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    Wyświetlanie 1-2 z 2
    Tytuł:
    The Problematic Nature of Gödel’s Disjunctions and Lucas-Penrose’s Theses
    Autorzy:
    Avron, Arnon
    Powiązania:
    https://bibliotekanauki.pl/articles/1796961.pdf
    Data publikacji:
    2020
    Wydawca:
    Polskie Towarzystwo Semiotyczne
    Tematy:
    Gödel disjunction
    Lucas-Penrose argument
    mechanism
    mind
    computationalism
    Opis:
    We show that the name “Lucas-Penrose thesis” encompasses several different theses. All these theses refer to extremely vague concepts, and so are either practically meaningless, or obviously false. The arguments for the various theses, in turn, are based on confusions with regard to the meaning(s) of these vague notions, and on unjustified hidden assumptions concerning them. All these observations are true also for all interesting versions of the much weaker (and by far more widely accepted) thesis known as “Gö- del disjunction”. Our main conclusions are that pure mathematical theorems cannot decide alone any question which is not purely mathematical, and that an argument that cannot be fully formalized cannot be taken as a mathematical proof.
    Źródło:
    Studia Semiotyczne; 2020, 34, 1; 83-108
    0137-6608
    Pojawia się w:
    Studia Semiotyczne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Martin-Löf’s Constructive Optimism
    Autorzy:
    Peluce, V. Alexis
    Powiązania:
    https://bibliotekanauki.pl/articles/1796975.pdf
    Data publikacji:
    2020
    Wydawca:
    Polskie Towarzystwo Semiotyczne
    Tematy:
    optimism
    pessimism
    Martin-Löf
    Gödel’s disjunction
    Opis:
    In his 1951 Gibbs Memorial Lecture, Kurt Gödel put forth his famous disjunction that either the power of the mind outstrips that of any machine or there are absolutely unsolvable problems. The view that there are no absolutely unsolvable problems is optimism, the view that there are such problems is pessimism. In his 1995—and, revised in 2013—Verificationism Then and Now, Per Martin-Löf presents an illustrative argument for a constructivist form of optimism. In response to that argument, Solomon Feferman points out that Martin-Löf’s reasoning relies upon constructive understandings of key philosophical notions. In the vein of Feferman’s analysis, one might be object to Martin-Löf’s argument for either its reliance upon constructivist (as opposed to classical) considerations, or for its appeal to non-unproblematically mathematical premises. We argue that both of these responses fall short. On one hand, to be critical of Martin-Löf’s reasoning for its constructiveness is to reject what would otherwise be a scientific advance on the basis of the assumption of constructivism’s falsehood or implausibility, which is of course uncharitable at best. On the other hand, to object to the argument for its use of non-unproblematically mathematical premises is to assume that there is some philosophically neutral mathematics, which is implausible. Martin-Löf’s argument relies upon his third law, the claim that from the impossibility of a proof of a proposition we can construct a proof of its negation. We close with a discussion of some ways in which this claim can be criticized from the constructive point of view. Specifically, we contend that Martin-Löf’s third law is incompatible with what has been called “Poincaré’s Principle of Epistemic Conservation”, the thesis that genuine increase in mathematical knowledge requires subject-specific insight.
    Źródło:
    Studia Semiotyczne; 2020, 34, 1; 233-242
    0137-6608
    Pojawia się w:
    Studia Semiotyczne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-2 z 2

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