Apologies. The purpose of the following talk is to give an overview of the present state of aims, methods and results in Pure Proof Theory. Shortage of time forces me to concentrate on my very personal views. This entails that I will emphasize the work which I know best, i.e., work that has been done in the triangle Stanford, Munich and Münster. I am of course well aware that there are as important results coming from outside this triangle and I (...) apologize for not displaying these results as well.Moreover the audience should be aware that in some points I have to oversimplify matters. Those who complain about that are invited to consult the original papers.1.1. General. Proof theory startedwithHilbert's Programme which aimed at a finitistic consistency proof for mathematics.By Gödel's Theorems, however, we know that we can neither formalize all mathematics nor even prove the consistency of formalized fragments by finitistic means. Inspite of this fact I want to give some reasons why I consider proof theory in the style of Gentzen's work still as an important and exciting field of Mathematical Logic. I will not go into applications of Gentzen's cut-elimination technique to computer science problems—this may be considered as applied proof theory—but want to concentrate on metamathematical problems and results. In this sense I am talking about Pure Proof Theory.Mathematicians are interested in structures. There is only one way to find the theorems of a structure. Start with an axiom system for the structure and deduce the theorems logically. These axiom systems are the objects of proof-theoretical research. Studying axiom systems there is a series of more or less obvious questions. (shrink)

Exploiting the fact that -definable non-monotone inductive definitions have the same closure ordinal as arbitrary arithmetically definable monotone inductive definitions, we show that the proof theoretic ordinal of an axiomatization of -definable non-monotone inductive definitions coincides with the proof theoretic ordinal of the theory of arithmetically definable monotone inductive definitions.

Apologies. The purpose of the following talk is to give an overview of the present state of aims, methods and results in Pure Proof Theory. Shortage of time forces me to concentrate on my very personal views. This entails that I will emphasize the work which I know best, i.e., work that has been done in the triangle Stanford, Munich and Münster. I am of course well aware that there are as important results coming from outside this triangle and I (...) apologize for not displaying these results as well.Moreover the audience should be aware that in some points I have to oversimplify matters. Those who complain about that are invited to consult the original papers.1.1. General. Proof theory startedwithHilbert's Programme which aimed at a finitistic consistency proof for mathematics.By Gödel's Theorems, however, we know that we can neither formalize all mathematics nor even prove the consistency of formalized fragments by finitistic means. Inspite of this fact I want to give some reasons why I consider proof theory in the style of Gentzen's work still as an important and exciting field of Mathematical Logic. I will not go into applications of Gentzen's cut-elimination technique to computer science problems—this may be considered as applied proof theory—but want to concentrate on metamathematical problems and results. In this sense I am talking about Pure Proof Theory.Mathematicians are interested in structures. There is only one way to find the theorems of a structure. Start with an axiom system for the structure and deduce the theorems logically. These axiom systems are the objects of proof-theoretical research. Studying axiom systems there is a series of more or less obvious questions. (shrink)

We prove that the boundedness theorem of generalized recursion theory can be derived from the ω-completeness theorem for number theory. This yields a proof of the boundedness theorem which does not refer to the analytical hierarchy theorem.

Apologies. The purpose of the following talk is to give an overview of the present state of aims, methods and results in Pure Proof Theory. Shortage of time forces me to concentrate on my very personal views. This entails that I will emphasize the work which I know best, i.e., work that has been done in the triangle Stanford, Munich and Münster. I am of course well aware that there are as important results coming from outside this triangle and I (...) apologize for not displaying these results as well.Moreover the audience should be aware that in some points I have to oversimplify matters. Those who complain about that are invited to consult the original papers.1.1. General. Proof theory startedwithHilbert's Programme which aimed at a finitistic consistency proof for mathematics.By Gödel's Theorems, however, we know that we can neither formalize all mathematics nor even prove the consistency of formalized fragments by finitistic means. Inspite of this fact I want to give some reasons why I consider proof theory in the style of Gentzen's work still as an important and exciting field of Mathematical Logic. I will not go into applications of Gentzen's cut-elimination technique to computer science problems—this may be considered as applied proof theory—but want to concentrate on metamathematical problems and results. In this sense I am talking about Pure Proof Theory.Mathematicians are interested in structures. There is only one way to find the theorems of a structure. Start with an axiom system for the structure and deduce the theorems logically. These axiom systems are the objects of proof-theoretical research. Studying axiom systems there is a series of more or less obvious questions. (shrink)

Wolfram Hogrebe examines the anthropological relevance of logomantic [divinational] precursors of philosophy and poetry along with the idea of the implicit citizen and the nature of implicit musical structures.".

A traditional view maintains that thought, while expressed in language, is non-linguistic in nature and occurs in non-linguistic beings as well. I assess this view against current theories of the evolutionary design of human grammar. I argue that even if some forms of human thought are shared with non-human animals, a residue remains that characterizes a unique way in which human thought is organized as a system. I explore the hypothesis that the cause of this difference is a grammatical way (...) of structuring semantic information, and I present evidence that the organization of grammar precisely reflects the organization of a specific mode of thought apparently distinctive of humans. Since there appears to be no known non-grammatical structuring principle for the relevant mode of thought, I suggest that grammar is that principle, with no independent ?Language of Thought? needed. (shrink)

Über das wesen der künstlerischen phantasie.--Über drei hymnen des Rig-Veda.--Über die bildwerke am Zeustempel von Olympia.--Mythenbildung um Alexander den Grossen.--Die anthroposophischen grundlagen des christentums.--Goethe und die goldene legende.--Die madonna der expressionisten.--Der mensch August Strindberg im spiegel seiner werke und das problem seines lebens als zeitproblem.--Das mysterium der Tristansage.

