10 found
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G. Aldo Antonelli
University of California, Davis
  1. Frege's Other Program.Aldo Antonelli & Robert May - 2005 - Notre Dame Journal of Formal Logic 46 (1):1-17.
    Frege's logicist program requires that arithmetic be reduced to logic. Such a program has recently been revamped by the "neologicist" approach of Hale and Wright. Less attention has been given to Frege's extensionalist program, according to which arithmetic is to be reconstructed in terms of a theory of extensions of concepts. This paper deals just with such a theory. We present a system of second-order logic augmented with a predicate representing the fact that an object x is the extension of (...)
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  2. Frege: Fra Estensionalismo E Logicismo.Aldo Antonelli - manuscript
    Due programmi diversi si intersecano nel lavoro di Frege sui fondamenti dell’aritmetica: • Logicismo: l’aritmetica `e riducibile alla logica; • Estensionalismo: l’aritmetica `e riducibile a una teoria delle estensioni. Sia nei Fondamenti che nei Principi, Frege articola l’idea che l’aritmetica sia riducibile a una teoria logica delle estensioni.
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    Grounded Consequence for Defeasible Logic.Aldo Antonelli - 2005 - Cambridge University Press.
    This is a title on the foundations of defeasible logic, which explores the formal properties of everyday reasoning patterns whereby people jump to conclusions, reserving the right to retract them in the light of further information. Although technical in nature the book contains sections that outline basic issues by means of intuitive and simple examples. This book is primarily targeted at philosophers interested in the foundations of defeasible logic, logicians, and specialists in artificial intelligence and theoretical computer science.
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    Completeness and Decidability of General First-Order Logic.Aldo Antonelli - 2017 - Journal of Philosophical Logic 46 (3):233-257.
    This paper investigates the “general” semantics for first-order logic introduced to Antonelli, 637–58, 2013): a sound and complete axiom system is given, and the satisfiability problem for the general semantics is reduced to the satisfiability of formulas in the Guarded Fragment of Andréka et al. :217–274, 1998), thereby showing the former decidable. A truth-tree method is presented in the Appendix.
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    The Complexity of Revision, Revised.Aldo Antonelli - 2002 - Notre Dame Journal of Formal Logic 43 (2):75-78.
    The purpose of this note is to acknowledge a gap in a previous paper — “The Complexity of Revision”, see [1] — and provide a corrected version of argument. The gap was originally pointed out by Francesco Orilia (personal communication and [4]), and the fix was developed in correspondence with Vann McGee.
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  6. Logicism, Quantifiers, and Abstraction.Aldo Antonelli - manuscript
    With the aid of a non-standard (but still first-order) cardinality quantifier and an extra-logical operator representing numerical abstraction, this paper presents a formalization of first-order arithmetic, in which numbers are abstracta of the equinumerosity relation, their properties derived from those of the cardinality quantifier and the abstraction operator.
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  7.  31
    Mathematical Methods in Philosophy: Editors' Introduction.Aldo Antonelli, Alasdair Urquhart & Richard Zach - 2008 - Review of Symbolic Logic 1 (2):143-145.
    Mathematics and philosophy have historically enjoyed a mutually beneficial and productive relationship, as a brief review of the work of mathematician–philosophers such as Descartes, Leibniz, Bolzano, Dedekind, Frege, Brouwer, Hilbert, Gödel, and Weyl easily confirms. In the last century, it was especially mathematical logic and research in the foundations of mathematics which, to a significant extent, have been driven by philosophical motivations and carried out by technically minded philosophers. Mathematical logic continues to play an important role in contemporary philosophy, and (...)
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  8. Gödel, Penrose, E I Fondamenti Dell'intelligenza Artificiale.Aldo Antonelli - 1997 - Sistemi Intelligenti 9 (3):353-376.
    Il dibattito sul ruolo e le implicazioni del teorema di Gödel per l'intelligenza artificiale ha recentemente ricevuto nuovo impeto grazie a due importanti volumi pubblicati da Roger Penrose, The Emperor's New Mind [1989] e Shadows of the Mind [1994]. Naturalmente, Penrose non è il primo né l'ultimo a usare il teorema di Gödel allo scopo di trarne conseguenze per i fondamenti dell'intelligenza artificiale. Tuttavia il recente dibattito suscitato dai due libri di Penrose è significativo sia per ampiezza sia per profondità. (...)
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  9. Virtuous Circles.Aldo Antonelli - 2000 - In Anil Gupta & Andre Chapuis (eds.), Circularity, Definition, and Truth. Indian Council of Philosophical Research.
    In the Posterior Analytics, Aristotle takes up the position of those who hold that all knowledge is demonstrable, and, hence, scientific. Such people are said to base their arguments on the fact that some demonstrations are circular or reciprocal (72b251). As Aristotle makes clear in the text, a circular demonstration consists of an argument (form) in which the conclusion is equivalent to one of the premises. But as Aristotle hastens to point out, demonstrations cannot be circular, for the essence of (...)
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  10. Il Teorema di G¨ Odel E la Filosofia Della Mente.Aldo Antonelli - unknown
    Kleene comincia la sezione §60 di Introduction to metamathematics considerando la questione se la matematica informale, e specialmente la teoria intuitiva dei numeri sia formalizzabile. Il classico teorema di G¨.
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