Switch to: References

Add citations

You must login to add citations.
  1. The Epsilon-Reconstruction of Theories and Scientific Structuralism.Georg Schiemer & Norbert Gratzl - 2016 - Erkenntnis 81 (2):407-432.
    Rudolf Carnap’s mature work on the logical reconstruction of scientific theories consists of two components. The first is the elimination of the theoretical vocabulary of a theory in terms of its Ramsification. The second is the reintroduction of the theoretical terms through explicit definitions in a language containing an epsilon operator. This paper investigates Carnap’s epsilon-reconstruction of theories in the context of pure mathematics. The main objective here is twofold: first, to specify the epsilon logic underlying his suggested definition of (...)
    No categories
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  • Hilberts Logik. Von der Axiomatik zur Beweistheorie.Volker Peckhaus - 1995 - NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 3 (1):65-86.
    This paper gives a survey of David Hilbert's (1862–1943) changing attitudes towards logic. The logical theory of the Göttingen mathematician is presented as intimately linked to his studies on the foundation of mathematics. Hilbert developed his logical theory in three stages: (1) in his early axiomatic programme until 1903 Hilbert proposed to use the traditional theory of logical inferences to prove the consistency of his set of axioms for arithmetic. (2) After the publication of the logical and set-theoretical paradoxes by (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  • A Categorical Interpretation of the Intuitionistic, Typed, First Order Logic with Hilbert’s $${\varepsilon}$$ ε -Terms.Fabio Pasquali - 2016 - Logica Universalis 10 (4):407-418.
    We introduce a typed version of the intuitionistic epsilon calculus. We give a categorical semantics of it introducing a class of categories which we call \-categories. We compare our results with earlier ones of Bell :323–337, 1993).
    $47.60 new   $52.55 used   $54.99 from Amazon    (collection)    View on Amazon.com
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • A characterization of those categories whose internal logic is Hilbert's ε-calculus.Fabio Pasquali - 2019 - Annals of Pure and Applied Logic 170 (4):446-464.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
    		•
  • The Epsilon Calculus and Herbrand Complexity.Georg Moser & Richard Zach - 2006 - Studia Logica 82 (1):133-155.
    Hilbert's ε-calculus is based on an extension of the language of predicate logic by a term-forming operator εx. Two fundamental results about the ε-calculus, the first and second epsilon theorem, play a rôle similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   14 citations  
  • Existence Assumptions and Logical Principles: Choice Operators in Intuitionistic Logic.Corey Edward Mulvihill - 2015 - Dissertation, University of Waterloo
    Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations