It is unfortunate for the philosophical community generally, and for those philosophers who pursue various versions of idealism in particular, that a logician of Kurt Goedel’s genius published very little of non-mathematical philosophical interest. Amongst his unpublished papers at Princeton there are, however, several versions of a paper he wrote on the relevance of contemporary relativity to the philosophy of Kant. The purpose of the present paper is to give a partial exposition and defence of Goedel’s view that contemporary (...) relativity supports a neo-Kantian idealistic position with regard to time. (shrink)

Hawking, in his book, A Brief History of Time, concludes with a conditional remark: If we find a complete theory to explain the physical world, then we will come to understand God’s mind. With Goedel in mind, we can raise questions about the completeness of our scientific understanding and the nature of our understanding with regard to God’s mind. We need to ask about the higher order of our understanding when we move to knowing God’s mind. We go onto develop (...) these problems with Nietzsche’s thoughts on the death of God, and the emergence of super human intelligences. Then, we come to Buddha, a logical genius, to see how the Buddhistic enlightenment exemplifies the super human intelligence, as well as the higher order understanding in our knowledge of God’s mind. (shrink)

"The Emperor's New Mind" by Roger Penrose has received a great deal of both praise and criticism. This review discusses philosophical aspects of the book that form an attack on the "strong" AI thesis. Eight different versions of this thesis are distinguished, and sources of ambiguity diagnosed, including different requirements for relationships between program and behaviour. Excessively strong versions attacked by Penrose (and Searle) are not worth defending or attacking, whereas weaker versions remain problematic. Penrose (like Searle) regards the notion (...) of an algorithm as central to AI, whereas it is argued here that for the purpose of explaining mental capabilities the architecture of an intelligent system is more important than the concept of an algorithm, using the premise that what makes something intelligent is not what it does but how it does it. What needs to be explained is also unclear: Penrose thinks we all know what consciousness is and claims that the ability to judge Go "del's formula to be true depends on it. He also suggests that quantum phenomena underly consciousness. This is rebutted by arguing that our existing concept of "consciousness" is too vague and muddled to be of use in science. This and related concepts will gradually be replaced by a more powerful theory-based taxonomy of types of mental states and processes. The central argument offered by Penrose against the strong AI thesis depends on a tempting but unjustified interpretation of Goedel's incompleteness theorem. Some critics are shown to have missed the point of his argument. A stronger criticism is mounted, and the relevance of mathematical Platonism analysed. Architectural requirements for intelligence are discussed and differences between serial and parallel implementations analysed. (shrink)

In “Minds, Machines, and Gödel”, J. R. Lucas claims that Goedel's incompleteness theorem constitutes a proof “that Mechanism is false, that is, that minds cannot be explained as machines”. He claims further that “if the proof of the falsity of mechanism is valid, it is of the greatest consequence for the whole of philosophy”. It seems to me that both of these claims are exaggerated. It is true that no minds can be explained as machines. But it is not (...) true that Goedel's theorem proves this. At most, Goedel's theorem proves that not all minds can be explained as machines. Since this is so, Goedel's theorem cannot be expected to throw much light on why minds are different from machines. Lucas overestimates the importance of Goedel's theorem for the topic of mechanism, I believe, because he presumes falsely that being unable to follow any but mechanical procedures in mathematics makes something a machine. (shrink)

My contribution to the symposium on Goedel’s philosophy of mathematics at the spring 2006 Association for Symbolic Logic meeting in Montreal. Provisional version: references remain to be added. To appear in an ASL volume of proceedings of the Goedel sessions at that meeting.

The volume contains twenty essays devoted to the philosophy of mathematics and the history of logic. They have been divided into four parts: general philosophical problems of mathematics, Hilbert's program vs. the incompleteness phenomenon, philosophy of mathematics in Poland, mathematical logic in Poland. Among considered problems are: epistemology of mathematics, the meaning of the axiomatic method, existence of mathematical objects, distinction between proof and truth, undefinability of truth, Goedel's theorems and computer science, philosophy of mathematics in Polish (...) mathematical and logical schools, beginnings of mathematical logic in Poland, contribution of Polish logicians to recursion theory. (shrink)

Contents: Acknowledgements. Conventions. Preface. Biographical sketch. 1 Introduction. 2 The Contributions. 3 Early work in analysis. 4 The Theory of Science . 5. Later mathematical studies. A On Kantian Intuitions. B The Bolzano-Cauchy Theorem.

Beginning with an introduction to the scriptural background of the Śaiva religion, this volume presents a translation accompanied by a re-edition of the Sanskrit text with the help of two manuscripts not consulted before, and a running commentary. A fragment of the Śrīkaṇṭī is transcribed in an appendix.

