By M. Deslauriers
This paintings examines Aristotles discussions of definition in his logical works and the Metaphysics , and argues for the significance of definitions of straightforward elements, drawing the relationship among definitions as first rules of demonstration and as statements of essence.
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Additional info for Aristotle on Definition
In saying this, Aristotle may have had in mind a passage such as the one I have already quoted from the Statesman, where the Stranger speaks of “the most honourable things” being demonstrable (δε κνυμι) only by reason (286a). Plato’s point is that ostensive deﬁnition is suitable for and adequate to embodied things, and that division is employed in the deﬁnition of embodied things only as practice for the deﬁnition of things without bodies. The implication is clearly that deﬁnition by division is a method of demonstrating (in the sense of “pointing out” or “showing”) forms in themselves, but not that it is a method of demonstration in the strict sense.
According to Aristotle deﬁnitions are the starting-points of demonstration, and division, which is not a system of proof, cannot oﬀer demonstrative conclusions, but only these starting points. At the same time, the deﬁnitions that are these starting-points are crucial in that the demonstration founded on them will be as vulnerable to criticism as are they. Since Aristotle insists on the certainty of demonstrative conclusions, he must have a means to ensure the certainty of deﬁnitions.
For every magnitude either has width or does not have width, because either the aﬃrmation or the denial is true in every case. 6 143b12–17). Privative divisions are, then, problematic in two ways: they cannot be further divided because they cannot be further speciﬁed, and they make necessary the identiﬁcation of the genus with one of its species (by appeal to the law of excluded middle). Both of these problems are indicative most immediately of incompleteness; if one divides initially privatively, one will likely end the procedure with an incomplete deﬁnition.