Generally Mill’s remark is true, that affirmation and denial stand for distinctions of fact that cannot be got rid of by manipulation of words.  Whether granite sinks in water, or not; whether the rook lives a hundred years, or not; whether a man has a hundred dollars in his pocket, or not; whether human bones have ever been found in Pliocene strata, or not; such alternatives require distinct forms of expression.  At the same time, it may be granted that many facts admit of being stated with nearly equal propriety in either Quality, as No man is proof against flattery, or All men are open to flattery.

But whatever advantage there is in occasionally changing the Quality of a proposition may be gained by the process of Obversion (chap. vii.  Sec. 5); whilst to use only one Quality would impair the elasticity of logical expression.  It is a postulate of Logic that the negative sign may be transferred from the copula to the predicate, or from the predicate to the copula, without altering the sense of a proposition; and this is justified by the experience that not to have an attribute and to be without it are the same thing.

Sec. 3.  A. I. E. O.—­Combining the two kinds of Quantity, Universal and Particular, with the two kinds of Quality, Affirmative and Negative, we get four simple types of proposition, which it is usual to symbolise by the letters A. I. E. O., thus: 

A. Universal Affirmative —­ All S is P.
I. Particular Affirmative —­ Some S is P.
E. Universal Negative —­ No S is P.
O. Particular Negative —­ Some S is not P.

As an aid to the remembering of these symbols we may observe that A. and I. are the first two vowels in affirmo and that E. and O. are the vowels in nego.

It must be acknowledged that these four kinds of proposition recognised by Formal Logic constitute a very meagre selection from the list of propositions actually used in judgment and reasoning.

Those Logicians who explicitly quantify the predicate obtain, in all, eight forms of proposition according to Quantity and Quality: 

[Transcriber’s Note:  The Greek characters used in the original are represented below by the name of the character in square brackets.]

U. Toto-total Affirmative —­ All X is all Y.
A. Toto-partial Affirmative —­ All X is some Y.
Y. Parti-total Affirmative —­ Some X is all Y.
I. Parti-partial Affirmative —­ Some X is some Y.
E. Toto-total Negative —­ No X is any Y.
[eta].  Toto-partial Negative —­ No X is some Y.
O. Parti-total Negative —­ Some X is not any Y.
[omega].  Parti-partial Negative —­ Some X is not some Y.

Here A. I. E. O. correspond with those similarly symbolised in the usual list, merely designating in the predicates the quantity which was formerly treated as implicit.