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)

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.

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)

Wilfred Sieg. Relative Consistency and Accesible Domains.

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

In many countries attention for fostering research integrity started with a misconduct case that got a lot of media exposure. But there is an emerging consensus that questionable research practices are more harmful due to their high prevalence. QRPs have in common that they can help to make study results more exciting, more positive and more statistically significant. That makes them tempting to engage in. Research institutions have the duty to empower their research staff to steer away from QRPs and (...) to explain how they realize that in a Research Integrity Promotion Plan. Avoiding perverse incentives in assessing researchers for career advancement is an important element in that plan. Research institutions, funding agencies and journals should make their research integrity policies as evidence-based as possible. The dilemmas and distractions researchers face are real and universal. We owe it to society to collaborate and to do our utmost best to prevent QRPs and to foster research integrity. (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..

Wilfried Sieg and John Byrnes. Gödel, Turing, and K-Graph Machines.

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

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the fifteenth publication in the Lecture Notes in Logic series, collects papers presented at the symposium 'Reflections on the Foundations of Mathematics' held in celebration of Solomon Feferman's 70th birthday (The 'Feferfest') at Stanford University, California in 1988. (...) Feferman has shaped the field of foundational research for nearly half a century. These papers reflect his broad interests as well as his approach to foundational research, which emphasizes the solution of mathematical and philosophical problems. There are four sections, covering proof theoretic analysis, logic and computation, applicative and self-applicative theories, and philosophy of modern mathematical and logic thought. (shrink)

Architecture has often served a variety of purposes in addition to that of mere functionality. Different categories of meanings can be distinguished. In this essay some aspects of political meaning in medieval architecture will be discussed. The architecture of churches commissioned for instance by bishops, archbishops, provosts or other high-ranking clerical patrons was often used to express views about the status and position of both patron and institution. Rivalling patrons could copy those parts of each other's churches that were considered (...) essential and characteristic. Buildings were thus often symbols, not only of the Church and of Heavenly Jerusalem, but also of an idealized history and an aspired status and position. (shrink)

The Belgian polyarchy has developed into a «particracy» in which the political parties have a preponderant impact on the political decisionmaking.As in every polyarchy, the political parties fulfill a set of vital functions in the Belgian system. But that does not explain its «particratie» particularity. The particracy arises as a consequence of four factors. The parties are fixed by the «zuilen» into an «internal-imperialistic» role. The power of the parties increased considerably, an increase of which the politization of the instruments (...) for, and the agencies of, policy is one of the most important, together with the capability of making and unmaking issues. The impact and power of the opponents of the parties in the decision-making process have been diminished to a considerable extent. This weakening involves the king, the parliament, theadministration, the electorate, and, ultimately, the cabinet because of the growing impact of the parties on policy design and policy output as well as on the appointment of ministers. Finally, the choice of the consociational pattern of politics of accomodation by the elite indicates the instrumental function of particracy in Belgian politics. (shrink)

W. Neumaier, Antike Rhythmustheorien, historische Form und aktuelle Substanz, Grüner, Amsterdam, 1989, 141 p. - Études grecques et latines.

Wilfred Sieg and Mark Ravaglia. David Hilbert and Paul Bernays, Grundlagen der Mathematik I and II: A Landmark.

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)

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

Academic journal publications may be retracted following institutional investigations that confirm allegations of research misconduct. Retraction notices can provide insight into the role institutional investigations play in the decision to retract a publication. Through a content analysis of 7,318 retraction notices published between 1927 and 2019 and indexed by the Web of Science, we found that most retraction notices (73.7%) provided no information about institutional investigations that may have led to retractions. A minority of the retraction notices (26.3%) mentioned an (...) institutional investigation either by journal authorities (12.1%), research performing organizations (10.3%), joint institutions (1.9%), research integrity and ethics governing bodies (1.0%), third-party institutions (0.5%), unspecified institutions (0.4%), or research funding organizations (0.1%). Comparing retraction notices issued before and after the introduction of retraction guidelines by the Committee on Publication Ethics (COPE) in 2009 revealed that those published after the guidelines’ publication were more likely to report investigations by journal authorities. Comparing retraction notices from different disciplines revealed that those from social sciences and the humanities were more likely to disclose investigations by research performing organizations than those from biomedical and natural sciences. Based on these findings, we suggest that the COPE retraction guidelines in the future make it mandatory to disclose in retraction notices institutional investigations leading to retractions. (shrink)

There is a tension between the idea of popular sovereignty and our understanding that basic constitutional rights and liberties have a normative authority which is independent from the results of democratic decision‐making procedures. On the one hand there is the claim that the content of political justice, at least as far as the basic liberties are concerned, is to be fixed solely by substantive moral and political argument, while on the other there is the claim that it is the people (...) who determine the specific scheme of basic liberties that they live under. The apparent tension between the two claims can be resolved by introducing, firstly, a distinction between the concept of justice and the concept of legitimacy and, secondly, between proto‐rights and constitutional rights. Unlike constitutional rights, proto‐rights are moral, not legal, rights, and they are less specific than constitutional rights: one set of proto‐rights allows for various schemes of legal constitutional rights. Proto‐rights are part of the principles of justice and can be established only by substantive argument while constitutional rights have to be established by the procedures of democratic legitimization, and, therefore, they are a result of the exercise of popular sovereignty. The correlated distinctions between justice and legitimacy, and between proto‐rights and constitutional rights, allow us to specify the scope of the two claims and, hence, to affirm both simultaneously. The philosophical and legal relevance of the distinctions made is elucidated by a brief discussion of the constitutional rights of freedom of speech in the US and Germany. (shrink)

Widespread scholarly agreement has it that Descartes' theory of judgment favors a compatibilist interpretation. This essay explains and rebuts the standard arguments made on behalf of compatibilist readings, while explaining and defending a libertarian interpretation. Along with relevant Fourth Meditation doctrines and texts, my analysis encompasses a much discussed 1645 letter discussing his account. Although some scholars view the letter as departing from the account of theMeditations, I argue that the two works present a consistent view – allowing us to (...) take at face value that the letter purports to elaborate Descartes' intended meaning in the associated Fourth Meditation passage. (shrink)

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 move towards having more teaching of business ethics comes in part from a tendency to view managers negatively, drawing on anti-management theories that are presently popular in business schools. This can lead to a misdiagnosis of the causes of contemporary business problems. Teaching business ethics can, however, be ineffectual and counter-productive. Education in ethical philosophy can lead managers to be indecisive, sceptical or to rationalize poor conduct. The ethics of academics become salient and lapses in them undercut their claims (...) to authority. The philosophical viewpoint that stresses free choice runs contrary to the social science mission to reveal the causes that determine human behaviour and provide solutions to problems. Pro-management theory offers a more positive appreciation of managers, with its three components of structural functionalism, strategic functionalism and stewardship. (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)

it, the idea of "substance-in-general". It is clear he accords a central role to collections of simple..

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)