Books by Francisco Antonio Doria
My book with Greg Chaitin and Newton da Costa. Heretic viewpoints.
Papers by Francisco Antonio Doria
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.
Lettere Al Nuovo Cimento Series 2, 1977
Review of Behavioral Economics, 2016
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
International Journal of Theoretical Physics, 1990
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Books by Francisco Antonio Doria
Papers by Francisco Antonio Doria