Aristotle on divisional definition and demonstration in Posterior Analytics 2

FABIAN MIE

Guadalajara

Workshop; Workshop The Greeks and Their Knowledge; 2022

Universidad de Guadalajara

In the Analytics, Aristotle presents a hard criticism against the current method of division; he mainly aims at showing that division is neither a deduction nor a demonstration and that, as it stands, cannot succeed in providing definitions (APo. 2.3-5). Now, Aristotle generally takes definitions to feature in demonstration as the explanatory middle (2.8 93b6), and thus he holds that definitions are the very principles through which all sciences come about (2.17 99a21-22). But he has serious concerns about divisional definition. For instance, he objects that division is a “weak deduction” (APr. 1.31 46a33) in that it begs the question by always deducing something higher or more general than what must be demonstrated (46a33-34), and that it includes in the premises what should be deduced (APo. 2.4. 91a24-32). The closing passage at the end of 2.7 summarizes the rather negative results achieved through the diaporematic examination of division and definition in 2.3-7:T1 From these considerations it appears that definitions and deductions are not the same, and that there cannot be deductions and definitions of the same thing; and further that definitions neither demonstrate nor prove anything, and that it is not possible to know what something is either by a definition or by a demonstration. (2.7 92b35-38) Since this involves a severe criticism of division, scholars have often been struck that in APo. 2.13 Aristotle seems to embrace division wholeheartedly, and, after making some formal precisions on the divisional procedure as well as introducing several important reformations on it in view of making division useful for demonstration, Aristotle does not hesitate to recommend division as the appropriate method for grasping the essence of species (91b33-35). My aims here are, first, to clarify Aristotle’s distinction between division, deduction, and demonstration in APo. 2.2-7. Second, I aim to show how Aristotle thinks that division turns out to be an integral part of causal inquiry and explanation in 2.13-14. A crucial issue for this project is to explain how does the account of essence reached by means of division relate to the role granted to definition as the main demonstrative principle in demonstrations. On this latter issue, Aristotle’s formal reformations of division will prove to be crucial. My claim will be that divisional definitions provide only a preliminary and partial account of the essence of subject-kinds, which must be placed in the pre-demonstrative framework stage of science. However, doing a division well is decisive for the aims of causal inquiry since the scientist aims at discovering which of the parts and features of a species’ essence already singled out in a division can play the role of explanantia. Thus, the formal amendments of division carefully introduced by Aristotle are intended to put to use the definitions grasped by that method as explanatory principles in working out next the demonstrations of attributes that are ultimately linked to the essence of the species.