Of the Canon of Reasoning.
& 569. The first figure was regarded by logicians as the only perfect type of syllogism, because the validity of moods in this figure may be tested directly by their complying, or failing to comply, with a certain axiom, the truth of which is self-evident. This axiom is known as the Dictum de Omni et Nullo. It may be expressed as follows—
Whatever may be affirmed or denied of a whole class may be affirmed or denied of everything contained in that class.
§ 570. This mode of stating the axiom contemplates predication as being made in extension, whereas it is more naturally to be regarded as being made in intension.
§ 571. The same principle may be expressed intensively as follows—
Whatever has certain attributes has also the attributes which invariably accompany them .[Footnote: Nota notae est nota rei ipsius. 'Whatever has any mark has that which it is a mark of.' Mill, vol. i, p. 201,]
§ 572. By Aristotle himself the principle was expressed in a neutral form thus—
'Whatever is stated of the predicate will be stated also of the subject [Footnote: [Greek: osa katà toû kategorouménou légetai pánta kaì katà toû hypokeiménou rhaetésetai]. Cat. 3, § I].'
This way of putting it, however, is too loose.
§ 573. The principle precisely stated is as follows—