form and saying that if he draws such and such figures, such and such properties will necessarily be found to be involved in them.

The general conclusion therefore which I am inclined to draw as to the distinctiveness, and the fixity of application, of these forms of speech is this. The distinction of facts, and of our mental attitude in relation to those facts, out of which the structural difference between the categorical and hypothetical forms of assertion has sprung, is a real and important one. So soon as men had begun to observe and to reason, this distinction must have forced itself into notice in every department of practical and speculative life. And the distinction thus early recognized has been imprinted upon our forms of speech, and has thus been enabled to emphasize and perpetuate itself. But, as in all cases where language is concerned, the forms of speech have shown a disposition to modify themselves with lapse of time and growing complexity of circumstance, and have thus become somewhat shifted from their original application. The hypothetical, it is true, has lost but very little of its primary import: that is, some trace of the conditions under which I conclude it to have originally developed itself may still be detected wherever it is employed. But the categorical form has shown a more decided tendency to extend its scope over what is really hypothetical ground. It has been driven into this course by the gradually increasing complication of the subjects of the propositions which advancing thought demands; for, as we have seen, complicated subject-terms cannot be considered to be bound by the assumption in virtue of which alone categorical propositions can be technically distinguished from hypothetical. This tendency finds its extreme development in the Symbolic Logic in which all distinction between the hypothetical and categorical forms is entirely obliterated.

CHAPTER XI.

DEFINITION.

WE have now reached a part of the subject in which the old technical terms have so worked their way, not only into the current language and treatment of the modern logicians, but even into the phraseology of common life, that a somewhat more historic explanation than has hitherto been adopted seems advisable. In treating of Definition we find ourselves forced to discuss the famous Predicables, or Five Words, which from the time of Porphyry onwards long formed the central part of Logic as commonly treated, and to the consideration of which indeed many entire treatises have been devoted. This introduces us to a certain difficulty. The old technical terms are far too thoroughly established to be lightly abandoned. But intimately connected as they are with decaying and obsolete doctrines, it is impossible not to make alterations in their meaning, and the extent to which this has been done by various modern writers has introduced an element of variety and confusion. Some of the more conservative writers have clung so closely to the old ways of thinking that we find them still taking for granted the scholastic distinction between necessary and contingent matter. Others, though retaining the old terms, have endeavoured to translate them into purely modern ideas, and have naturally found it very difficult to find a suitable and consistent usage for them all.

The following is the plan I propose to adopt. We will first explain what may be regarded as the customary modern usage of sound and sober logicians. It will then be attempted to give a slight sketch of the old account, in order to realise how wide is the transition which is thus bridged over by a common phraseology. So much refers mainly to the province

of Formal Logic. We will therefore, thirdly, consider whether any of the old terms are still capable, and if so in what direction and under what limitations, of answering the past and present wants of the Inductive logician.

The five words with which we have to deal, it need hardly be said, are Genus, Species, Property, Difference, and Accident.

(i, ii) First then, as regards the Genus and Species, which it will be best to take together. These are now commonly regarded as class names; or rather, to speak more accurately, as the classes themselves denoted by the names. And no further or deeper distinction is recognized between them than that of greater and less denotation. That is, whenever two classes of things are found, with names corresponding to them, of which one includes the other, they may be respectively so regarded: the wider being considered a genus, and the narrower a species.

In saying this it must be understood that when we talk of the wider class including the narrower, we mean that it does so formally: i.e. that the connotation of the latter includes that of the former. It would not generally be considered correct to select any two classes of which one happened to lie inside the other, and call the former a species of the latter. Thus, even if all kangaroos were as a matter of fact natives of Australia, the kangaroo would not be technically regarded by the logician,-and still less by the naturalist, as a species of Australian thing, because its residence or place of origin is in no sense a part of the meaning of its name. But for the same reason it would rightly be regarded as a species of marsupial, of mammal, and of animal, because its distinctive attributes include those of each of these classes.

(iii) The account generally given of the Differentia follows simply and immediately from that of the Genus and Species. The species, as we have seen, is a narrower class selected from the broader by the addition of some further attribute or attributes. The surplus connotation thus involved in the species over the genus is regarded as the Differentia of the former.

Regarded formally, that is, without enquiry whether there are really to be found things corresponding to each such selec

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tion,-it is obvious that every species will have corresponding to it not one, but a number of differentiæ. It contains of course a plurality of attributes, any one of which may be conceived to have been added on to the group consisting of the remaining ones. Each of these groups, that is, might be conceived as a genus of a differentia.

from which we select a species by means

(iv) So far there is but little opening to variety or difficulty for those who only seek a reasonable and consistent usage of the old terms. The three words referred to, or at least the distinctions which they are intended to express, are absolutely requisite for accurate discussion. Indeed, we might say that even the looser discourse of common life could not be conveniently carried on without some resort to them. The next term however, Property or Proprium, seems of less importance, and has retained its place along with the rest mainly from traditional reasons. It is moreover that one of the five words as to which the widest difference of interpretation is to be found amongst the old logicians. If it is still to be retained, I think the best interpretation is that of Mill and some others. On this view the 'property' is regarded as being any attribute which is not explicitly considered as forming part of the connotation of the term in question, but which can be shown to follow from what is a part of such connotation. The reader may be supposed to know, it is a point to which we shall have to recur presently,-that the logical connotation of any term comprises a limited number only of those attributes which the objects themselves comprising that class actually possess in common. Of the remaining attributes some will probably be deducible from others. If so, and these others are themselves included in the connotation, then the derivative ones will be considered as properties. Thus, for instance, the Differentia of a Bill of Exchange consists mainly in the fact that it only becomes due after a certain assigned date. That is, this is the principal distinguishing attribute which differentiates it from other instruments of credit. Now it is a consequence of this characteristic that Bills of Exchange will be more liable to fluctuations in value than cheques, which are payable at sight. Accordingly the fluctuation of value may be regarded as a 'property' of a Bill of

Exchange. It is no part strictly of the meaning, but follows from that which is a part.

(v) Accident. Here again we come upon a term indicating a generally recognized distinction, and one consequently which has worked its way into even popular phraseology. On the whole it is still accepted in a sense which departs but slightly from its original signification.

Every class of objects, as just remarked, contains many attributes, besides those connoted by the name, which are common to every member of the class. And every individual object contains an infinite number of attributes which are in no way involved in the meaning of any single class name which we may happen to apply to it. These attributes may be of various degrees of fixity and universality. Some may only just have fallen short of being included in the connotation, on the ground that though not included in the meaning of the term they are always present, and are inevitably suggested by it. Others may be very generally present. very generally present. And others again may be of the most casual character, mere temporary qualifications, or so forth. But they all agree in the fact that they cannot strictly be inferred from anything contained in the connotation of the name. These attributes are called accidents. They fall naturally into two classes. Sometimes they will, as a matter of fact, be found to be present in all the objects of the class in question: they are then called 'inseparable' accidents. Sometimes, and of course much more often, they will only be found present in certain individuals of the class, or only present at certain times or under certain conditions. They are then called 'separable' accidents.

Thus among the inseparable accidents of the Bill of Exchange might be included the facts that it is in great part printed or lithographed, and that it is on paper: among its separable accidents may be included the size, date, value, &c., in fact, all the innumerable qualities by which one bill is distinguished from another.

Having cleared the ground by the foregoing brief discussion we are now in a position to say what is to be meant by Definition. Revert for a moment to the distinction between denotation and connotation. We have already seen the necessity of assuming that every significant name (with some