Books (Monographs) by Vincenzo De Risi
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Edited Volumes by Vincenzo De Risi
Articles by Francesco Ademollo, Fabrizio Amerini, Maria Rosa Antognazza, Richard T.W. Arthur, Car... more Articles by Francesco Ademollo, Fabrizio Amerini, Maria Rosa Antognazza, Richard T.W. Arthur, Carla Bagnoli, Francesco Belardinelli, Sergio Bernini, Irene Binini, Andrea Borghini, Andrea Cantini, Graziana Ciola, Paolo Crivelli, Marcello D’Agostino, Vincenzo De Risi, Hykel Hosni, Giorgio Lando, Pierluigi Minari, Daniele Mundici, Calvin Normore, Chris Martin, Fabrizio Mondadori, Claude Panaccio, Enrico Pasini, Mario Piazza, Riccardo Strobino, Monica Ugaglia.
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Chapters by Marko Malink, Anubav Vasudevan, Massimo Mugnai, Richard Arthur, Vincenzo De Risi, Dav... more Chapters by Marko Malink, Anubav Vasudevan, Massimo Mugnai, Richard Arthur, Vincenzo De Risi, David Rabouin, Valérie Debuiche, Davide Crippa, Jürgen Jost, Nabeel Hamid.
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Chapters by Henry Mendell, Alexander Jones, David Rabouin, Franco Farinelli, Gary Hatfield, Dougl... more Chapters by Henry Mendell, Alexander Jones, David Rabouin, Franco Farinelli, Gary Hatfield, Douglas Jesseph, Andrew Janiak, Daniel Garber, Graciela De Pierris, Jeremy Gray, Michael Friedman.
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Articles by Daniel Garber, Anne-Lise Rey, François Duchesneau, Mathieu Gibier, Andrea Costa, Enri... more Articles by Daniel Garber, Anne-Lise Rey, François Duchesneau, Mathieu Gibier, Andrea Costa, Enrico Pasini, Laurynas Adomaitis.
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Editions of Texts by Vincenzo De Risi
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Papers by Vincenzo De Risi
Science in Context (forthcoming), 2023
The Fourth Postulate of Euclid's Elements states that all right angles are equal. This principle ... more The Fourth Postulate of Euclid's Elements states that all right angles are equal. This principle has always been considered as extremely problematic in the deductive economy of the treatise, and even the ancient interpreters were confused about its mathematical role and its epistemological status. The present essay reconsiders the ancient testimonies on the Fourth Postulate, showing that there is no certain evidence for its authenticity, nor for its spuriousness. The paper also considers modern mathematical interpretations of this postulate, pointing out various anachronisms. It further discusses the validity of the ancient proof by superposition of the Fourth Postulate. Finally, the article proposes an interpretation of the history of the concept of angle in Greek mathematics between Euclid and Apollonius, and puts forward a conjecture on the interpolation of the Fourth Postulate in the Hellenistic age.
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Thinking and Calculating. Essays on Logic, its History and its Applications, Berlin, Springer, pp. 53-82., 2022
Aristotle claimed that each science is grounded in principles that are proper to it. He also reco... more Aristotle claimed that each science is grounded in principles that are proper to it. He also recognized, however, the existence of principles that are common to many sciences, that he called axioms. The sources of Aristotle's theory of axioms seem to have been both philosophical and mathematical, and the outcomes of the theory are some very refined views on the analogy between different scientific domains, and possibly a theory of nonsyllogistic inferences. I sketch here Aristotle's theory of axioms, its motivations, its developments, and its applications to the theory of science. Finally, I offer a tentative interpretation of axioms that may shed some light on several open interpretative questions in Aristotle's epistemology.
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Perché studiare la logica, ed. E. Montuschi, P.D. Omodeo, 2021
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Foundations of Science, 2021
The "common notions" prefacing the Elements of Euclid are a very peculiar set of axioms, and thei... more The "common notions" prefacing the Elements of Euclid are a very peculiar set of axioms, and their authenticity, as well as their actual role in the demonstrations, have been object of debate. In the first part of this essay, I offer a survey of the evidence for the authenticity of the common notions, and conclude that only three of them are likely to have been in place at the times of Euclid, whereas others were added in Late Antiquity. In the second part of the essay, I consider the meaning and uses of the common notions in Greek mathematics, and argue that they were originally conceived in order to axiomatize a theory of equivalence in geometry. I also claim that two interpolated common notions responded to different epistemic needs and regulated diagrammatic inferences.
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This chapter deals with the philosophy of space and the theory of geometry developed by the Renai... more This chapter deals with the philosophy of space and the theory of geometry developed by the Renaissance philosopher Francesco Patrizi da Cherso. Patrizi's metaphysics of space shares several common features with other similar constructions (by Bruno, Campanella, and others) aimed at radically rethinking the notions of space and place present in Aristotelian traditions. The uniqueness of Patrizi's proposal, however, is to be found in his attempt to ground geometry in this new conception of space, thus claiming for the first time in history that geometry is the science of space rather than the "science of continuous magnitudes" as it had been conceived from Antiquity to his day and age.
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Books (Monographs) by Vincenzo De Risi
Edited Volumes by Vincenzo De Risi
Editions of Texts by Vincenzo De Risi
Papers by Vincenzo De Risi