order. One is a discipline to be assimilated by the mind, the other a drug to be absorbed by the body. 4. The definition must consist of terms more elementary than the term defined-i.e., it must be such that no one can reasonably expect to understand the term to be defined without first understanding what the defining terms themselves mean. This rule must be applied with reference to the given interest-e.g., that of Geometry. I may be quite right in defining a circle as follows: ' A circle is a plane figure contained by a line of which all the points are equidistant from a fixed point within it,' since the specific mark contains only such terms as 'line,' 'point,' 'equidistant,' all of which express more elementary geometrical ideas than that of the circle. Hence a definition is not invalidated because the untrained mind finds its terms less simple than the term it defines. 'Man' is to most people, no doubt, a much simpler and more familiar term, much easier to understand, than its definition 'rational animal,' but these defining words are more elementary than the more obvious term they serve to define. Example. A fine is a pecuniary mulct. This is, scientifically, a correct definition, as a mulct is any forfeiture or penalty. But from the purely practical point of view it would be a breach of this fourth rule, or, in technical language, an 'ignotum per ignotius.' 5. A term should not be defined by the aid of terms which cannot themselves be appropriately defined without first defining the original term. To break this rule is to commit a 'circulus in definiendo'or 'vicious circle.' E.g.: 'Man is a human being.' 'The sun is the centre of the solar system.' Example. Cheese is a caseous preparation of milk. 'Here caseous' means 'cheesy,' and we still want the definition of 'cheesy.' We wish to know by what kind of preparation cheese can be obtained out of milk. The differentia should indicate the recipe for transforming milk into cheese. A vicious circle in definition is more than a mere blemish. It destroys not only the value of the definition, but the definition itself. The 'statement' that 'cheese is cheesy' is, in fact, no statement at all. It does not predicate anything of cheese, but stops at the concept which is to be defined. 'Cheese is cheesy' takes us no further than 'cheese.' The definition is, therefore, to this extent non-existent. We must be careful, however, not to be too hasty in accusing a definition of involving a vicious circle. Example. A Lilliputian is an inhabitant of the island of Lilliput. Taking 'Lilliputian' in its primary sense (in its derived sense it is a synonym for 'dwarf'), we should have to meet the objection that if Lilliput is defined as the land of the Lilliputians, then to define the Lilliputian as an inhabitant of Lilliput is to shut oneself up within a vicious circle. But if 'Lilliput' is defined in such a way that its definition does not introduce the Lilliputian-e.g., by its geographical position-then there is no vicious circle at all, and the definition is correct. Such definitions as 'A sovereign is a gold coin equal in value to twenty shillings' and 'A day is a period of time consisting of twenty-four hours' are liable under similar limitations to the fallacy of vicious circle, the former if a shilling is defined as the twentieth part of a sovereign, the latter if an hour is defined as the twenty-fourth part of a day. As a particular case of circular definition, we have the attempt to define a term by means of its correlative. In the case of correlatives in the case, that is, of such terms as 'whole' and 'part,' genus' and 'species,' 'first' and 'second,' 'cause' and 'effect,' the two terms must be defined together. We cannot define one by the other. A whole cannot be logically defined as 'an aggregate of parts,' if by 'a part' we mean 'a fraction of a whole.' The definition here is, in fact, the definiendum itself. To define a 'whole' is to define a 'whole of parts.' It is a unity of some kind, of which the nature varies with the form of relation between whole and part. In specifying this form of relation, whether spatial, organic, or spiritual, we define the type of unity we have in mind, and specify the general meaning of 'whole.' We may therefore define a 'whole' or 'whole of parts' by means of the genus 'unity' and the indeterminate differentia 'possessing some kind and some degree of self-coherence.' Mill, in his 'Logic' (Bk. I., ch. ii., § 7), clearly points out why it is that certain words go in pairs, as in the case of the instances mentioned above. It is because the meaning of both terms is derived from the same fact or set of facts. Thus, taking the relation of 'father' to 'son,' he writes: 'The paternity of A and the filiety of B are not two facts, but two modes of expressing the same fact.' The terms 'father' and 'son,' however, are not strictly correlatives as are the terms 'parent' and 'child.' They are semi-correlatives. Fatherhood does not necessarily imply sonship, though sonship implies fatherhood. Sheep' and 'shepherd' are semi-correlatives in a precisely similar sense. There can be no shepherd unless there are sheep to be herded and tended, but there can be sheep without a shepherd. So, again, a third implies a first and a second, but these do not imply a third. Hence no circle is committed by defining a shepherd as 'a person who looks after sheep,' for we may very well define a sheep without introducing its relation to a shepherd. But we cannot, without a circle, define a sheep as 'the kind of animal which a shepherd looks after.' 