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The Aristotelian conception of geometric demonstration from the Posterior Analytics

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Rafael Cavalcanti de Souza
Total Authors: 1
Document type: Master's Dissertation
Press: Campinas, SP.
Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Filosofia e Ciências Humanas
Defense date:
Examining board members:
Lucas Angioni; Breno Andrade Zuppolini; Mateus Ricardo Fernandes Ferreira
Advisor: Lucas Angioni

In Posterior Analytics I. 14, 79a16-21 Aristotle states that mathematical demonstrations are expressed in first-figure syllogisms. I present a reading of the theory of the scientific demonstration set out in Posterior Analytics I (with greater emphasis on chapters 2-6) that is consistent with the Aristotelian text and explains examples of geometric demonstrations present in the Corpus. In general terms, I argue that the Aristotelian demonstration is a procedure of analysis that explains a given explanandum through the conversion of a previously established proposition. In a syllogistic structure, the previously established proposition is the major premise and the middle term must be commensurate with the explanandum. The conjunct of the major premise and the minor premise (the explanans) is coextensive with the explanandum, but there is an intensional asymmetry between the explanans and the explanadum, so that only the former explains the latter. Finally, I argue that the element identified in the middle term must be the most appropriate to explain precisely what a certain explanandum is (AU)

FAPESP's process: 20/00155-8 - Dependence and independence of mathematical entities on sensitive substances: ontological and logical aspect of abstraction in Aristotle
Grantee:Rafael Cavalcanti de Souza
Support Opportunities: Scholarships in Brazil - Master