PART II.-PROPOSITIONS.

CHAPTER I.

THE DEFINITION AND DIVISIONS OF PROPOSITIONS.

ined as an affirmation or

§ 1. A PROPOSITION may be denial of a certain relation betr. en terms. It thus consists/ of two terms and of a word, or words, or part of a word expressed or understood, as a sign of affirmation or denial. That which is affirmed or denied is called the Predicate, that of which it is affirmed or denied is called the Subject, and that which stands as a sign of affirmation or denial is called the Copula, of the proposition. For example, in the proposition "All men are mortal,” 'all men' is the subject, 'mortal' the predicate, and 'are' the copula or the sign of affirmation; in the proposition "Some men are not wise," 'some men' is the subject, 'wise' the predicate, 'are not' the copula or the sign of denial; in the proposition "The sun rises," 'the sun' is the subject, 'rise' the predicate, and the letter 's' is the copula; here the affirmation of the predicate of the subject is expressed by a slight alteration, called an inflection of the word 'rise.' When fully expressed, the last proposition stands thus :-"The sun is rising," in which the sign of affirmation is explicitly stated, and is the same as in the first example given above.

The subject or the predicate of a proposition may consist of a single word or of any combination of words constituting a term.

In the propositions "Chalk is white," "The virtuous are happy,” "That all men are mortal is known to everybody," "To know any subject thoroughly is not easy," &c., 'chalk,' 'the virtuous,' ‘that all men are mortal,' 'to know any subject thoroughly' are, respectively, the subjects, and 'white,' 'happy,' 'known to everybody,' 'easy' are, respectively, the predicates.

The copula of a proposition, when stated in the logical form, consists usually of the parts of the verb 'to be' with or without the negative particle 'not.' It should be carefully noticed that the copula merely expresses a certain relation between the subject and the predicate, and does not imply the existence of either. For example, in the symbolical proposition 'A is B,' 'A' is the subject, 'B' the predicate, and 'is' the copula which, in the affirmative form, merely expresses the presence of a particular relation between A and B, and does not imply the existence of either the subject or the predicate. Similarly, in the proposition 'A is not B,' the copula 'is not' is merely a sign of the absence of a particular relation between A and B, and does not signify either the existence or the non-existence of A or B. The verb 'to be' used as copula should be distinguished from the same verb used as copula and predicate in a proposition. In the latter case, it implies the existence of the subject. In the proposition, ‘A is,' for example, 'is' means 'exists' and is equivalent to 'is existing.' In this sense, also, the verb 'to be' is ambiguous; for the words 'is,' 'are,' 'being,' &c., like 'exists,' 'existing,' 'existence,' &c., may, according to context, mean either existing in Thought, that is, free from self-contradiction, or existing in Nature, that is, corresponding to actual existence, and free not only from selfcontradiction but also from disagreement with fact or reality. The proposition, 'A is,' may mean simply that the idea or concept A exists in Thought without any reality or fact corresponding to it, or it may mean that the idea A exists in Thought and agrees with fact or reality. The subject of a proposition may exist in neither of these senses. In the proposition, “A square circle is not," the subject 'a square circle' has existence neither in Nature nor in Thought.

According to some logicians the copula consists of the verb 'to be' without the negative particle 'not.' They attach this particle not to the copula but to the predicate, and thus make all propositions apparently affirmative. They cannot of course get rid of the not, or of the fact of negation or absence of something; and what is excluded from the copula must be included in some form in the predicate. In the proposition 'A is not B,' 'not-B' is, according to them, the predicate, and 'is' the copula; the 'not' of the copula being thus attached to the predicate. In abolishing the 'not' of the copula, they only multiply unnecessarily the number of negative terms, and make the meaning of propositions with such terms vague and indefinite.

