not cold '; 'he laughed'; 'he is asleep'. The subject of such propositions is always a demonstrative term; the predicate is always descriptive, but its meaning may be expressed either by the verb to be or its equivalent (i.e., to seem, to appear, or some other similar verb) followed by an adjective or its equivalent (i.e., some descriptive noun or phrase), or merely by an intransitive verb (with or without a completing or modifying adverb), e.g.: 'He is insane'; 'he is a lunatic'; 'he raves'; 'he acts insanely'.

3. The third kind of relation affirmed or denied by propositions is the action of one thing upon another, or the mutual relations of two things as active beings. Propositions expressing such relations involve two demonstrative terms and a transitive verb or its equivalent, e.g.: John strikes his horse'; ́ A. and B. are quarreling'; 'C. is D.'s landlord', i.e., rents a house to him; E. walks on the grass', i.e., treads the grass. These relations may be called causal or dynamic.

Whether a proposition belongs to this third class or to the second is often a mere question of interest. A man cannot walk without treading upon something, but we are not usually interested in the effect upon the object beneath his feet, and so we regard the statement that he walks as merely descriptive. When we are interested enough to tell what he walks upon the dynamic relation becomes prominent. Further, as Sigwart says in his " Logic": "When a man walks he moves his legs; that which from one point of view is mere action appears from another as an effect upon his limbs, which are relatively independent things." Here, again, the classification of the proposition depends upon the interest which one can reasonably be supposed to take in some particular aspect of the whole fact stated.

Sometimes, but not usually, it is proper to regard a statement of a thing's color, taste, smell, or other perceptible

* Vol. I, p. 37 (Macmillan)

quality as dynamic rather than merely descriptive; for to have a certain color is to reflect light in a certain way, and to have a certain smell is to act chemically in a certain way upon an olfactory organ. But when the ultimate nature of things is not under discussion it is more convenient to ignore these facts and regard such statements as merely descriptive.

4. Propositions of the fourth kind affirm or deny the existence of various non-dynamic or non-causal relations between two or more different things or other objects of thought. They express our comparisons between them rather than the action of one upon another. We may say, for example, that several objects are similar or dissimilar; that things or events coexist or succeed each other in time; that they bear to each other various relations in space; that one thing is more or less beautiful, one musical note 'higher' or 'lower', or one man morally better or worse than another, without supposing the objects whose relations we discuss to affect each other in any way whatever. The number of relations of this kind which anything bears to anything else is limited only by the ability of beings that know them both to compare them together in various respects; and whether many or few such relations be discovered or exist has not the slightest effect upon the things compared or their activities. Causal relations, on the

other hand, engross more or less of a thing's energy, and may thus interfere with each other. Anything, A, might resemble B, coexist with C, be heavier than D, lighter than E and beside F, all at once; but if A were a man he could not at any one time fight with B, dance with C, and discuss philosophy with D. Causal relations exist directly for the things related, and seem to penetrate into and affect their inmost being; non-dynamic relations concern nothing and nobody but the being that discovers them.

The most important of the non-dynamic relations are those of Space and Time, without which the mathematical sciences would be impossible. They are so important that many eminent writers give them a separate place in their

lists of relations.
often supposed to comprehend causal relations.
tion is one of metaphysics which cannot be discussed here.*
When we speak of the color or of any other attribute of an
object as identical with that which exists elsewhere, the rela-
tion asserted is really a relation of resemblance rather than of
individual identity. We merely mean that the similarity is
complete. We must not be deceived by a merely verbal
resemblance between two propositions. If I say that your
clothes are the same as mine the relation in question is one of
resemblance; if I say that they are the same that you wore a
year ago the relation is one of identity. If I say the house has
the same color it had ten years ago the relation indicated by
the word 'same' is one of similarity; if I say it has the same
paint the relation is probably intended to be one of individual
identity. The distinction here pointed out between the same
thing and the same kind of thing is very important, though
sometimes lost sight of, in metaphysical discussions. In which
sense, for example, do we see the same rainbow when the sun
comes out again, and have the same idea or make the very
same' remark as somebody else?

