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BOOK II.

CHAP. I.

On the number and arrangements of Questions

The objects of knowledge are four in number:—a thing’s existence, its cause, the question whether it is, and its nature.

The subjects of enquiry are equal in number to the objects of scientific knowledge. We enquire about four things, the fact of the phenomenon, its cause, whether it exists and what its nature is. Now when we ask whether a thing is this or that, taking two alternatives, e.g. asking whether the sun is eclipsed or not, we ask about the fact. A proof of this is that when we find that it is eclipsed we abandon this line of enquiry. Also if we know from the first that it is eclipsed we do not ask whether it is eclipsed or not. Next, after learning the fact of the phenomenon we seek for the cause of it. For example, when we know that the sun is eclipsed or that the earth does move, we go on to seek for the cause of the eclipse or of the movement.

These questions concerning the fact and cause stand towards each other in the relation here stated, but in some questions the enquiry proceeds differently: namely whether a thing exists at all or not; e.g. as to whether or not a centaur or a god is. By ‘whether it is or not’ I mean is absolutely, not whether a thing is, e.g., white or not white. When we know that the thing does exist we enquire about its nature, asking, for instance, ‘What then is a god, or what is a man?’

CHAP. II.

Every question is concerned with the discovery of a Middle Term

The first and third of these questions and also the second and fourth may be identified. Hence all scientific enquiry consists in investigating whether there is a middle term, and what the middle term is, for the middle is identical with the cause.

These or such as these are the subjects about which we enquire and which we know when we have found what we sought. Now when we ask about the fact, or enquire whether the thing has absolute existence, we enquire whether it has a middle term, but when we have learned the fact and solved the question as to its absolute or partial existence, then we ask what the middle term is. My phrase ‘partial existence’ would be illustrated by the questions ‘Does the moon wax?’ or ‘Is the moon eclipsed?’ In questions of this sort we do really ask whether a thing exists or not. ‘Absolute existence’ might be illustrated by the questions ‘Does a moon, or does night, exist or not?’

Hence it follows that in every enquiry we really ask if a middle term for the subject in question is or else what this middle term is. The reason is that the middle term contains the cause, and it is the cause that we look for in all cases. For instance we ask first ‘Is the moon eclipsed?’ Then, ‘Is there any cause of the eclipse or not?’ Next, on learning that some cause of it is known we enquire what the cause is. Now the cause of a thing’s being, (not of its being this or that, but of its being absolutely) or again the cause why a thing has no absolute existence but is an essential or accidental attribute of something else, is nothing but the middle term. When speaking of absolute existence I refer to the existence of the subject, whether it be moon, earth, sun, or triangle; examples of attributes would be eclipse, equality, inequality, interposition or non-interposition of the earth.

In all these cases it is clear that the nature of the thing and its cause are the same. To the question ‘What is an eclipse?’ the answer is ‘An exclusion of light from the moon owing to the interposition of the earth.’ ‘Why does an eclipse take place, or why is the moon eclipsed?’ ‘Because the light fails when the earth excludes it.’ ‘What is harmony?’ ‘An arithmetical proportion between sharp and flat.’ ‘Why does sharp harmonize with flat?’ ‘Because they are in a certain arithmetical proportion.’ Thus the question ‘Can sharp and flat harmonize?’ is equivalent to ‘Is there an arithmetical proportion between them?’ On learning that there is we proceed to ask, ‘What then is the proportion?’ That the object of our enquiry is really the middle term is clearly displayed by those cases in which the middle term is perceptible to the senses. We make an enquiry about it only when we have not perceived it. Thus, in the case of eclipse, we ask whether there is such a thing or not. If, however, we were on the moon we should not enquire whether an eclipse does occur, nor yet why it occurs, for the answers to both these questions would become visible simultaneously. We should in fact have learned the universal as a result of sense perception. Sense perception would shew that the earth was at a particular moment excluding the sun’s light; and since it would also be obvious that the moon was then being eclipsed, knowledge of the universal would have been attained immediately. Thus, as we have said, knowing the nature of a thing is the same as knowing its cause. The former of these may either have or not have an independent existence. E.g. ‘One thing is larger, or smaller, than another.’ ‘The three angles of a triangle are equal to two right angles.’

It has now been made clear that every kind of enquiry involves a search after the middle term.

CHAP. III.

The distinction between Definition and Demonstration

Definitions and demonstration are not identical. Denfiitions are always general and affirmative, while some syllogisms may be particular or negative. Even universal affirmative syllogisms cannot always be replaced by definitions. The principles of demonstration, which are themselves indemonstrable, may be definitions, but the two processes differ. Definition states a thing’s essence, Demonstration presupposes it.

