15 found
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  1.  18
    Decoding Gentzen's Notation.Luca Bellotti - 2018 - History and Philosophy of Logic 39 (3):270-288.
    In this note we consider Gentzen's first ordinal notation, used in his first published proof of the consistency of Peano Arithmetic. It is a decimal notation, quite different from our current notations. We give a rule to translate this notation into our usual set-theoretic notation and we show some of its peculiarities. Then we indicate how to decode Gentzen's assignment of ordinal notations to derivations and give some examples. Finally, we go through his proof of their decrease after the application (...)
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  2.  61
    Putnam and Constructibility.Luca Bellotti - 2005 - Erkenntnis 62 (3):395-409.
    I discuss and try to evaluate the argument about constructible sets made by Putnam in ‘ ”Models and Reality”, and some of the counterarguments directed against it in the literature. I shall conclude that Putnam’s argument, while correct in substance, nevertheless has no direct bearing on the philosophical question of unintended models of set theory.
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  3.  75
    Tarski on Logical Notions.Luca Bellotti - 2003 - Synthese 135 (3):401 - 413.
    We try to explain Tarski's conception of logical notions, as it emerges from alecture of his, delivered in 1966 and published posthumously in 1986 (Historyand Philosophy of Logic 7, 143–154), a conception based on the idea ofinvariance. The evaluation of Tarski's proposal leads us to consider an interesting(and neglected) reply to Skolem in which Tarski hints at his own point of view onthe foundations of set theory. Then, comparing the lecture of 1966 with Tarski'slast work and with an earlier paper (...)
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  4.  84
    Skolem, the Skolem 'Paradox' and Informal Mathematics.Luca Bellotti - 2006 - Theoria 72 (3):177-212.
  5.  56
    Formalization, Syntax and the Standard Model of Arithmetic.Luca Bellotti - 2007 - Synthese 154 (2):199-229.
    I make an attempt at the description of the delicate role of the standard model of arithmetic for the syntax of formal systems. I try to assess whether the possible instability in the notion of finiteness deriving from the nonstandard interpretability of arithmetic affects the very notions of syntactic metatheory and of formal system. I maintain that the crucial point of the whole question lies in the evaluation of the phenomenon of formalization. The ideas of Skolem, Zermelo, Beth and Carnap (...)
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  6.  10
    Tarski On Logical Notions.Luca Bellotti - 2003 - Synthese 135 (3):401-413.
    We try to explain Tarski's conception of logical notions, as it emerges from a lecture of his, delivered in 1966 and published posthumously in 1986, a conception based on the idea of invariance. The evaluation of Tarski's proposal leads us to consider an interesting reply to Skolem in which Tarski hints at his own point of view on the foundations of set theory. Then, comparing the lecture of 1966 with Tarski's last work and with an earlier paper written with Lindenbaum, (...)
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  7. Woodin on the Continuum Problem: An Overview and Some Objections.Luca Bellotti - 2005 - Logic and Philosophy of Science 3 (1).
  8. On the Consistency of ZF Set Theory and Its Large Cardinal Extensions.Luca Bellotti - 2006 - Epistemologia 29 (1):41-60.
  9.  27
    On the Circularity of Set-Theoretic Semantics for Set Theory.Luca Bellotti - 2014 - Epistemologia 37 (1):58-78.
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  10.  12
    A Neo-Kantian Approach in the Philosophy of Mathematics.Luca Bellotti - 2013 - In Margit Ruffing, Claudio La Rocca, Alfredo Ferrarin & Stefano Bacin (eds.), Kant Und Die Philosophie in Weltbürgerlicher Absicht: Akten des Xi. Kant-Kongresses 2010. De Gruyter. pp. 3-6.
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  11.  6
    Von Neumann’s Consistency Proof.Luca Bellotti - 2016 - Review of Symbolic Logic 9 (3):429-455.
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  12.  13
    Naturalismo e realismo nella teoria degli insiemi.Luca Bellotti - 1998 - Rivista di Filosofia 89 (3):445-476.
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  13. Some Attempts at a Direct Reduction of the Infinite to the (Large) Finite.Luca Bellotti - 2008 - Logique Et Analyse 51 (201):3.
  14. Third Pisa Colloquium in Logic, Language and Epistemology.Luca Bellotti, Luca Gili, Giacomo Turbanti & Enrico Moriconi (eds.) - 2019
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  15. Third Pisa Colloquium in Logic, Language and Epistemology.Luca Bellotti, Luca Gili, Enrico Moriconi & Giacomo Turbanti (eds.) - 2019 - Edizioni ETS.
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