The leading principles ofDivisionmay be stated as follows:—
I. Every division is made on the ground of differences in some attribute common to all the members of the whole to be divided.
This is merely a way of stating what a logical division is. It is a division of a generic whole orgenus, an indefinite number of objects thought of together as possessing some common character or attribute. All have this attribute, which is technically called thefundamentum divisionis, or generic attribute. But the whole is divisible into smaller groups (species), each of which possesses the common character with a difference (differentia). Thus, mankind may be divided into White men, Black men, Yellow men, on ground of the differences in the colour of their skins: all have skins of some colour: this is thefundamentum divisionis: but each subdivision or species has a different colour: this is thedifferentia. Rectilineal figures are divided into triangles, quadrangles, pentagons, etc., on the ground of differences in the number of angles.
Unless there is afund. div.,i.e., unless the differences are differences in a common character, the division is not a logical division. To divide men into Europeans, opticians, tailors, blondes, brunettes, and dyspeptics is not to make a logical division. This is seen more clearly in connexion with the second condition of a perfect division.
II. In a perfect division, the subdivisions or species are mutually exclusive.
Every object possessing the common charactershould be in one or other of the groups, and none should be in more than one.
Confusion between classes, or overlapping, may arise from two causes. It may be due (1) to faulty division, to want of unity in thefundamentum divisionis; (2) to the indistinct character of the objects to be defined.
(1) Unless the division is based upon a single ground, unless each species is based upon some mode of the generic character, confusion is almost certain to arise. Suppose the field to be divided, the objects to be classified, are three-sided rectilineal plane figures, each group must be based upon some modification of the three sides. Divide them into equilateral, isosceles, and scalene according as the three sides are all of equal length, or two of equal length, or each of different length, and you have a perfect division. Similarly you can divide them perfectly according to the character of the angles into acute-angled, right-angled and obtuse-angled. But if you do not keep to a single basis, as in dividing them into equilateral, isosceles, scalene, and right-angled, you have a cross-division. The same triangle might be both right-angled and isosceles.
(2) Overlapping, however, may be unavoidable in practice owing to the nature of the objects. There may be objects in which the dividing characters are not distinctly marked, objects that possess the differentiæ of more than one group in a greater or less degree. Things are not always marked off from one another by hard and fast lines. They shade into one another by imperceptible gradations. A clear separation of them may be impossible. In that case you must allow a certain indeterminate margin betweenyour classes, and sometimes it may be necessary to put an object into more than one class.
To insist that there is no essential difference unless a clear demarcation can be made is a fallacy. A sophistical trick called theSoritesor Heap from the classical example of it was based upon this difficulty of drawing sharp lines of definition. Assuming that it is possible to say how many stones constitute a heap, you begin by asking whether three stones form a heap. If your respondent says No, you ask whether four stones form a heap, then five, and so on and he is puzzled to say when the addition of a single stone makes that a heap which was not a heap before. Or you may begin by asking whether twenty stones form a heap, then nineteen, then eighteen, and so on, the difficulty being to say when what was a heap ceases to be so.
Where the objects classified are mixed states or affections, the products of interacting factors, or differently interlaced or interfused growths from common roots, as in the case of virtues, or emotions, or literary qualities, sharp demarcations are impossible. To distinguish between wit and humour, or humour and pathos, or pathos and sublimity is difficult because the same composition may partake of more than one character. The specific characters cannot be made rigidly exclusive one of another.
Even in the natural sciences, where the individuals are concrete objects of perception, it may be difficult to decide in which of two opposed groups an object should be included. Sydney Smith has commemorated the perplexities of Naturalists over the newly discovered animals and plants of Botany Bay, in especial with theOrnithorynchus,—"a quadruped as big as alarge cat, with the eyes, colour, and skin of a mole, and the bill and web-feet of a duck—puzzling Dr. Shaw, and rendering the latter half of his life miserable, from his utter inability to determine whether it was a bird or a beast".
III. The classes in any scheme of division should be of co-ordinate rank.
The classes may be mutually exclusive, and yet the division imperfect, owing to their not being of equal rank. Thus in the ordinary division of the Parts of Speech, parts, that is, of a sentence, Prepositions and Conjunctions are not co-ordinate in respect of function, which is the basis of the division, with Nouns, Adjectives, Verbs, and Adverbs. The preposition is a part of a phrase which serves the same function as an adjective,e.g.,royalarmy, armyof the king; it is thus functionally part of a part, or a particle. So with the conjunction: it also is a part of a part,i.e., part of a clause serving the function of adjective or adverb.
