§ 8. Mill then shows that the Denotative or Class Theory of Predication accordingly to which predication consists in referring something to a class, i.e., in placing an individual under a class or one class under another, is hardly better than the theory of Hobbes. "There is," says he, "no real difference, except in language, between this theory of predication and the theory of Hobbes. For a class is absolutely nothing but an indefinite number of individuals denoted by a general name. The name given to them in common is what makes them a class. To refer anything to a class, therefore, is to look upon it as one of the things which are called by that common name. To exclude it from a class, is to say that the common name is not applicable to it." The Class Theory of Predication is, argues Mill, moreover psychologically false. For in the proposition 'snow is white,' I am not thinking of 'white objects' as a class, but only of 'snow' as an object and the sensation of 'white' which it gives me.

§ 9. A view that is closely connected with the Denotative or Class Theory of Predication, and is, in fact, only a special development of it, is the equational view of propositions. According to this view, the proposition 'A is B' is an equation, 'A' and 'B' corresponding to the two sides of the equation, and 'is' to the sign of equality between them; and the meaning of the proposition is that the things denoted by 'A' are identical with those denoted by 'B.' This view is adopted by Hamilton in his later writings. It is the direct consequence of the doctrine of the Quantification of the Predicate. This doctrine is, that in thought the quantity of the predicate as well as that of the subject is implicitly contained, and that, according to the principle, that "Logic postulates to be allowed to state explicitly in language all that is implicitly contained in the thought," it may be expressed by such words as 'some,' 'all,' &c., before the predicate.

Adopting this doctrine, Hamilton obtains the following eight

1 Mill's Logic, Vol. 1. p. 104.

forms of propositions instead of the four we have given in a previous chapter:

Mill objects to the adoption of the above view on the following grounds1:-(1) The theory is psychologically false, because the predicate of a proposition is not thought of in its extension, but only in its comprehension. In the proposition "all oxen ruminate," nobody thinks of other ruminating animals, and none ever asks the question whether or not there are other animals that ruminate; all that anyone is thinking of is the phenomenon or attribute of ruminating in reference to ‘oxen.' (2) All reasoning being carried on in the ordinary forms of expression, it is desirable that every proposition in logical form should be the exact equivalent of some proposition in the common form. On this ground the proposition "all A is all B" is inadmissible, because there are none corresponding to it in ordinary language, because it is really a compound of two ordinary propositions, viz., “all A is B” and “all B is A"; since it can never be accepted without proving these two. Similarly, if you take "some A is B" to mean "some A is some B only," you not only change the real logical meaning of 'some' as meaning 'not none,' it may be 'all,' into a part only,' 'not the whole,' but you make the proposition "some A is some B” really a double judgment, an implicit expression of the two explicit judgments, viz., “ some A is some B" and " some other A is not any B." (3) Logic should start with the simplest or most elementary judgments. But "all A is all B," "some A is

1 Mill's Examination of Hamilton's Philosophy, Chap. XXII.

some B" are complex, consisting of two as we have just seen, while “A is B” is the simplest and most elementary, than which there cannot be any simpler.

66

as

Hamilton anticipates some of Mill's objections. He says:But, in fact, ordinary language quantifies the predicate so often as this determination becomes of the smallest import. This it does either directly, by adding all, some, or their equivalent predesignations, to the predicate; or it accomplishes the same end indirectly, in an exceptive or limitative form. (a) Directly,— as Peter, John, James, &c., are all the Apostles,” “Mercury, Venus, &c., are all the planets." (b) But this is more frequently accomplished indirectly, by the equipollent forms of limitation or inclusion, and exception. For example, by the limitative designations, alone or only, we say, "God alone is good," which is equivalent to saying, God is all good, that is, God is all that is good; "Virtue is the only nobility," that is, virtue is all noble, that is, all that is noble. "Faith, hope, charity, alone justify.” "Of animals man alone is rational," that is, man is all rational animal. "What is rational is alone or only risible," that is, “all rational is all risible, &c." Of the exceptive form Hamilton gives the following examples:- "On earth there is nothing great but man," which means "Man is all earthly great." "In man there is nothing great but mind," which means "Mind is all humanly great," that is, "all that is great in man1."

