13 found
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  1. What is Tarski's Common Concept of Consequence?Ignacio Jané - 2006 - Bulletin of Symbolic Logic 12 (1):1-42.
    In 1936 Tarski sketched a rigorous definition of the concept of logical consequence which, he claimed, agreed quite well with common usage-or, as he also said, with the common concept of consequence. Commentators of Tarski's paper have usually been elusive as to what this common concept is. However, being clear on this issue is important to decide whether Tarski's definition failed (as Etchemendy has contended) or succeeded (as most commentators maintain). I argue that the common concept of consequence that Tarski (...)
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  2.  14
    Aproximaciones admisibles dentro de teorías empíricas.Ignacio Jane & C. Ulises Moulines - 1981 - Critica 13 (38):53-75.
  3. Remarks on Second-Order Consequence.Ignacio Jané - 2003 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 18 (2):179-187.
    Tarski’s definition of logical consequence can take different forms when implemented in second order languages, depending on what counts as a model. In the canonical, or standard, version, a model is just an ordinary structure and the second-order variables are meant to range over all subsets of its domain. We discuss the dependence of canonical second-order consequence on set theory and raise doubts on the assumption that canonical consequence is a definite relation.
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  4.  86
    A Critical Appraisal of Second-Order Logic.Ignacio Jané - 1993 - History and Philosophy of Logic 14 (1):67-86.
    Because of its capacity to characterize mathematical concepts and structures?a capacity which first-order languages clearly lack?second-order languages recommend themselves as a convenient framework for much of mathematics, including set theory. This paper is about the credentials of second-order logic:the reasons for it to be considered logic, its relations with set theory, and especially the efficacy with which it performs its role of the underlying logic of set theory.
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  5. The Role of the Absolute Infinite in Cantor's Conception of Set.Ignacio Jané - 1995 - Erkenntnis 42 (3):375 - 402.
  6. Well- and Non-Well-Founded Fregean Extensions.Ignacio Jané & Gabriel Uzquiano - 2004 - Journal of Philosophical Logic 33 (5):437-465.
    George Boolos has described an interpretation of a fragment of ZFC in a consistent second-order theory whose only axiom is a modification of Frege's inconsistent Axiom V. We build on Boolos's interpretation and study the models of a variety of such theories obtained by amending Axiom V in the spirit of a limitation of size principle. After providing a complete structural description of all well-founded models, we turn to the non-well-founded ones. We show how to build models in which foundation (...)
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  7.  8
    Observaciones sobre el concepto de aproximación empírica.Ignacio Jane - 1980 - Critica 12 (35):3-14.
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  8.  98
    Theoremhood and Logical Consequence.Ignacio Jane - 1997 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 12 (1):139-160.
    In this paper, Tarskis notion of Logical Consequence is viewed as a special case of the more general notion of being a theorem of an axiomatic theory. As was recognized by Tarski, the material adequacy of his definition depends on having the distinction between logical and non logical constants right, but we find Tarskis analysis persuasive even if we dont agree on what constants are logical. This accords with the view put forward in this paper that Tarski indeed captures the (...)
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  9.  82
    Review of C. Badesa, The Birth of Model Theory: Löwenheim's Theorem in the Frame of the Theory of Relatives[REVIEW]Ignacio Jané - 2005 - Philosophia Mathematica 13 (1):91-106.
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  10.  58
    Lógica Y Ontología.Ignacio Jané - 1988 - Theoria 4 (1):81-106.
    In this paper we discuss the way logical consequence depends on what sets there are. We try to find out what set-theoretical assumptions have to be made to determine a logic, i.e., to give a definite answer to whether any given argument is correct. Consideration of second order logic -which is left highly indetermined by the usual set-theoretical axioms- prompts us to suggest a slightly different but natural nation of logical consequence, which reduces second order logic indeterminacy without interfering with (...)
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  11.  20
    Lógica y Ontología.Ignacio Jané - 1988 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 4 (1):81-106.
    In this paper we discuss the way logical consequence depends on what sets there are. We try to find out what set-theoretical assumptions have to be made to determine a logic, i.e., to give a definite answer to whether any given argument is correct. Consideration of second order logic -which is left highly indetermined by the usual set-theoretical axioms- prompts us to suggest a slightly different but natural nation of logical consequence, which reduces second order logic indeterminacy without interfering with (...)
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  12.  8
    Remarks on Second-Order Consequence.Ignacio Jané - 2010 - Theoria : An International Journal for Theory, History and Fundations of Science 18 (2):179-187.
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  13. El universo de la teoría de conjuntos.Ignacio Jané - 1981 - Dianoia 27:207-222.
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