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

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.

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

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.

This chapter contains section titled: Human Rights in Rawls's The Law of Peoples Human Rights as Universal Claim Rights Human Rights Minimalism and the Problem of Justification Acknowledgments Notes.

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)

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)

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)

Dieser Artikel widerspricht der Deutung der sog. Schriftkritik am Ende des Phaidros, wie sie von den Vertretern der esoterischen Platoninterpretation vorgetragen wird. In esoterischer Sicht handelt es sich um den einzigen Abschnitt in den Dialogen, der ausdrücklich auf eine mündliche Lehre Platons hinweist. Der Hinweis soll in Sokrates' These liegen, im Unterschied zu anderen Autoren übertreffe der Philosoph seine Schriften mit wertvolleren Inhalten, die er nur mündlich lehre.Der Einwand gegen diese Interpretation lautet, daß Platon den inhaltlichen Wertunterschied nicht zwischen Schriften (...) und mündlichen Reden von Philosophen sieht, sondern zwischen kunstlosen Reden und Schriften konventioneller Autoren einerseits und kunstgerechten, d.h. dialektischen Reden und Schriften von Philosophen andererseits. Philosophische Reden unterscheiden sich von philosophischen Schriften in formaler Hinsicht: nur Reden belehren, Schriften sind Erinnerungshilfe. (shrink)

Wilfred Sieg and John Byrnes. K-Graph Machines: Generalizing Turing's Machines and Arguments.

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 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)

This commentary focuses on Hommel et al.'s inferences on action planning. It discusses the relevance of anticipated extrinsic movement effects for action control, the problems of a feature-based representation of actions, and the necessity of the acquisition of conditional movement-effect associations.

The covariant and relativistic generalization of the Helmholtz integral vorticity theorems and Thomson's circulation theorem are derived.

Wilfred Sieg and Rosella Lupiccini. Computing Machines: Entry for the Second Edition of the Encyclopedia of Philsophy.

— via appropriate substitutions — syntactically identical. The method can be applied directly to quantifierfree formulae and, in this paper, will b e extended in a natural and strai ghlforward way to quantified formulae.

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)

Contemporary philosophy is said to focus on particular issues, rather than on comprehensive syntheses. The following contribution intends to join this trend by offering some reflections on the “animal rights” debate, which is to be situated within the wider context of environmental philosophy. While classical Western concepts of man were anthropocentric, recent cultural developments have triggered a rediscovery of Nature, especially of nonhuman animals, while focusing on their affiliations with us, humans. Appropriate relations with those animals require a respectful attitude (...) on the human side, as if those animals had full moral and legal rights. But is this not an illusion? Can we talk about real “rights” for animals, or should we just remain aware of them having their own feelings and take care not to hurt them, unless for a “serious” cause? While taking note of the wide variety of animal species and habitats , the answer to this question may have its bearings on one’s personal choices regarding food, clothing, entertainment, etc. (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)