IV.

ANALYSIS OF THE LOGICAL PROPOSITION AS STATEMENT OF MEANING.

(i.) Kinds of Proposition (ch. xi.).

(ii.) Analysis of the Categorical Proposition (ch. xii.).

(iii.) The Meaning of Possibility (ch. xiii.).

(iv.) The Disjunctive Proposition (ch. xiv.).

(v.) The Hypothetical Proposition (ch. xv.).

CHAPTER XI.

IV. (i.) KINDS OF PROPOSITION.

THERE are three main kinds of proposition :

1. Categorical: 'S is P,' 'Sis-not P.'

2. Disjunctive: 'Either A is B, or C is D, or E is F.'

3. Hypothetical: 'If A is B, then C is D.'

If we examine the structure of these three main types of proposition, we notice that the elements out of which each type is constructed are different in the three cases.

1. The Categorical Proposition is a synthesis of the two elements which, in their verbal form, are called Terms* -the Subject-Term and the Predicate-Term. The subject of a categorical proposition is that about which something is being said; the predicate is that which is being said or stated about the subject of the proposition.

Examples: (The next examination) is (held in June).

It is (a tiresome thing) (to fail in an examination).

= (The possibility of passing) is (in the hands of

As the proposition is the true logical unit, and the term a mere derivative or abstract from the proposition, it follows that the term has meaning only in relation to the part it plays in a proposition. But this does not mean that we are logically precluded from discussing terms except in so far as they actually exist within given propositions. A word, or a word-complex such as 'The Science of Logic' or 'The Cat and Fiddle,' may justly be called 'a term,' provided it can play the part of subject or predicate in a proposition. A term is, in fact, just a potential subject or predicate, so that even in abstraction from the proposition it still remains'intrinsically related

* On the etymological significance of the word 'term,' vide Joseph, 'An Introduction to Logic,' ch. ii., p. 13, footnote.

to it. Though it need not be doing actual service within a proposition, it must at least belong to the reserve.

2. In the case of the Disjunctive Proposition-e.g., 'Either the earth moves or Copernicus was mistaken '-the main elements are clauses, not terms; and they stand to each other in the relation of alternatives a relation very different from that of Subject to Predi

cate.

3. In the case of the Hypothetical Proposition, again, it is evident that we cannot call its main elements 'terms.' Take, for instance, the proposition 'If the weather is fine, we shall go for a picnic.' Here we have two main elements; but these do not stand to each other as Subject to Predicate, nor are they terms. They are clauses, and stand to each other as Antecedent to Consequent, the antecedent being represented by the 'if' clause.

We conclude that propositional elements are of three kinds : Terms: 1. Subject and Predicate in Categorical propositions. Clauses:

:

{

2. Alternative possibilities in Disjunctive propositions. 3. Antecedent and Consequent in Hypothetical propositions.

The types of proposition that we have been considering may be connected together as different stages in the process through which the human mind passes on its way from question to answer. Every process of reflective activity which is guided, however vaguely, by the logical ideal of clear and consistent thinking is a process of which the essence is to give a more determinate form to what, at the outset, is relatively indeterminate. 'The action of thought,' it has been said, 'is excited by the irritation of doubt, and ceases when belief is attained.'* So, we might add, an act of judgment is excited by the discomfort of a question to which we do not at once foresee the answer, and it crystallizes into the form of a proposition only when some answer, however partial, has been definitely formulated. As Belief is to Doubt, so is the Answer which a judgment expresses to the Question out of which it arises.

Now, a question, if it is to be more than a vague unprogressive state of wonder or curiosity, is already, by the very fact of its being a question, partially determinate. It takes its start from a more or less vague conception, and the motive which prompts a more determinate answer is the pressure which the idea of the determinate necessarily exercises upon the undetermined whenever the logical interest is in any degree awake. This pressure exerts itself most naturally in the work of transforming the vague possibility of a solution which is implied in the existence of the question into a set of definite alternative possibilities. If I am told that a happy

* C. S. Peirce, 'Illustrations of the Logic of Science, Popular Science Monthly, xii., p. 289.

event has raised me to the dignity of an uncle, but am not further informed, the knowledge I have is, in its indeterminateness, itself a question which tends to determine itself forthwith in the form of the disjunctive proposition: 'Either it is a nephew or it is a niece.'

A further stage of determination is reached when I make an assumption as to the sex, and proceed to define my mental attitude, prospectively, on that assumption. 'If it is a boy, my brother-inlaw will perhaps be sorry; but my sister, I know, will be pleased. If it is a girl, there is no reasonable possibility of its being called after me.' And so forth. The second stage is thus that of the Hypothetical Proposition.

The third stage in the process is reached when the news arrives that my sister is pleased, and that the infant is to be called after me. The question 'What sex ?' with which the whole thoughtprocess started now receives the definite answer 'The child is a boy.' The disjunctive proposition passes into a categorical proposition which asserts the one alternative to the exclusion of the other.

It must not, however, be supposed that the Disjunctive Proposition, which is logically prior to the Hypothetical, is logically prior to the Categorical as well. It is certainly prior to the more determinate form of categorical which asserts one out of many alternative possibilities; but it is posterior to the more indefinite categorical out of which the question and the disjunction sprang. Thus, the proposition that the being is a human child is the necessary preface to the question 'What sex ?' and to all that follows between the question and the determinate categorical answer, 'The child is a boy.'*

In many cases, indeed, a categorical statement possesses no indeterminateness at all, hence suggests no question, and therefore no disjunction as the first step towards a more determinate answer. Moreover, there is another class of cases in which we have a categorical proposition which, though determinate, cannot have been reached through the cancelling of alternatives in a disjunctive proposition. The statement 'The part is not greater than the whole' cannot have been preceded by a disjunctive proposition stating an alternative to the assertion in question. The proposition is selfevident, and in the case of all self-evident propositions the categorical statement cannot be considered in the light of an answer at all. Where there can be no doubt there can be no question, and therefore no answer.

* The Categorical Proposition is, in fact, implied all through. It mediates the transitions from the question to the disjunctive, and from the disjunctive to the hypothetical. Thus the statement 'Either it is a nephew or it is a niece' presupposes the categorical 'A baby is either a boy or a girl'; and the statement 'If it is a boy... my sister... will be pleased' presupposes the categorical 'My sister has a preference for boys.'