After stating some other additional difficulties which seem to leave the work of Definition inexplicable, Aristotle relinquishes the dubitative treatment, and looks out for some solution of the puzzle: How may it be possible that the Definition shall become known?17 He has already told us that to know the essence of a thing is the same as to know the cause or reason of its existence; but we must first begin by knowing that the definiendum exists; for there can be no definition of a non-entity, except a mere definition of the word, a nominal or verbal definition. Now sometimes we know the existence of the subject by one or other of its accidental attributes; but this gives us no help towards finding the definition.18 Sometimes, however, we obtain a partial knowledge of its essence along with the knowledge of its existence; when we know it along with some constant antecedent, or through some constant, though derivative, consequent. Knowing thus much, we can often discover the cause or fundamental condition thereof, which is the essence or definition of the subject.19 Indeed, it may happen that the constant derivative, and the fundamental essence on which it depends, become known both together; or, again, the cause or fundamental condition may perhaps not be the essence of the subject alone, but some fact including other subjects also; and this fact may then be stated as a middle term. Thus, in regard to eclipse of the moon, we know the constant phenomenal fact about it, that, on a certain recurrence of the time of full moon, the moon casts no light and makes no shadow. Hence we proceed to search out the cause. Is it interposition of the earth, or conversion of the moon’s body, or extinction of her light, &c.? The new fact when shown, must appear as a middle term, throwing into syllogistic form (in the First figure) the cause or rational explanation of a lunar eclipse; showing not merely that there is an eclipse, but what an eclipse is, or what is its definition.20

Aristotle has thus shown how the Essence or Quiddity (τί ἐστι) may become known in this class of cases. There is neither syllogism nor demonstration thereof, yet it is declared through syllogism and demonstration: though no demonstration thereof is possible, yet you cannot know it without demonstration, wherever there is an extraneous cause.21

But the above doctrine will hold only in cases where there is a distinct or extraneous cause; it will not hold in cases where there is none. It is only in the former (as has been said) that a middle term can be shown; rendering it possible that Quiddity or Essence should be declared by a valid formal syllogism, though it cannot be demonstrated by syllogism. In the latter, where there is no distinct cause, no such middle term can be enunciated: the Quiddity or Essence must be assumed as an immediate or undemonstrable principium, and must be exposed or set out in the best manner practicable as an existent reality, on Induction or on some other authority. The arithmetician makes his first steps by assuming both what a monad is and that there exists such a monad.22

We may distinguish three varieties of Definition. 1. Sometimes it is the mere explanation what a word signifies; in this sense, it has nothing to do with essence or existence; it is a nominal definition and nothing more.23 2. Sometimes it enunciates the Essence, cause, or reason of the definitum; this will happen where the cause is distinct or extraneous, and where there is accordingly an intervening middle term: the definition will then differ from a demonstration only by condensing into one enunciation the two premisses and the conclusion which together constitute the demonstration.24 3. Sometimes it is an immediate proposition, an indemonstrable hypothesis, assuming Essence or Quiddity; the essence itself being cause, and no extraneous cause — no intervening middle term — being obtainable.25

To know or cognize is, to know the Cause; when we know the Cause, we are satisfied with our cognition. Now there are four Causes, or varieties of Cause:—

1. The Essence or Quiddity (Form) — τὸ τί ἦν εἶναι.

2. The necessitating conditions (Matter) — τό τίνων ὄντων ἀνάγκη τοῦτ’ εἶναι.

3. The proximate mover or stimulator of change (Efficient) — ἡ τί πρῶτον ἐκίνησε.

4. That for the sake of which (Final Cause or End) — τὸ τίνος ἕνεκα.

All these four Causes (Formal, Material, Efficient, Final) appear as middle terms in demonstrating. We can proceed through the medium either of Form, or of Matter, or of Efficient, or of End. The first of the four has already been exemplified — the demonstration by Form. The second appears in demonstrating that the angle in a semi-circle is always a right angle; where the middle term (or matter of the syllogism, (τὸ ἐξ οὗ) is, that such angle is always the half of two right angles.26 The Efficient is the middle term, when to the question, Why did the Persians invade Athens? it is answered that the Athenians had previously invaded Persia along with the Eretrians. (All are disposed to attack those who have attacked them first; the Athenians attacked the Persians first; ergo, the Persians were disposed to attack the Athenians.) Lastly, the Final Cause serves as middle term, when to the question, Why does a man walk after dinner? the response is, For the purpose of keeping up his health. In another way, the middle term here is digestion: walking after dinner promotes digestion; digestion is the efficient cause of health.27

