must be divided in a different way, and give rise to new subclasses.

The concept, like the term, has its content or comprehension, and its extent or extension. The extent of a concept consists of the individual conceptions or things in which its content is found. The content of a concept consists of the elementary notions or ideas which constitute its very essence and meaning. The statement in words of all or any of these elements, is the definition of the concept; and the grouping of the individual conceptions into minor divisions according to their resemblance and difference, is the division of the concept. The extent and the content of a concept, and the relation between them, may be represented by circles, and capital and small letters of the alphabet, just as in the case of a term.

§ 7. Definition as a logical process is the process of determining the connotation of a term, or the attributes possessed in common by the things denoted by the term. It implies observation, analysis, abstraction, comparison, and even generalization, and is a most important process in science. A definition as a product of thought is the product of this process. In a complete treatise on Logic, Definition would deserve a most prominent place. Here I shall give only the rules to which a definition ought to conform, noting, by the way, the faults to which the violation of them gives rise. A definition should conform to the following rules or conditions :—

(1) That it be an analytical statement of the connotation of the term defined. This rule includes the one given by the older logicians, that a definition should be per genus et differentiam, that is, a statement of the genus and a differentia of the term. If a part of the connotation is stated, the definition is partial or incomplete; and if the whole of it is stated, the definition is complete. An incomplete definition, if it serves to distinguish the things denoted by the term from others belonging to the same higher class, corresponds to a definition per genus et differentiam, while a complete definition corresponds to a definition per genus et differentias. The violation of this rule gives rise to

what has been called an accidental definition, or a mere description of the things denoted by the term as well as to redundant and incomplete definitions. When any attribute not possessed by all the things denoted by the term, or not forming a part of its connotation, is stated in the definition, it is accidental; and when some attributes that follow from its connotation are stated, it is redundant. For example, 'a triangle is a figure which is bounded by three straight lines, and which has all its angles together equal to two right angles' is a redundant definition; 'water is a liquid substance' is incomplete; 'man is a cooking animal' and ‘iron is the cheapest metal' are accidental; and ‘a plant is an organism having roots, branches, leaves, flowers, fruits, &c.,' is a mere description.

(2) That it exactly coincide in extent with the denotation of the term defined. In other words, it should not include things other than those to be defined, nor should it exclude any of them. The violation of this rule gives rise to the fault of too great width or narrowness. For example, the definitions 'man is a sentient being,' 'a metal is a solid substance,' are too wide; while 'man is a civilized animal,' ‘a metal is a heavy element,' are too narrow.

(3) That it do not contain the term to be defined, or any of its synonyms. The violation of this rule gives rise to the fault of the circle in definition. For example, when a term is defined by itself, as 'man is a human being,' 'a plant is a vegetable organism,' 'life is the sum of the vital functions,' or when a term is defined by a second term, and the second again by the first, as 'man is a rational animal'; and, again, ‘a rational animal is a human being,' 'matter is an extended substance'; and, again, ‘an extended substance is a material body.' From this rule it is evident that a term connoting an elementary attribute cannot be defined. For its definition will contain either the term itself or its synonym, or be merely a description of it. Hence such terms as 'consciousness,' 'feeling,' 'pleasure,' 'pain,' 'colour,' 'smell,' &c., connoting elementary attributes, cannot be defined. The definitions or rather descriptions and analyses that

are given of them, consist of a statement of the circumstances or conditions under which they are produced.

(4) That it be expressed in clear and unambiguous language. In other words, it should not be expressed in obscure, figurative, or ambiguous language. The violation of this rule gives rise to obscure and figurative definitions, which are misunderstood, often bear more than one interpretation, and are a source of much trouble and misunderstanding both to the teacher and the pupil, as well as to the general reader. 'The intuitive reason is the eye of the soul,' 'The mind is a tabula rasa,' 'The ideas are the images of external objects,' 'The soul is the first entelecheia of a natural body which has potential life1,' will serve as examples.

(5) That it be not negative, where it can be affirmative. The violation of this rule gives rise to negative definitions which are often almost meaningless. 'Mind is not matter,' 'mind is the non-extended,' 'evil is that which is not good,' 'vice is that which is not virtue,' 'virtue is that which is not vice,' are negative definitions that are almost useless.

Exercises on Definition.

I. Test the following definitions:

(1) Logic is the science of thought.

(2) Logic is the science of reasoning.

(3) A triangle is a three-sided figure, of which any two sides together are greater than the third.

(4) (a) "A power is a force which tends to produce motion," -Ganot.

(b) "Porosity is the property which bodies possess of having pores."-Ganot.

(c) "Matter is any thing whose existence can be determined by one or more of our senses."-Ganot.

(5) A force is a power that can produce motion.

(6) A plant is an insentient organized being.

(7) A crystal is a solid substance of a definite geometrical form.

1 Aristotle's definition of the soul quoted by Reid in his Inquiry.

(8) An equilateral triangle is a three-sided figure, having all its angles and sides respectively equal to each other.

(9)

A triangle is a figure bounded by three straight lines. (10) Logic is the science of human knowledge.

(11) Gold is a precious metal.

(12) Diamond is a kind of carbon.

(13) Oxygen is a supporter of combustion.

(14) A rock is a hard substance.

(15) Inorganic substances are dead material bodies.

(16) Mind is a thinking substance.

(17) A plant is a being possessing vegetable life. (18) A glacier is a river of ice.

II. Define the following terms :—

(1) Student, (2) College, (3) University, (4) Library, (5) Class, (6) Term, (7) Mind, (8) Matter, (9) Thing, (10) Food, (11) Bird, (12) Lake, (13) Book, (14) Free, (15) Plant, (16) Flower, (17) Animal, (18) Virtue, (19) Religion, (20) Science.

§ 8. Logical division is to be distinguished, on the one hand, from what is called physical division, or the analysis or separation of an individual thing into its component parts; and, on the other, from what is called metaphysical division, or the analysis of an individual thing into its constituent attributes, qualities, or properties.

The division of a plant into its roots, trunk, branches, and leaves, or of an animal into its head, trunk, limbs, &c., is physical; while the division into the qualities which constitute a plant or an animal is metaphysical. The division of a piece of gold into two or more parts is physical, while the division or rather the analysis of it into the qualities, yellow colour, a certain specific gravity, a certain form, size, solidity, &c., which are possessed by every particle of it, is metaphysical. Similarly, every individual object may be divided physically into its component particles or parts, and metaphysically into its qualities, properties, or attributes. But both these kinds of division should be distinguished from logical division, which cannot be

applied to an individual thing or attribute, but only to a class of things or attributes.

The rules or conditions to which a logical division ought to conform are the following:

(1) That what is to be divided be a class and not an individual. In other words, a singular term cannot be divided, and only a general term is capable of logical division. The violation of this rule gives rise either to physical partition, or to metaphysical analysis. A collective term, such as 'a nation,' 'a library,' 'a forest,' 'the universe,' 'the animal kingdom,' being really singular in signification, is also incapable of logical division.

(2) That the division be founded upon the presence or absence, or upon the varying degree, of a certain fundamental attribute; in other words, that there be only one fundamentum divisionis or principle of division. The violation of this rule gives rise to the fault of cross-division.

(3) That the name of the class divided be applicable, in the same sense, to each of the sub-divisions or smaller classes into which the whole is divided. The violation of this rule also gives rise to physical partition, or to metaphysical analysis.

(4) That the sub-divisions be together equal to the class divided. In other words, the denotations of the dividing terms should together exactly coincide with the denotation of the divided term. The violation of this rule gives rise to the fault of incomplete or over-complete (too narrow or too wide) division.

(5) That the sub-divisions do not overlap, but completely exclude each other. In other words, any individual included in the denotation of one dividing term, should not be included in the denotation of another. The violation of this rule gives rise to the fault of over-lapping division.

I shall illustrate the above rules by a few examples :-(1) A division of rectilineal triangles is into (i) equilateral, (ii) isosceles, and (iii) scalene. Here the term divided is general; the principle of division is the equality or inequality of the sides; the divided term 'rectilineal triangle' is applicable to each sub