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Paola Cantù
Università degli Studi di Genova
  1. Aristotle’s Prohibition Rule on Kind-Crossing and the Definition of Mathematics as a Science of Quantities.Paola Cantù - 2010 - Synthese 174 (2):225-235.
    The article evaluates the Domain Postulate of the Classical Model of Science and the related Aristotelian prohibition rule on kind-crossing as interpretative tools in the history of the development of mathematics into a general science of quantities. Special reference is made to Proclus’ commentary to Euclid’s first book of Elements , to the sixteenth century translations of Euclid’s work into Latin and to the works of Stevin, Wallis, Viète and Descartes. The prohibition rule on kind-crossing formulated by Aristotle in Posterior (...)
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  2. Grassmann’s Epistemology: Multiplication and Constructivism.Paola Cantù - 2010 - In Hans-Joachim Petsche (ed.), From Past to Future: Graßmann's Work in Context.
    The paper aims to establish if Grassmann’s notion of an extensive form involved an epistemological change in the understanding of geometry and of mathematical knowledge. Firstly, it will examine if an ontological shift in geometry is determined by the vectorial representation of extended magnitudes. Giving up homogeneity, and considering geometry as an application of extension theory, Grassmann developed a different notion of a geometrical object, based on abstract constraints concerning the construction of forms rather than on the homogeneity conditions required (...)
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  3. Bolzano Versus Kant: Mathematics as a Scientia Universalis.Paola Cantù - 2011 - Philosophical Papers Dedicated to Kevin Mulligan.
    The paper discusses some changes in Bolzano's definition of mathematics attested in several quotations from the Beyträge, Wissenschaftslehre and Grössenlehre: is mathematics a theory of forms or a theory of quantities? Several issues that are maintained throughout Bolzano's works are distinguished from others that were accepted in the Beyträge and abandoned in the Grössenlehre. Changes are interpreted as a consequence of the new logical theory of truth introduced in the Wissenschaftslehre, but also as a consequence of the overcome of Kant's (...)
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  4. The Role of Epistemological Models in Veronese's and Bettazzi's Theory of Magnitudes.Paola Cantù - 2010 - In M. D'Agostino, G. Giorello, F. Laudisa, T. Pievani & C. Sinigaglia (eds.), New Essays in Logic and Philosophy of Science. College Publications.
    The philosophy of mathematics has been accused of paying insufficient attention to mathematical practice: one way to cope with the problem, the one we will follow in this paper on extensive magnitudes, is to combine the `history of ideas' and the `philosophy of models' in a logical and epistemological perspective. The history of ideas allows the reconstruction of the theory of extensive magnitudes as a theory of ordered algebraic structures; the philosophy of models allows an investigation into the way epistemology (...)
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  5. Life and Works of Giovanni Vailati.Paola Cantù & De Zan Mauro - 2009 - In Arrighi Claudia, Cantù Paola, De Zan Mauro & Suppes Patrick (eds.), Life and Works of Giovanni Vailati. CSLI Publications.
    The paper introduces Vailati’s life and works, investigating Vailati’s education, the relation to Peano and his school, and the interest for pragmatism and modernism. A detailed analysis of Vailati’s scientific and didactic activities, shows that he held, like Peano, a a strong interest for the history of science and a pluralist, anti-dogmatic and anti-foundationalist conception of definitions in mathematics, logic and philosophy of language. Vailati’s understanding of mathematical logic as a form of pragmatism is not a faithful interpretation of Peano’s (...)
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  6. Is Common Ground a Word or Just a Sound?Paola Cantù - 2007 - In H. V. Hanson (ed.), Proceedings of the International Conference: Dissensus & The Search for Common Ground. Ontario Society for the Study of Argumentation. pp. 1--9.
    The paper analyses the role played by the concept of ‘common ground’ in argumentation theories. If a common agreement on all the rules of a discursive exchange is required, either at the beginning or at the end of an argumentative practice, then no violation of the rules is possible. The paper suggests an alternative understanding of ‘common ground’ as something that can change during the development of the argumentative practice, and in particular something that can change without the practice being (...)
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