no farther than to the occurrence of the phenomenon at some time or other, leaving the particular time undecided1." The relation asserted here between the two sets of phenomena is one of either co-existence or succession. Similarly in the propositions 'A generous person is worthy of honor,' 'Thoughtlessness is dangerous,' 'Prudence is a virtue,' the relation expressed is coexistence or succession, and the things between which the relation exists are the attributes connoted or signified by the subject and the predicate of the proposition, or rather the phenomena and actions upon which they are grounded.

Besides co-existence and sequence propositions may express causation or mere existence, as in the case of nöumena, or resemblance, as in such propositions as this, 'The heat of to-day is equal to the heat of yesterday? These relations are expressed not only between phenomena, but also between nöumena, and between phenomena and nöumena. The relation of causation is only provisionally recognized, subject to the analysis of it under the head of causation.

Mill thus sums up the result of his investigation:

"Existence, co-existence, sequence, causation, resemblance, one or other of these is asserted or denied in every proposition which is not merely verbal. This five-fold classification is an exhaustive classification of matters of fact, of all things that can be believed or tendered for belief; of all questions that can be propounded and all answers that can be returned to them?" On the suggestion of Professor Bain that co-existence is of two kinds,—one in different places at the same time, and the other in the same part or place, as the co-existence or co-inherence in every atom of gold, of the attributes of a certain specific gravity, tenacity, fusibility, lustre, colour, &c., Mill divides all co-existence and succession into Order in Time and Order in Place, the former including Bain's Coinhering Attributes. Of the five classes given by Mill, Bain adopts only three :-(1) Co-existence, (2) Succession, including Causation, (3) Equality or Inequality.

1 Logic, Vol. 1. p. 110.

2 Ibid. p. 116.

§ 11. A few remarks on Mill's Theory:

The first remark to be made on Mill's theory is, that he does not show, either deductively or inductively, either from the nature of relations or from an enumeration of them, that his five-fold classification is an exhaustive one; that every possible relation between attributes has been included in his list.

The second remark is, that Mill does not give a sufficient account of the meaning of those propositions which he calls verbal. By calling them verbal, a name not without a touch of contempt, he seems to consider them as of no importance. But they are as important as those which he calls real propositions. Kant calls the two classes analytical and synthetical, respectively, and these two terms seem to express the distinction between them much better than Mill's names. What is the meaning of a verbal proposition even on Mill's own theory? It is that the connotation of the predicate is a part of the connotation of the subject, that is, the phenomena on which the attribute signified by the predicate is grounded are a part of the phenomena on which the attributes connoted by the subject are grounded. The meaning of the proposition 'Man is rational,' for example, is that the phenomena on which the attribute, rationality, is grounded are a part of, or included in, the phenomena on which the attributes signified by the term 'man' are grounded. Thus it would seem, that, to the five heads given by Mill, a sixth, namely, inclusion or containing of attributes, should be added. This last is different from any that are mentioned by Mill. It is not the same as co-existence, for two phenomena or attributes may co-exist without one forming a part of the other. Thus gravity and inertia co-exist, but one is not contained in the other; while animality is contained in humanity. A verbal proposition does not merely explain the meaning of a name, but expresses, like a real proposition, a relation between phenomena or attributes. The relation expressed by it is that of containing or inclusion. The different relations between phenomena or attributes may be thus shown in a tabular view:

Co-existence, Sequence, Causation, Existence, Resemblance.

When both the subject and the predicate of a proposition are taken in intension, Hamilton seems to recognize only one relation between them, namely, the relation of containing or inclusion; and this he does by enlarging the intension of the subject, that is, by putting into it all that is known of the thing or things denoted by the subject. Thus, according to him, all judgments are analytical or verbal, the attribute signified by the predicate being a part of the intension of the subject. He says in the Lectures, Vol. II. p. 336, quoting with approval from Crousary:—

"Every time we judge, we compare a total conception with a partial, and we recognize that the latter really constitutes a part of the former.” Again, "when we judge, we must have, in the first place, at least two notions; in the second place we compare these; in the third, we recognize that the one contains or excludes the other; and in the fourth, we acquiesce in the recognition." "When I say, 'body is divisible,' among the notions which occur in forming my conception of body, I particularly attend to that of 'divisible,' and finding that it really agrees with the others, I judge accordingly that the body is divisible."

