vol 7: Notes
2004
2 May
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... to restore theology to the mainstream of science
Notes
[Notebook: Transfinite field theory DB 56]
[Sunday 2 May 2004 - Saturday 8 May 2004]
Sunday 2 May 2004
Monday 3 May 2004
[page 78]
Tuesday 4 May 2004
Chaitin/Turing/Goedel: our minds are not (and can never be) complex enough to control themselves. Chaitin, Turing, Goedel. This holds even for god, ie the universe has on irreducible uncontrolled (probabilistic) element, the root of creativity.
Wednesday 5 May 2004
The deterministic metaphysics of old believes in a closed universe, with a fixed partitioning of human acts into 'bad', 'indifferent' and 'good'. In an open, dynamic universe, the boundaries between these categories may move. In particular if we recognize the mind as beyond control we should open ourselves to all possible states, leaving only a constraint (justice) on the physical realization of these states.
Thursday 6 May 2004
Friday 7 May 2004
Saturday 8 May 2004
Books
| Chaitin, Gregory J, Information, Randomness & Incompleteness: Papers on Algorithmic Information Theory, World Scientific 1987 Jacket: 'Algorithmic information theory is a branch of computational complexity theory concerned with the size of computer programs rather than with their running time. ... The theory combines features of probability theory, information theory, statistical mechanics and thermodynamics, and recursive function or computability theory. ... [A] major application of algorithmic information theory has been the dramatic new light it throws on Goedel's famous incompleteness theorem and on the limitations of the axiomatic method. ...' Amazon back |
| Chaitin, Gregory J, Algorithmic Information Theory, Cambridge UP 1987 Foreword: 'The crucial fact here is that there exist symbolic objects (i.e., texts) which are "algorithmically inexplicable", i.e., cannot be specified by any text shorter than themselves. Since texts of this sort have the properties associated with random sequences of classical probability theory, the theory of describability developed ... in the present work yields a very interesting new view of the notion of randomness.' J T Schwartz Amazon back |
| Chaitin, Gregory J, "Goedel's Theorem and Information" in Information, Randomness & Incompleteness: Papers on Algorithmic Information Theory, World Scientific 1987 Reprinted from the International Journal of Theoretical Physics (1982) 22, 941-954. Amazon back |
| Davis, Martin, Computability and Unsolvability, Dover 1982 Preface: 'This book is an introduction to the theory of computability and non-computability ususally referred to as the theory of recursive functions. The subject is concerned with the existence of purely mechanical procedures for solving problems. ... The existence of absolutely unsolvable problems and the Goedel incompleteness theorem are among the results in the theory of computability that have philosophical significance.' Amazon back |
| Davis, Martin, The Undecidable : Basic Papers on Problems Propositions Unsolvable Problems and Computable Functions, Raven Press 1965 Description: '[Includes] ... the basic papers of Goedel, Church, Turing, and Post in which the class of recursive functions was singled out and seen to be just the class of functions that can be computed by terminating processes. Also presented is the work of Church, Turing, and Post in which problems from the theory of abstract computing machines, from mathematical logic, and finally from algebra are shown to be unsolvable in the sense that there is no terminating process for dealing with them. Finally, the book presents the work of Kleene and of Post initiating the classification theory of unsolvable problems. Already the standard reference work on the subject, The Undecidable is also ideally suited as a text or supplementary text for courses in logic, philosophy, and foundations of mathematics. Amazon back |
| Goedel, Kurt, and Solomon Feferman et al (eds), Kurt Goedel: Collected Works Volume 1 Publications 1929-1936, Oxford UP 1986 Jacket: 'Kurt Goedel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory and the consistency of the axiom of choice and the continuum hypotheses. ... The first volume of a comprehensive edition of Goedel's works, this book makes available for the first time in a single source all his publications from 1929 to 1936, including his dissertation. ...' Amazon back |
| Goedel, Kurt, and B Meltzler (translator), R B Braithwaite (Introduction), On Formally Undecidable Propositions of Principia Mathematica and Related Systems, Dover 1992 A translation of Uber Formal Unentscheidbare Satze der Principia Mathematica und Verwandter Systeme I, Monatshefte fur Mathematik und Physic, 38(1931) 173-198. Jacket: 'In 1931 a young Austrian mathematician published an epoch making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Gödel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will mot give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th century mathematics.' Amazon back |
| Goedel, Kurt, "On formally undecidable propositions of Principia Mathematica and related systems, I" in Solomon Fefferman et al (eds) Kurt Goedel: Collected Works Volume 1 Publications 1929-1936, Oxford UP 1986 Jacket: 'Kurt Goedel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory and the consistency of the axiom of choice and the continuum hypotheses. ... The first volume of a comprehensive edition of Goedel's works, this book makes available for the first time in a single source all his publications from 1929 to 1936, including his dissertation. ...' Amazon back |
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