Division and DeFinition. Aristotle's Criticism and Use of Platonic Division

FABIAN MIE

Santa Fe

Workshop; V workshop sobre la filosofía de Aristóteles: aspectos de ética, metafísica y metodología. Interpretaciones y discusiones medievales y contemporáneas.; 2019

Universidad Nacional del Litoral

Famously, Aristotle rejected division as a weak deduction (Prior Analytics I 31, 46a33) because, according to him, division begs the question by always deducing something higher or more general than the attribute to be demonstrated (46a33-34). Aristotle?s hard criticism is not independent from his own theory of deduction and of science; in fact, he sees division as a deductive argument and objects against Plato?s divisions both that they do not know what can be deduced, and that the ?deduction according to division? cannot really proceed in the way the Platonists make it proceed. He generally objects that essence cannot be proved, implying therewith that the Platonic division (wrongly) aims at deducing or demonstrating essence. This is a topic Aristotle elaborates further in APo. II 5-10. It could be surprising that after his devastating criticism in APo. II 3-5, Aristotle comes to accept that, if we follow some recommendations (which basically coincide with those given by Plato) and even though division will never be a deduction properly, it will permit us to know the essence (91b33-35):It is possible to solve the difficulties if you assume everything in what the thing is, make the division consecutive by postulating what is primitive, and leave nothing out (APo. II 5.91b29-30). I hold that the recommendations for division contained here are four (possibly, none of them was ignored by Plato): (i) assume every term in what the thing is (λαμβάνειν ἐν τῷ τί ἐστι πάντα) (i.e. every term must be essential to the definiendum or part of its essence); (ii) divide in order or consecutively (καὶ τὸ ἐφεξῆς τῇ διαιρέσει ποιεῖν) (i.e. one term must come after the other in a series); (iii) postulate what comes first (αἰτούμενον τὸ πρῶτον) (i.e. identify the genus and, perhaps, what is prior at each cut); (iv) do not leave something out (μηδὲν παραλείπειν) (i.e. include all the essential features). In this presentation, I would like to consider Aristotle?s attitude towards Platonic division in order to find out why, after having criticized division in APr. I 31 and APo. II 3-5, he can still hold (in APo. II 13) that division is a useful procedure for grasping the essence and getting to the principles of science. If it is true that Aristotle grants the method such a performance within his own theory of science, it may be important to get a clearer view on the constraints Aristotle sets on the practice of division for achieving his own epistemological goals (i.e. the grasping of definitions). My presentation will focus mainly on some relevant texts of the Analytics in a very basic way and as a preliminary to a far-reaching discussion on demonstrative knowledge and the grasping of its principles.