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  1.  3
    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. We formulate an abstract version of this postulate and derive it from some selected principles for magnitudes. We also formulate and derive an abstract version of Euclid’s Common Notion 5, and analyze its logical relation to the former proposition. These results prove (...)
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    Dedekind and Wolffian Deductive Method.José Ferreirós & Abel Lassalle-Casanave - forthcoming - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie:1-21.
    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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    From Magnitudes to Geometry and Back: De Zolt's Postulate.Eduardo N. Giovannini & Abel Lassalle-Casanave - forthcoming - Wiley: Theoria.
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    From Magnitudes to Geometry and Back: De Zolt's Postulate.Eduardo N. Giovannini & Abel Lassalle-Casanave - forthcoming - Theoria.
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    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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    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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