Posterior Analytics (Bouchier)/Book II/Chapter XIII
Chapter XIII: On the search for a Definition
- The part of definition is to examine essentially attributes which, individually, may be either co-extensive with their subjects or more comprehensive. The sum of these attributes must however exactly equal the subject. As to the arrangements of attributes, none must be omitted, and that one must be placed first which is the consequence of all the rest. All definitions are universal; truth and clearness must be aimed at, ambiguous and metaphorical language must be avoided.
It has already been stated how a thing’s essence is expressed in definition, and in what ways the essence can or cannot be demonstrated or defined. We will now explain how one should discover the essential attributes of a subject. Of the attributes of every subject some are always more comprehensive than that subject, though keeping within the limits of the genus to which the subject itself belongs. As an instance of more comprehensive attributes I might mention those qualities which are universal attributes of the subject in question but are attributes of some other thing as well. Thus a quality may belong to every triad but also to something other than triad. E.g. Existence belongs to triad, but also to other things not numbers at all. ‘Odd’ is also an attribute of every triad but is more comprehensive, for it also belongs to a pentad. Yet this latter quality remains within the limits of the same genus; a pentad being a number, while nothing outside number can be odd. In defining such terms we should reckon in so many qualities as, when taken collectively, may be equivalent to the thing defined, though separatedly they may have a wider comprehension, and we shall then be in possession of the thing’s substance.
For instance ‘number’ is true of every triad, also ‘odd’ and ‘primary’ in both senses; that of not being the multiple of another number and not being a compound number. The following then is the definition of triad:—an odd number, primary, and primary in a certain sense. Each of the first two qualities is true of all odd numbers, while the last quality of primariness is true of the dyad also, but no number except the triad possesses all these qualities together. Since we have shewn above that all the attributes which express the essence of any subject are necessary, while it is the universal which is always necessary; since also the attributes established in the case of triad, or similar attributes of any other subject, are part of the essence, it follows that the attributes predicated of it in the definition must necessarily constitute a triad. That they form its substance is clear from the following considerations. If these attributes are not the essence of triad they must form a kind of genus of triad either named or unnamed, which will be consequently more comprehensive than triad, seeing that we assumed that the genus is such as potentially to be more comprehensive. If then the definition be applicable to nothing wider than individual triads it must form the essence of triad. This rests on the assumption that the essence of every subject is the lowest predication of attributes, or one applying only to individuals and to no class higher than that of the subject. Hence the essence of any other subject will consist of the attributes predicated of it in a definition of this kind.
When one is engaged with any complete whole one ought to cut up the genus into primary indivisible species, e.g. to divide the genus number into triad and dyad, and then endeavour to establish the definitions of these species, considering the cases of straight line, circle, or right angle. Next after establishing the nature or sphere of the genus, for instance whether it concerns quantities or qualities, one should search for its peculiar properties in the light of its common primary principles.
The definition will suffice to shew what are the properties of those species which serve to make up the genus, because definition and unity form the basis of all things, and because accidental qualities are only essentially true of the simple species, and of the others only from their relation to those simple species. Divisions also, if conducted according to the specific differences of the subject, are of service for the establishment of a definition.
In what way division is capable of producing demonstration has already been stated (II, c. 5); namely that it can only serve to deduce the essence of the subject. It might however seem as if it were of no value for obtaining definition, since one might assume all the qualities of the subject at the outset, such assumptions being made without any division.
On the other hand we must remark that the nature of the result varies according to the order in which the attributes in a definition are predicated; e.g. whether one says ‘Man is a tame animal with two feet,’ or ‘a two-footed tame animal’; for if the whole definition be composed of two elements of which the first is ‘tame animal,’ and if from this, combined with the specific difference ‘two-footed,’ the concept ‘Man’ be formed (or whatever else may be the unit which results from the definition), one must discover the parts of a definition by means of a division.
Moreover division is the only method which can ensure that definition shall omit no essential attribute of the subject. Thus if, after taking the most comprehensive genus, one proceed to some of the subordinate divisions, not everything which belongs to the whole genus will fall within one of those subdivisions. For instance not every animal has either undivided or divided wings, but only every winged animal, and this possession of wings constitutes its difference. On the other hand, in the case of the genus animal, the primary difference of animal must be of such a kind as to be applicable to every kind of animal. In the same way the primary divisions in every genus must be conducted, whether these be genera outside of and co-ordinate with the genus ‘animal’ already referred to or subordinate to it. For instance, the term Bird ought to be so divided that every separate bird shall be included in the division, and every fish in the division of Fish. If our division be thus conducted we may feel sure that nothing has been omitted, otherwise we must omit some essential quality in our definition without observing our omission.
