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The correlation between definition and demonstration in Aristotle's Posterior Analytics

Grant number: 21/01029-9
Support Opportunities:Scholarships in Brazil - Doctorate
Effective date (Start): January 01, 2022
Effective date (End): July 31, 2025
Field of knowledge:Humanities - Philosophy - History of Philosophy
Principal Investigator:Luiz Henrique Lopes dos Santos
Grantee:Mariane Farias de Oliveira
Host Institution: Faculdade de Filosofia, Letras e Ciências Humanas (FFLCH). Universidade de São Paulo (USP). São Paulo , SP, Brazil


In the Posterior Analytics, after having exposed, in book A, his investigation on scientific knowledge and its expression through demonstration, Aristotle presents, in book B, how and if it is possible to have demonstration and definition of the same object. After going through several puzzles between the section of chapters B.3-7, Aristotle develops in B.8 an interpretation about this interdependence between practices from the introduction of the notion of causality. That is, the cause, which is the very expression of "what is it" (the definition) of the object, figures as a middle term of demonstration for scientific knowledge. The problem, however, is that at the end of the chapter, having intended to have presented how the definition is known, Aristotle presents us with an apparent inconsistency. This consists of three propositions presented (93b15ff) at the end of the chapter: (i) There is knowledge of "what is it" (definition); (ii) One cannot know "what is it" without demonstration; (iii) There is no demonstration of "what is it". Our main question, therefore, is the following: after all, can the definition, whose possibility of knowledge has already been guaranteed in (i), only be known through demonstration (ii), without, however, being able to have demonstration of it (iii)? We intend to explore the hypothesis that there is knowledge of the definition through the explanatory power expressed by the cause, instantiated in the middle term, in the structure of demonstration. That is, we know the definition because it is nothing more than the exposure of the causal and necessary relationship that the items of the demonstration maintain among themselves. It is not the result of the demonstration, that is, what it proves, that reveals the definition, but a certain "disposition of the terms " in the demonstrative structure that makes possible the causal explanatory power of it. Thus we can summarize our hypothesis that it is this causal explanatory power among the ordered terms, determined by an appropriate middle term that presents the efficient cause, which reveals or shows the definition without demonstrating it. The fact is that both the demonstration and the definition that is manifested in it seem to be one and the same thing: the expression of scientific knowledge. It can be said that they complement each other because while the definition shows the essence, the demonstration proves the existence.

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