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35
Gödel's Theorem and Information
, 1982
"... Gödel's theorem may be demonstrated using arguments having an informationtheoretic flavor. In such an approach it is possible to argue that if a theorem contains more information than a given set of axioms, then it is impossible for the theorem to be derived from the axioms. In contrast with the tr ..."
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Cited by 52 (6 self)
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Gödel's theorem may be demonstrated using arguments having an informationtheoretic flavor. In such an approach it is possible to argue that if a theorem contains more information than a given set of axioms, then it is impossible for the theorem to be derived from the axioms. In contrast with the traditional proof based on the paradox of the liar, this new viewpoint suggests that the incompleteness phenomenon discovered by Gödel is natural and widespread rather than pathological and unusual.
Quantum Mechanics as a Principle Theory
, 2000
"... I show how quantum mechanics, like the theory of relativity, can be understood as a 'principle theory' in Einstein's sense, and I use this notion to explore the approach to the problem of interpretation developed in my book ..."
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Cited by 5 (0 self)
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I show how quantum mechanics, like the theory of relativity, can be understood as a 'principle theory' in Einstein's sense, and I use this notion to explore the approach to the problem of interpretation developed in my book
Reconstruction of Quantum Theory
"... What belongs to quantum theory is no more than what is needed for its derivation. Keeping to this maxim, we record a paradigmatic shift in the foundations of quantum mechanics, where the focus has recently moved from interpreting to reconstructing quantum theory. Several historic and contemporary re ..."
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Cited by 4 (0 self)
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What belongs to quantum theory is no more than what is needed for its derivation. Keeping to this maxim, we record a paradigmatic shift in the foundations of quantum mechanics, where the focus has recently moved from interpreting to reconstructing quantum theory. Several historic and contemporary reconstructions are analyzed, including the work of Hardy, Rovelli, and Clifton, Bub and Halvorson. We conclude by discussing the importance of a novel concept of intentionally incomplete reconstruction.
When champions meet: Rethinking the Bohr–Einstein debate
, 2006
"... Einstein’s philosophy of physics (as clarified by Fine and Howard) was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed “physical thought ” and “physical laws ” to be impossible. Bohr’s philosophy (as elucidated by Hooker, Scheibe, Folse, Howa ..."
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Cited by 4 (2 self)
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Einstein’s philosophy of physics (as clarified by Fine and Howard) was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed “physical thought ” and “physical laws ” to be impossible. Bohr’s philosophy (as elucidated by Hooker, Scheibe, Folse, Howard, and others), on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio’s Theorem in algebraic quantum theory that within a suitable class of physical theories Einstein’s doctrine is mathematically equivalent to Bohr’s, so that quantum mechanics accommodates Einstein’s Trennungsprinzip if and only if it is interpreted à la Bohr through classical physics. Unfortunately, the protagonists themselves failed to discuss their differences in a constructive way, since in its early phase their debate was blurred by an undue emphasis on the uncertainty relations, whereas in its second stage it was dominated by Einstein’s flawed attempts to establish the “incompleteness ” of quantum mechanics. These two aspects of their debate may still be understood and appreciated, however, as reflecting a much deeper and insurmountable disagreement between Bohr and Einstein on the knowability of Nature. Using the theological controversy on the knowability of God as a analogy, Einstein was a Spinozist, whereas Bohr could be said to be on the side of Maimonides. Thus Einstein’s offthecuff characterization of Bohr as a ‘Talmudic philosopher ’ was spoton.
Representational formalisms: What they are and why we haven’t had any, submitted to a special issue of Pattern Recognition (2007) http://www.cs.unb.ca/~goldfarb/ETS special issue/Repr formalisms.pdf
, 2006
"... Abstract. Currently, the only discipline that has dealt with scientific representations— albeit nonstructural ones—is mathematics (as distinct from logic). I suggest that it is this discipline, only vastly expanded based on a new, structural, foundation, that will also deal with structural represen ..."
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Cited by 3 (3 self)
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Abstract. Currently, the only discipline that has dealt with scientific representations— albeit nonstructural ones—is mathematics (as distinct from logic). I suggest that it is this discipline, only vastly expanded based on a new, structural, foundation, that will also deal with structural representations. Logic (including computability theory) is not concerned with the issues of various representations useful in natural sciences. Artificial intelligence was supposed to address these issues but has, in fact, hardly advanced them at all. How do we, then, approach the development of representational formalisms? It appears that the only reasonable starting point is the primordial point at which all of mathematics began, i.e. we should start with the generalization of the process of construction of natural numbers, replacing the identical structureless units, out of which numbers are built, by structural ones, each signifying an atomic “transforming ” event. This paper is conceived as a companion to [1], and is a revised version of [2]. Mathematics is the science of the infinite, its goal is the symbolic comprehension of the infinite with human, that is finite, means.