Though some maintain that it is impossible to know the true Difference of a thing without knowing every other thing also, it is not really necessary for either definition or division to possess universal knowledge. They hold that, if no difference be known between the thing observed and other things, we cannot know that the former is not identical with the latter, and one thing can only be said to differ from another when it has a recognized difference. Now firstly this is untrue. Not every difference renders things diverse, and many differences exist between things specifically the same, namely differences which are neither inherent nor essential.
Secondly, when one has established pairs of opposites in a division, and also the difference between them, in such a way that every individual instance must fall under one or the other class, and further has assumed that the thing which one is seeking is in one of the classes, and is able to recognize it, it is of no importance whether one knows or does not know all the other subjects to which the difference in question also belongs. If one proceed in this manner to a point where no further specific difference is found, one must clearly be in possession of the definition of the subject. That everything must fall under the division if pairs of opposites have been discovered admitting of no further alternative is not an assumption but is necessarily true, if the difference we have selected be really the primary difference of the genus in question.
In order to construct a definition by means of division, three points must be kept in view. We must admit only essential attributes, must arrange them in their right order, and must not omit a single one.
The first of these depends on whether we are able to make an essential predication with the help of the generic notion, as we predicate accidental attributes in the syllogism. The right order of attributes will result from the correct selection of the first attribute. This will be the case if an attribute be found which is the consequence of all the others, although the others are not all consequences of it, for some attributes of the former kind must exist. When such an attribute has been discovered the same method must be pursued with the less general attributes, for the following term will be primary among the remainder and the third term primary in relation to those next below, since, when the highest term has been set aside, the next term will be primary among those remaining. The same method applies to the subsequent attributes. The enumeration of attributes is complete so long as the primary genus has been taken in the division (so that e.g. every animal must fall under one or other of the divisions of the genus Animal), and also the primary difference belonging to that entire genus; so long also as no further difference appears in the last term of the division, or when the last term combined with the last difference does not differ specifically from the entire genus. It is clear that in such definitions nothing is superfluous, for all the attributes here mentioned form part of the essence of the thing defined, nor is anything wanting, for any such thing would have to be either genus or difference. But here the highest genus has taken the first place in the division together with the difference. Further the subordinate differences all follow in order, and no later term in the series can remain. Otherwise the last term would be specifically divisible, which has been said not to be the case. In searching for a definition we ought to enquire first what common element is possessed by similar individual instances of the subject, and then examine another class of instances homogeneous to the first class and specifically the same among themselves but specifically different from the former instances. When some element has been found which exists equally in all the individuals of the first class, and an element which exists in all those of the second, we ought next to consider whether anything exists alike in both cases. This process must continue until we attain a single conception, which will form the definition of the subject. If no such single conception be arrived at, but only two or more, we may feel sure that the object of our search is not single but manifold. For instance, if we are enquiring into the nature of Magnanimity we should examine the cases of certain magnanimous persons whom we know of, in order to discover what common quality they all possess in virtue of their magnanimity. Thus supposing Alcibiades, Achilles and Ajax to be all of them magnanimous, what common quality did they all possess? We find that it consisted in impatience of insult. The first made war on his country, the second brooded over his wrath, the third slew himself. We next consider other cases such as those of Lysander and Socrates. If we find that their magnanimity induced them to remain unchanged amidst prosperity and adversity we must take these two aspects of magnanimity and consider what common element exists between disregard of external fortune and impatience of dishonour. If no such element be found, these must constitute two distinct species of magnanimity.
Every definition must have a universal application. The physician does not tell what is beneficial for some particular eye, but either for every eye, or else he divides eyes into different classes. In definition it is easier to assert something of the particular than of the universal; one ought therefore to pass from particulars to universals. Also equivocal expressions are more easily concealed in universals than in individuals. As in demonstrations we must look to the correctness of our syllogistic argument, so in definitions perspicuity is to be studied. This will be attained if it be possible, by means of particular instances quoted, to define that which belongs to each separate genus. For instance, when defining similarity, we should not define all kinds of similarity at once, but should take the common attribute of sharpness belonging to colours, forms and tones, and then proceed to a universal expression, taking care however to admit no ambiguity of phrase. If we ought not to use metaphors in argument, it is clear that we should not define either in metaphors or metaphorical expressions. Otherwise we shall be obliged to use metaphors in argument also.
- Viz. Speusippus (Diog. Laert., IV, § 5).