For 50 years, Star Trek has been an inspiration to its fans around the world, helping them to dream of a better future. This inspiration has entered our culture and helped to shape much of the technology of the early 21st Century. The contributors to this volume are researchers and teachers in a wide variety of disciplines; from Astrophysics to Ethnology, from English and History to Medicine and Video Games, and from American Studies to the study of Collective Computing Systems. (...) What the authors have in common is that some version of Star Trek has inspired them, not only in their dreams of what may be, but in the ways in which they work - and teach others to work - here in the real world. Introduced with references to Star Trek films and television shows, and illustrated with original cartoons, each of the 15 chapters included in this volume provides insights into research and teaching in this range of academic fields. (shrink)

Using the concept of notations for infinitary derivations we give an explanation of Takeuti's reduction steps on finite derivations (used in his consistency proof for Π1 1-CA) in terms of the more perspicious infinitary approach from [BS88].

On June 4, 1925, Hilbert delivered an address to the Westphalian Mathematical Society in Miinster; that was, as a quick calculation will convince you, almost exactly sixty years ago. The address was published in 1926 under the title Über dasUnendlicheand is perhaps Hilbert's most comprehensive presentation of his ideas concerning the finitist justification of classical mathematics and the role his proof theory was to play in it. But what has become of the ambitious program for securing all of mathematics, once (...) and for all? What of proof theory, the very subject Hilbert invented to carry out his program? The Hilbertian ambition reached out too far: in its original form, the program was refuted by Gödel's Incompleteness Theorems. And even allowing more than finitist means in metamathematics, the Hilbertian expectations for proof theory have not been realized: a constructive consistency proof for second-order arithmetic is still out of reach. Nevertheless, remarkable progress has been made. Two separate, but complementary directions of research have led to surprising insights: classical analysis can be formally developed in conservative extensions of elementary number theory; relative consistency proofs can be given by constructive means for impredicative parts of second order arithmetic. The mathematical and metamathematical developments have been accompanied by sustained philosophical reflections on the foundations of mathematics. This indicates briefly the main themes of the contributions to the symposium; in my introductory remarks I want to give a very schematic perspective, that is partly historical and partly systematic. (shrink)

Two young logicians, whose work had a dramatic impact on the direction of logic, exchanged two letters in early 1931. Jacques Herbrand initiated the correspondence on 7 April and Kurt Gödel responded on 25 July, just two days before Herbrand died in a mountaineering accident at La Bérarde (Isère). Herbrand's letter played a significant role in the development of computability theory. Gödel asserted in his 1934 Princeton Lectures and on later occasions that it suggested to him a crucial part of (...) the definition of a general recursive function. Understanding this role in detail is of great interest as the notion is absolutely central. The full text of the letter had not been available until recently, and its content (as reported by Gödel) was not in accord with Herbrand's contemporaneous published work. Together, the letters reflect broader intellectual currents of the time: they are intimately linked to the discussion of the incompleteness theorems and their potential impact on Hilbert's Program. (shrink)

We introduce a system of simply typed lambda terms and show that a rather comprehensive class of recursion equations on streams or non-wellfounded trees can be solved in our system. Moreover certain conditions are presented which guarantee that the defined functionals are primitive recursive. As a major example we give a co-recursive treatment of Mints’ continuous cut-elimination operator.

Abstract:The shutdown due to the COVID-19 pandemic has accelerated the implementation of digital technology to advance many new applications. Digital applications were believed to be indispensable for changes in learning environments and strategies that would enhance the capacity and quality of learning through focused motivation, communicative interaction, and stronger self-determination. This text will discuss prominent arguments for digital learning and digital technologies that might initiate a digital turn. To this end, this paper reflects on the psychological and mental conditions of (...) human learning, evaluates the potential opportunities of digital tools within the context of teaching and learning, and concludes with consequences for music learning in public schools. (shrink)

In carm. 55, Catullus supposes his friend Camerius may be caught in erotic adventure:num te lacteolae tenent puellae?si linguam clauso tenes in ore,fructus proicies amoris omnes:uerbosa gaudet Venus loquella. 20uel, si uis, licet obseres palatum,dum nostri sis particeps amoris.