We may now state in what ways the essential nature of a thing may be proved, and also what definition is and what are its objects; and we may first mention the difficulties connected with these subjects. We will begin with a point closely connected with the matters last treated of, namely the question which might be raised as to whether it is possible to know the same thing and know it in the same way by means of Definition and by means of Demonstration. Ought not this to be held impossible? Definition would seem to express a thing’s essential nature, which is invariably universal and affirmative. Some syllogisms however are negative, others not universal; for instance all in the second figure are negative, those in the third are other than universal. Then too definition is not invariably practicable even in the case of the affirmative syllogisms in the first figure; e.g. the proposition ‘Every triangle has its angles equal to two right angles,’ cannot be arranged as a definition. The reason of this is that knowing a thing demonstratively is equivalent to having a demonstration. Hence if such cases are capable of demonstration they clearly cannot admit of definition as well. Otherwise one would acquire knowledge by means of the definition without possessing any demonstration; for it is quite possible to have a definition without drawing any demonstration from it. An inductive proof will lead to the same conclusion. We never know anything either of the essential or accidental attributes of a thing from merely defining it. Moreover definition is a method of making known substances, while propositions like the above concerning the triangle clearly do not contain the substance of the subject. It is clear then that not everything which is capable of demonstration also admits of being defined; but then the further question arises:—When a thing is definable is it invariably capable of demonstration or not?

One argument against the possibility of this latter suggestion has already been mentioned, namely, that a single subject is, as such, treated of by a single science. Hence if demonstrative knowledge of a thing consists in having a demonstration of it we are placed in a dilemma, as one who possesses a definition without demonstration will have real knowledge.

Further, the elementary principles of demonstration are definitions, and it has been shewn before that these principles admit of no demonstration. Either then these principles must be demonstrable and also the principles of the principles, and the like process will go on to infinity; or else the primary principles will be indemonstrable definitions.

But if the objects of definition and demonstration be not entirely the same, may they not be partly the same? Or is that impossible, nothing which can be defined being capable of demonstration? Definition expresses the nature of a thing and its substance, but demonstrations all clearly assume the nature of a thing as a hypothesis, as, e.g. mathematical demonstrations assume the nature of Unit or Odd, and so with other demonstrations. Further, every demonstration proves something of a subject: e.g. that it exists or does not exist; but in a definition no one thing is predicated of another: e.g. animal is not predicated of biped nor biped of animal; nor figure of superficies; for superficies is not what figure is nor is figure what superficies is.

By this I mean, e.g. that we have already proved that an isosceles triangle has its angles equal to two right angles if we have proved that every triangle has that quality, for isosceles triangle is a part, triangle in general a whole. But a thing’s Nature and its Existence are not thus related to one another, since neither is a part of the other. It is clear then that a demonstration is not invariably attainable in cases which admit of definition, and that definition does not invariably accompany demonstration.

Hence, generally speaking, one cannot have both for any one subject. It is therefore clear that definition and demonstration cannot be identical, nor can one be part of another, for then their objects would have borne a like relation to one another.

This may be regarded as the answer to the present difficulties.

CHAP. IV.

The Essence of a thing cannot be attained by Syllogism

A syllogism could only be expressed as a definition if a middle term convertible with the two other terms were employed. This, however, would involve a Petitio Principii.

Can a syllogism or a demonstration treating of a thing’s Nature be arrived at, or, as our recent argument assumed, is that impossible? Syllogism proves one thing of another by means of a middle term, but a thing’s Nature is a property and is predicated as part of its essence. Further, definition must be convertible with the thing defined; for if A be a property of B, and that again of C, each term is a property of the other. Further, if A be an essential attribute of B, and B be essentially universally and distributively predicable of C, A must be essentially predicable of C.

If, however, one do not thus make use of A twice over, it will not of necessity be predicable of C; that is to say when A is an essential attribute of B, but not of everything of which B is predicable. Both A and B then form part of the essence of C. Hence too B is essentially predicable of C; but if both A and B be essential attributes of the subject C, and also of the formal cause of C, the formal cause will be present in the middle term before the syllogism is formed.

In general then if one have to prove, e.g. What man’s essence is; let C be ‘man,’ and A the essence, whether this be ‘biped animal’ or something else. If then a syllogism is to be formed, A must be predicated distributively of B, and further a middle term is required, and this will be predicable of the essence A. Thus one will be assuming what one ought to prove, seeing that B will also denote man’s essence.

One ought to consider this phenomenon both in the two premises and in the primary and ultimate proposition, as it will appear most plainly in them. In fact, those who prove by means of a convertible proposition what is the essence of Soul, of Man, or of any other existing thing, are guilty of begging the question.

Thus, suppose it were asserted that the soul is a thing which is the cause of its own life, and that this cause is a number which moves itself. Here one would have to assume that the soul is like a number which moves itself, and is actually identical with it. A will not in fact be essentially predicable of C because A is a consequence of B, and B of C, though it may be conventionally so denoted; nor yet, if A exists, is it thereby made essentially and distributively predicable of B.