Curve fitting, the reliability of inductive inference, and the errorstatistical approach
 Philosophy of Science
, 2007
"... The main aim of this paper is to revisit the curve fitting problem using the reliability of inductive inference as a primary criterion for the ‘fittest ’ curve. Viewed from this perspective, it is argued that a crucial concern with the current framework for addressing the curve fitting problem is, o ..."
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The main aim of this paper is to revisit the curve fitting problem using the reliability of inductive inference as a primary criterion for the ‘fittest ’ curve. Viewed from this perspective, it is argued that a crucial concern with the current framework for addressing the curve fitting problem is, on the one hand, the undue influence of the mathematical approximation perspective, and on the other, the insufficient attention paid to the statistical modeling aspects of the problem. Using goodnessoffit as the primary criterion for ‘best’, the mathematical approximation perspective undermines the reliability of inference objective by giving rise to selection rules which pay insufficient attention to ‘accounting for the regularities in the data’. A more appropriate framework is offered by the errorstatistical approach, where (i) statistical adequacy provides the criterion for assessing when a curve captures the regularities in the data adequately, and (ii) the relevant error probabilities can be used to assess the reliability of inductive inference. Broadly speaking, the fittest curve (statistically adequate) is not determined by the smallness if its residuals, tempered by simplicity or other pragmatic criteria, but by the nonsystematic (e.g. white noise) nature of its residuals. The advocated errorstatistical arguments are illustrated by comparing the Kepler and Ptolemaic models on empirical grounds. 1. Introduction. The
Virtual Reality: Consciousness Really Explained
, 1995
"... I argue that the evolutionary rationale for the brains of organisms was not representation nor reactive parallelism as is generally proposed, but was specifically an internal operational organization of blind biologic process instead. I propose that our cognitive objects are deep metaphors of primit ..."
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Cited by 2 (2 self)
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I argue that the evolutionary rationale for the brains of organisms was not representation nor reactive parallelism as is generally proposed, but was specifically an internal operational organization of blind biologic process instead. I propose that our cognitive objects are deep metaphors of primitive biological response rather than informational referents to environment. A concise operational organization was an evolutionary necessity to enable an adroit functioning of profoundly complex metacellular organisms in a hostile and overwhelmingly complex environment. It was, however, antithetical to a representative role. This hypothesis, in concert with ancillary logical and epistemological hypotheses, opens the very first real possibility for an actual and adequate solution of the problem of "consciousness".
Representational formalisms: why we haven’t had one
 Proc. ICPR 2004 Satellite Workshop on Pattern Representation and the Future of Pattern Recognition
, 2004
"... Abstract. Currently, the only discipline that deals with scientific representations— albeit nonstructural ones—is mathematics (as distinct from logic). I suggest that it is this discipline, only vastly expanded based on a new, structural, foundation, that will also be dealing with structural repres ..."
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Cited by 2 (2 self)
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Abstract. Currently, the only discipline that deals with scientific representations— albeit nonstructural ones—is mathematics (as distinct from logic). I suggest that it is this discipline, only vastly expanded based on a new, structural, foundation, that will also be dealing with structural representations. Logic (including computability theory) is not concerned with the issues of various representations useful in natural sciences. Artificial intelligence was supposed to address these issues but has, in fact, hardly advanced them at all. How do we, then, approach the development of representational formalisms? It appears that the only reasonable starting point is the primordial point at which all of mathematics began, i.e. we should start with the generalization of the process of construction of natural numbers, replacing the identical structureless units, out of which numbers are built, by structural ones, each signifying an elementary “transforming” event. Mathematics is the science of the infinite, its goal is the symbolic comprehension of the infinite with human, that is finite, means.
Bell's Theorem, NonSeparability and SpaceTime Individuation in Quantum Mechanics
"... We first examine Howard's analysis of the Bell factorizability condition in terms of 'separability' and 'locality' and then consider his claims that the violations of Bell's inequality by the statistical predictions of quantum mechanics should be interpreted in terms of 'nonseparability' rather tha ..."
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We first examine Howard's analysis of the Bell factorizability condition in terms of 'separability' and 'locality' and then consider his claims that the violations of Bell's inequality by the statistical predictions of quantum mechanics should be interpreted in terms of 'nonseparability' rather than 'nonlocality' and that 'nonseparability' implies the failure of spacetime as a principle of individuation for quantummechanical systems. And I find his arguments for both claims to be lacking.