Russkiĭ kosmizm v poiskakh absoli︠u︡ta : paralleli i peresechenii︠a︡ v muzykalʹnom, poėticheskom i izobrazitelʹnom tborchestve 1910-1920-kh godov -- Liki Moderna -- Putʹ k modernu : Georgiĭ Lʹvovich Katuar -- Stilʹ modern v tvorchestve Frederika Diliusa : kont︠s︡ert dli︠a︡ fortepiano s orkestrom do minor -- Stilʹ modern i tvorchestvo Bely Bartoka (na primere opery "Zamok gert︠s︡oga Sini︠a︡i︠a︡ Boroda") -- Frit︠s︡ Kreĭsler i stilʹ modern -- Klod Debi︠u︡ssi i Moris Ravelʹ : muzyka dli︠a︡ arfy -- Klod Debi︠u︡ssi : dvenadt︠s︡atʹ ėti︠u︡dov dli︠a︡ fortepiano (...) : ot ėkzersisa do installi︠a︡t︠s︡ii -- O dikhotomii "muzhskogo" i "zhenskogo" v Pi︠a︡toĭ sonate A.N. Skri︠a︡bina (na primere motivnoĭ metriki) -- Pod znakom moderna : A.N. Skri︠a︡bin i S.S. Prokofʹev v 1913 godu -- Avangard i modern v retrospektive -- O proi︠a︡vlenii︠a︡kh "modernizma" v ispolnitelʹskom iskusstve : F. Buzoni, M. I︠U︡dina, G. Gulʹd -- Sudʹba providt︠s︡a : fortepiannai︠a︡ muzyka Ėrika Sati v sovremennom akademicheskom muzykalʹnom mire -- Otgoloski ėpokhi modern : o nekotorykh smyslovykh osobennosti︠a︡kh sovremennykh fortepiannykh sochineniĭ (Ė. Denisov, S. Slonimskiĭ, G. Zaĭt︠s︡ev) -- Zapadnye pianisty - ispolniteli russkogo avangarda pervoĭ volny : Sh. Shleĭermakher, Kh. Khenk, M.-A. Amlen -- Muzyka k filʹmu "Kabinet doktora Kaligari" : mezhdu tvorcheskoĭ rekonstrukt︠s︡ieĭ i istoricheskoĭ imitat︠s︡ieĭ -- Podvodi︠a︡ itogi -- "Pozdniĭ modernizm" v muzyke kont︠s︡a XX - nachala XXI veka : nekotorye nabli︠u︡denii︠a︡ -- Po sledam konferent︠s︡ii "Ot moderna k futurizmu" (virtualʹnai︠a︡ beseda za kruglym stolom). (shrink)

Much of what once was praised as scientific and technological progress has shown itself to be in conflict with the world, the world man has inherited, that we hold in trust.

Much of what once was praised as scientific and technological progress has shown itself to be in conflict with the world, the world man has inherited, that we hold in trust.

The Star of Redemption, * which presents Franz Rosenzweig's system of philosophy, begins with the sentence "from death, (vom Tode) , from the fear of death, originates all cognition of the All" and concludes with the words "into life. " This beginning and this conclusion of the book signify more than the first and last words of philosophical books usually do. Taken together - "from death into life" - they comprise the entire meaning of Rosenzweig's philosophy. The leitmotif (...) of this philosophy is the life and death of the human being and not the I of philosophical idealism, where man ultimately signifies "for ethics" no more than" . . . a point to which it (ethics) relates its problems, as for science also he (man) is only a particular case of its general laws. "l Rosenzweig deals with the individual's actual existence, that which is termi nated by death; he speaks of the individual's hic et nunc, of his actions and decisions in the realm of concrete reality. This philosophy is not an exposition of theoretical principles. It is not concerned with man in general in abstract time, but rather with the individual human being, designated by a proper name, living in his particular time. ** Human existence in its finiteness and temporalness forms the focus in which Rosenzweig's motif can be gathered together. (shrink)

Commentary on Śārīrakamīmāṃsābhāṣya of Śaṅkarācārya, work on Vedanta philosophy.

This is the first English translation of the seminar Martin Heidegger gave during the Winter of 1934-35, which dealt with Hegel's Philosophy of Right. This remarkable text is the only one in which Heidegger interprets Hegel's masterpiece in the tradition of Continental political philosophy while offering a glimpse into Heidegger's own political thought following his engagement with Nazism. It also confronts the ideas of Carl Schmitt, allowing readers to reconstruct the relation between politics and ontology. The book is (...) enriched by a collection of interpretations of the seminar, written by select European and North American political thinkers and philosophers. Their essays aim to make the seminar accessible to students of political theory and philosophy, as well as to open new directions for debating the relation between the two disciplines. A unique contribution, this volume makes available key lectures by Heidegger that will interest a wide readership of students and scholars. (shrink)