No. 2 represents the special case where S and P are coextensive, as in All equiangular triangles are equilateral.
S and P being general names, they are said to be distributed when the proposition applies to them in their whole extent, that is, when the assertion covers every individual in the class.
In E, the Universal Negative, both terms are distributed: "No S is P" wholly excludes the two classes one from the other, imports that not one individual of either is in the other.
In A, S is distributed, but not P. S is wholly in P, but nothing is said about the extent of P beyond S.
In O, S is undistributed, P is distributed. A part of S is declared to be wholly excluded from P.
In I, neither S nor P is distributed.
It will be seen that the Predicate term of a Negative proposition is always distributed, of an Affirmative, always undistributed.
A little indistinctness in the signification of P crept into mediæval text-books, and has tended to confuse modern disputation about the import of Predication. Unless P is a class name, the ordinary doctrine of distribution is nonsense; and Euler's diagrams are meaningless. Yet many writers who adopt both follow mediæval usage in treating P as the equivalent of an adjective, and consequently "is" as identical with the verb of incomplete predication in common speech.
It should be recognised that these syllogistic forms are purely artificial, invented for a purpose, namely, the simplification of syllogising. Aristotle indicated the precise usage on which his syllogism is based (Prior Analytics, i. 1 and 4). His form[2] for All S is P, is S is wholly in P; for No S is P, S is wholly not in P. His copula is not "is," but "is in," and it is a pity that this usage was not kept. "All S is in P" would have saved much confusion. But, doubtless for the sake of simplicity, the besetting sin of tutorial handbooks, All S is P crept in instead, illustrated by such examples as "All men are mortal".
Thus the "is" of the syllogistic form became confused with the "is" of common speech, and the syllogistic view of predication as being equivalent to inclusion in, or exclusion from a class, was misunderstood. The true Aristotelian doctrine is not that predication consists in referring subjects to classes, but only that for certain logical purposes it may be so regarded. The syllogistic forms are artificial forms. They were not originally intended to represent the actual processes of thought expressed in common speech. To argue that when I say "All crows are black," I do not form a class of black things, and contemplate crows within it as one circle is within another, is to contradict no intelligent logical doctrine.