Francisco Antonio Doria | Universidade Federal do Rio de Janeiro (UFRJ) (original) (raw)
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Books by Francisco Antonio Doria
My book with Greg Chaitin and Newton da Costa. Heretic viewpoints.
Papers by Francisco Antonio Doria
The Frontiers Collection
Science is a constructed narrative of the natural world based on information gathering and its su... more Science is a constructed narrative of the natural world based on information gathering and its subsequent analysis. In this essay, we develop a novel approach to the epistemic foundations of the scientific narrative, as based on our experiential interactions with the natural world. We first review some of the basic aspects of both Bayesian statistics and Shannon's information theory as applied to the construction of meaningful conceptualization of the natural world. This conceptualization is rendered through the maps we construct of the world based on our limited knowledge of reality. We propose a path from experience to information and physics based on the notion that information is experience that induces change in an Epistemic Agent (EA): the change may be local and focused to a minor aspect of reality or it may be broad and worldview-changing. We illustrate our approach through an analysis of a measure of spatial complexity proposed by one of us called Configuration Entropy (CE), and establish a link between experience at the cognitive level and information content, showing that the CE is a quantitative measure of how much information in spatial-complexity the external world hides from an EA. All philosophy is based on two things only: curiosity and poor eyesight. The trouble is, we want to know more than we can see. Bernard le Bovier de Fontenelle a To appear in Map and Territory-Exploring the Foundations of Science, Thought and Reality, ed.
Space, Time and the Limits of Human Understanding, 2016
We show how widespread are metamathematical phenomena in mathematics and in the sciences which re... more We show how widespread are metamathematical phenomena in mathematics and in the sciences which rely on mathematics. We will consider specific examples of undecidable sentences in mathematics, physics and economics. Our presentation is informal; rigorous developments can be found in the references.
We introduce a formal sentence noted P NPŠ F (the ‘‘exotic definition’’) that is intuitively equi... more We introduce a formal sentence noted P NPŠ F (the ‘‘exotic definition’’) that is intuitively equivalent to P NP; however P NP and P NPŠ F may not be equivalent in ZFC for some choices of F. Again for some F we show that P NPŠ F is consistent with ZFC, and so is the equivalence P NPŠ F $P NPŠ. We finally derive a consistency result for P NP itself.
We prove here a lemma that connects some properties of the so-called "counterexample function" to... more We prove here a lemma that connects some properties of the so-called "counterexample function" to the P = N P conjecture over the Baker-Gill-Solovay set of polynomial Turing machines to the behavior of the same function "at large," over the set of all polynomial Turing machines.
Lettere Al Nuovo Cimento Series 2, 1977
Review of Behavioral Economics, 2016
We present and discuss the O'Donnell 1979 algorithm for the solution of N P-complete problems. If... more We present and discuss the O'Donnell 1979 algorithm for the solution of N P-complete problems. If P < N P is proved in a theory with greater "provability strength" than Primitive Recursive Arithmetic, the O'Donnell algorithm turns out to be almost polynomial. We elaborate on how close to polynomial it might be. As an application, we show that follows from Maymin's theorem on efficient markets that, given our metamathematical condition above, there are "almost efficient" markets (that is to say, markets where information about their operation is known in almost polynomial time).
Lettere Al Nuovo Cimento Series 2, 1973
Lettere Al Nuovo Cimento Series 2, 1975
Randomness and Complexity, From Leibniz to Chaitin, 2007
Philosophy of Latin America, 2003
We summarize in an intuitive vein a few recent results by the authors on the incompleteness of el... more We summarize in an intuitive vein a few recent results by the authors on the incompleteness of elementary real analysis and its consequences to the axiomatized sciences, from chaos theory to the dynamics of populations.
The Handbook on Reasoning-Based Intelligent Systems, 2013
Lecture Notes in Computer Science, 1993
We prove that stability is undecidable for dynamical systems whose right-hand side is explicitly ... more We prove that stability is undecidable for dynamical systems whose right-hand side is explicitly written in the language of elementary analysis.
