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Aristotle on the middle term in deduction and demonstration

Grant number: 13/22513-0
Support Opportunities:Scholarships abroad - Research Internship - Post-doctor
Effective date (Start): January 01, 2014
Effective date (End): May 31, 2014
Field of knowledge:Humanities - Philosophy - History of Philosophy
Principal Investigator:Marco Antônio de Ávila Zingano
Grantee:Jean-Louis André Bernard Hudry
Supervisor: Ahmed Hasnaoui
Host Institution: Faculdade de Filosofia, Letras e Ciências Humanas (FFLCH). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Research place: Université Paris Diderot - Paris 7, France  
Associated to the scholarship:11/03425-7 - Aristotle on the intellect, BP.PD


Aristotle's conception of the intellect (nous) plays a central role in the Posterior Analytics, in so far as a process of intellection provides justifications for the indemonstrable premises of a scientific demonstration. These premises are an immediate first (major) premise and a last (minor) premise introduced by a middle term. My research project for the BEPE scholarship aims to show how the demonstrative middle term accounts for the distinction between deduction and demonstration. In any deduction simpliciter, the middle term holds a formal position between a first term and a last term. Yet, with respect to demonstration, the middle term is more than a formal term, as it is the proof or explanation that accounts for the demonstrative conclusion. The Prior Analytics (cf. B, 23, 68b15-37) introduces two kinds of deduction: the deduction through the (demonstrative) middle term and the deduction through induction (epagôgê). In a deduction through the middle term, the first premise is immediate (amesos), and the last premise mediates the first premise through the middle term (meson). In a deduction through induction, the first premise is never immediate, as it is the deduced conclusion of another deduction. Nor does the last premise introduce a demonstrative middle term (namely a proof or explanation), as it is a premise justified though mere induction. This research project aims to explain why the deduction through the middle term is prior to the deduction through induction. While the former is more cognizable by nature, the latter is more accessible through perception. The contrast of what is prior by nature with what is prior to us is introduced in the Posterior Analytics (A, 2, 71b33-72a5), and Aristotle repeats this view in many of his other works. The primacy of the deduction through the middle term implies that this kind of deduction may be demonstrative knowledge, as the middle term provides an abstract proof or explanation. On the other hand, it is impossible for the deduction through induction to be demonstrative knowledge. It is only a dialectical deduction, which Aristotle's Topics investigates. Induction is often required for demonstrative knowledge, but is not sufficient on its own, since knowledge has to deal with abstract universals, namely genera and their differentiae. If demonstrative knowledge has to define an apple tree, it will do it under the abstract genus 'plant', for which induction on its own cannot account. At best, induction will tell that an apple tree is a tree or a fruit tree. In other words, if what is prior and better cognized is indirectly related to perception, it does not mean that it is directly accessible through it, and this contrast perfectly illustrates Aristotle's distinction between the deduction through the middle term and the deduction through induction. In that respect, the middle term is the cornerstone of Aristotle's conception of demonstrative knowledge. (AU)

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