10 found
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  1. On the Incompleteness of Axiomatized Models for the Empirical Sciences.Newton C. A. da Costa & Francisco Antonio Doria - 1992 - Philosophica 50.
     
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  2. Theoretical Physics: A Primer for Philosophers of Science.Francisco Antonio Doria - 2009 - Principia: An International Journal of Epistemology 13 (2):195-232.
    We give a overview of the main areas in theoretical physics, with emphasis on their relation to Lagrangian formalism in classical mechanics. This review covers classical mechanics; the road from classical mechanics to Schrodinger's quantum mechanics; electromagnetism, special and general relativity, and (very briefly) gauge field theory and the Higgs mechanism. We shun mathematical rigor in favor of a straightforward presentation.
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  3.  73
    Informal Versus Formal Mathematics.Francisco Antonio Doria - 2007 - Synthese 154 (3):401-415.
    We discuss Kunen’s algorithmic implementation of a proof for the Paris–Harrington theorem, and the author’s and da Costa’s proposed “exotic” formulation for the P = NP hypothesis. Out of those two examples we ponder the relation between mathematics within an axiomatic framework, and intuitive or informal mathematics.
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  4.  2
    The Map and the Territory: Exploring the Foundations of Science, Thought and Reality.Shyam Wuppuluri & Francisco Antonio Doria (eds.) - 2018 - Springer.
    This volume presents essays by pioneering thinkers including Tyler Burge, Gregory Chaitin, Daniel Dennett, Barry Mazur, Nicholas Humphrey, John Searle and Ian Stewart. Together they illuminate the Map/Territory Distinction that underlies at the foundation of the scientific method, thought and the very reality itself. It is imperative to distinguish Map from the Territory while analyzing any subject but we often mistake map for the territory. Meaning for the Reference. Computational tool for what it computes. Representations are handy and tempting that (...)
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  5.  38
    Mathematics is Dramatically Incomplete.Francisco Antonio Doria - 1992 - Theoria 7 (1/2/3):411-422.
    We state and comment our recent results on the incompleteness of elementary real analysis and their relevance for the axiomatized sciences.
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  6.  48
    Is There a Simple, Pedestrian Arithmetic Sentence Which is Independent of Zfc?Francisco Antonio Doria - 2000 - Synthese 125 (1-2):69-76.
    We show that the P 2 0 sentence, and explore some of theconsequences of that fact. This paper summarizes recent workby the author with N. C. A. da Costa on the P
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  7.  18
    On Formal Treatments for General Relativity.Francisco Antonio Doria & Manuel Doria - 2009 - Philosophia Naturalis 46 (1):115-132.
  8.  7
    Theoretical Physics: A Primer for Philosophers of Science.Francisco Antonio Doria - 2009 - Principia: An International Journal of Epistemology 13 (2):195-232.
    We give a overview of the main areas in theoretical physics, with emphasis on their relation to Lagrangian formalism in classical mechanics. This review covers classical mechanics; the road from classical mechanics to Schrödinger’s quantum mechanics; electromagnetism, special and general relativity, and gauge field theory and the Higgs mechanism. We shun mathematical rigor in favor of a straightforward presentation.
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  9.  2
    El Aleph, Or a Monster Lurks in the Belly of Computer Science.Francisco Antonio Doria - 2018 - In Wuppuluri Shyam & Francisco Antonio Dorio (eds.), The Map and the Territory: Exploring the Foundations of Science, Thought and Reality. Springer. pp. 403-417.
    In 1962 Tibor Radó uncovered a monster hiding in the midst of innocent-looking Turing machines.
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  10.  1
    Two Algorithms for NP-Complete Problems and Their Relevance to Economics.C. A. Cosenza & Francisco Antonio Doria - 2018 - In Wuppuluri Shyam & Francisco Antonio Dorio (eds.), The Map and the Territory: Exploring the Foundations of Science, Thought and Reality. Springer. pp. 419-429.
    Maps and territory suggest problems which have to do with the opening of pathways in some poorly explored domain.
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