Philosophical Logic and Logical Philosophy, 1996
An old and important question concerning physical theories has to do with their axiomatization [4... more An old and important question concerning physical theories has to do with their axiomatization [47]. The sixth problem in Hilbert’s celebrated list of mathematical problems deals with its desirable (or ideal) contours [31]:
Lettere al Nuovo Cimento, 1973
ABSTRACT
Patrick Suppes: Scientific Philosopher, 1994
We first review our previous work on Suppes predicates and the axiomatization of the empirical sc... more We first review our previous work on Suppes predicates and the axiomatization of the empirical sciences. We then state some undecidability and incompleteness results in classical analysis that lead to the explicit construction of expressions for characteristic functions in all complete arithmetical degrees. Out of those results we show that for any degree there are corresponding ‘meaningful’ unsolvable problems in
The Handbook on Reasoning-Based Intelligent Systems, 2013
Progress of Theoretical Physics, 1986
We construct Dirac-like equations on a principal bundle over spacetime which is also the setting ... more We construct Dirac-like equations on a principal bundle over spacetime which is also the setting for the standard gauge field theories. We see that they describe other fields besides the. usual gauge fields, and impose certain degeneracies on the fields over a bifurcation domain.
International Journal of Theoretical Physics, 1990
We summarize ideas from Zermelo-Fraenkel set theory up to an axiomatic treatment for general rela... more We summarize ideas from Zermelo-Fraenkel set theory up to an axiomatic treatment for general relativity based on a Suppes predicate. We then examine the meaning of set-theoretic genericity for manifolds that underlie the Einstein equations. A physical interpretation is finally offered for those set-theoretically generic manifolds in gravitational theory.
My book with Greg Chaitin and Newton da Costa. Heretic viewpoints.
The Frontiers Collection
Science is a constructed narrative of the natural world based on information gathering and its su... more Science is a constructed narrative of the natural world based on information gathering and its subsequent analysis. In this essay, we develop a novel approach to the epistemic foundations of the scientific narrative, as based on our experiential interactions with the natural world. We first review some of the basic aspects of both Bayesian statistics and Shannon's information theory as applied to the construction of meaningful conceptualization of the natural world. This conceptualization is rendered through the maps we construct of the world based on our limited knowledge of reality. We propose a path from experience to information and physics based on the notion that information is experience that induces change in an Epistemic Agent (EA): the change may be local and focused to a minor aspect of reality or it may be broad and worldview-changing. We illustrate our approach through an analysis of a measure of spatial complexity proposed by one of us called Configuration Entropy (CE), and establish a link between experience at the cognitive level and information content, showing that the CE is a quantitative measure of how much information in spatial-complexity the external world hides from an EA. All philosophy is based on two things only: curiosity and poor eyesight. The trouble is, we want to know more than we can see. Bernard le Bovier de Fontenelle a To appear in Map and Territory-Exploring the Foundations of Science, Thought and Reality, ed.
Space, Time and the Limits of Human Understanding, 2016
We show how widespread are metamathematical phenomena in mathematics and in the sciences which re... more We show how widespread are metamathematical phenomena in mathematics and in the sciences which rely on mathematics. We will consider specific examples of undecidable sentences in mathematics, physics and economics. Our presentation is informal; rigorous developments can be found in the references.
We introduce a formal sentence noted P NPŠ F (the ‘‘exotic definition’’) that is intuitively equi... more We introduce a formal sentence noted P NPŠ F (the ‘‘exotic definition’’) that is intuitively equivalent to P NP; however P NP and P NPŠ F may not be equivalent in ZFC for some choices of F. Again for some F we show that P NPŠ F is consistent with ZFC, and so is the equivalence P NPŠ F $P NPŠ. We finally derive a consistency result for P NP itself.
We prove here a lemma that connects some properties of the so-called "counterexample function" to... more We prove here a lemma that connects some properties of the so-called "counterexample function" to the P = N P conjecture over the Baker-Gill-Solovay set of polynomial Turing machines to the behavior of the same function "at large," over the set of all polynomial Turing machines.
