definition and demonstration

see also: http://eidetisch.tumblr.com/post/43126760887/5-definition-horismos-categories-ch-1-what

Closely related to this is the discussion, in Posterior Analytics II.3-10, of the question whether there can be both definition and demonstration of the same thing.

Since the definitions Aristotle is interested in are statements of essences, knowing a definition is knowing, of some existing thing, what it is.

Consequently, Aristotle’s question amounts to a question whether defining and demonstrating can be alternative ways of acquiring the same knowledge.

His reply is complex:

1. Not everything demonstrable can be known by finding definitions, since all definitions are universal and affirmative whereas some demonstrable propositions are negative.

2. If a thing is demonstrable, then to know it just is to possess its demonstration; therefore, it cannot be known just by definition.

3. Nevertheless, some definitions can be understood as demonstrations differently arranged.

As an example of case 3, Aristotle considers the definition “Thunder is the extinction of fire in the clouds”.

He sees this as a compressed and rearranged form of this demonstration:

– Sound accompanies the extinguishing of fire.
– Fire is extinguished in the clouds.
– Therefore, a sound occurs in the clouds.

We can see the connection by considering the answers to two questions:

“What is thunder?”

“The extinction of fire in the clouds” (definition).

“Why does it thunder?”

“Because fire is extinguished in the clouds” (demonstration).

As with his criticisms of Division, Aristotle is arguing for the superiority of his own concept of science to the Platonic concept.

Knowledge is composed of demonstrations, even if it may also include definitions; the method of science is demonstrative, even if it may also include the process of defining.

via: http://plato.stanford.edu/archives/spr2012/entries/aristotle-logic/

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