IV. The basis of division (fundamentum divisionis) should be an attribute admitting of important differences.
The importance of the attribute chosen as basis may vary with the purpose of the division. An attribute that is of no importance in one division, may be important enough to be the basis of another division. Thus in a division of houses according to their architectural attributes, the number of windows or the rent is of little importance; but if houses are taxed or rated according to the number of windows or the rent, these attributes become important enough to be a basis of division for purposes of taxation or rating. They then admit of important differences.
That the importance is relative to the purpose of the division should be borne in mind because there is a tendency to regard attributes that are of importance in any familiar or pre-eminent division as if they had an absolute importance. In short, disregard of this relativity is a fallacy to be guarded against.
In the sciences, the purpose being the attainment and preservation of knowledge, the objects of study are divided so as to serve that purpose. Groups must be formed so as to bring together the objects that have most in common. The question, Who are to be placed together? in any arrangement for purposes of study, receives the same answer for individuals and for classes that have to be grouped into higher classes, namely, Those that have most in common. This is what Dr. Bain happily calls "the golden rule" of scientific classification: "Of the various groupings of resembling things, preference is given to such as have the greatest number of attributes in common". I slightly modify Dr. Bain's statement: he says "the most numerous and the most important attributes in common". But for scientific purposes number of attributes constitutes importance, as is well recognised by Dr. Fowler when he says that the test of importance in an attribute proposed as a basis of classification is the number of other attributes of which it is an index or invariable accompaniment. Thus in Zoology the squirrel, the rat, and the beaver are classed together as Rodents, the difference between their teeth and the teeth of other Mammalia being the basis of division, because the difference in teeth is accompanied by differences in many other properties. So the hedge-hog, the shrew-mouse, and the mole, though very unlike in outward appearance and habits, are classed together as Insectivora,the difference in what they feed on being accompanied by a number of other differences.
The Principles ofDefinition. The word "definition" as used in Logic shows the usual tendency of words to wander from a strict meaning and become ambiguous. Throughout most of its uses it retains this much of a common signification, the fixing or determining of the boundaries of a class3by making clear its constituent attributes. Now in this making clear two processes may be distinguished, a material process and a verbal process. We have (1) the clearing up of the common attributes by a careful examination of the objects included in the class: and we have (2) the statement of these common attributes in language. The rules of definition given by Dr. Bain, who devotes a separate Book in his Logic to the subject of Definition, concern the first of these processes: the rules more commonly given concern mainly the second.
One eminent merit in Dr. Bain's treatment is that it recognises the close connexion between Definition and Classification. His cardinal rules are reduced to two.
I.Assemble for comparison representative individuals of the class.
II.Assemble for comparison representative individuals of the contrasted class or classes.
Seeing that the contrasted classes are contrasted on some basis of division, this is in effect to recognise that you cannot clearly define any class except in a scheme of classification. You must have a widegenuswith itsfundamentum divisionis, and, within this,speciesdistinguished by their severaldifferentiæ.
Next, as to the verbal process, rules are commonly laid down mostly of a trifling and obvious character. That "a definition should state neither more nor less than the common attributes of the class," or than the attributes signified by the class-name, is sometimes given as a rule of definition. This is really an explanation of what a definition is, a definition of a definition. And as far as mere statement goes it is not strictly accurate, for when the attributes of a genus are known it is not necessary to give all the attributes of the species, which include the generic attributes as well, but it is sufficient to give the generic name and the differentia. Thus Poetry may be defined as "a Fine Art having metrical language as its instrument". This is technically known as definitionper genus et differentiam. This mode of statement is a recognition of the connexion between Definition and Division.
The rule that "a definition should not be a synonymous repetition of the name of the class to be defined," is too obvious to require formal statement. To describe a Viceroy as a man who exercises viceregal functions, may have point as an epigram in the case of afaineantviceroy, but it is not a definition.