Lettere Al Nuovo Cimento Series 2, 1977
Review of Behavioral Economics, 2016
We present and discuss the O'Donnell 1979 algorithm for the solution of N P-complete problems. If... more We present and discuss the O'Donnell 1979 algorithm for the solution of N P-complete problems. If P < N P is proved in a theory with greater "provability strength" than Primitive Recursive Arithmetic, the O'Donnell algorithm turns out to be almost polynomial. We elaborate on how close to polynomial it might be. As an application, we show that follows from Maymin's theorem on efficient markets that, given our metamathematical condition above, there are "almost efficient" markets (that is to say, markets where information about their operation is known in almost polynomial time).
Lettere Al Nuovo Cimento Series 2, 1973
Lettere Al Nuovo Cimento Series 2, 1975
Randomness and Complexity, From Leibniz to Chaitin, 2007
Philosophy of Latin America, 2003
We summarize in an intuitive vein a few recent results by the authors on the incompleteness of el... more We summarize in an intuitive vein a few recent results by the authors on the incompleteness of elementary real analysis and its consequences to the axiomatized sciences, from chaos theory to the dynamics of populations.
The Handbook on Reasoning-Based Intelligent Systems, 2013
Lecture Notes in Computer Science, 1993
We prove that stability is undecidable for dynamical systems whose right-hand side is explicitly ... more We prove that stability is undecidable for dynamical systems whose right-hand side is explicitly written in the language of elementary analysis.
Philosophical Logic and Logical Philosophy, 1996
An old and important question concerning physical theories has to do with their axiomatization [4... more An old and important question concerning physical theories has to do with their axiomatization [47]. The sixth problem in Hilbert’s celebrated list of mathematical problems deals with its desirable (or ideal) contours [31]:
Lettere al Nuovo Cimento, 1973
ABSTRACT
Patrick Suppes: Scientific Philosopher, 1994
We first review our previous work on Suppes predicates and the axiomatization of the empirical sc... more We first review our previous work on Suppes predicates and the axiomatization of the empirical sciences. We then state some undecidability and incompleteness results in classical analysis that lead to the explicit construction of expressions for characteristic functions in all complete arithmetical degrees. Out of those results we show that for any degree there are corresponding ‘meaningful’ unsolvable problems in
The Handbook on Reasoning-Based Intelligent Systems, 2013
Progress of Theoretical Physics, 1986
We construct Dirac-like equations on a principal bundle over spacetime which is also the setting ... more We construct Dirac-like equations on a principal bundle over spacetime which is also the setting for the standard gauge field theories. We see that they describe other fields besides the. usual gauge fields, and impose certain degeneracies on the fields over a bifurcation domain.
International Journal of Theoretical Physics, 1990
We summarize ideas from Zermelo-Fraenkel set theory up to an axiomatic treatment for general rela... more We summarize ideas from Zermelo-Fraenkel set theory up to an axiomatic treatment for general relativity based on a Suppes predicate. We then examine the meaning of set-theoretic genericity for manifolds that underlie the Einstein equations. A physical interpretation is finally offered for those set-theoretically generic manifolds in gravitational theory.
Complexity, 1995
We summarize in a n intuitiue vein a few concepts froin recursion theory and fi-om the theory ofj... more We summarize in a n intuitiue vein a few concepts froin recursion theory and fi-om the theory ofjormal systems and then state and comment our recent 1-esults on the incoinpleteness of elementary real analysis and its consequences. Their relation to forcing is also dealt with. 0 1995 John Wiiviley & Sons, Inc.
We define a complete market to be one in which complete contracts can be algorithmically written ... more We define a complete market to be one in which complete contracts can be algorithmically written and executed. We define a free market to be a market where private ownership is positively valued by market members. In an economy with zero transaction costs, if the market is algorithmically complete, ownership will be worthless. Accordingly, the market can be either free or complete, but not both. For the same reason, the market can be either efficient or complete, but not both.