6. A definition should not be given in a negative form if a positive idea is intended. As Professor Read reminds us, a natural historian would not define a lion by saying that it was not a vegetarian. So, in the positive interests of Geometry, it would be better to define a curve as 'a line that is always changing its direction' than to define it as 'a line in no part straight.' On the other hand, where the word to be defined stands for a distinctly negative idea, this form of definition-i.e., negative definition-is to be preferred to any other. E.g., 'An alien is a person who is not a citizen,' ' A bachelor is a man who is not married.' Examples on the Testing of Definitions. I. A circle is a figure of which all the points are equidistant from its centre. Purpose of the definition: To give a geometrical definition of a circle. Criticism of the definition as given. (a) The word 'centre' is not more elementary than the term 'circle,' therefore should be avoided. Correction: A circle is a figure of which all points are equidistant from a certain fixed point within the figure. (b) It is not true that all points of a circular area are equidistant from the centre; one point of the area is, in fact, the centre itself. Correction: A circle is a figure enclosed by one line, the circumference, of which all points, etc. If by 'line' we understand 'continuous line,' this correction should quiet the suspicion that the circumference might be punctiform, a discontinuous aggregate of points. (c) The 'one line' of this definition may still meander freely over any surface of which all points are equidistant from a certain point within the figure. In mathematical phrase, its locus may be the surface of a sphere. Final Reconstruction : A circle is a plane figure, enclosed by one line (the circumference), of which all points are equidistant from a certain fixed point within the figure. II. Work is the salt of life. Verbal Division :* By 'work' we may understand either an activity or its product. The former sense is evidently intended here. Purpose: To define Work as an activity having relation to moral life. Criticism: The definition is metaphorical. We must get rid of the metaphor. Reconstruction: (i.) Work is a type of purposive activity (genus) which stimulates, purifies, and sustains the life (differentia). Query: Is 'work' here sufficiently distinguished from 'play'? (ii.) Work is a purposive activity which, when regarded in the light of a moral obligation, stimulates, purifies and sustains the life. III. A chair is an article of furniture with four legs and a back. Purpose: To define a chair by the use to which it is put. Criticism: (a) Proximate genus not given. Correction: A chair is a seat. (b) The differentia is not satisfactorily given. Correction: If we compare a chair with a stool, we obtain as genus 'moveable seat,' and as differentia 'having a back.' If we compare a chair with a sofa, the differentia is 'intended to seat one person.' (c) 'Four legs' is a mere 'accident' or problematical property of the occasional type. Reconstruction: Proximate genus (of chair, sofa, stool) 'Moveable seat.' Differentia: 'Intended to accommodate one person at a time, and having a back.' IV. A cow is a ruminant with cloven feet and sweet-smelling breath. Comparing 'cow' with 'bull,' we obtain as genus (b) 'With cloven feet' is a characteristic property. Reconstruction: A cow is a female ox. * By 'Verbal Division' we understand the division of an equivocal or manymeaninged word into its various alternative significations. Thus the division of 'box' into 'covered case, partition in a theatre, blow with the fist, shrub, or driver's seat' would be a verbal division. V. A candle is a kind of light used before gas was invented. Purpose: To define a candle from the point of view of its use as a light and the structure which subserves that use. Criticism: (a) Genus inexact; a candle is not a kind but a means of light. : In (b) The specifying mark leaves the definition in one respect too wide, for other things besides candles were used for lighting before gas came into use. another respect it is too narrow, for candles are still used, though gas has been 'invented.' 'Used before' implies that candles ceased to be used when gas came into fashion. (c) Further, gas was not 'invented' but 'manufactured.' The specific mark must, therefore, be cancelled as flat and irrelevant, and a radical reconstruction is called for. Reconstruction: A candle is a means of lighting, consisting of a stick of fatty matter traversed by a wick. VI. The Sun is the star that shines by day. Purpose: To define the sun from the point of view of its appearance (Ptolemaic point of view). Criticism: Can 'day' be defined without involving a vicious circle ? Is not 'day' that time during which the sun is above the horizon ?* Reconstruction: Comparing the sun with moon and stars, which agree in giving forth no perceptible heat, we obtain: The sun is a celestial luminary which warms the earth. VII. 'A soldier is a brave man who is ready to die for his country. Purpose: To define a soldier as such-i.e., from the point of view of his military office. Objection: (a) 'Brave' superfluous, as the essential kind of bravery that a soldier requires is implied in 'ready to die.' Correction: (i.) A soldier is a man who is ready to die Objection: (b) 'Man' makes the definition too narrow. Correction: (ii.) A soldier is a person who is ready to Objection: (c) The definition is still too narrow. It excludes mercenaries, organized revolutionists, etc. Correction: (iii.) A soldier is a person who is ready to die for country, cause, or material reward. * This criticism, as Mr. Joseph points out (ibid., p. 100), is given by Aristotle himself. |