So with the rule that "a definition should not be couched in ambiguous unfamiliar, or figurative language". To call the camel "the ship of the desert" is a suggestive and luminous description of a property, but it is not a definition. So with the noble description of Faith as "the substance of things hoped for, the evidence of things not seen". But if one wonders why so obvious a "rule" should be laid down, the answer is that it has its historical origin in the caprices of two classes of offenders, mystical philosophers and pompous lexicographers.4
That "the definition should be simply convertible with the term for the class defined," so that we may say, for example, either: "Wine is the juice of the grape," or, "The juice of the grape is wine," is an obvious corollary from the nature of definition, but should hardly be dignified with the name of a "rule".
The Principles ofNaming. Rules have been formulated for the choice of names in scientific definition and classification, but it may be doubted whether such choice can be reduced to precise rule. It is enough to draw attention to certain considerations obvious enough on reflection.
We may take for granted that there should be distinct names for every defining attribute (aTerminology) and for every group or class (aNomenclature). What about the selection of the names? Suppose an investigator is struck with likenesses and differences that seem to him important enough to be the basis of a new division, how should he be guided in his choice of names for the new groups that he proposes? Shouldhe coin new names, or should he take old names and try to fit them with new definitions?
The balance of advantages is probably in favour of Dr. Whewell's dictum that "in framing scientific terms, the appropriation of old words is preferable to the invention of new ones". Only care must be taken to keep as close as possible to the current meaning of the old word, and not to run counter to strong associations. This is an obvious precept with a view to avoiding confusion. Suppose, for example, that in dividing Governments you take the distribution of political power as your basis of division and come to the conclusion that the most important differences are whether this power is vested in a few or in the majority of the community. You want names to fix this broad division. You decide instead of coining the new wordPollarchyto express the opposite ofOligarchyto use the old wordsRepublicandOligarchy. You would find, as Sir George Cornewall Lewis found, that however carefully you defined the word Republic, a division under which the British Government had to be ranked among Republics would not be generally understood and accepted. Using the word in the sense explained above, Mr. Bagehot maintained that the constitution of Great Britain was more Republican than that of the United States, but his meaning was not taken except by a few.
The difficulty in choosing between new words and old words to express new meanings is hardly felt in the exact sciences. It is at least at a minimum. The innovator may encounter violent prejudice, but, arguing with experts, he can at least make sure of being understood, if his new division is based uponreal and important differences. But in other subjects the difficulty of transmitting truth or of expressing it in language suited for precise transmission, is almost greater than the difficulty of arriving at truth. Between new names and old names redefined, the possessor of fresh knowledge, assuming it to be perfectly verified, is in a quandary. The objects with which he deals are already named in accordance with loose divisions resting on strong prejudices. The names in current use are absolutely incapable of conveying his meaning. He must redefine them if he is to use them. But in that case he runs the risk of being misunderstood from people being too impatient to master his redefinition. His right to redefine may even be challenged without any reference to the facts to be expressed: he may simply be accused of circulating false linguistic coin, of debasing the verbal currency. The other alternative open to him is to coin new words. In that case he runs the risk of not being read at all. His contribution to verified knowledge is passed by as pedantic and unintelligible. There is no simple rule of safety: between Scylla and Charybdis the mariner must steer as best he may. Practically the advantage lies with old words redefined, because thereby discussion is provoked and discussion clears the air.
Whether it is best to attempt a formal definition or to use words in a private, peculiar, or esoteric sense, and leave this to be gathered by the reader from the general tenor of your utterances, is a question of policy outside the limits of Logic. It is for the logician to expound the method of Definition and the conditions of its application: how far there are subjects that do not admit of its application profitably must bedecided on other grounds. But it is probably true that no man who declines to be bound by a formal definition of his terms is capable of carrying them in a clear unambiguous sense through a heated controversy.
Footnote 1:Except, perhaps, in new offices to which the name is extended, such asClerkof School Board. The name, bearing its most simple and common meaning, may cause popular misapprehension of the nature of the duties. Any uncertainty in meaning may be dangerous in practice: elections have been affected by the ambiguity of this word.
Footnote 2:Sidgwick'sPolitical Economy, pp. 52-3. Ed. 1883.
Footnote 3:Some logicians, however, speak of defining a thing, and illustrate this as if by a thing they meant a concrete individual, the realistic treatment of Universals lending itself to such expressions. But though the authority of Aristotle might be claimed for this, it is better to confine the name in strictness to the main process of defining a class. Since, however, the method is the same whether it is an individual or a class that we want to make distinct, there is no harm in the extension of the word definition to both varieties. See Davidson'sLogic of Definition, chap. ii.
