In every proposition P must be either affirmed or denied of S. This alternative determines the Quality of the proposition, which must be either (I) affirmative, or (2) negative. This division is ultimate.

Some logicians have, it is true, endeavoured to reduce all propositions to the affirmative form by writing S is not-P. But the difference cannot be thus bridged. S is not-P is, of course, equivalent to S is not P. But they differ the one from the other: since in S is not P we deny the positive concept P of S, and in S is not-P we affirm the negative concept not-P of S. The negative and affirmative forms remain radically distinct.

Kant admits three forms, Affirmative, Negative, Infinite, S is P. S is not P, S is not-P. His motive in assigning the Infinite judgment to a separate class, instead of reckoning them with the Affirmatives to which they rightly belong, seems to have been the desire that his scheme of Categories should present an harmonious appearance. A triple division was required in its other portions, and a triple division must perforce be found for the Quality of judgments.

In any affirmation or negation, P may be affirmed or denied, (1) of all the objects denoted by the subject-term, e.g. 'All men are mortal'; or (2) of only some of these objects, e.g. 'Some men are negroes': or (3) there may be no sign to mark whether the predicate refers to some only or to all, e.g. 'Pleasure is not a good' : or (4) the subject may be a singular term, e.g. 'Socrates is wise,' 'The highest of the Alps has been scaled.' These various alternatives lead to the division of propositions according to quantity.

We have already explained that when a subject is employed distributively, the predicate is affirmed of every individual denoted by the subject. When we say, 'All sparrows are winged,' we mean that every individual sparrow is possessed of wings.

A proposition in which the subject is understood collectively is not universal. Thus the proposition, 'All the slates covered the roof,' is not a universal proposition. The predicate is not affirmable of each individual denoted by the subject, but of the individuals as forming one group. Hence, whenever the word All (and not Every) is employed to qualify the subject, care must be taken to observe whether it be understood collectively or distributively.

It is plain that though the Affirmative Universal is of the form All S is P, the Negative Universal will not be All S is not P, but No S is P. The form All S is not P does not exclude P from each and every individual S, as at once appears in the proposition 'All soldiers are not generals’. If, however, I say, 'No Englishmen are negroes,' I deny the attribute of every Englishman.

The employment of the plural in a universal proposition, e.g. 'All men are mortal,' may possibly mislead the student into supposing that in the subject the intellect conceives a number of individuals. This is, of course, impossible. Mentally the whole class is expressed by the universal concept 'man.' But the grammatical form 'All men are mortal,' shows that we have under our consideration, not the universal nature viewed in abstraction from particulars, but the concrete individuals. Man is mortal' is the purely logical form. 'All men are mortal' puts us in touch with concrete reality.

The form of the Particular proposition is Some S are (or are not) P; for instance, 'Some soldiers are brave,' 'Some rich men are not generous’. The sense, in which the word 'some' is here used, differs in certain respects from that in which it is ordinarily employed. In ordinary use, when we speak, e.g. of 'some' men, we are under stood to mean more than one, and also to exclude the supposition that what we say may be true of all men.

'Some' means 'several but not all.' In Logic, the ‘some' of a particular proposition, may be used even where the predicate might be truly affirmed of all: and it may be used also even if there be but one individual to whom it could be applied.

Thus I may say, 'Some birds have wings,' even though it be the case that all birds possess them: and 'Some men are eight feet high,' though in fact there be but one such man. 'Some' leaves the extension to which reference is made indeterminate.¹

The essential distinction then between Universal and Particular propositions lies in this, that Universals deal with the whole class, Particulars with an indeterminate portion of the class.

And here it is well to call attention to the fact, that universal propositions are of two sorts. The majority of them cannot be attained by mere enumeration of instances. Some indeed can. I can arrive at the universal truth, that 'All the apostles were Jews,' by a process of counting. But propositions of this character are of minor moment. Enumeration will not serve me in regard to such propositions as, 'All men are mortal,' 'All birds are oviparous.' Here, I refer not merely to an incalculable number of past instances, but also to the future. All laws of nature known to science are propositions of this character.

The aim and object of scientific enquiry is to establish such universal truths.

How is it that we can affirm a predicate of individuals, which have not come within our experience? The explanation lies in the fact, that in these propositions we know the predicate to be invariably connected with the universal class-notion employed in the subject. In a later part of Logic, we shall consider how we reach this knowledge. It is sufficient here to observe that to what ever individuals the notion 'man ' is applicable, the predicate 'mortal' is applicable also. In virtue of their being men, they possess the attribute of mortality. The universality of these propositions rests not on enumeration, but on our knowledge of the constant connection between the concepts of the subject and predicate.

It remains to consider Indesignate and Singular pro positions.

Indesignate propositions are such as have no sign of quantity. As far as form is concerned, they may be universal, or they may be particular. If I say, 'Old men are melancholy,' it does not appear, whether I am speaking of all old men, or of some only. Hence indesignate propositions have no place in Logic, until a sign of quantity is affixed to them. In some cases indeed the Indesignate is used to signify that the predicate is connected necessarily with the subject, e.g. 'Man is mortal’.

Here the proposition is of course equivalent to a universal. For these judgments in which the Indesignate form stands not for individuals, but for the class-nature, some authors employ the convenient term Generic judgments. But it should be observed that we do not know their universal character from the logical form, but from our previous acquaintance with the matter under consideration.

Very often the Indesignate is used for what are termed moral universals, as in the example already given', Old men are melancholy'.

A moral universal admits exceptions, and hence is logically a particular.

The Singular proposition is, as we have said, one whose subject is either a significant Singular term or a proper name. These propositions present some anomalies. On the one hand, the individual object is a member of a class, and it appears incongruous to treat it as though it were itself a class. On the other, the definition of a Universal proposition is applicable to them, for the predicate is affirmed of the subject in its whole extension, the extension in this case being restricted to a single individual. Modern logicians have resolved to treat this proposition as a Universal, and it will be convenient to adhere to that arrangement.

The older logicians classify the Singular proposition separately, and assign it neither to the Universal nor to the Particular.^²

This was, it would seem, the more scientific course. For the Universal and Particular are distinguished by the manner in which the concept employed as subject is understood in regard to extension. But as we have explained above we have no singular concepts. Hence there is a fundamental difference between such a proposition as, 'All men are mortal,' and 'Socrates is a philosopher.'

Propositions whose subject is a Collective term are Singular propositions. Thus if I say,' All the apples filled the bowl,' it is clear that I refer to this group of apples considered as a single object.