The Final Cause or End is prior in the order of nature, but posterior to the terms of the conclusion in the order of time or generation; while the Efficient is prior in the order of time or generation. The Formal and Material are simultaneous with the effect, neither prior nor posterior.28 Sometimes the same fact may proceed both from a Final cause, and from a cause of Material Necessity; thus the light passes through our lantern for the purpose of guiding us in the dark, but also by reason that the particles of light are smaller than the pores in the glass. Nature produces effects of finality, or with a view to some given end; and also effects by necessity, the necessity being either inherent in the substance itself, or imposed by extraneous force. Thus a stone falls to the ground by necessity of the first kind, but ascends by necessity of the second kind. Among products of human intelligence some spring wholly from design without necessity; but others arise by accident or chance and have no final cause.29

That the middle term is the Cause, is equally true in respect to Entia, Fientia, Præterita, and Futura; only that in respect to Entia, the middle term or Cause must be an Ens; in respect to Fientia it must be a Fiens; in respect to Præterita, a Præteritum; and in respect to Futura, a Futurum; that is, in each case, it must be generated at the corresponding time with the major and minor terms in the conclusion.30 What is the cause of an eclipse of the moon? The cause is, that the earth intervenes between moon and sun; and this is true alike of eclipses past, present, and future. Such an intervention is the essence or definition of a lunar eclipse: the cause is therefore Formal, and cause and effect are simultaneous, occurring at the same moment of time. But in the other three Causes — Material, Efficient, Final — where phenomena are successive and not simultaneous, can we say that the antecedent is cause and the consequent effect, time being, as seems to us, a continuum? In cases like this, we can syllogize from the consequent backward to the antecedent; but not from the antecedent forward to the consequent. If the house has been built, we can infer that the foundations have been laid; but, if the foundations have been laid, we cannot infer that the house has been built.31 There must always be an interval of time during which inference from the antecedent will be untrue; perhaps, indeed, it may never become true. Cause and causatum in these three last varieties of Cause, do not universally and necessarily reciprocate with each other, as in the case of the Formal cause. Though time is continuous, events or generations are distinct points marked in a continuous line, and are not continuous with each other.32 The number of these points that may be taken is indeed infinite; yet we must assume some of them as ultimate and immediate principia, in order to construct our syllogism, and provide our middle term.33 Where the middle term reciprocates and is co-extensive with the major and the minor, in such cases we have generation of phenomena in a cycle; e.g., after the earth has been made wet, vapour rises of necessity: hence comes a cloud, hence water; which again falls, and the earth again becomes wet.34 Finally, wherever our conclusion is not universally and necessarily true, but true only in most cases, our immediate principia must also be of the same character, true in most cases, but in most cases only.35

How are we to proceed in hunting out those attributes that are predicated in Quid,36 as belonging to the Essence of the subject? The subject being a lowest species, we must look out for such attributes as belong to all individuals thereof, but which belong also to individuals of other species under the same genus. We shall thus find one, two, three, or more, attributes, each of which, separately taken, belongs to various individuals lying out of the species; but the assemblage of which, collectively taken, does not belong to any individual lying out of the species. The Assemblage thus found is the Essence; and the enunciation thereof is the Definition of the species. Thus, the triad is included in the genus number; in searching for its definition, therefore, we must not go beyond that genus, nor include any attributes (such as ens, &c.) predicable of other subjects as well as numbers. Keeping within the limits of the genus, we find that every triad agrees in being an odd number. But this oddness belongs to other numbers also (pentad, heptad, &c.). We therefore look out for other attributes, and we find that every triad agrees in being a prime number, in two distinct senses; first, that it is not measured by any other number; secondly, that it is not compounded of any other numbers. This last attribute belongs to no other odd number except the triad. We have now an assemblage of attributes, which belong each of them to every triad, universally and necessarily, and which, taken all together, belong exclusively to the triad, and therefore constitute its essence or definition. The triad is a number, odd, and prime in the two senses.37 The definitum and the definition are here exactly co-extensive.

Where the matter that we study is the entire genus, we must begin by distributing it into its lowest species; e.g. number into dyad, triad, &c.; in like manner, taking straight line, circle, right angle, &c.38 We must first search out the definitions of each of these lowest species; and these having been ascertained, we must next look above the genus, to the Category in which it is itself comprised, whether Quantum, Quale, &c. Having done thus much we must study the derivative attributes or propria of the lowest species through the common generalities true respecting the larger. We must recollect that these derivative attributes are derived from the essence and definition of the lowest species, the complex flowing from the simple as its principium: they belong per se only to the lowest species thus defined; they belong to the higher genera only through those species.39 It is in this way, and not in any other, that the logical Division of genera, according to specific differences, can be made serviceable for investigation of essential attributes; that is, it can only be made to demonstrate what is derivative from the essence. We have shown already that it cannot help in demonstrating essence or Definition itself. We learn to marshal in proper order the two constituent elements of our definition, and to attach each specific difference to the genus to which it properly belongs. Thus we must not attempt to distribute the genus animal according to the difference of having the wing divided or undivided: many animals will fall under neither of the two heads; the difference in question belongs to the lower genus winged animal, and distributes the same into two species. The characteristic or specific difference must be enunciated and postulated by itself, and must be attached to its appropriate genus in order to form the definition. It is only by careful attention to the steps of legitimate logical Division that we can make sure of including all the particulars and leaving out none.40

