upon the real characteristics of the distinction between the two elements. The predicate here is clearly first in the mind in the order of time; in fact there it stands, waiting, possibly in vain, for its desired subject. But as soon as the mind has got possession of both the elements, we see that the person is the more important, and therefore the determining one, whilst the comparatively less substantial qualification or character is the one which is employed to supplement it.

A third possibility, of course, is that both terms were already present to the mind, the only doubt being whether they should be joined together; that is, the supposed question might have been, Is Gladstone a statesman? Any proposition may of course be apprehended doubtfully; and the ordinary grammatical form for expressing such doubt, coupled with a desire to have it dispelled, is that which we call a question.

Affirmation and Negation. For logical purposes, the distinction between affirmation and negation ought not to offer any real difficulty. In fact the perplexities which unfortunately have sometimes crept into the subject have mainly arisen from an almost wanton love of subtlety or paradox on the part of logicians.

The simple and obvious distinction which forms the ground of the separation of propositions into affirmative and negative, in itself needs no explanation, at least when we are dealing with the class of propositions which are most suitable for the predicative form. The predicate element which is, so to say, held out before us for the moment, for comparison with the subject, must either be found in it or not; it must either be a constituent member of the group or not. If the proposition be what is called an analytical or verbal one the alternative is, that in making an affirmation, we have extracted the predicate from a group of which we already know it to be a member; in making the negative we have looked in vain for some element which we knew not to be there. If the proposition be a synthetical or real one, the alternative is that in affirmation we are going to add on some predicate to the group, whilst in denial we equally hold it out before us and say we are not going to put it there.

The only point here which seems to deserve any notice is that one particular difficulty which we saw might attend affir

mative predication is absent from the negative form. We saw that affirmation consisted in separating one member from a group to which it belonged, and yet in regarding, or rather in naming, that group as if this member were still there. We found in fact that in certain cases where the predicated members constituted a large proportion of the total group, the predication was apt to assume an almost fictitious form, as for instance when we spoke of the weather by enumerating all the attributes which constituted it. From this anomaly negation is generally clearly free. I may picture as many qualities as I like which are not to be found in the subject group, and it is obvious that in so doing we are in no way tampering with the integrity of that group or reducing it to a fiction.

The way in which the ingenuity of logicians has been most successful in creating difficulties here is in trying to evade the fundamental distinction above indicated by employing one form for both affirmation and denial. This it is attempted to do by the use of negative predicates, retaining only one form of copula. Thus, instead of saying, The stone is not black, some would phrase it, The stone is not-black, thereby securing the semblance of an affirmation. We need hardly pause to point out that nothing is effected in this way except so far as the mere expression of our propositions is concerned. Recur for a moment to what was said when we were dealing with the distinction. between positive and negative terms. We saw that 'not-black' denoted the whole class of things of which 'black' was denied, or could be denied; its connotation or characteristic distinction was the absence of black, and nothing else. To assert the absence of black, or to deny its presence, are merely varying verbal expressions of one and the same fact.

In itself, any such attempt to do away with the form of negation by transferring it from the copula to the predicate in the hope that it could better be stowed away out of sight in the latter than in the former, is utterly trivial. But it may serve to direct us to two considerations of some importance.

(1) Fully admitting the merely formal character of the transformation in question, there is a certain development of Logic which, dealing exclusively with the form, finds it convenient to adopt this transformation. This is that development of Formal Logic which I have proposed to call Symbolic. The

object of adopting this course here is to secure simplification. Whereas common speech makes use (universally) of positive and negative copulas, and also makes use (not unfrequently) of positive and negative terms as well; the Symbolic scheme finds it economical to employ one form only of copula,—at least so far as universal propositions are concerned,-viz. the negative form, marking the distinctions of affirmation and negation in the predicate. To carry this out it adopts a thorough-going class interpretation of every proposition, declaring that such and such a class is empty, that is, non-existent. Thus when it wants to assert that, All cruciferæ are edible, it frames the statement in the form, There are no cruciferæ non-edible; that is, it declares this class or compartment to be unoccupied. If it wanted to state that, No orchids have opposite leaves, it frames the statement thus, There are no orchids opposite-leaved.

The transformation thus made use of is adopted entirely for simplification, and for the symbolic power which comes of simplification. No one who uses it should ever suppose that he is abrogating the fundamental distinction between affirmation and denial of any specified fact, however optional he may have rendered it which form shall be preferred for the purposes in hand.

(2) The other point to be noticed is that though the distinction between affirmation and negation is always peremptory and unambiguous, yet it may often be difficult in any given case to say which of two propositions best deserves to be called the affirmative. By this I mean that given a proposition which we have decided to consider as being intrinsically affirmative, it is easy enough to state the corresponding negative, and conversely; but the decision, as to any single proposition, whether it is most reasonably to be termed positive or negative, may often be a difficult decision. The antithesis, in fact, often comes to be a relative rather than an absolute one. If we revert to what may be called the typical primitive case of predication, viz. that of a substance with simple attributes, here indeed there is seldom much difficulty. As between the statements that the picture is square, and that it is not square, no verbal arrangement would disguise the fact that the former is the affirmative. But as between the statements that a certain mountain summit is accessible and that it is not accessible, the case does not seem

so plain. When we picture the facts implied in the statements we can do so by imagining a climbing party reaching the top after many efforts, in the former case, and turning back or falling down in the latter. Is the latter intrinsically more of a negation than the former?

The fact that it should be so difficult to give an offhand answer in some of these cases reminds us how widely the conception of predication must be extended. We may begin, as was pointed out at the commencement of this chapter, by taking substances and their sensible qualities, but we find that the same formal framework will serve to indicate syntheses of an exceedingly complex character. Now so long as we deal with such elements as colour or weight, the non-possession of these attributes offers a very wide and heterogeneous field as compared with their possession. The difficulty of saying which is, and which is not, in itself a negative quality is helped out by the fact that the one is by comparison definitely limited whilst the other opens out an indefinitely wide scope. The distinction was clearly marked by the old logicians when they described terms which merely marked the non-possession of some quality as 'infinite'. They were right enough as regards the bulk of such simple attributes as mostly present themselves in common life, but we should greatly underrate the range over which the act of predication may extend if we were to suppose that this must always be the case. The non-possession of a quality may really, when we look at the facts denoted by the terms, in certain cases be the simpler conception of the two.

CHAPTER IX.

THE SCHEDULE OF PROPOSITIONS.

HAVING So far discussed the general nature and functions of Propositions we must next enquire into their subdivisions; that is, we must ask how many kinds of propositions there are, and how these stand related to each other. I take it for granted that the reader knows something of the familiar logical doctrines on this subject; and therefore instead of spending the time in an exposition of the common view we will rather work round about the subject, raising such questions as these, How and why does it come to pass that there should be just four forms of proposition generally accepted? Are there any other systems of logical science which would naturally lead to a different scheme of propositions? In particular, is it necessary for inductive purposes to enlarge the accepted scheme? and so forth.

I. First then, as regards the origin and justification of the familiar and traditional scheme. This scheme seems to me to be unquestionably selected from the propositions of common life. It contains, as we shall presently see, but a small selection from the propositions actually current amongst ordinary people, but the general view underlying it seems to be substantially the same.

In order to settle this point a previous question must be raised, which is best phrased as follows. In what way,-that is, in what kind of form, whether of substantive or adjective or otherwise, do the subject and predicate present themselves to the mind when we make assertions? This question, like many others raised in Logic, subdivides into several branches, according as we enquire (1) how the matter is decided spontaneously, i.e. how the logical habits implicit in human thought have