Footnote 4:See Davidson'sLogic of Definition, chap. iii.
We give a separate chapter to this topic out of respect for the space that it occupies in the history of Logic. But except as an exercise in subtle distinction for its own sake, all that falls to be said about the Predicables might be given as a simple appendix to the chapter on Definition.
Primarily, the Five Predicables or Heads of Predicables—Genus, Species, Differentia, Proprium, and Accidens—are not predicables at all, but merely a list or enumeration of terms used in dividing and defining on the basis of attributes. They have no meaning except in connexion with a fixed scheme of division. Given such a scheme, and we can distinguish in it the whole to be divided (thegenus), the subordinate divisions (thespecies), the attribute or combination of attributes on which each species is constituted (thedifferentia), and other attributes, which belong to some or all of the individuals but are not reckoned for purposes of division and definition (PropriaandAccidentia). The list is not itself a logical division: it is heterogeneous, not homogeneous; the two first are names of classes, the three last of attributes. But corresponding to it we might make a homogeneous division of attributes, as follows:—
Attributes chart
The origin of the title Predicables as applied to these five terms is curious, and may be worth noting as an instance of the difficulty of keeping names precise, and of the confusion arising from forgetting the purpose of a name. Porphyry in hisεἰσαγωγὴor Introduction explains the five words (φωναὶ) simply as terms that it is useful for various purposes to know, expressly mentioning definition and division. But he casually remarks that Singular names, "This man," "Socrates," can be predicated only of one individual, whereasGenera,Species,Differentiæ, etc., are predicables of many. That is to say he describes them as Predicables simply by contradistinction from Singular names. A name, however, was wanted for the five terms taken all together, and since they are not a logical division, but merely a list of terms used in dividing and defining, there was no apt general designation for them such as would occur spontaneously. Thus it became the custom to refer to them as the Predicables, a means of reference to them collectively being desiderated, while the meaning of this descriptive title was forgotten.
To call the five divisional elements orDivisoriaPredicables is to present them as a division of Predicate Terms on the basis of their relation to the Subject Term: to suggest that every Predicate Term must be either a Genus or a Species, or a Differentia, or aProprium, or an Accidens of the Subject Term. They are sometimes criticised as such, and it is rightly pointed out that the Predicate is never a species of or with reference to the Subject. But, in truth, the five so-called Predicables were never meant as a division of predicates in relation to the subject: it is only the title that makes this misleading suggestion.
To complete the confusion it so happens that Aristotle used three of the Five terms in what was virtually a division of Predicates inasmuch as it was a division of Problems or Questions. In expounding the methods of Dialectic in the Topica he divided Problems into four classes according to the relation of the Predicate to the Subject. The Predicate must either be simply convertible with the subject or not. If simply convertible, the two must be coextensive, and the Predicate must be either a Proprium or the Definition. If not simply convertible, the Predicate must either be part of the Definition or not. If part of the Definition it must be either a Generic Property or a Differentia (both of which in this connexion Aristotle includes under Genus): if not part of the Definition, it is an Accident. Aristotle thus arrives at a fourfold division of Problems or Predicates:—γένος(Genus, includingDifferentia,διαφορὰ);ὄρος(Definition);τὸἴδιον(Proprium); andτὸσυμβεβηκὸς(Accidens). The object of it was to provide a basis for his systematic exposition; each of the four kinds admitted of differences in dialectic method. For us it is a matter of simple curiosity and ingenuity. It serves as a monument of how much Greek dialectic turned on Definition, and it corresponds exactly to the division of attributes into Defining and Non-defining given above. It is sometimes said that Aristotle showed a more scientific mindthan Porphyry in making the Predicables four instead of five. This is true if Porphyry's list had been meant as a division of attributes: but it was not so meant.
The distinction betweenVerbalorAnalyticandRealorSyntheticPredication corresponds to the distinction between Defining and Non-defining attributes, and also has no significance except with reference to some scheme of Division, scientific and precise or loose and popular.
When a proposition predicates of a subject something contained in the full notion, concept, or definition of the subject term, it is called Verbal, Analytic, or Explicative:verbal, inasmuch as it merely explains the meaning of a name;explicativefor the same reason;analytic, inasmuch as it unties the bundle of attributes held together in the concept and pays out one, or all one by one.
