§ 6. Division according to Quantity.

The fourth division of propositions is into (1) Universal, and (2) Particular, founded on their quantity. A categorical proposition is universal or particular according as its subject is taken in its entire or in its partial extent. Its quantity is determined by the quantity of its subject. "All A is B" and "No A is B" are both universal, because, in the former, 'B' is affirmed, and, in the latter, B is denied, of the whole of 'A,' that is, of every individual thing denoted by 'A.' "Some A is B," "" 66 some A is not B" are both particular, because, in the former, B is affirmed, and, in the latter, B is denied, of a part of the subject 'A.' The logical meaning of the proposition "Some A is B" is that 'at least one A is B,' that 'B' is affirmed of at least one individual, if not of more, belonging to the class 'A.'

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A proposition of the form "A is B" or "A is not B" is said to be an indesignate or indefinite proposition, because its quantity, or rather the quantity of its subject, is not stated explicitly; the propositions "Metals conduct electricity," "animals have a nervous system," "plants have flowers," "material bodies have weight," &c., belong to this class. The quantity of these propositions cannot be determined without a reference to the sciences to which they respectively belong; or, in other words, without a knowledge of their matter as distinguished from their form; but it is, in reality, either universal or particular, that is, the predicate in each of them is affirmed either of the whole of the subject, or of at least a part of it—of every individual thing denoted by it, or of at least one individual.

When the subject of a proposition is a singular, or a collective term, the proposition is said to be Singular. A singular proposition should be referred to the class of universal propositions, when the subject denotes definitely an individual or a collection of individuals, as the predicate is, in that case, affirmed of the whole of the subject; and to the class of particular propositions, when the subject does not definitely refer to an individual or a collection of individuals. For example, the proposition "A Germán was there" is a singular proposition belonging to the

class of particular propositions, while the proposition "A German whom I had met at Leipzig was there" is a singular proposition, belonging to the class of universal propositions. "One metal is liquid" is a singular proposition belonging to the former class, while "Mercury is a liquid metal" is a singular proposition belonging to the latter class. In like manner, when by any descriptive words, or demonstrative pronouns, any individuals of a class forming the subject of a proposition are definitely pointed out, the proposition is universal and not particular: “These three men were there," "These metals belong to the Copper Group," "All metals except mercury are solid substances," "Those metals that do not rust are noble metals,” “The following fifteen elements are non-metals,” are all universal propositions.

We have explained above the quantity of categorical propositions, when the subject is taken in its denotation or extent. We get the same two-fold division, when the subject is taken in its connotation or intension, for the attribute signified by the predicate B may accompany the attribute connoted by the subject A in every case, or in some cases,-under all circumstances universally, or under particular circumstances contingently. In the former case, the proposition "A is B" is universal, and in the latter case, it is particular. For example, the proposition "All men are mortal" is universal, and means, when the subject is taken in its connotation; that mortality accompanies humanity under all circumstances, that wherever humanity is, mortality is. The proposition "Some men are wise" is particular, and means, when the subject is taken in its connotation, that in some cases, or under certain circumstances, wisdom accompanies humanity, that in at least one case, where humanity is, wisdom is.

The hypothetical proposition is universal, when, in every case, the antecedent is followed by the consequent; and it is particular, when the consequent follows the antecedent in some cases, or in at least one case. The universal proposition "If A is, B is,” or, more explicitly, “In all cases, if A is, B is,” means that wherever 'A' exists 'B' exists, that under whatever circum

stances 'A' happens, it is followed by the happening of 'B'; and the particular proposition "In some cases, if A is, B is,' means that, in at least one case, the existence of 'A' is followed by the existence of 'B.'

3.

If mercury is heated, it rises in temperaturé.

4.

UNIV
CALITA

If water is heated to 100° C. under a pressure of 760 mm., boils.

5. This animal is either a vertebrate, or an invertebrate. 6. The soul is either mortal or immortal.

7. Space is either finite or infinite.

it

2.

Some elements are not metals.

3. In some cases, if water is heated, it contracts.

4. In many cases, if there is a sensation, there is a perception. 5. In some cases, if there is a sensation, there is no perception.

6. Some men are either philosophers or prophets.

§ 7. The Propositional Forms according to Quality and Quantity.

Propositions are divided into affirmative and negative according to their quality. The affirmative propositions, as well as the negative, may again be divided into universal and particular according to their quantity. Thus we get the following classes or forms of propositions :—

Every universal affirmative proposition is called A, every universal negative proposition E, every particular affirmative proposition I, and every particular negative O, that is, A, E, I, and O are the symbols for the propositions of those classes respectively. The words 'all,' 'the whole,' 'any,' 'each,' 'every,' 'a few' and 'certain" used definitely, 'no,' 'none,' &c., are signs of A or E. The words 'some,' 'not all,' 'at least one,' 'not none,' 'a few' and 'certain' used indefinitely, 'many,' 'most,' &c., are signs of I or O.

The quality and quantity of a proposition cannot always be determined from its form. Without a knowledge of the subjectmatter, we cannot, in many cases, say whether it is universal or particular, affirmative or negative. For example, the proposition "Every man is not learned" would seem to be E from its form, but from its meaning it is really or I, that is, it means that some men are not learned, and implies that some men are. Thus it may be taken, from its meaning, to be indifferently O or I; but in Logic, it is usually regarded as a mere negation of the proposition "All men are learned,” and treated as O rather than as I. Similarly, the propositions "Every mistake is not a proof of ignorance," "Some of the most valuable books are seldom read," "Few know both physics and metaphysics," ," "All that glitters is not gold,” “All elements are not metals,” “All scientific books are not difficult," are to be regarded as O, rather than as I. The proposition "Some acids have no oxygen" would seem from its form to be affirmative, “having no oxygen" being affirmed of some acids, but, in reality, it is negative, and means that 'having oxygen' is denied of some acids. Similarly, "None were there," "Nothing is annihilated," "Many objects of imagination have no objective existence," should be regarded as negative rather than as affirmative.

Similarly, the modality of a proposition cannot, in every case, be determined from its form only. For example, the proposition "All triangles have three angles together equal to two right angles" would appear from its form to be assertory, but, in reality, it is necessary.

Exercise.

Reduce each of the following propositions to the logical form, and give its quantity and quality, that is, state in respect to each whether it is A, E, I, or 0:—

(1) Two straight lines cannot inclose a space.

(2) Matter is anything whose existence can be determined by one
or more of our senses.

́(3) A nail driven into wood is not a true case of penetration.
(4) Liquids have no shape of their own.

(5) Gases are eminently compressible and expansive.

(6) Strictly speaking, impenetrability only applies to the atoms of bodies.

(7) Two portions of matter cannot simultaneously occupy the same portion of space.

(8) If a pint of water and a pint of alcohol be mixed together, the volume of the mixture is less than two parts.

(9) Very few of these elements occur in nature in the free state. (10) No absolute rest is known in the universe.

(11) Inertia is a purely negative property of matter.

(12) Consciousness involves judgment.

(13) The province of physics is at present much more restricted. (14) To have the objective essence of a thing is to think clearly what is in it and omit what is not.

(15) Not all our ideas consist of the objective essences of things. (16) Some of our ideas represent only the partial or accidental affections of things.

(17) If you know what a circle is, and what a square, you cannot make a compound out of them.

§ 8. The mutual relations of A, E, I, and O, or, Opposition of Propositions.

Two propositions having the same subject and predicate, but differing in quality, are said to be opposed to each other, and their mutual relation is called opposition.

The relation of A and E to each other is called Contrary Opposition. That is, two universal propositions having the same subject and predicate, but differing in quality, are said to be