[5] Definition (horismos) [Categories, ch. 1]

What is definition?

Before attempting to answer this question Aristotle draws attention to the possibility of ambiguity.

He discusses two kinds:

(i) synonymy — as when different entities share the same name (for example, ‘animal’ may refer to man, horse, dog, and so on);

(ii) homonymy — when a word has different meanings (for example, ‘plain’).

He is particularly concerned with the word ‘esti‘ (‘is’), from ‘einai (‘to be’), and hence with ‘being’ — a central concept in his metaphysics.

Given such possible ambiguities there are, he says [Posterior Analytics II, 13], difficulties with the view of definition as a process of analysis (or ‘division’) of a genus into subgenera by means of ‘differentia’ [a], for example, the definition of man (species) as an animal (genus) characterized by being two-footed (difference).

He does, however, allow a role to definition by division in so far as

(a) it ensures that we take the relevant characteristics in the right order, and

(b) enables us to determine when our definition of the ‘lowest species’ (infima species) has been reached.

(In his later writings [for example, Metaphysics, Ζ 12 and Η 6] he modifies and expands on this account.

To avoid problems raised by Plato’s treatment of ‘participation’ of genera and differentia [b] in the Forms he appeals to the concepts of potentiality and actuality [b].

He supposes the genus exists potentially in the species as its ‘matter’ on which the form of the lowest species is imposed.

Hence, he believes, a unity of genus and differentia is achieved.)

He starts his own account of definition [Posterior Analytics II, 9-10] by distinguishing between a nominal (or verbal) definition and a real (or ‘essential’) one.

The former relates to a conventional usage in ordinary discourse — what is signified by a name and which may be an incomplete definition of a basic term in natural science, or a definition of some event or quality as contained in the conclusion of a syllogism (if we leave out the premisses).

Real definitions, however, give us an explanation of why and what a thing is [c].

This leads on to methodology.

[6] To discover real definitions we must make use of demonstration.

Aristotle says [Post. An. II, 1 and 2] that before undertaking a demonstration we need to set out the objects of the enquiry, that is, we have to know:

– what the name means;

– that the corresponding thing ‘is’;

– that it has such and such properties; and

why it has them.

There are also a number of requirements the premisses (as archai) of a demonstration must meet.

They must be true, primary, more ‘intelligible’, and prior to the conclusions we draw from them; and they must be causes (aitiai — ‘explanatory factors’) of the conclusions.

He identifies four such factors: formal, material, efficient, and final [a] [see further in sec. 9 below].

Premisses, moreover, are of several kinds.

(1) There are axioms, such as the principle of contradiction, in accordance with which our inferences are drawn; and

(2) theses or ‘posits’: these vary from science to science.

They include hypotheses and definitions.

A hypothesis is an assumption that something is or is not, whereas if we know what something is, or why it occurs we have a (real) definition — which, in the case of a primary substance, will give us its material, formal, or final ‘causes’.

It is the aim of a given science to reach such definitions.

This is done by constructing a scientific or ‘cognitive’ syllogism.

Thus, suppose we wish to define thunder [see Post. An. II, 10].

We must first produce the nominal definition of the fundamental species by collecting common qualities which we suppose are coextensive with and essential to it.

For thunder one such quality is noise in the clouds.

(Here Plato’s method of division is relevant.)

Aristotle’s procedure (the epagoge) here is roughly what later came to be called inductive — a move from particulars to the universal.

However, his account is not fully worked out and is not always consistent [see Post. An. II, 23].

Secondly, we search for the reference of the middle term of the syllogism.

‘Extinguishing of fire’ is suitable here and constitutes the efficient cause.

Finally the real definition — thunder is a noise in the clouds caused by the extinguishing of fire in them — can be established when the complete syllogism is constructed — a deductive procedure of universal to particular [b].

(This would not of course be regarded as the correct explanation by scientists today.)

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