Indeed relations of time and space are
The ques-

5. So far we have discussed the various relations which exist between the things we know or think about, but we have said nothing about our knowledge of these relations. It is one thing for the frog that exists to-day to be identical with the tadpole that existed six months ago, and quite another thing for you or me to recognize that it is identical; one thing for

* It may occur to the reader that the non-dynamic relations between several objects can be affirmed or denied only because the things compared act upon the person making the comparison, e.g., that we say one thing is prettier than another because it acts upon our senses in such a way as to give us more æsthetic enjoyment. This is often the case, but we must not infer from it that the non-dynamic relations can be resolved into dynamic, for even if we suppose that to be pretty means merely to please the beholder, in the example given there is still a comparison expressed between the amount of enjoyment present in the two cases. We cannot therefore get rid of the element of mere comparison.

a man to be angry, and quite another thing for us or even for the man himself to know that he is angry; one thing for A to be larger than B, or to be near B, or to influence B, and quite another thing for us to know or think about these relations.

We have thus a new kind of relation to deal with, namely, that between a person thinking and the thing he thinks about -between thought and its object. This relation can be called noetic.

This noetic relation, or relation between thought and its object, can be affirmed or denied like any other: e.g., I was thinking of you; I love you or fear you; I do not desire a certain end; he knew, or was mistaken, or was doubtful about a certain matter; your ideas about it are consistent, or contradictory, or absurd; he is right about it; he thought he knew; I mean you. In all these cases something is said about some aspect of the relation between a thinker or his thought and the object thought about.

In the history of philosophy much has been made of the distinction between real and verbal propositions (otherwise called Synthetic and Analytic, Ampliative and Explicative, Accidental and Essential). A Real proposition tells something about an object, e.g. A thrush is in the tree', 'Tully is dead'. A Verbal proposition tells the meaning or part of the meaning of a word, e.g.: A thrush is a kind of bird', 'Tully is Cicero'. Every definition is thus a verbal proposition. Euclid's definitions are supposed to be merely verbal-telling nothing more than the meaning of words; his axioms and postulates to be real-telling something more than the names of various figures strictly imply, though perhaps not more than everybody knows. Real propositions may belong to any one of our five classes. Verbal propositions are always noetic; for to tell the meaning of a word is to tell of what I

* Contrast with these propositions such a one as this: 'That man's name is Washington Jefferson Madison Stokes'. Here the name is regarded as a kind of appendage, and the proposition is as descriptive as if it had been said that the man had thirteen fingers,

am thinking and of what I wish my hearer to think when I use it.*

It is probable that we can never speak or think of a relation not included in this list: Individual Identity, Subject and Attribute, Causal relations between several things, Non-dynamic, or Non-causal, relations between several things, and relations between thought and its object or Noetic relations. These then are the so-called categories; but it must be remembered that the fourth class includes a great many different relations which agree in only one respect, namely, that they involve at least two objects without involving any action of the one upon the other.†

* The terms Real and Verbal seem to me preferable to Kant's Synthetic and Analytic, partly because as Mansel says, "propositions in which the predicate is a single term synonymous with the subject” cannot possibly involve any analysis or splitting up of the meaning of the subject; e.g., Tully is Cicero (see Keynes, "Logic ", p. 43, 3d ed.); but mainly because the term Analytic implies that both subject and predicate of verbal propositions are always used in a connotative or descriptive sense and that the function of such propositions is to analyze ideas rather than to identify things spoken of. In a word, Kant's terminology does not suggest any clear distinction between thought and its object.

Aristotle's list of categories is as follows: Substance, Quantity, Quality, Relation, Action, Passion, Place, Time, Posture, Habit.

Hume gives Resemblance, Identity, Space and Time, Quantity or Number, Degree of Quality, Contrariety, Cause and Effect.

Kant gives Space and Time and four sets of 'pure conceptions', viz., Quantity, including Unity, Plurality, Totality; Quality, including Reality, Negation, Limitation; Relation, including Substance and Accident, Cause and Effect, Reciprocity between the active and the passive; Modality, including Possibility and Impossibility, Existence and Nonexistence, Necessity and Contingency.

Mill gives Sequence, Coexistence, Simple Existence, Causation, Resemblance.

For an explanation of Aristotle's list see Minto's "Logic", Chap. III. Hume's categories, called by him "philosophical relations", are enumerated and explained in the "Treatise of Human Nature", Bk. I, Pt. I, Sec. V. But his discussion of Space and Time and Causation runs through the first three 'Parts'. Kant's categories, which he makes to correspond with the formal differences between propositions as set forth