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  1. On the Concepts of Function and Dependence.André Bazzoni - 2015 - Principia: An International Journal of Epistemology 19 (1):01-15.
    This paper briefly traces the evolution of the function concept until its modern set theoretic definition, and then investigates its relationship to the pre-formal notion of variable dependence. I shall argue that the common association of pre-formal dependence with the modern function concept is misconceived, and that two different notions of dependence are actually involved in the classic and the modern viewpoints, namely effective and functional dependence. The former contains the latter, and seems to conform more to our pre-formal conception (...)
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  2. The Inadequacy of a Proposed Paraconsistent Set Theory.Frode Bjørdal - 2011 - Review of Symbolic Logic 4 (1):106-108.
    We show that a paraconsistent set theory proposed in Weber (2010) is strong enough to provide a quite classical nonprimitive notion of identity, so that the relation is an equivalence relation and also obeys full substitutivity: a = b -> F(b)). With this as background it is shown that the proposed theory also proves the negation of x=x. While not by itself showing that the proposed system is trivial in the sense of proving all statements, it is argued that this (...)
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  3. Gestalt, Equivalency, and Functional Dependency. Kurt Grelling’s Formal Ontology.Arkadiusz Chrudzimski - 2013 - In Nikolay Milkov & Volker Peckhaus (eds.), The Berlin Group and the Philosophy of Logical Empiricism. Springer. pp. 245--261.
    In his ontological works Kurt Grelling tries to give a rigorous analysis of the foundations of the so-called Gestalt-psychology. Gestalten are peculiar emergent qualities, ontologically dependent on their foundations, but nonetheless non reducible to them. Grelling shows that this concept, as used in psychology and ontology, is often ambiguous. He distinguishes two important meanings in which the word “Gestalt” is used: Gestalten as structural aspects available to transposition and Gestalten as causally self-regulating wholes. Gestalten in the first meaning are, according (...)
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  4. Set Theory: Constructive and Intuitionistic Zf.Laura Crosilla - 2010 - Stanford Encyclopedia of Philosophy.
    Constructive and intuitionistic Zermelo-Fraenkel set theories are axiomatic theories of sets in the style of Zermelo-Fraenkel set theory (ZF) which are based on intuitionistic logic. They were introduced in the 1970's and they represent a formal context within which to codify mathematics based on intuitionistic logic. They are formulated on the basis of the standard first order language of Zermelo-Fraenkel set theory and make no direct use of inherently constructive ideas. In working in constructive and intuitionistic ZF we can thus (...)
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  5. Arithmetic, Set Theory, Reduction and Explanation.William D'Alessandro - forthcoming - Synthese:1-31.
    Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In defense (...)
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  6. Die Axiome der Arithmetik mit besonderer Berücksichtigung der Beziehungen zur Mengenlehre.Kurt Grelling - 1910 - Dissertation, Georg-Augusts-Universität Göttingen
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  7. La Dinamica Delle Teorie Scientifiche. Strutturalismo Ed Interpretazione Logico-Formale Dell’Epistemologia di Kuhn, with a Preface of C. Ulises Moulines.Tommaso Perrone - 2012 - Franco Angeli.
    Philosophy of science in the 20th century is to be considered as mostly characterized by a fundamentally systematic heuristic attitude, which looks to mathematics, and more generally to the philosophy of mathematics, for a genuinely and epistemologically legitimate form of knowledge. Rooted in this assumption, the book provides a formal reconsidering of the dynamics of scientific theories, especially in the field of the physical sciences, and offers a significant contribution to current epistemological investigations regarding the validity of using formal (especially: (...)
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