While the Historische Kulturwissenschaft is introduced as a new way of writing history the question has to be answered what Kultur means or how it should be interpreted. The paper deals primarily with the special German notion of ‘Kultur’. The distinction between ‘intension’ and ‘extension’ is made and contrasted with both the narrow and the wide concept of ‘Kultur’. Writing history as new cultural history is shaped at least by five aspects: space, perspective, language, acting and time which are discussed (...) in this thesis. The intension of ‘Kultur’ in Historische Kulturwissenschaft leads to popularisation. The sense of the popular approach to history emphasizes modality in the conception and writing of history. (shrink)

Zuerst im 2CV, dann im umgebauten VW-Bus: Das Zürcher Fotografenpaar Margrit und Ernst Baumann, 1929 bzw. 1928 geboren, begann in den 1950er-Jahren rund um den Erdball zu reisen. Ihre Fotografien publizierten sie in Zeitschriften und Zeitungen wie Stern, Neue Zürcher Zeitung oder Das gelbe Heft und brachten so die Welt in die Wohnzimmer. Kosmopolitan und neugierig kamen sie zu Motiven mit Seltenheitswert: Farbporträts von Che Guevara gehören ebenso dazu wie Reportagen über die letzten Kopfjäger im ecuadorianischen Urwald. Ein Schwerpunkt dieser (...) reich bebilderten Doppelmonografie ist ihre Reise entlang der “Panamericana” 1957-1959, die Süd- und Nordamerika verbindet. Sie fotografierten Reportagen, Porträts und Landschaftsbilder und drehten den wohl ersten Farbfilm über den legendären Verkehrsweg. Dieser Film und ein Filporträt über die beiden Fotografen sind dem Buch auf DVD beigefügt. Das Buch präsentiert Funde aus ihrem Fotoarchiv - viele Bilder erstmals im Originalausschnitt - sowie Publikationen in Zeitschriften. Der Historiker und Schriftsteller Wilfried Meichtry erzählt vom ereignisreichen Leben des Paars, das sich zeitlebens als journalistische Handwerker verstanden hat. Der Fotohistoriker Markus Schürpf ordnet ihr Werk in die Foto- und Pressegeschichte ein, Nadine Olonetzky verfasst Begleittexte zu den Bildern. Eine Entdeckung in der Schweizer Fotogeschichte. (shrink)

Wilfried Sieg. Calculations by Man and Machine: Mathematical Presentation.

In this rapid commentary, a mini-review is given of the present state-of-knowledge regarding the etiology and epidemiology of the new coronavirus 2019-nCoV and the risks for developing Acute respiratory distress syndrome. The available knowledge on the viral genomics, molecular biology and pathogenicity of viruses of the Coronaviridae family and other Nidovirales, forms a helpful template for understanding the present pandemic outbreak. However, important questions remain unanswered about the underlying mechanism causing the very high case fatality ratios and mechanisms regarding severe (...) reactions like ARDS, fatal cardiac and renal failures, associated with a number of important comorbidity factors. Immunological reactions to lung alveoles in particular in late phase ARDS in SARS-like CoV diseases, so far may not have received enough attention. Finally a shortlist of questions for high priority further research is suggested. (shrink)

David Hilbert was one of the great mathematicians who expounded the centrality of their subject in human thought. In this collection of essays, Wilfried Sieg frames Hilbert's foundational work, from 1890 to 1939, in a comprehensive way and integrates it with modern proof theoretic investigations.

The Carnegie Mellon Proof Tutor project was motivated by pedagogical concerns: we wanted to use a "mechanical" (i.e. computerized) tutor for teaching students..

Wilfred Sieg. Mechanical Procedures and Mathematical Experience.