When the attributes of the Predicate are not contained in the concept of the Subject, the proposition is calledReal,Synthetic, orAmpliative, for parallel reasons.
Thus: "A triangle is a three-sided rectilinear figure" is Verbal or Analytic; "Triangles have three angles together equal to two right angles," or "Triangles are studied in schools," is Real or Synthetic.
According to this distinction, predications of the whole Definition or of a Generic attribute or of a Specific attribute are Verbal; predications of Accident are Real. A nice point is whether Propria are Verbal or Real. They can hardly be classed with Verbal, inasmuch as one may know the full meaning of the name without knowing them: but it might be argued that they are Analytic, inasmuch as they are implicitlycontained in the defining attributes as being deducible from them.
Observe, however, that the whole distinction is really valid only in relation to some fixed or accepted scheme of classification or division. Otherwise, what is Verbal or Analytic to one man may be Real or Synthetic to another. It might even be argued that every proposition is Analytic to the man who utters it and Synthetic to the man who receives it. We must make some analysis of a whole of thought before paying it out in words: and in the process of apprehending the meaning of what we hear or read we must add the other members of the sentence on to the subject. Whether or not this is super-subtle, it clearly holds good that what is Verbal (in the sense defined) to the learned man of science may be Real to the learner. That the horse has six incisors in each jaw or that the domestic dog has a curly tail, is a Verbal Proposition to the Natural Historian, a mere exposition of defining marks; but the plain man has a notion of horse or dog into which this defining attribute does not enter, and to him accordingly the proposition is Real.
But what of propositions that the plain man would at once recognise as Verbal? Charles Lamb, for example, remarks that the statement that "a good name shows the estimation in which a man is held in the world" is a verbal proposition. Where is the fixed scheme of division there? The answer is that by a fixed scheme of division we do not necessarily mean a scheme that is rigidly, definitely and precisely fixed. To make such schemes is the business of Science. But the ordinary vocabulary of common intercourse as a matter of fact proceeds upon schemes of division, though the names used in common speechare not always scientifically accurate, not always the best that could be devised for the easy acquisition and sure transmission of thorough knowledge. The plain man's vocabulary, though often twisted aside by such causes as we have specified, is roughly moulded on the most marked distinguishing attributes of things. This was practically recognised by Aristotle when he made one of his modes of definition consist in something like what we have called verifying the meaning of a name, ascertaining the attributes that it signifies in common speech or in the speech of sensible men. This is to ascertain the essence,οὐσία, orSubstantia, of things, the most salient attributes that strike the common eye either at once or after the closer inspection that comes of long companionship, and form the basis of the ordinary vocabulary. "Properly speaking," Mansel says,1"All Definition is an inquiry intoAttributes. Our complex notions of Substances can only be resolved into various Attributes, with the addition of an unknownsubstratum: a something to which we are compelled to regard these attributes as belonging.Man, for example, is analysed into Animality, Rationality, and the something which exhibits these phenomena. Pursue the analysis and the result is the same. We have a something corporeal, animated, sensible, rational. An unknown constant must always be added to complete the integration." This "unknown constant" was what Locke called theRealEssence, as distinguished from theNominalEssence, or complex of attributes. Itis upon this nominal essence, upon divisions of things according to attributes, that common speech rests, and if it involves many cross-divisions, this is because the divisions have been made for limited and conflicting purposes.
Footnote 1:Aldrich's Compendium, Appendix, Note C. The reader may be referred to Mansel's Notes A and C for valuable historical notices of the Predicables and Definition.
In deference to tradition a place must be found in every logical treatise for Aristotle's Categories. No writing of the same length has exercised a tithe of its influence on human thought. It governed scholastic thought and expression for many centuries, being from its shortness and consequent easiness of transcription one of the few books in every educated man's library. It still regulates the subdivisions of Parts of Speech in our grammars. Its universality of acceptance is shown in the fact that the wordscategory(κατηγορία) andpredicament, its Latin translation, have passed into common speech.
The Categories have been much criticised and often condemned as a division, but, strange to say, few have inquired what they originally professed to be a division of, or what was the original author's basis of division. Whether the basis is itself important, is another question: but to call the division imperfect, without reference to the author's intention, is merely confusing, and serves only to illustrate the fact that the same objects may be differently divided on different principles of division. Ramus was right in saying that the Categories had no logical significance, inasmuch asthey could not be made a basis for departments of logical method; and Kant and Mill in saying that they had no philosophical significance, inasmuch as they are founded upon no theory of Knowing and Being: but this is to condemn them for not being what they were never intended to be.
