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Articles 1 - 6 of 6
Full-Text Articles in Arts and Humanities
The Varieties Of Indispensability Arguments, Marco Panza, Andrea Sereni
The Varieties Of Indispensability Arguments, Marco Panza, Andrea Sereni
MPP Published Research
The indispensability argument (IA) comes in many different versions that all reduce to a general valid schema. Providing a sound IA amounts to providing a full interpretation of the schema according to which all its premises are true. Hence, arguing whether IA is sound results in wondering whether the schema admits such an interpretation. We discuss in full details all the parameters on which the specification of the general schema may depend. In doing this, we consider how different versions of IA can be obtained, also through different specifications of the notion of indispensability. We then distinguish between schematic and …
Introduction To Functions And Generality Of Logic. Reflections On Frege's And Dedekind's Logicisms, Hourya Benis Sinaceur, Marco Panza, Gabriel Sandu
Introduction To Functions And Generality Of Logic. Reflections On Frege's And Dedekind's Logicisms, Hourya Benis Sinaceur, Marco Panza, Gabriel Sandu
MPP Published Research
This book examines three connected aspects of Frege’s logicism: the differences between Dedekind’s and Frege’s interpretation of the term ‘logic’ and related terms and reflects on Frege’s notion of function, comparing its understanding and the role it played in Frege’s and Lagrange’s foundational programs. It concludes with an examination of the notion of arbitrary function, taking into account Frege’s, Ramsey’s and Russell’s view on the subject. Composed of three chapters, this book sheds light on important aspects of Dedekind’s and Frege’s logicisms. The first chapter explains how, although he shares Frege’s aim at substituting logical standards of rigor to intuitive …
Wallis On Indivisibles, Antoni Malet, Marco Panza
Wallis On Indivisibles, Antoni Malet, Marco Panza
MPP Published Research
The present chapter is devoted, first, to discuss in detail the structure and results of Wallis’s major and most influential mathematical work, the Arithmetica Infinitorum (Wallis 1656). Next we will revise Wallis’s views on indivisibles as articulated in his answer to Hobbes’s criticism in the early 1670s. Finally, we will turn to his discussion of the proper way to understand the angle of contingence in the first half of the 1680s. As we shall see, there are marked differences in the status that indivisibles seem to enjoy in Wallis’s thought along his mathematical career. These differences correlate with the changing …
Newton On Indivisibles, Antoni Malet, Marco Panza
Newton On Indivisibles, Antoni Malet, Marco Panza
MPP Published Research
Though Wallis’s Arithmetica infinitorum was one of Newton’s major sources of inspiration during the first years of his mathematical education, indivisibles were not a central feature of his mathematical production.
The Logical System Of Frege’S Grundgesetze : A Rational Reconstruction, Méven Cadet, Marco Panza
The Logical System Of Frege’S Grundgesetze : A Rational Reconstruction, Méven Cadet, Marco Panza
MPP Published Research
This paper aims at clarifying the nature of Frege's system of logic, as presented in the first volume of the Grundgesetze . We undertake a rational reconstruction of this system, by distinguishing its propositional and predicate fragments. This allows us to emphasise the differences and similarities between this system and a modern system of classical second-order logic.
Pruebas Entimemáticas Y Pruebas Canónicas En La Geometría Plana De Euclides, Marco Panza, Abel Lassalle Casanave
Pruebas Entimemáticas Y Pruebas Canónicas En La Geometría Plana De Euclides, Marco Panza, Abel Lassalle Casanave
MPP Published Research
Dado que la aplicación del Postulado I.2 no es uniforme en Elementos, ¿de qué manera debería ser aplicado en la geometría plana de Euclides? Además de legitimar la pregunta misma desde la perspectiva de una filosofía de la práctica matemática, nos proponemos esbozar una perspectiva general de análisis conceptual de textos matemáticos que involucra una noción ampliada de la teoría matemática como sistema de autorizaciones o potestades y una noción de prueba que depende del auditorio.
Since the application of Postulate I.2 in the Elements is not uniform, one could wonder in what way should it be applied in Euclid’s …