legal principles will usually be lacking in hard cases. One may then argue, as Brouwer does, that where conventions are lacking there is no law and the judge is not bound by the law. But then exceptions to rules are also allowed where there are no conventional principles to justify these exceptions. This contradicts Brouwer’s starting point that exceptions to the application of rules are possible on the basis of legal principles. (shrink)

This article is a comment on Carel Smith’s paper. Smith rightly argues that the study of law has a hermeneutic character. But his interpretation of legal hermeneutics includes the thesis that in hard cases there is no right or true legal decision. This seems to have negative implications for the scholarly character of the study of law: in hard cases any solution goes. This paper argues, against Smith, that the study of law defends right answers for hard cases. It is (...) also normative in another sense: legal answers, in easy cases as well as in hard cases, always presuppose a normative interpretation of the legal sources. This contributes to the differences of opinion under lawyers. But it is no obstacle to the scholarly character of the study of law, as long as a rational debate about these legal answers and the underlying values and principles is possible. Smith’s rejection of the right answer thesis, however, prevents the possibility of such a rational debate. (shrink)

L’ouvrage d’A. Wenger est la version remaniée de sa thèse de doctorat complétée par certains développements parus dans des revues spécialisées, Clio. Histoire, Femmes et Sociétés, Dix-huitième Siècle… La reprise de travaux antérieurs a entraîné parfois quelques redondances – sur l’onanisme ou la lectrice, par exemple – qu’une lecture plus attentive aurait pu éviter. Cette restriction est mineure au regard de l’intérêt de cette étude dont « l’objectif est de faire bouger les objets d’analyse t...

L’auteur a pris le risque de traiter d’une question qui, aujourd’hui encore, fait polémique : celle du rapport qu’entretient le philosophe et romancier Jean-Jacques Rousseau avec la différence sexuelle. L’un des mérites de l’étude de Laure Challandes est d’argumenter, avec une grande précision, sur la nécessaire frontière qui existe entre les textes théoriques, Lettre à d’Alembert sur les spectacles, Du contrat social, Émile ou de l’éducation, entre autres, et les textes fictifs, parmi lesque...

This report explores the relationship between philosophy and medicine in the Netherlands. In Section 1 we outline the ups and downs of medico-philosophical research in our country: pre-war flourishing, post-war decline, and modern renaissance. In Section 2 we review recent Dutch literature in the philosophy of medicine. The topics dealt with include methodology of medical science, alternative medicine, the basic concepts of medicine, anthropological medicine, medicalization, medicine and culture, and health care ethics.

This article presents the results of a qualitative study on the ethical aspects of inclusion practice for radiotherapy patients taking part in clinical research. The study focused on the standards and values of this process. Patients and physicians were interviewed about their views and experiences. Analysis of these interviews showed that candidate research participants need better protection from unwanted factors that could influence their choice about participation. Researchers need proper education about regulation, codes and directives in the field of research (...) ethics, and they should be aware of the underlying ethical concepts of these regulations. A sound institutional ethics policy is necessary in order to guide medical staff in decisions about the inclusion of patients in trials. (shrink)