The sentence in which Aristotle states the objects to be divided, and his division of them is so brief and bold that bearing in mind the subsequent history of the Categories, one first comes upon it with a certain surprise. He says simply:—
"Of things expressed without syntax (i.e., single words), each signifies either substance, or quantity, or quality, or relation, or place, or time, or disposition (i.e., attitude or internal arrangement), or appurtenance, or action (doing), or suffering (being done to)."1
The objects, then, that Aristotle proposed to classify were single words (thethemata simpliciaof the Schoolmen).He explains that by "out of syntax" (ἄνευ συμπλοκῆς)*he means without reference to truth or falsehood: there can be no declaration of truth or falsehood without a sentence, a combination, or syntax: "man runs" is either true or false, "man" by itself, "runs" by itself, is neither. His division, therefore, was a division of single words according to their differences of signification, and without reference to the truth or falsehood of their predication.2
Signification was thus the basis of division. Butaccording to what differences? The Categories themselves are so abstract that this question might be discussed on their bare titles interminably. But often when abstract terms are doubtful, an author's intention may be gathered from his examples. And when Aristotle's examples are ranged in a table, certain principles of subdivision leap to the eyes. Thus:—
In looking at the examples, our first impression is that Aristotle has fallen into a confusion. He professes to classify words out of syntax, yet hegives words with the marks of syntax on them. Thus his division is accidentally grammatical, a division of parts of speech, parts of a sentence, into Nouns, Adjectives, Adverbs, and Verbs. And his subdivisions of these parts are still followed in our grammars. But really it is not the grammatical function that he attends to, but the signification: and looking further at the examples, we see what differences of signification he had in his mind. It is differences relative to a concrete individual, differences in the words applied to him according as they signify the substance of him or his attributes, permanent or temporary.
Take any concrete thing, Socrates, this book, this table. It must be some kind of a thing, a man, a book. It must have some size or quantity, six feet high, three inches broad. It must have some quality, white, learned, hard. It must have relations with other things, half this, double that, the son of a father. It must be somewhere, at some time, in some attitude, with some "havings," appendages, appurtenances, or belongings, doing something, or having something done to it. Can you conceive any name (simple or composite) applicable to any object of perception, whose signification does not fall into one or other of these classes? If you cannot, the categories are justified as an exhaustive division of significations. They are a complete list of the most general resemblances among individual things, in other words, of thesumma genera, thegenera generalissimaof predicates concerning this, that or the other concrete individual. No individual thing issui generis: everything is like other things: the categories are the most general likenesses.
The categories are exhaustive, but do they fulfil another requisite of a good division—are they mutually exclusive? Aristotle himself raised this question, and some of his answers to difficulties are instructive. Particularly his discussion of the distinction between Second Substances or Essences and Qualities. Here he approximates to the modern doctrine of the distinction between Substance and Attribute as set forth in our quotation from Mansel at p. 110. Aristotle's Second Essences (δεύτεραι οὐσίαι) are common nouns or general names, Species and Genera,man,horse,animal, as distinguished from Singular names,this man,this horse, which he calls First Substances (πρῶται οὐσίαι), essencespar excellence, to which real existence in the highest sense is attributed. Common nouns are put in the First Category because they are predicated in answer to the question, What is this? But he raises the difficulty whether they may not rather be regarded as being in the Third Category, that of Quality (τὸποιὸν). When we say, "This is a man," do we not declare what sort of a thing he is? do we not declare his Quality? If Aristotle had gone farther along this line, he would have arrived at the modern point of view that a man is a man in virtue of his possessing certain attributes, that general names are applied in virtue of their connotation. This would have been to make the line of distinction between the First Category and the Third pass between First Essence and Second, ranking the Second Essences with Qualities. But Aristotle did not get out of the difficulty in this way. He solved it by falling back on the differences in common speech. "Man" does not signify the quality simply, as "whiteness" does. "Whiteness" signifies nothing but the quality. Thatis to say, there is no separate name in common speech for the common attributes of man. His further obscure remark that general names "define quality round essence"περὶ οὐσίαν, inasmuch as they signify what sort a certain essence is, and that genera make this definition more widely than species, bore fruit in the mediæval discussions between Realists and Nominalists by which the signification of general names was cleared up.