Another remark suggested by Mill's theory is, that it makes the meaning of a proposition depend upon what is more or less variable, indefinite, and uncertain. Take, for example, the proposition 'Man is mortal.' According to Mill its meaning is that 'mortality' co-exists with 'humanity,' that whatever has the attribute 'humanity' has the attribute 'mortality.' Now, what is meant by 'humanity'? What are the essential elements of it? Is it possible to give a final definition of it? If not, how am I to know what does and what does not possess it? Again,

the connotation of the term 'man' is not the same to all persons, being different to different classes according to the kind and degree of their education and experience. Nor is it anything constant and fixed. On the contrary, it must vary with the progress in our knowledge of man in all his aspects. Or take the proposition 'All material bodies gravitate.' Its meaning, according to Mill, is that whatever has the attribute of a 'material body' has also the attribute of 'gravitating.' Now, what are the attributes of a material body? How am I to know whether a particular body is material or not? Is the luminiferous ether (the medium of light), for example, material? Thus the connotation of terms being variable and uncertain, the meaning of a proposition, on Mill's theory, must partake of its uncertainty, variability, and indefiniteness.

The last remark that I will make on Mill's theory is connected with the import or real meaning of a term, and should, perhaps, have been made first. In the chapter on Terms, Mill says that a common or general term directly signifies objects or things, and implies or indirectly signifies attributes; so the connotation of a term is taken in that chapter to be its implied or indirect meaning, and its denotation the direct or explicit meaning1. But in his theory of the Proposition, the former is taken as the direct or essential meaning, while the latter is entirely passed over. Consistency seems to require that Mill should have regarded the connotative or rather attributive meaning of a term as its direct and explicit meaning, and the denotative meaning as indirect and implicit.

§ 12. From what we have given above of the views of Logicians, it is evident that they differ (1) as to the relation of A and B (subject and predicate) and (2) as to the way in which A and B are to be interpreted (that is, the meaning of subject and predicate).

1 Mill's Logic, Vol. 1. pp. 31, 32.-"A connotative term is one which denotes a subject, and implies an attribute," p. 31. Again, “The name is, therefore, said to signify the subjects directly, the attributes indirectly, &c.," p. 32.

As regards the first point, Hamilton, for instance, recognizes the relation of containing or not-containing (inclusion or exclusion) either in the quantity of extension or in the quantity of comprehension, arising from the 'relation of congruence or confliction.' Mansel holds that the two sets of attributes expressed by A and B must be capable of existing together in some possible object of intuition, that is, the relation of A and B is that of compatibility or incompatibility. According to Ueberweg the relation of A and B must correspond to an objective relation, that is, to a relation really existing among things. Martineau recognizes the relation of substance and attribute, and, also, the relations of time and space, of cause and effect, and of resemblance and difference. Mill gives the relations expressed by all propositions under five heads: (1) Existence, (2) Co-existence, (3) Succession, (4) Causation, (5) Resemblance. Bain includes all under three classes, (1) Co-existence, (2) Succession, (3) Equality or Inequality.

The different views arising from difference on the second point, namely, the way in which A and B are interpreted by Logicians, may be noted as follows:-(1) The Ordinary or Predicative View in which A is taken in denotation (or extension) and B in connotation (or comprehension), and the relation of A and B is that of subject and attribute. "The light," says Dr Venn, “in which a proposition has to be consistently interpreted on this view is that of predication. We distinguish between subject and attribute here, and we assert that a given subject does or does not possess certain attributes1." Of the four forms A, E, I, O, arising from this view of propositions, Dr Venn says, "These forms appear to be naturally determined by the ordinary needs of mankind, and the ordinary pre-logical modes of expressing those needs; all that Logic has done being to make them somewhat more precise in their signification than they conventionally are?" Again, “As just remarked, these forms of proposition certainly seem to represent the most primitive and natural 2 Ibid. p. 3.

1 Symbolic Logic, p. 3.