§ 566. It will be well to explain by an instance the meaning of the assertion previously made, that a difference of figure is internal to a difference of mood. We will take the mood EIO, and by varying the position of the terms, construct a syllogism in it in each of the four figures. I. E No wicked man is happy. I Some prosperous men are wicked. O .'. Some prosperous men are not happy. II. E No happy man is wicked. I Some prosperous men are wicked. O .'. Some prosperous men are not happy. III. E No wicked man is happy. I Some wicked men are prosperous. O .'. Some prosperous men are not happy. IV. E No happy man is wicked. I Some wicked men are prosperous. O .'. Some prosperous men are not happy. § 567. In the mood we have selected, owing to the peculiar nature of the premisses, both of which admit of simple conversion, it happens that the resulting syllogisms are all valid. But in the great majority of moods no syllogism would be valid at all, and in many moods a syllogism would be valid in one figure and invalid in another. As yet however we are only concerned with the conceivable combinations, apart from the question of their legitimacy. § 568. Now since there are four different figures and sixty-four different moods, we obtain in all 256 possible ways of arranging three terms in three propositions, that is, 256 possible forms of syllogism. CHAPTER X. _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-- Whatever may be affirmed or denied universally of the predicate of an affirmative proposition, may be affirmed or denied also of the subject.