Another difficulty about the mutual exclusiveness of the Categories was started by Aristotle in connexion with the Fourth Category, Relation (πρός τιAd aliquid,To something). Mill remarks that "that could not be a very comprehensive view of the nature of Relation which would exclude action, passivity, and local situation from that Category," and many commentators, from Simplicius down to Hamilton, have remarked that all the last six Categories might be included under Relation. This is so far correct that the word Relation is one of the vaguest and most extensive of words; but the criticism ignores the strictness with which Aristotle confined himself in his Categories to the forms of common speech. It is clear from his examples that in his Fourth Category he was thinking only of "relation" as definitely expressed in common speech. In his meaning, any word is a relative which is joined with another in a sentence by means of a preposition or a case-inflection. Thus "disposition" is a relative: it is the dispositionofsomething. This kind of relation is perfect when the related terms reciprocate grammatically; thus "master," "servant," since we can say either "the master of the servant," or "the servant of the master". In mediæval logic the termRelatawas confined to these perfect cases, but theCategory had a wider scope with Aristotle. And he expressly raised the question whether a word might not have as much right to be put in another Category as in this. Indeed, he went further than his critics in his suggestions of what Relation might be made to include. Thus: "big" signifies Quality; yet a thing is big with reference to something else, and is so far a Relative. Knowledge must be knowledge of something, and is a relative: why then should we put "knowing" (i.e., learned) in the Category of Quality. "Hope" is a relative, as being the hopeofa man and the hope of something. Yet we say, "I have hope," and there hope would be in the category of Having, Appurtenance. For the solution of all such difficulties, Aristotle falls back upon the forms of common speech, and decides the place of words in his categories according to them. This was hardly consistent with his proposal to deal with separate words out of syntax, if by this was meant anything more than dealing with them without reference to truth or falsehood. He did not and could not succeed in dealing with separate words otherwise than as parts of sentences, owing their signification to their position as parts of a transient plexus of thought. In so far as words have their being in common speech, and it is their being in this sense that Aristotle considers in the Categories, it is a transient being. What being they represent besides is, in the words of Porphyry, a very deep affair, and one that needs other and greater investigation.
Footnote 1:τῶν κατὰ μηδεμίαν συμπλοκὴν λεγομένων ἕκαστον ἢτοι οὐσίαν σημαίνει, ἢ ποσὸν, ἢ ποιὸν, ἢ πρός τι, ἢ ποῦ, ἢ ποτὲ, ἢ κεῖσθαι, ἢ ἔχειν, ἢ ποιεῖν, ἢ πάσχειν(Categ. ii. 5.)
Footnote 2:To describe the Categories as a grammatical division, as Mansel does in his instructive Appendix C to Aldrich, is a little misleading without a qualification. They are non-logical inasmuch as they have no bearing on any logical purpose. But they are grammatical only in so far as they are concerned with words. They are not grammatical in the sense of being concerned with the function of words in predication. The unit of grammar in this sense is the sentence, a combination of words in syntax; and it is expressly with words out of syntax that Aristotle deals, with single words not in relation to the other parts of a sentence, but in relation to the things signified. In any strict definition of the provinces of Grammar and Logic, the Categories are neither grammatical nor logical: the grammarians have appropriated them for the subdivision of certain parts of the sentence, but with no more right than the logicians. They really form a treatise by themselves, which is in the main ontological, a discussion of substances and attributes as underlying the forms of common speech. In saying this I use the word substance in the modern sense: but it must be remembered that Aristotle'sοὐσία, translated substantia, covered the word as well as the thing signified, and that his Categories are primarily classes of words. The union between names and things would seem to have been closer in the Greek mind than we can now realise. To get at it we must note that every separate wordτὸ λεγόμενονis conceived as having a being or thingτὸ ὄνcorresponding to it, so that beings or thingsτὰ ὄνταare coextensive with single words: a being or thing is whatever receives a separate name. This is clear and simple enough, but perplexity begins when we try to distinguish between this nameable being and concrete being, which last is Aristotle's category ofοὐσία, the being signified by a Proper or a Common as distinguished from an Abstract Noun. As we shall see, it is relatively to the highest sense of this last kind of being, namely, the being signified by a Proper name, that he considers the other kinds of being.