Hilbert's finitist program was not created at the beginning of the twenties solely to counteract Brouwer's intuitionism, but rather emerged out of broad philosophical reflections on the foundations of mathematics and out of detailed logical work; that is evident from notes of lecture courses that were given by Hilbert and prepared in collaboration with Bernays during the period from 1917 to 1922. These notes reveal a dialectic progression from a critical logicism through a radical constructivism toward finitism; the progression has (...) to be seen against the background of the stunning presentation of mathematical logic in the lectures given during the winter term 1917/18. In this paper, I sketch the connection of Hilbert's considerations to issues in the foundations of mathematics during the second half of the 19th century, describe the work that laid the basis of modern mathematical logic, and analyze the first steps in the new subject of proof theory. A revision of the standard view of Hilbert's and Bernays's contributions to the foundational discussion in our century has long been overdue. It is almost scandalous that their carefully worked out notes have not been used yet to understand more accurately the evolution of modern logic in general and of Hilbert's Program in particular. One conclusion will be obvious: the dogmatic formalist Hilbert is a figment of historical (de)construction! Indeed, the study and analysis of these lectures reveal a depth of mathematical-logical achievement and of philosophical reflection that is remarkable. In the course of my presentation many questions are raised and many more can be explored; thus, I hope this paper will stimulate interest for new historical and systematic work. (shrink)

The incompleteness theorems constitute the mathematical core of Gödel’s philosophical challenge. They are given in their “most satisfactory form”, as Gödel saw it, when the formality of theories to which they apply is characterized via Turing machines. These machines codify human mechanical procedures that can be carried out without appealing to higher cognitive capacities. The question naturally arises, whether the theorems justify the claim that the human mind has mathematical abilities that are not shared by any machine. Turing admits that (...) non-mechanical steps of intuition are needed to transcend particular formal theories. Thus, there is a substantive point in comparing Turing’s views with Gödel’s that is expressed by the assertion, “The human mind infinitely surpasses any finite machine”. The parallelisms and tensions between their views are taken as an inspiration for beginning to explore, computationally, the capacities of the human mathematical mind. (shrink)

The highly ordered neuronal projections from the retina to the tectum mesencephali (optic tectum) in several vertebrate groups have been intensively studied. Several hypotheses so far have been proposed, suggesting mechanisms to explain the topographical and biochemical specificity of the retinotectal projections during ontogeny. In the present paper we compare the main hypotheses of retinotectal development with respect to the nature of specificity envisaged, the activity-dependence versus inheritance criterium and the strategy of argument, in casu the descriptive versus interferential type (...) of argument. Matching of the current developmental hypotheses and mechanisms for elimination or persistance of contralateral, respectively ipsilateral connections, is attempted with respect to the known neuroanatomical connectivity data in the amphibian optic tectum and with respect to the symmetry relations between ipsilateral and contralateral connection patterns described in amphibians and other vertebrate groups. Local mechanisms influencing the survival potential of synaptic contacts between retinal afferents and tectal neurons are probably essential for generating global symmetry patterns. Finally, a global topological approach is discussed with respect to its applicability in the amphibian retinotectal projection system. Basic assumptions of topological modeling appear to rely on anatomical and functional properties of the visual system like left-right symmetry, dichotomy, (absence of) convergence and segregation of fibers and neurons into columnar information units. It is concluded however, that more neuroanatomical, physiological and ultrastructural data are needed to establish a formalized operation model of the amphibian retinotectal system. (shrink)

In Hume’s Of Miracles the person movecl by faith is put in a dilemma between faith and reason. Can one resolve this dilemma as a compleat Humean? The answer is yes. Within the Humean context different approaches can be developed ta overcome Hume’s dilemma. One uses Hume’s theory of utility to defend the belief in the afterlife. The other requires Hume to place faith on a par with beauty and therefore among the passions to which reason must be a slave. (...) Historically there was at least one compleat Humean who was also moved by faith --- Johann Georg Hamann [1730- 1788]. (shrink)

