[178] With extensive definitions we might similarly work out the relations between the terms of a proposition in exemplification and comprehension; and with either intensive or extensive definitions, we might consider them in denotation and comprehension. The discussion in the text will, however, be limited to connotation and denotation, except that a separate [section] will be devoted to the case in which both subject and predicate are read in comprehension.
As an example, we may take the proposition, All men are mortal.[179] According to our point of view, this proposition may be read in any of the following ways:
(1) The objects denoted by man possess the attributes connoted by mortal ;
(2) The objects denoted by man are included within the class of objects denoted by mortal ;
(3) The attributes connoted by man are accompanied by the attributes connoted by mortal ;
(4) The attributes connoted by man indicate the presence of an object belonging to the class denoted by mortal.
[179] A distinction may perhaps be drawn between the four following types of propositions; (a) All men are mortal ; (b) All men are mortals ; (c) Man is mortal ; (d) Man is a mortal. Of these, (a) naturally suggests the reading of subject in denotation and predicate in connotation as meaning, the three other readings being implications ; (b) is similarly related to the reading numbered (2) above; (c) to (3); and (d) to (4).
It should be specially noticed that a different relation between subject and predicate is brought out in each of these four modes of analysing the proposition, the relations being respectively (i) possession, (ii) inclusion, (iii) concomitance, (iv) indication.
It may very reasonably be argued that a certain one of the above ways of regarding the proposition is (a) psychologically the most prominent in the mind in predication; or (b) the most fundamental in the sense of making explicit that relation which ultimately determines the other relations; or (c) the most convenient for a given purpose, e.g., for dealing with the problems of formal logic. We need not, however, select the same mode of interpretation in each case. There would, for example, be nothing inconsistent in holding that to read the 179 subject in denotation and the predicate in connotation is most correct from the psychological standpoint; to read both terms in connotation the most ultimate, inasmuch as connotation determines denotation and not vice versâ, and to read both terms in denotation the most serviceable for purposes of logical manipulation. To say, however, that a certain one of the four readings alone can be regarded as constituting the import of the proposition to the exclusion of the others cannot but be erroneous. They are in truth so much implicated in one another, that the difficulty may rather be to justify a treatment which distinguishes between them.[180]
[180] The true doctrine is excellently stated by Mrs Ladd Franklin in an article in Mind, October, 1890, pp. 561, 2.
(1) Subject in denotation, predicate in connotation.
If we read the subject of a proposition in denotation and the predicate in connotation, we have what is sometimes called the predicative mode of interpreting the proposition. This way of regarding propositions most nearly corresponds in the great majority of cases with the course of ordinary thought;[181] that is to say, we naturally contemplate the subject as a class of objects of which a certain attribute or complex of attributes is predicated. Such propositions as All men are mortal, Some violets are white, All diamonds are combustible, may be taken as examples. Dr Venn puts the point very clearly with reference to the last of these three propositions: “If I say that ‘all diamonds are combustible,’ I am joining together two connotative terms, each of which, therefore, implies an attribute and denotes a class; but is there not a broad distinction in respect of the prominence with which the notion of a class is presented to the mind in the two cases? As regards the diamond, we think at once, or think very speedily, of a class of things, the distinctive attributes of the subject being mainly used to carry the mind on to the contemplation of the objects referred to by them. But as regards the combustibility, the attribute itself is the prominent thing … Combustible things, other than the diamond itself, come scarcely, if at all, under 180 contemplation. The assertion in itself does not cause us to raise a thought whether there be other combustible things than these in existence” (Empirical Logic, p. 219).
[181] Though perhaps what is actually present to the mind is usually rather more complex than what is represented by any one of the four readings taken by itself.
Two points may be noticed as serving to confirm the view that generally speaking the predicative mode of interpreting propositions is psychologically the most prominent:
(a) The most striking difference between a substantive and an attributive (i.e., an adjective or a participle) from the logical point of view is that in the former the denotation is usually more prominent than the connotation, even though it may be ultimately determined by the connotation, whilst in the latter the connotation is the more prominent, even though the name must be regarded as the name of a class of objects if it is entitled to be called a name in the strict logical sense at all. Corresponding to this we find that the subject of a proposition is almost always a substantive, whereas the predicate is more often an attributive.
(b) It is always the denotation of a term that we quantify, never the connotation. Whether we talk of all men or of some men, the complex of attributes connoted by man is taken in its totality; the distinction of quantity relates entirely to the denotation of the term. Corresponding to this, we find that we naturally regard the quantity of a proposition as pertaining to its subject, and not to its predicate. It will be shewn in the following [chapter] that the doctrine of the quantification of the predicate has at any rate no psychological justification.
There are, however, numerous exceptions to the statement that the subject of a proposition is naturally read in denotation and the predicate in connotation; for example, in the classificatory sciences. The following propositions may be taken as instances: All palms are endogens, All daisies are compositae, None but solid bodies are crystals, Hindoos are Aryans, Tartars are Turanians. In such cases as these most of us would naturally think of a certain class of objects as included in or excluded from another class rather than as possessing or not possessing certain definite attributes; in other words, as Dr Venn puts it, “the class-reference of the predicate is no less definite than that of the subject” (Empirical Logic, p. 220). 181 In the case of such a proposition as No plants with opposite leaves are orchids, the position is even reversed, that is to say, it is the subject rather than the predicate that we should more naturally read in connotation. We may pass on then to other ways of regarding the categorical proposition.