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)

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].

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.

This is a rich, dense book. Hines provides sensible analyses of the communications networks that unite systematics—the science devoted to understanding and standardizing descriptions of the relationships among living things—and systematists in the 21st century. This work will be useful for introducing graduate students to these aspects of modern systematics and to the sociology of this science.

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)

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

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.

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

Introduction By the late fifth century BCE Panini had composed the Astadhyayi, consisting of nearly 4000 rules giving a precise and fairly complete ...

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)

In this article we give a unifying approach to the theory of fundamental sequences and their related Hardy hierarchies of number-theoretic functions and we show the equivalence of the new approach with the classical one.

Wilfred Sieg. Mechanical Procedures and Mathematical Experience.

It is a puzzle of long standing in Indo-Iranian studies that the cognates of the Vedic devás and their eventual rivals and eternal enemies, the ásuras, have entirely opposite valuations in Old Iranian, where Ahura Mazdāh is the chief of the pantheon and the daēuuas are considered demons. This puzzle is complicated by the fact that in early Vedic the ásuras do not have the demonic role they play in later Vedic and in fact are themselves sometimes identified as devás. (...) Numerous solutions to this problem have been advanced. This article re-examines the evidence in detail and suggests a new explanation, set in the larger Near Eastern cultural context. (shrink)

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)

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)

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 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)

The Ethics Committee at Memorial Sloan Kettering Cancer Center (MSK) developed a Bioethics Ambassador Program (BAP); a yearlong educational program to assist clinical and non-clinical staff develop the skills to identify and address common burgeoning ethical issues that can arise during the provision of care to patients with cancer. The goal was to provide greater awareness of the role and services of Ethics, particularly at the institution’s geographically-diverse outpatient care centers and to better-instill a culture of preventative ethics. This article (...) discusses the design and implementation of the first two years of the program and analyzes its strengths, weaknesses, and impact on MSK. (shrink)

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

Clinical ethics consultations exist to support patients, families and clinicians who are facing ethical or moral challenges related to patient care. They provide a forum for open communication, where all stakeholders are encouraged to express their concerns and articulate their viewpoints. Ethics consultations can be requested by patients, caregivers or members of a patient’s clinical or supportive team. Althoughpatientsand by extension their families (especially in cases of decisional incapacity) are the common denominators in most ethics consultations, these constituents are theleastlikely (...) to request them. At many healthcare organisations in the USA, ethics consultations are overwhelmingly requested by physicians and other clinicians. We believe it is vital that healthcare institutions bridge the knowledge gaps and power imbalances over access to ethics consultation services through augmented policies, procedures and infrastructure. With enhanced education and support, patients and families may use ethics consultation to elevate their voices and prioritise their unique characteristics and preferences in the delivery of their healthcare. Empowering patients and families to request ethics consultation can only strengthen the patient/family–clinician relationship, enhance the shared decision-making model of care and ultimately lead to improved patient-centred care. (shrink)

We establish by elementary proof-theoretic means the conservativeness of two subsystems of analysis over primitive recursive arithmetic. The one subsystem was introduced by Friedman [6], the other is a strengthened version of a theory of Minc [14]; each has been shown to be of considerable interest for both mathematical practice and metamathematical investigations. The foundational significance of such conservation results is clear: they provide a direct finitist justification of the part of mathematical practice formalizable in these subsystems. The results are (...) generalized to relate a hierarchy of subsystems, all contained in the theory of arithmetic properties, to a corresponding hierarchy of fragments of arithmetic. The proof theoretic tools employed there are used to re-establish in a uniform, elementary way relationships between various fragments of arithmetic due to Parsons, Paris and Kirby, and Friedman. (shrink)

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