Some contemporaries of Aristotle, and among them Speusippus, maintained that it was impossible either to define, or to divide logically, unless you knew all particulars without exception. You cannot (they said) know any one thing, except by knowing its differences from all other things; which would imply that you knew also all these other things.41 To these reasoners Aristotle replies: It is not necessary to know all the differences of every thing; you know a thing as soon as you know its essence, with the properties per se which are derivative therefrom. There are many differences not belonging to the essence, but distinguishing from each other two things having the same essence: you may know the thing, without knowing these accidental differences.42 When you divide a genus into two species, distinguished by one proximate specific difference, such that there cannot be any thing that does not fall under one or other of these membra condividentia, and when you have traced the subject investigated under one or other of these members, you can always follow this road until no lower specific difference can be found, and you have then the final essence and definition of the subject; even though you may not know how many other subjects each of the two members may include.43 Thus does Aristotle reply to Speusippus, showing that it is not necessary, for the definition of one thing, that you should know all other things. His reply, as in many other cases, is founded on the distinction between the Essential and the Accidental.

To obtain or put together a definition through logical Division, three points are to be attended to.44 Collect the predicates in Quid; range them in the proper order; make sure that there are no more, or that you have collected all. The essential predicates are genera, to be obtained not otherwise than by the method (dialectical) used in concluding accidents. As regards order, you begin with the highest genus, that which is predicable of all the others, while none of these is predicable of it, determining in like fashion the succession of the rest respectively. The collection will be complete, if you divide the highest genus by an exhaustive specific difference, such that every thing must be included in one or other of the two proximate and opposed portions; and then taking the species thus found as your dividendum, subdivide it until no lower specific difference can be found, or you obtain from the elements an exact equivalent to the subject.45

When the investigation must proceed by getting together a group of similar particulars, you compare them, and note what is the same in all; then turn to another group which are the same in genere yet differ in specie from the first group, and have a different point of community among themselves. You next compare the point of community among the members of the first group, and that among the members of the second group. If the two points of community can be brought under one rational formula, that will be the definition of the subject; but if at the end of the process, the distinct points of community are not found resolvable into any final one, this proves that the supposed definiendum is not one but two or more.46 For example, suppose you are investigating, What is the essence or definition of magnanimity? You must study various magnanimous individuals, and note what they have in common quâ magnanimous.47 Thus, Achilles, Ajax, Alkibiades were all magnanimous. Now, that which the three had in common was, that they could not endure to be insulted; on that account Alkibiades went to war with his countrymen, Achilles was angry and stood aloof from the Greeks, Ajax slew himself. But, again, you find two other magnanimous men, Sokrates and Lysander. These two had in common the quality, that they maintained an equal and unshaken temper both in prosperity and adversity. Now when you have got thus far, the question to be examined is, What is the point of identity between the temper that will not endure insult, and the temper that remains undisturbed under all diversities of fortune? If an identity can be found, this will be the essence or definition of magnanimity; to which will belong equanimity as one variety, and intolerance of insult as another. If, on the contrary, no identity can be found, you will then have two distinct mental dispositions, without any common definition.48

Every definition must be an universal proposition, applicable, not exclusively to one particular object, but to a class of greater or less extent. The lowest species is easier to define than the higher genus; this is one reason why we must begin with particulars, and ascend to universals. It is in the higher genera that equivocal terms most frequently escape detection.49 When you are demonstrating, what you have first to attend to is, the completeness of the form of syllogizing: when you are defining, the main requisite is to be perspicuous and intelligible; i.e. to avoid equivocal or metaphorical terms.50 You will best succeed in avoiding them, if you begin with the individuals, or with examples of the lowest species, and then proceed to consider not their resemblances generally, but their resemblances in certain definite ways, as in colour or figure. These more definite resemblances you will note first; upon each you will found a formula of separate definition; after which you will ascend to the more general formula of less definite resemblance common to both. Thus, in regard to the acute or sharp, you will consider the acute in sound, and in other matters (tastes, pains, weapons, angles, &c.), and you will investigate what is the common point of identity characterizing all. Perhaps there may be no such identity; the transfer of the term from one to the other may be only a metaphor: you will thus learn that no common definition is attainable. This is an important lesson; for as we are forbidden to carry on a dialectical debate in metaphorical terms, much more are we forbidden to introduce metaphorical terms in a definition.51