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 a _faineant_ viceroy, 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 of_ NAMING. 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 (a _Terminology_) and for every group or class (a _Nomenclature_). 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?

Should he 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 word _Pollarchy_ to express the opposite of _Oligarchy_ to use the old words _Republic_ and _Oligarchy_. 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 upon real 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 be decided 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 as _Clerk_ of 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's _Political 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's _Logic of Definition_, chap. ii.]

[Footnote 4: See Davidson's _Logic of Definition_, chap. iii.]

CHAPTER II.

THE FIVE PREDICABLES.--VERBAL AND REAL PREDICATION.

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 (the _genus_), the subordinate divisions (the _species_), the attribute or combination of attributes on which each species is constituted (the _differentia_), and other attributes, which belong to some or all of the individuals but are not reckoned for purposes of division and definition (_Propria_ and _Accidentia_). 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 ___________ ____________ Defining Non-defining _____ ______ ____ __________ Generic Specific Proprium Accidens (Differentia)

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 his [Greek: eisagoge] or Introduction explains the five words ([Greek: phonai]) 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, whereas _Genera_, _Species_, _Differentiae_, 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 or _Divisoria_ Predicables 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 a Proprium, 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:--[Greek: genos] (_Genus_, including _Differentia_, [Greek: diaphora]); [Greek: horos] (Definition); [Greek: to idion]

(_Proprium_); and [Greek: to symbebekos] (_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 mind than 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 between VERBAL or ANALYTIC and REAL or SYNTHETIC Predication 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; _explicative_ for 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 called _Real_, _Synthetic_, or _Ampliative_, 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 implicitly contained 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 speech are 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, [Greek: ousia], or _Substantia_, 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 into _Attributes_. Our complex notions of Substances can only be resolved into various Attributes, with the addition of an unknown _substratum_: 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 the _Real_ Essence, as distinguished from the _Nominal_ Essence, or complex of attributes. It is 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.]

CHAPTER III.

ARISTOTLE'S CATEGORIES.

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 words _category_ ([Greek: kategoria]) and _predicament_, 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 as they 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 (the _themata simplicia_ of the Schoolmen). He explains that by "out of syntax" ([Greek: aneu symplokes]) 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. But according 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:--

Substance Man } COMMON { Substance ([Greek: ousia]) ([Greek: anthropos]) } NOUN { (_Substantia_) -------------------------------------------------------------- Quantity Five-feet-five } { ([Greek: poson]) ([Greek: tripechu]) } { (_Quantitas_) } { Quality Scholarly } { Permanent ([Greek: poion]) ([Greek: grammatikon])} ADJECTIVE { Attribute (_Qualitas_) } { Relation Bigger } { ([Greek: pros ti]) ([Greek: meizon]) } { (_Relatio_) } { -------------------------------------------------------------- Place In-the-Lyceum } { ([Greek: pou]) ([Greek: en Lykeio]) } { (_Ubi_) } ADVERB { Temporary Time Yesterday } { Attribute ([Greek: pote]) ([Greek: chthes]) } { (_Quando_) } { -------------------------------------------------------------- Disposition Reclines } { ([Greek: keisthai]) ([Greek: anakeitai]) } { (_Positio_) } { Appurtenance Has-shoes-on } { ([Greek: echein]) ([Greek: hypodedetai])} { (_Habitus_) } VERB { Action Cuts } { Temporary ([Greek: poiein]) ([Greek: temnei]) } { Attribute (_Actio_) } { Passion Is cut } { ([Greek: paschein]) ([Greek: temnetai]) } { (_Passio_) } {

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 he gives 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 the _summa genera_, the _genera generalissima_ of predicates concerning this, that or the other concrete individual. No individual thing is _sui 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 ([Greek: deuterai ousiai]) 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 ([Greek: protai ousiai]), essences _par 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 ([Greek: to poion]). 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. That is 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" [Greek: peri ousian], inasmuch as they signify what sort a certain essence is, and that genera make this definition more widely than species, bore fruit in the mediaeval discussions between Realists and Nominalists by which the signification of general names was cleared up.