Aristotle proposes a solution that applies to definitions reached by the "method of division".
He criticises the method of division, for example, in Parts of Animals (I, 2-3).
In this work, we present an efficient parallelization of the method by division among the processors of the plane-wave components for each state.
Although many have criticised the method of division, most notably, Ryle (1966), who wished to distinguish it from genuine philosophy or dialectic, it does seem that, properly understood, it forms the heart of Plato's later methodology.
What we have in ancient Greek thought, then, is a complex web of methodologies, of which the most important are Socratic definition, which Plato elaborated into his method of division, his related method of hypothesis, which drew on geometrical analysis, and the method(s) that Aristotle developed in his Analytics.
(CEE, 57/46) {§2.2} [Euclid's Elements] contains all the dialectical methods: the method of division for finding kinds, definitions for making statements of essential properties, demonstrations for proceeding from premises to conclusions, and analysis for passing in the reverse direction from conclusions to principles.
Leibniz's conception of analysis can thus be seen as combining aspects of Plato's method of division, in the centrality accorded to the definition of concepts, of ancient Greek geometry and Aristotelian logic, in the emphasis placed on proof and working back to first principles, and of Cartesian geometry and the new algebra, in the value attributed to symbolic formulations.
Its five chapters pursue this purpose, discussing the appropriate level of generality for such studies, the modes of causality and of necessity to be used in biological explanations, the relation of form to matter in living things, the proper method of division for this subject matter, the means of identifying kinds and their activities at the proper level of abstraction, and much more.
The interconnections between these alone are complex; but there were other influential conceptions in antiquity as well most notably, Galen's amalgam of previous methodologies in the context of medicine, and the Neoplatonists' theological transformation of Plato's method of division.
The task of this strategy is to find the method of division in which the areas of all groups are all the same.