1 The following note by Hamilton on the import of what are called exclusive and exceptive particles is worth quoting:-They are, 66 one, only, alone, exclusively, precisely, just, sole, solely; nothing but— not-except, beyond. (1) These particles annexed to the subject predesignate the predicate universally, or to its whole extent, denying its particularity or indefinitude, and definitely limiting it to the subject alone; as, 'man alone philosophises,' 'the dog alone barks,' 'man only is rational,' ' of material things there is nothing living (but) not organized, and nothing organized not living,' 'God alone is to be worshipped,' 'some men only are elect.' (2) Annexed to the predicate, they limit the subject to the predicate, but do not define its quantity, or exclude it from other subjects; as, 'Peter only plays,' 'the sacra

"The non-quantification of the predicate in thought," argues Hamilton, "is given up by the logicians themselves, but only in certain cases where they were forced to admit, and to the amount which they could not possibly deny. The predicate, they confess, is quantified by particularity in affirmative, by universality in negative, propositions. But why the quantification, formal quantification, should be thus restricted in thought, they furnish us with no valid reason1."

§ 10. Mill's own theory, which may be called the Connotative or Attributive Theory of Predication, is that the proposition 'A is B' expresses a certain relation between the attributes connoted by 'A' and 'B' respectively, or, more properly, a certain connection or relation between the phenomena on which the attributes are respectively founded and through which they are known, and that the relation expressed by it is that of co-existence, succession, causation, resemblance, or mere existence2. Take, for example, the proposition "All men are mortal":

ments are only two,' 'the categories are only ten,' 'John drinks only water.' (3) Sometimes the particles sole, solely, single, alone, only, &c., are annexed to the predicate as a predesignation tantamount to 'all'; as, 'God is the single,-one,-alone,-only,-exclusive,―adequate,-object of worship.'"

1 Hamilton's Lectures, Vol. IV. pp. 261-5.

2 In the case of a proposition whose subject is a proper name and has, therefore, according to Mill, no signification in connotation, the meaning of the proposition, according to him, is, that the attribute or attributes connoted by the predicate belong to the individual thing denoted by the subject. For example, the proposition "Socrates is a philosopher" means that the attributes of being a philosopher belong to the individual denoted by the proper name Socrates. If both the subject and the predicate of a proposition are proper names, then, according to Mill, Hobbes's theory is a sufficient account of it: as examples of such propositions he gives :-'Tully is Cicero,' 'Hyde was Clarendon,' &c., the whole meaning of such propositions is, that the predicate is a name or meaningless mark for the same thing for which the subject is a mark.

its meaning is that the objects denoted by the subject possess the attributes connoted by the predicate. The objects are not, however, individually designated. "They are pointed out only by some of their attributes; they are the objects called 'men,' that is possessing the attributes connoted by the term 'man,' and the only thing known of them may be these attributes; indeed the proposition is general, and the objects denoted by the subject are, therefore, indefinite in number, most of them are not known individually at all. The assertion is, * therefore, that the attributes which the predicate connotes are possessed by each and every individual possessing certain other attributes, that whatever has the attributes connoted by the subject has also those connoted by the predicate, that the latter set of attributes constantly accompanies the former set. Whatever has the attributes of man has the attribute of mortality; mortality constantly accompanies the attributes of man1"

*

To the objection that we naturally construe the subject of a proposition in its extension, and the predicate in its intention, Mill replies that "though it is true that we naturally construe the subject of a proposition in its extension, this extension, or, in other words, the extent of the class denoted by the name is not apprehended or indicated directly, and that it is both apprehended and indicated solely through the attributes.”

The

But what is an attribute? "Every attribute," says Mr Mill, "is grounded on some fact or phenomenon, either of outward sense or of inward consciousness; and to possess an attribute is another phrase for being the cause of, or forming part of, the fact or phenomenon upon which the attribute is grounded?" proposition 'All men are mortal,' therefore, really means that "wherever the various physical and mental phenomena on which the attributes of 'man' are grounded are all found, there we have assurance that the other physical and mental phenomenon, called death, will not fail to take place. The proposition does not affirm when; for the connotation of the word 'mortal' goes

1 Mill's Logic, Vol. 1. p. 109.

2 Ibid. p. 109.