Switch to: References

Add citations

You must login to add citations.
  1. On the Intuitionistic Background of Gentzen's 1935 and 1936 Consistency Proofs and Their Philosophical Aspects.Yuta Takahashi - 2018 - Annals of the Japan Association for Philosophy of Science 27:1-26.
    Gentzen's three consistency proofs for elementary number theory have a common aim that originates from Hilbert's Program, namely, the aim to justify the application of classical reasoning to quantified propositions in elementary number theory. In addition to this common aim, Gentzen gave a “finitist” interpretation to every number-theoretic proposition with his 1935 and 1936 consistency proofs. In the present paper, we investigate the relationship of this interpretation with intuitionism in terms of the debate between the Hilbert School and the Brouwer (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  • Semantic Values for Natural Deduction Derivations.Göran Sundholm - 2006 - Synthese 148 (3):623-638.
    Drawing upon Martin-Löf’s semantic framework for his constructive type theory, semantic values are assigned also to natural-deduction derivations, while observing the crucial distinction between consequence among propositions and inference among judgements. Derivations in Gentzen’s format with derivable formulae dependent upon open assumptions, stand, it is suggested, for proof-objects, whereas derivations in Gentzen’s sequential format are proof-acts.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  • Science without reduction.Helmut F. Spinner - 1973 - Inquiry: An Interdisciplinary Journal of Philosophy 16 (1-4):16 – 94.
    The aim of this essay is a criticism of reductionism ? both in its ?static? interpretation (usually referred to as the layer model or level?picture of science) and in its ?dynamic? interpretation (as a theory of the growth of scientific knowledge), with emphasis on the latter ? from the point of view of Popperian fallibilism and Feyerabendian pluralism, but without being committed to the idiosyncrasies of these standpoints. In both aspects of criticism, the rejection is based on the proposal of (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  • An Analysis of the Rules of Gentzen’s _Nj__ and __Lj_.Mirjana Borisavljević - 2018 - Review of Symbolic Logic 11 (2):347-370.
    The connection between the rules and derivations of Gentzen’s calculiNJandLJwill be explained by several steps (i.e., systems), and an analysis of the well-known problems of the connection between reduction steps of normalization and cut elimination, from Zucker (1974) and Urban (2014), will be given.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • Reading Gentzen's Three Consistency Proofs Uniformly.Ryota Akiyoshi & Yuta Takahashi - 2013 - Journal of the Japan Association for Philosophy of Science 41 (1):1-22.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation