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Objection: (d) Many units in an army are not ready so to die. In this respect the definition is again too

narrow.

Correction: (iv.) A soldier is a person pledged to fight -to the death if need be-for country, cause, or material reward.

N.B. In the above, it has been found convenient to merge the two stages of criticism and reconstruction under a single process of reconstructive criticism through successive objections and corrections. A tendency in this same direction may already have been noticed in connexion with the discussion of some of the preceding definitions.

CHAPTER IV.

II. (iv.) DEFINITION AND DIVISION: LOGICAL DIVISION.

THE process of comparison by which definitions are framed to meet the logical need of the occasion gives, as a result, a genus with two or more species included under it. In a word, the definition of the species through a process of comparison results in the division of a genus into two or more of its species. Definition and Division are thus closely connected from the point of view of logical origin. They are also closely connected from the point of view of logical function. Definition and Division are both necessary to the full understanding of the meaning of a word. Definition gives us

(a) The more general class under which the class in question falls.

(b) A specific distinguishing mark.

Division continues the process of supplying information by giving us the alternative sub-classes.

The problem of meaning, then, covers both Definition and Division, and the principle of Non-Ambiguity is regulative of both processes. (Cf. the illustration of p. 18 borrowed from Mr. Sidgwick.) Hence, if we identify the Principle of Non-Ambiguity with the principle of Definition, we must understand the term 'Definition' in that wider sense of a complete definition of meaning which includes Division as well.

Logical Division.

The term 'Division,' which is the established designation of the procedure we have now to examine, is not happily chosen. We cannot appropriately speak of dividing a word, or the meaning of a word, for meanings are 'differentiated' rather than divided. The very term 'Division' (as also such other metaphorical expressions as 'parts,' 'joints,' etc.) seems almost to imply a physical division, a division of some individual thing into its component parts.* The use of the word has the further disadvantage of prejudicing the interpretation to be put upon the process in its logical aspect. For this process essentially concerns the relation between a genus and its species, and the term 'Division' in this connexion naturally suggests that logical Division consists in the splitting up of a genus into its constituent species. If this is the way in which we are to conceive the process, then the true formula for the relation between genus G and species S1, S2, S3 is G = S1 and S2 and S3. Plane triangles, we should have to say, are divided into equilateral, isosceles, and scalene. These are the parts of which 'plane triangle' is the whole. But when I say that ABC is a plane triangle, I certainly do not mean to say that it is an equilateral triangle and an isosceles triangle and a scalene triangle, that it is S1 and S2 and S3; I mean that it is S1 or S2 or S3. It is this disjunctive formulation which alone truly represents the nature of logical Division.

Logical Division is in no sense a splitting up of things into their parts. For the thing is not a genus, nor are its parts species. The division of an animal (mentally, of course) into head, trunk, and limbs, or of a book into parts or chapters, is a purely physical division. The part here does not stand to the whole in the relation of species to genus. We cannot say that the head or trunk or limb of an animal is itself a sort of animal. But in logical Division the genus divided must be predicable of each of the species into which it is divided. If we divide 'human being' into 'man or woman,' each of the two species into which the genus 'human being' is divided is itself a sort or kind of human being.

There is another species of non-logical Division usually referred to as 'Metaphysical Division.' This is the mental division of an object into its several attributes, as when I analyze 'organism' into its genus, differentia, and various properties. These are not parts of the concept 'organism' in the sense in which head, trunk, and limbs are parts of an animal, for the qualities could not really be separated from each other as head or limb could be separated from the trunk, nor are they collectively equivalent to the object divided.

* Cf. Plato's admonition that 'the philosopher must divide by the joints, and not hack anywhere like a clumsy cook'; and Seneca's remark that a genus 'should be divided, not cut into shreds.'

The true significance of logical Division can best be gauged by considering the relation of Division to Definition in connexion with what we may call the logical development of meaning. To this development, as we have seen, both processes are essential, and we may define their respective functions within this development by saying that Division serves to render determinate those elements of meaning in the definition which are still left indeterminate, and therefore capable of further specification. Division, in a word, is just the further differentiation of the definition in so far as it contains indeterminate elements. Given the definition of a plane triangle as a three-sided rectilinear plane figure, the relations between the three sides are not determined except to this extent that we know, from the geometrical definition of 'figure,' that the three sides must include an area; there is otherwise an indeterminateness in the side-relations, an indeterminateness which is rendered determinate by the division or differentiation into equilateral, isosceles, or scalene.

Illustration of the Logical Development of Meaning through
Definition and Division.

A government may be defined as the ruling power in a society consolidated through some dominating interest, the form of rule varying in every case with the structural character of the body wherein the ultimate authority is vested.

The consolidating interest may be either political or non-political. If non-political, it may be either ecclesiastical (Church-government) or non-ecclesiastical. We restrict ourselves to developing, through division, the meaning of a State-government.

In the case of a State-government, the structural character of the ruling body may take any one of three forms: it may consist of an individual,* or it may consist of a privileged class, or of the community itself. A State-government, that is, may be either an Autocracy, an Oligarchy, or a Democracy. If it is autocratic, the form of government will vary according as the 'rule by one is limited or unlimited. An Autocracy, that is, may be either a Limited or a Constitutional Monarchy, or else an Absolute Monarchy or Despotism, passing, when degenerate, into a Tyranny.

,

If the government is a class-government, the form will vary according to the nature of the ruling qualification. If this is rank, the government will be an Aristocracy; if wealth, a Plutocracy.

If the government is a government by the people, its form will vary with the method of self-government. This may be direct, as in the Citizen-Rule of ancient Athens, or representative, as in the case of modern Democracies, the form of representative govern

* Perhaps two or three, as in the case of the two Kings of Sparta, or of the Roman Triumvirates.

ment varying again with the conditions of the franchise and the number and nature of the representative bodies.

Thus we see that a logical division is not necessarily exhausted by a single division of a genus into its alternative species. The interest which prompts the division may require for its fulfilment the further division of the species into sub-species, and these, again, may require to be divided. These further divisions of species and sub-species would at the same time be subdivisions of the genus.

The conception or genus with which the division starts is known as the summum genus of the division; the ultimate subdivisions of this genus-ultimate, that is, in respect to the purpose of the division-are its infimæ species. The intermediate classes are sometimes called 'subaltern genera '-genera, because every species except the infima species is a genus to the classes into which it is divided. Just as the infima species is a species which is not also a genus, so the summum genus is a genus which is not also a species. Every subaltern class in a continued division is at once species and genus.

The logical interest which prompts and guides a division may be either formal or real. It is 'formal' (with a small 'f'; vide p. 16) when it is 'practical' and 'occasional' in character. It is 'real' when the divisions are drafted in the sole interest of scientific research. This distinction between formal and real may be applied to the divisions themselves. A real division might then be regarded as a Scientific Classification. There is, however, a reason for not identifying the two terms 'Classification' and 'Real Division.' Real Division proceeds always downwards from 'genus' to 'species.' In the process of Classification, on the other hand, we may move in either of two directions: we may move from the 'species' upwards, or from the 'genus' downwards.

Every separate classification has its own summum genus, so that a summum genus cannot profitably denote anything absolute, as the 'being' of Porphyry's tree is not unusually supposed to do. Thus the summum genus of the classification scheme in Zoölogy is the kingdom 'Animal,' and not 'Living Being,' which would include Plants as well, and might even be extended to Metals, if we may trust certain recent scientific research.

The 'infima species,' again, is by no means a fixed distinction in any given system of classification, but is relative to the limit of purposiveness in the making of class distinctions. The African Lion, which is classed as a 'variety' in Animal Classification, may be regarded as an infima species, but if it became useful to distinguish sub-varieties, these latter would in their turn become the infimæ species.

Logical Division must be carefully distinguished from Enumeration. Enumeration is a summing up of the individuals which answer to a given class-designation, whether that class be a summum genus, subaltern genus, or infima species. It is therefore a process which runs parallel to the development of meaning through logical Division. At any stage of that development it may be purposive to turn from the conceptual ordering of fact to the counting up of the individual units which the concepts serve to include under classes. When we consider facts from the point of view of their number or quantity, the process is an Enumeration. From the logical point of view the interest in Enumeration centres mainly, as we shall see, in questions relating to its completeness or its incompleteness.

Basis of Division, or Fundamentum Divisionis.

Every division is based upon and guided by a fundamentum divisionis-i.e., by some character of the group or genus which is a source of difference amongst its members. Thus, in the botanical division of Angiosperms into Monocotyledons and Dicotyledons, the fundamentum divisionis, or F.D., is the number of primary leaves possessed by the plant-embryo. It will readily be seen that the fundamenta divisionis are simply indeterminate attributes of the genus. If 'Man' is divided into 'White man,' 'Black man,' 'Yellow man,' ' Brown man,' 'Red man,' the F.D. is 'skin-colour.' But the genus 'Man' is here relevantly defined as 'a rational animal (det.) possessing a skin-colour of some kind (indet.).' The F.D. cannot be a determinate attribute of the genus, qua determinate, for the simple reason that, in so far as it is determinate, it ceases to be specifiable. At the same time, most so-called determinate attributes are only partially determinate, and, in so far as they are indeterminate, may serve as fundamenta divisionis or bases of division.

From the point of view of the interest we have in dividing or differentiating the meaning of a concept these fundamenta divisionis are essential characteristics of the concept, and must therefore be included within its definition. Thus, suppose we desire to define the statistical unit from the point of view of a statistical inquiry which purposes to class the citizens of a country according to means and occupation. The definition would take some such form as this: The 'statistical man' is 'a citizen of a certain means and occupation'; and the full meaning of this unit can be made clear only when we specify the divisions we intend to draw under these two heads. Thus the 'statistical man' may be regarded as (1) 'a citizen who has an income that is either under £50 a year or under £500, or over that amount'; and as (2) ' a citizen who is an artisan or is engaged in business, or is in a profession, or falls outside these three classes.'

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