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negative, as “man is not perfect;” “no miser is happy,"
Another division* of propositions is accord- Qnantity. ing to their quantity (or extent : )if the predicate is said of the whole of the subject, the proposition is Universal : if of a part of it only, the proposition is Particular (or partial ;)
England is an island;" “ all tyrants are miserable ;” “no miser is rich ;” are Universal propositions, and their subjects are therefore said to be distributed, being understood to stand, each, for the whole of its Significates : but, “ some islands are fertile ; ” "all tyrants are not assassinated;" are Particular, and their subjects, consequently, not distributed, being taken to stand for a part only of their Significates.
As every proposition must be either Affirmative or Negative, and must also be either universal or particular, we reckon, in all, four kinds of pure categorical propositions, (i. e. considered as to their quantity and quality both;) viz. Universal Affirmative, whose symbol (used for brevity) is A; Universal Negative, E; Particular Affirmative, I; Particular Negative, O.
§ 2. When the subject of a proposition is a Common-term, the universal signs (“all, no, every")
* See Chap. v. 9 5.
are used to indicate that it is distributed, (and the proposition consequently is universal ;) the particular signs (“some, &c.”) the contrary; should there be no sign at all to the common term, the quantity of the proposition (which is called an Indefinite proposition) is ascertained by the matter; i.e. the nature of the connexion between the extremes : which is either Neces
sary, Impossible, or Contingent. In necessary Indefinites. and in impossible matter, an Indefinite is un
derstood as a universal : e. g. “ birds have wings;" i. e. all: “ birds are not quadrupeds;" i. e. none : in contingent matter, (i. e. where the terms partly (i. e. sometimes) agree, and partly not) an Indefinite is understood as a particular; e. g. “food is necessary to life ;' i. e. some food; "birds sing;" i. e. some do ; “birds are not carnivorous ;" i. e. some are not, or, all are not.*
As for singular propositions, (viz. those whose subject is either a proper name, or a common term with a singular sign) they are reckoned as Universals, (see Book IV. Ch. iv. § 2.) because in them we speak of the whole of the subject; e.g. when we say, “ Brutus was a Roman,” we
It is very perplexing to the learner, and needlessly so, to reckon indefinites as one class of propositions in respect of quantity. They must be either universal or particular, though it is not declared which. Such a mode of classifi. cation resembles that of some grammarians, who, among the Genders, enumerate the doubtful gender !
mean, the whole of Brutus : this is the general rule; but some singular propositions may fairly be reckoned particular ; i.e. when some qualifying word is inserted, which indicates that you are not speaking of the whole of the subject; e. g. “ Cæsar was not wholly a tyrant ;" “ this man is occasionally intemperate;" “ non omnis moriar.”*
It is evident, that the subject is distributed in every universal proposition, and never in a particular; (that being the very difference between universal and particular propositions :) but the distribution or non-distribution of the predicate, depends (not on the quantity, but) on the quality, of the proposition ; for, if any part of the predicate agrees with the subject, it must be affirmed and not denied of the subject; therefore, for an affirmative proposition to be true, it is sufficient that some part of the predicate agree with the subject; and (for the same reason) for a negative to be true, it is necessary that the whole of the predicate should disagree with the subject : e.g. it is
It is not meant that these may not be, and that, the most naturally, accounted Universals; but it is only by viewing them in the other light, that we can regularly state the Contradictory to a Singular proposition. Strictly speaking, when we regard such propositions as admitting of a variation in Quantity, they are not properly considered as Singular; the subject being, e. g. not Cæsar, but the parts of his character.
true that "
learning is useful,” though the whole of the term “ useful” does not agree with the term “ learning,” (for many things are useful besides learning,) but “no vice is useful,” would be false, if any part of the term “useful” agreed with the term “vice;" (i.e. if you could find any one useful thing which was a vice.) The two practical rules then to be observed respecting distribution, are,
1st. All universal propositions (and no particular) distribute the subject.
2d. All negative (and no affirmative) the
* Hence, it is matter of common remark, that it is difficult to prove a Negative. At first sight this appears very obvious, from the circumstance that a Negative has one more Term distributed than the corresponding Affirmative. But then, again, a difficulty may be felt in accounting for this, inasmuch as any Negative may be expressed (as we shall see presently) as an Affirmative, and vice versa. The proposition, e.g. that “such a one is not in the Town," might be expressed by the use of an equivalent term," he is absent from the Town."
The fact is, however, that in every case where the observation as to the difficulty of proving a Negative holds good, it will be found that the proposition in question is contrasted with one which has really a term the less, distributed, or a term of less extensive sense. E. G. It is easier to prove that a man has proposed wise measures, than that he has never proposed an unwise measure.
In fact, the one would be, to prove that “ Some of his measures are wise ;" the other, that “ All his measures are wise.” And numberless such examples are to be found.
But it will very often happen that there shall be Nega
It may happen indeed, that the whole of the predicate in an affirmative may agree with the subject; e. g. it is equally true, that “all men are rational animals ;” and “all rational animals are men :" but this is merely accidental, and is not at all implied in the form of expression, which alone is regarded in Logic. *
Two propositions are said to be opposed to each other, when, having the same subject and predicate, they differ, in quantity, or quality, or both.f It is evident, that with any given subject and predicate, you may state four distinct propositions, viz. A, E, I, and 0; any two of which are said to be opposed ; hence there are four different kinds of opposition, viz. 1st. the two universals (A and E)
tive propositions much more easily established than certain Affirmative ones on the same subject. E. G. That “ The cause of animal-heat is not respiration,” has been established by experiments ; but what the cause is, remains doubtful. See Note to Chap. III. $ 5.
* When, however, a Singular Term is the Predicate, it must, of course, be co-extensive with the subject; as “ Romulus was the founder of Rome.” # For Opposition of Terms, see Chap. V.