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  1.  17
    Dedekind and Wolffian Deductive Method.José Ferreirós & Abel Lassalle-Casanave - 2022 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 53 (4):345-365.
    Dedekind’s methodology, in his classic booklet on the foundations of arithmetic, has been the topic of some debate. While some authors make it closely analogue to Hilbert’s early axiomatics, others emphasize its idiosyncratic features, most importantly the fact that no axioms are stated and its careful deductive structure apparently rests on definitions alone. In particular, the so-called Dedekind “axioms” of arithmetic are presented by him as “characteristic conditions” in the _definition_ of the complex concept of a _simply infinite_ system. Making (...)
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  2.  16
    De Zolt’s Postulate: An Abstract Approach.Eduardo N. Giovannini, Edward H. Haeusler, Abel Lassalle-Casanave & Paulo A. S. Veloso - 2022 - Review of Symbolic Logic 15 (1):197-224.
    A theory of magnitudes involves criteria for their equivalence, comparison and addition. In this article we examine these aspects from an abstract viewpoint, by focusing on the so-called De Zolt’s postulate in the theory of equivalence of plane polygons (“If a polygon is divided into polygonal parts in any given way, then the union of all but one of these parts is not equivalent to the given polygon”). We formulate an abstract version of this postulate and derive it from some (...)
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  3.  20
    From Magnitudes to Geometry and Back: De Zolt's Postulate.Eduardo N. Giovannini & Abel Lassalle-Casanave - 2022 - Theoria 88 (3):629-652.
    Theoria, Volume 88, Issue 3, Page 629-652, June 2022.
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  4.  4
    Enthymemathical Proofs and Canonical Proofs in Euclid’s Plane Geometry.Marco Panza & Abel Lassalle-Casanave - 2018 - In Hassan Tahiri (ed.), The Philosophers and Mathematics: Festschrift for Roshdi Rashed. Springer Verlag. pp. 127-144.
    Since the application of Postulate I.2 in Euclid’s Elements is not uniform, one could wonder in what way should it be applied in Euclid’s plane geometry. Besides legitimizing questions like this from the perspective of a philosophy of mathematical practice, we sketch a general perspective of conceptual analysis of mathematical texts, which involves an extended notion of mathematical theory as system of authorizations, and an audience-dependent notion of proof.
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  5.  7
    On Comparison, Equivalence and Addition of Magnitudes.Paulo A. Veloso, Abel Lassalle-Casanave & Eduardo N. Giovannini - 2019 - Principia: An International Journal of Epistemology 23 (2):153-173.
    A theory of magnitudes involves criteria for their comparison, equivalence and addition. We examine these aspects from an abstract viewpoint, stressing independence and definability. These considerations are triggered by the so-called De Zolt’s principle in the theory of equivalence of plane polygons.
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