Some logicians make the copula consist of the present tense only of the verb 'to be' with or without the negative particle, that is, of ‘is,' ‘are,' ‘is not,' 'are not,' and exclude the other tenses. Hamilton, Mansel, Fowler, &c., have adopted this view, while Mill contends that the element of time, or modifications of tense are as much a part of the copula as the particle 'not' or the fact of negation. Just as we cannot, he would argue, exclude the latter, so we cannot exclude the former; its exclusion from the copula would require it to be included in the predicate as in the case of the particle 'not.' This question does not seem to be of any great importance; and the copula may be indifferently regarded to consist of the present tense only or of any of the tenses of the verb 'to be.'

A judgment is the mental recognition of a certain relation between two concepts. It consists of two concepts, the Subject and the Predicate, and of a recognition of a certain relation, agreement or disagreement, congruence or incongruence, &c., between them, the Copula. When the two concepts are true, that is, correspond exactly to the attributes and things actually existing, and when the relation between them is also true, that is, corresponds exactly to the relation between the attributes and things, then the judgment is true; otherwise the judgment must be regarded as false. (A true judgment is the subjective aspect of an objective relation between attributes and things. A rela

tion between two attributes or things may be considered (1) in itself, without any reference to our thought or any mode of our thinking of it, (2) as thought by us independently of any mode of expression in language, and (3) as thought and expressed by i us in language. A judgment is the relation as thought by us. A proposition is the relation as thought and expressed by us in language. By some logicians it is regarded as the objective relation itself, or expressed in language without any reference to our thought or any mode of our thinking of it. § 2. The Divisions of Propositions.

A proposition in Logic usually corresponds to a simple or to a complex sentence in grammar, while a compound sentence in Grammar generally corresponds to a plurality of propositions in Logic.

SYMBOLICAL EXAMPLES OF PROPOSITIONS.

I. Propositions (single).

1. A is B, a simple sentence.

2. A that is C is B, a complex sentence.

3. A that is C is B that is D, a complex sentence.

4. If A is, B is, a compound sentence.

5. A is either B or C, a compound sentence.

II. Combinations of Propositions (also called Compound Propositions).

1. A is B and C; or A is B as well as C.

2. A and D are B; or A as well as D is B.

5.

A that is E, and D that is F, are B which is G.

6. A is B, and C is D.

7. A is B, but C is D.

8. A is neither B nor C.

9. Neither A nor D is C.

The various divisions of propositions are founded upon certain aspects possessed by every proposition. A tabular view of the divisions is given below:

Propositions.

I. Relation

...

A is B, A is not B.

Conditional: If A is, B is.

Affirmative: A is B.

II. Quality ...Negative: A is not B.

Necessary: A must be B.

III. Modality...Assertory: A is B.

Problematic: A may be B.

IV. Quantity ...{Universal: All A is B.

V. Import

Particular: Some A is B.

Verbal, Analytical: All men
animals.

Real, Synthetical: All men
mortal.

We shall now proceed to explain these divisions in order.

§ 3. Division of Propositions according to Relation.

are

are

The first division of propositions is into (1) Categorical (also called Simple), and (2) Conditional (also called Hypothetical, or Complex), founded on the relation between the two terms, or on the nature of affirmation or denial. A categorical proposition is one in which the relation between the subject and the predicate is a simple, unconditional one, in which the predicate is simply affirmed or denied of the subject, without any condition being laid down. For example, in "A is B," "All metals are elements," B is affirmed of 'A' unconditionally, 'elements' is affirmed of 'all metals' under all circumstances without any restriction or condition. Similarly, in the proposition "Some men are wise,” 'wise' is affirmed absolutely or unconditionally of 'some men.' A conditional proposition, on the other hand, is one in which an affirmation or denial is made under a certain condition. In the proposition "if A is B, C is D," for example, the assertion 'C is D' depends on the assertion 'A is B,' or D is affirmed of C, provided B is affirmed of A. The truth of the second clause depends 'upon that of the first. Hence the latter is called the antecedent, condition, or reason, and the former the consequent. The dependence of the one upon the other, or the conditional nature of