La dissolution assez inattendue des Chambres, le 24 septembre 1971 impliquait une promesse d'élection directe du gouvernement. Cette promesse s'est cependant vite volatilisée. Des élections calmes et traditionnelles ont pris le relais, le gouvernement ayant choisi uniquement le moment le moins défavorable pour les partis de la majorité.La composition des listes s'effectue dans un plus grand calme que de coutume et se déroule davantage par le biais de petits comités ou d'assemblées peu nombreuses. Cependant un grand changement de personnel se (...) réalise par le retrait plus au mains forcé de 65 parlementaires sortants; ce chiffre est, d'après la tradition établie depuis plusieurs élections, très élevé.En dehors de Bruxelles la campagne est calme. Une personnification se manifeste de plus en plus, aussi bien en Wallonie qu'en Flandre.En ce qui concerne la personnification, Bruxelles a une longueur d'avance. Le penchant pour l'«argumentation» symbolique est une autre caractéristique de la campagne. On ne s'oppose pas sur les points litigieux, on ne les expose même pas.Les résultats électoraux en W allonie et à Bruxelles diffèrent fondamentalement de ceux de la Flandre. En Wallonie et à Bruxelles de grands changements se font jour : le P.L.P. est le grand perdant tandis que le F.D.F./R.W. sort des élections en grand vainqueur. En Flandre, par contre, il y a peu de changements dans les chiffres globaux, mais de région à région de petits gains et de petites pertes sant enregistrés.Ceux-ci cependant vont dans des sens divers et même souvent radicalement opposés. L'explication de ces changements reste encore à fournir. Une fois de plus, le nombre des votes blanc et non valables à augmenté. La composition de la Chambre des Représentants et du Sénat issue de ces élections ne permet qu'une bipartite entre C.V.P. -P.S.C. et P.S.B. Les trois partis traditionnels possèdent encore numériquement plus des 2/3 des sièges. Certaines complications dans la réorganisation de l'Etat établie par la révision constitutionnelle, se font déjà entrevoir. Et cela n'est qu'un des problèmes que ces élections ont portés à l'attention de l'opinion publique. (shrink)

We still lack an operational theory for a complete analysis of early socialization processes. Bourdieu has stressed their bodily dimension but has done so at the expense of more symbolic aspects. This theoretical option corresponds to a very general goal of the Bourdieusian theory of practice: analysing sociality without suffering an intellectualist bias. However, symbolic activity and socializing language in particular can be approached as a practical phenomenon (i.e. habitual, informal, unconscious, etc.). From this viewpoint, the sociology of embodiment may (...) have much to learn from cultural psychology, which has focused on early language as it is naturally performed – when people speak to children, and when children speak. The work of cultural psychologists on the role of everyday words and narratives in the making of the self can be extended through a sociological ethnography of language. The features and interests of such an ethnography are discussed in the final section of the article, on the basis of fieldwork conducted in a nursery. This final development illustrates and analyses the concrete appropriation of caregiver injunctions by 2- to 3-year-old children. (shrink)

Thema der vorliegenden Arbeit ist der dialektische Gehalt der wichtigsten bildungstheoretischen Abhandlungen des padagogischen Theoretikers Josef Derbolav. Ergebnis der zum grossten Teil immanent durchgefuhrten Analyse ist der Aufweis, dass Derbolav die dialektische Fassung didaktischer, anthropologischer und handlungstheoretischer Prinzipien aufgrund metaphysischer Denkstrukturen nicht oder nur teilweise gelingt. Inwieweit einige dieser Prinzipien dialektisches Potential enthalten konnten, zeigt der Verfasser anhand der Entwicklung eines eigenen, an der hermeneutischen Philosophie orientierten dialektischen Standpunktes.".

Wilfred Sieg and Dirk Schlimm. Dedekind's Analysis of Number: Systems and Axioms.

