BEING CLEAR ABOUT THE EXPLANATION: A MATHEMATICAL EXAMPLE IN ARISTOTLE, <i>METAPHYSICA</i> Θ.9, 1051A26–9

Hasper, Pieter Sjoerd

doi:10.1017/s000983881000042x

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The Geometrical Example1

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“…The version of the proof of Metaphysics Θ 9 is incomplete, since Aristotle thinks he has shown that there is 'universally a right angle'. On this problem see Mendell (1994) and Hasper (2011). perpendicular to the diameter AB is erected from centre O. AO, OB and OC are all radii and form the isosceles triangles ABO and OBC.…”

Section: The Geometrical Examplementioning

confidence: 99%

Material Cause and Syllogistic Necessity in Posterior Analytics Ii 11

Fait

2019

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The paper examines Posterior Analytics II 11, 94a20-36 and makes three points. (1) The confusing formula 'given what things, is it necessary for this to be' [τίνων ὄντων ἀνάγκη τοῦτ᾿ εἶναι] at a21-22 introduces material cause, not syllogistic necessity. (2) When biological material necessitation is the only causal factor, Aristotle is reluctant to formalize it in syllogistic terms, and this helps to explain why, in II 11, he turns to geometry in order to illustrate a kind of material cause that can be expressed as the middle term of an explanatory syllogism. (3) If geometrical proof is viewed as a complex construction built on  I thank Fabio Acerbi, Lucas Angioni, Giulio Di Basilio and Breno Zuppolini for their help and their comments. I am particularly indebted to Diana Quarantotto for invaluable written remarks on a very short notice.

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Section: The Geometrical Examplementioning

confidence: 99%