Life's Solution builds a persuasive case for the predictability of evolutionary outcomes. The case rests on a remarkable compilation of examples of convergent evolution, in which two or more lineages have independently evolved similar structures and functions. The examples range from the aerodynamics of hovering moths and hummingbirds to the use of silk by spiders and some insects to capture prey. Going against the grain of Darwinian orthodoxy, this book is a must read for anyone grappling with the meaning of (...) evolution and our place in the Universe. Simon Conway Morris is the Ad Hominen Professor in the Earth Science Department at the University of Cambridge and a Fellow of St. John's College and the Royal Society. His research focuses on the study of constraints on evolution, and the historical processes that lead to the emergence of complexity, especially with respect to the construction of the major animal body parts in the Cambrian explosion. Previous books include The Crucible of Creation (Getty Center for Education in the Arts, 1999) and co-author of Solnhofen (Cambridge, 1990). Hb ISBN (2003) 0-521-82704-3. (shrink)

A soaring intellectual narrative starring the radical, brilliant, and provocative philosophers Simone de Beauvoir, Hannah Arendt, Simone Weil, and Ayn Rand by the critically acclaimed author of Time of the Magicians, Wolfram Eilenberger The period from 1933 to 1943 was one of the darkest and most chaotic in human history, as the Second World War unfolded with unthinkable cruelty. It was also a crucial decade in the dramatic, intersecting lives of some of history's greatest philosophers. In particular, four women (...) whose parallel ideas would come to dominate the twentieth century-at once in necessary dialogue and striking contrast with one another. Simone de Beauvoir, already in a deep emotional and intellectual partnership with Jean-Paul Sartre, was laying the foundations for nothing less than the future of feminism. Born Alissa Rosenbaum in St. Petersburg before emigrating to the US in 1926, Ayn Rand was honing one of the most politically influential voices of the 20th century. Her novels The Fountainhead and Atlas Shrugged would reach the hearts and minds millions of Americans in the decades to come, becoming canonical libertarian texts, which continue to echo today among Silicon Valley's tech elite. Hannah Arendt was developing some of today's most important leftwing ideas, culminating with the publication of The Origins of Totalitarianism and her arrival as a peerless intellectual celebrity. Perhaps the greatest thinker of all was a classmate of de Beauvoir: Simone Weil, who turned away from fame to devote herself entirely to refugee aid and the resistance movement during the war. Ultimately, in 1943, she would starve to death in England, a martyr and true saint in the eyes of many. Few authors can synthesize gripping storytelling with sophisticated philosophy like Wolfram Eilenberger. The Visionaries tells the story of four singular philosophers-indomitable women who were refugees and resistance fighters-each putting forward a vision of a truly free and open society at a time of authoritarianism and war. (shrink)

In this, his latest book, Wolfram Hogrebe continues to unfold his project of an informal epistemology with an analysis of ties ("ligatures") to be found below the level of theoretically discussed norms, laws, and institutional regulations and nevertheless indispensable for a humane coexistence. Risks associated with such often hidden constellations of knowledge are also discussed. Master thinkers such as Schelling, Hegel, Heidegger, but also more marginal figures such as Felix Hausdorff alias Paul Mongré or artists such as Beuys are (...) discussed. In his inimitable style of concise yet succinct sketches, Hogrebe thus causes thinking to confront the often subtle nuances of being in a state of wonderment"--Publisher's website. (shrink)

Es gehort zu den Aufgaben unserer Gegenwart, das Format einer neuen Metaphysik zu entwickeln. In diesem Buch wird der Versuch unternommen, aus exemplarischen philosophischen Fragestellungen Klarungsstrategien zu entfalten, die allesamt anigmatische Grenzzonen erkunden, aus denen niemand herauszufinden vermag. Abwesenheiten in kreativen Prozessen, die Geburt der Intentionalitat, der switch vom ungeheuren Objekt zum ungeheuren Subjekt, die Entbindung von Kreativitat aus unscharfen semantischen Verhaltnissen, die Bedeutung von Bildung in Prozessen eines konzilianten Geltenlassens, Formen als Augen der Dinge und schliealich Kosmologie als Poetik: (...) Die Rettung einer unvermeidlichen Ratselhaftigkeit ist das Sujet einer neuen Metaphysik. (shrink)

Über die Methoden der Lehre und die Lehrstätten der Philosophen der spätklassischen Zeit kursieren abenteuerliche Vorstellungen. Trotz einseitiger Quellenlage lassen sich die Wege von Sokrates in Athen, Platons Reisen nach Syrakus und Aristoteles Aufenthalte in Makedonien aber erstaunlich genau nachvollziehen. Philosophen nutzten für ihre Lehre bestimmte schattige Rundwege, um sich bei gleichmässiger Bewegung mit einem oder zwei Schülern auf einen dialogos zu konzentrieren. Schon für die Historiker der sp̈aten Antike wie Diogenes Laertius war dieses Verhalten zum Rätsel geworden. Das Phänomen (...) lässt sich dennoch erklären und sogar topographisch festlegen. Das Hauptaugenmerk gilt den Schulen der Philosophen. In vielen Fällen war damit der Peripatos gemeint, ein Bau-Typus, den Platon in der Akademie kreiert hatte. Wie er aussah, welche Räumlichkeiten vertreten waren und wie lange solche Lehrstätten Bestand hatten, ist Thema dieses Buches"--Publisher's website. (shrink)