The paper discusses the problem of global distributive justice. It proposes to distinguish between principles for the domestic and for the global or intersocietal distribution of wealth. It is argued that there may be a plurality of partly diverging domestic conceptions of distributive justice, not all of which need to be liberal egalitarian conceptions. It is maintained, however, that principles regulating the intersocietal distribution of wealth have to be egalitarian principles. This claim is defended against Rawls's argument in The Law (...) of Peoples that egalitarian principles of distributive justice should not be applied globally. Moreover, it is explained in detail, why Rawls's “duty of assistance to burdened societies” cannot be an appropriate substitute for a global principle of distributive justice. (shrink)

The paper discusses tools for teaching logic used in Logic & Proofs, a web-based introduction to modern logic that has been taken by more than 1,300 students since the fall of 2003. The tools include a wide array of interactive learning environments or cognitive mini-tutors; most important among them is the Carnegie Proof Lab. The Proof Lab is a sophisticated interface for constructing natural deduction proofs and is central, as strategically guided discovery of proofs is the distinctive focus of the (...) course. My discussion makes explicit the broader intellectual context, but also the pursuit of pedagogical goals and their experimental examination. The intellectual context includes i) the theoretical background for the proof search algorithm AProS and its use for a dynamic Proof Tutor, and ii) the programmatic expansion of the course to Computational Logic. 1. (shrink)

The Hygiene Hypothesis has been recognized as an important cornerstone to explain the sudden increase in the prevalence of asthma and allergic diseases in modernized culture. The recent epidemic of allergic diseases is in contrast with the gradual implementation of Homo sapiens sapiens to the present-day forms of civilization. This civilization forms a gradual process with cumulative effects on the human immune system, which co-developed with parasitic and commensal Helminths. The clinical manifestation of this epidemic, however, became only visible in (...) the second half of the twentieth century. In order to explain these clinical effects in terms of the underlying IgE-mediated reactions to innocuous environmental antigens, the low biodiversity of antigens in the domestic environment plays a pivotal role. The skewing of antigen exposure as a cumulative effect of reducing biodiversity in the immediate human environment as well as in changing food habits, provides a sufficient and parsimonious explanation for the rise in allergic diseases in a highly developed and helminth-free modernized culture. Socio-economic tendencies that incline towards a further reduction of environmental biodiversity may provide serious concern for future health. This article explains that the “Hygiene Hypothesis”, the “Old Friends Hypothesis”, and the “Skewed Antigen Exposure Hypothesis” are required to more fully explain the rise of allergy in modern societies. (shrink)

Natural Formalization proposes a concrete way of expanding proof theory from the meta-mathematical investigation of formal theories to an examination of “the concept of the specifically mathematical proof.” Formal proofs play a role for this examination in as much as they reflect the essential structure and systematic construction of mathematical proofs. We emphasize three crucial features of our formal inference mechanism: (1) the underlying logical calculus is built for reasoning with gaps and for providing strategic directions, (2) the mathematical frame (...) is a definitional extension of Zermelo–Fraenkel set theory and has a hierarchically organized structure of concepts and operations, and (3) the construction of formal proofs is deeply connected to the frame through rules for definitions and lemmas. To bring these general ideas to life, we examine, as a case study, proofs of the Cantor–Bernstein Theorem that do not appeal to the principle of choice. A thorough analysis of the multitude of “different” informal proofs seems to reduce them to exactly one. The natural formalization confirms that there is one proof, but that it comes in two variants due to Dedekind and Zermelo, respectively. In this way it enhances the conceptual understanding of the represented informal proofs. The formal, computational work is carried out with the proof search system AProS that serves as a proof assistant and implements the above inference mechanism; it can be fully inspected at (see link below). (shrink)

Wilfried Sieg and John Byrnes. AnModel for Parallel Computation: Gandy's Thesis.

