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Set Theory and Physics
 FOUNDATIONS OF PHYSICS, VOL. 25, NO. 11
, 1995
"... Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of soli ..."
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Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of solid threedimensional objects, (iii) in the theory of effective computability (ChurchTurhrg thesis) related to the possible "solution of supertasks," and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for" physical applications are discussed: Cantorian "naive" (i.e., nonaxiomatic) set theory, contructivism, and operationalism, hr the arrthor's ophrion, an attitude of "suspended attention" (a term borrowed from psychoanalysis) seems most promising for progress. Physical and set theoretical entities must be operationalized wherever possible. At the same thne, physicists shouM be open to "bizarre" or "mindboggling" new formalisms, which treed not be operationalizable or testable at the thne of their " creation, but which may successfully lead to novel fields of phenomenology and technology.
Turing Oracle Machines, Online Computing, and Three Displacements in Computability Theory
, 2009
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Incomputability after Alan Turing
"... The year 2012 marks the 100th anniversary of the birth of Alan Turing. The following two articles were inspired by the work ..."
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The year 2012 marks the 100th anniversary of the birth of Alan Turing. The following two articles were inspired by the work
The Incomputable Alan Turing
 In the Proceedings of
"... The last century saw dramatic challenges to the Laplacian predictability which had underpinned scientific research for around 300 years. Basic to this was Alan Turing’s 1936 discovery (along with Alonzo Church) of the existence of unsolvable problems. This paper focuses on incomputability as a power ..."
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The last century saw dramatic challenges to the Laplacian predictability which had underpinned scientific research for around 300 years. Basic to this was Alan Turing’s 1936 discovery (along with Alonzo Church) of the existence of unsolvable problems. This paper focuses on incomputability as a powerful theme in Turing’s work and personal life, and examines its role in his evolving concept of machine intelligence. It also traces some of the ways in which important new developments are anticipated by Turing’s ideas in logic. This paper is based on the talk given on 5th June 2004 at the conference at Manchester University marking the 50th anniversary of Alan Turing’s death. It is published by the British Computer Society on
GÖDELIAN PLATONISM
, 2009
"... The members of the Comittee appointed to examine the thesis of TEPPEI HAYASHI ..."
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The members of the Comittee appointed to examine the thesis of TEPPEI HAYASHI
My fourty years on his shoulders
, 2007
"... Gödel's legacy is still very much in evidence. We will not attempt to properly discuss the full impact of his work and all of the ongoing important research programs that it suggests. This would require a book length manuscript. Indeed, there are several books discussing the Gödel legacy from m ..."
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Gödel's legacy is still very much in evidence. We will not attempt to properly discuss the full impact of his work and all of the ongoing important research programs that it suggests. This would require a book length manuscript. Indeed, there are several books discussing the Gödel legacy from many points of view, including, for example, [Wa87], [Wa96], [Da05], and the historically comprehensive five volume set [Go,8603]. In sections 27 we briefly discuss some research projects that are suggested by some of his most famous contributions. In sections 811 we discuss some highlights of a main recurrent theme in our own research, which amounts to an expansion of the Gödel incompleteness phenomenon in a critical direction.
Gödel's incompleteness theorems and artificial life
, 1997
"... In this paper I discuss whether Gödel's incompleteness theorems have any implications for studies in Artificial Life (AL). Since Gödel's incompleteness theorems have been used to argue against certain mechanistic theories of the mind, it seems natural to attempt to apply the theorems to ce ..."
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In this paper I discuss whether Gödel's incompleteness theorems have any implications for studies in Artificial Life (AL). Since Gödel's incompleteness theorems have been used to argue against certain mechanistic theories of the mind, it seems natural to attempt to apply the theorems to certain strong mechanistic arguments postulated by some AL theorists. We find that an argument using the incompleteness theorems can not be constructed that will block the hard AL claim, specifically in the field of robotics. However, we will see that the beginnings of an argument casting doubt on our ability to create living systems entirely resident in a computer environment might be suggested by looking at the incompleteness theorems from the point of view of Gödel's belief in mathematical realism.