Dedekind’s structuralism is a crucial source for the structuralism of mathematical practice—with its focus on abstract concepts like groups and fields. It plays an equally central role for the structuralism of philosophical analysis—with its focus on particular mathematical objects like natural and real numbers. Tensions between these structuralisms are palpable in Dedekind’s work, but are resolved in his essay Was sind und was sollen die Zahlen? In a radical shift, Dedekind extends his mathematical approach to “the” natural numbers. He creates (...) the abstract concept of a simply infinite system, proves the existence of a “model”, insists on the stepwise derivation of theorems, and defines structure-preserving mappings between different systems that fall under the abstract concept. Crucial parts of these considerations were added, however, only to the penultimate manuscript, for example, the very concept of a simply infinite system. The methodological consequences of this radical shift are elucidated by an analysis of Dedekind’s metamathematics. Our analysis provides a deeper understanding of the essay and, in addition, illuminates its impact on the evolution of the axiomatic method and of “semantics” before Tarski. This understanding allows us to make connections to contemporary issues in the philosophy of mathematics and science. (shrink)

The Federation of Belgian companies is a confederation which groups 36 branch associations covering 30. 000 individual firms. About 85 % are small and medium-sizedfirms occupying less than 50 employees. The VBO/FEB is the most important exponent of the high degree of affiliation on the employers' side. The process of decision making reflects the structure of the federation. The mandate is defined in the board of the VBO/FEB, composed by a representative ofeach branch association. This representative holds his mandate on (...) the basis of the deliberations held in the elected board of his association. The guiding principle is consensus, which is not synonymous of unanimity. When a consistent and representative majority emerges from the debate, the members holding another opinion join that majority in a spirit ofemployers' solidarity. The decision making process aims in this way to combine efficiency and democracy. This is particularly important for the VBO/FEB, as that organisation not only acts as a lobby but also as a social partner able to conclude agreements. In the Belgian system, social partners are consulted by the authorities, because of their representativeness. It must however be clear that they may not interfere with the political decisions which in our democratic system rest with government and parliament. (shrink)

The amalgamation of the municipalities has had profound effects on the municipal character in Belgium : the village has disappeared as a political entity. The «municipality» since 1976 is at least the political and administrative amalgamation of a number of villages.The effect of this amalgamation on the municipal council elections is expressed first of all in the shift in the election form. Uncontested elections disappeared in 1976. The exclusively local election form occurred rarely in 1976, even though this form was (...) still the most common in 1970. However, the mixed election form increased very considerably. Parallel with the amalgamation of the municipalities, the national party pattern penetrated increasingly into the municipal polities : there occurred a gradual «nationalisation» of the municipal polities. The «urban citizens» became more «state citizens», also in municipal matters. Regarding direct municipal executive appointment, the amalgamation led to a less far-reaching and less decisive character of the input, which are characteristics that also tend to follw the national pattern more strongly. The number of municipalities in which no coalition executive needed to be formed clearly declined in 1976.The amalgamation has reduced the uniqueness of the municipal council elections and the decisionmaking capacity of the urban citizens and introduced more national political content. (shrink)

According to an opinion poll which was carried out in the middle of 1975 with a representative sample of Belgian citizens, the problems which most imposed themselves about that time were economie problems, viz.inflation and employment. These two problems were perceived as the most pressing by the more active part of the population as well. However, the solutions that citizens favour for a broad range of problems are not logically consistent, and demonstrate that many citizens have but very little insight (...) in the problems' structure. Yet, those who do feel more concerned, generally favour the same solutions as does the average citizen ; there is no polarization to be noticed.Considerable differences are brought forward by splitting up the results in two main regions : Flanders vs. Wallonia. The ethnic and linguistic difference appears to be also a political difference as far as problem-solving is concerned. The type of solutions citizens favour also shows that the stereotype «conservative Flanders» vs. «progressist Wallonia» is not valid any longer. (shrink)

The available studies and opinion polls are examined for indications of the degree and the content of political knowledge of the Belgian citizens. Political knowledge differs strikingly depending on the components of decision making : political parties, office bolders and their competence, power relations, institutional settings, pressure groups, corporatism and policy measures. Proceeding from personification to content and from more important to less important aspects, the knowledge declines noticeably. A marked portion of the populationshows a lack of even the most (...) elementary knowledge. (shrink)