For instance, the essence ‘animal’ is predicated of the essence ‘man,’ and it is true to say that every essential attribute of man is an essential attribute of animal, (just as it is true to say that every man is an animal) but not in the sense that man and animal are identical.

If the terms are not so stated one cannot infer that A constitutes the essential nature and substance of C. If they are so stated there will be a preliminary assumption that B, the thing which ought to be proved, constitutes the essential nature of C. Thus no demonstration of this latter fact will have been given, but we shall have begged the question.

CHAP. V.

Knowledge of the Essence cannot be attained by Division

Nor can demonstration be attained by means of Division, which never proves necessary connection, and can never give the cause. Thus definitions founded on division are invalid as lacking the element of necessity.

Nor does the method of Division produce syllogistic conclusions, as has been pointed out in the analysis of the figures of the syllogism (Pr. An. I. 31). There is never any necessity that the thing to be defined should be exactly what it is stated to be because the other terms of the division are so; and the method of division is even less demonstrative than induction. One ought not to ask that the conclusion should be admitted, nor ought it to be held to be true because another admits it, but it must necessarily be true if those particular premises are true, even though our companion refuses to accept it. Thus, in division the question might be asked. ‘Is Man an animate or inanimate creature?’ Though the other may decide in favour of ‘animate,’ yet no real conclusion has been arrived at. Suppose the question to follow, ‘As every animate creature is terrestrial or aquatic, which is man?’ and the other decides for terrestrial. Yet it is not a necessary consequence of these admissions that man is a terrestrial animate creature, but that also is an assumption.

It makes no difference whether the division has many or few parts; for the same charge may be brought against every instance of it. Even in the case of arguments which might proceed syllogistically, when division is resorted to the method is not syllogistic. There is in fact nothing to shew that these qualities, though they may all be true of man, really express his Nature or essential Form. Also there is nothing to prevent Division from adding to, subtracting from, or entirely passing over the substance of the thing.

It is in this connection that mistakes are generally made; but the difficulty may be solved by taking all the essential attributes of the thing, arranging them in order by means of division, making a postulate of the first attribute and passing over none of the later ones. Here necessity will be secured so long as everything falls within the division, nothing being omitted, and so long as no term is admitted which is capable of a further subdivision. This process, however, involves no regular syllogism, or if division does convey scientific knowledge it conveys it in a different way from syllogism. Nor is there anything strange in this; for Induction does not properly speaking demonstrate, but yet it makes something known. In the present case, however, one who announces a definition after an inspection of a division does not really give us a syllogism. Just as in the case of conclusions without any middle term, if it be asserted that this conclusion must follow from this premise, one is entitled to ask, ‘Why so?’ so also with definitions which depend on division. E.g. ‘What is man?’ ‘A mortal, footed, biped, featherless animal.’ ‘Why?’ will be asked at every additional attribute. The answer will be that it may, as the speaker supposes, be proved by division that everything is either mortal or immortal. No reasoning of this kind can have any of the characteristics of definition. Hence even if division did demonstrate something, definition would not thereby become the same as syllogism.

CHAP. VI.

The Essence cannot be proved by the Definition of the thing itself or by that of its opposite

Division supplies no common attribute by means of which the various attributes may be bound together, so as to produce one predication instead of several.

Is it possible to demonstrate the real essence of a subject when one has assumed hypothetically that the essential nature of that subject is one of the properties which constitute its formal cause, and that only those particular qualities, all being peculiar to the subject, are so included? (That is the meaning of the essence of a subject).

Has one not however really used the same term, the notion of formal cause, twice over? for one must effect the proof by means of the middle term which ought itself to be proved. Further, just as in a syllogism there is no assumption as to the nature of inference, for the premises on which the syllogism is based always bear the relation of whole or of part to each other, so the essential form of syllogism ought not to be included in the syllogism, but to remain outside the particular premises.

One should meet an objector who questions whether an inference is syllogistic or not, by saying, ‘that at least is the process which we meant by syllogism,’ and to one who asserts that we have not the essential form of syllogism, we should answer with a denial, saying that this was what we meant by the essential form of syllogism. Thus some conclusion may be arrived at without any definition of its essence or of its essential form being given.

Neither can a definition be proved by means of a hypothesis, as illustrated by the following example. Assuming that Evil consists in the quality of ‘the manifold,’ and, in the case of subjects which have an opposite, the opposite of evil, is the opposite of manifold; it might be inferred that good, as being the opposite of evil will possess the quality which is the opposite of manifold, and the essence of good will be proved to be the same as the essence of indivisible. Here too, however, the proof is effected by assuming the essential form of the subject and then proving it, and this assumption is made for the express purpose of effecting the proof. It may be objected that the same term is not really used both in the definition of evil and in the proof, and that there is difference. This may be admitted; for in demonstrations also it is assumed that one thing is predicable of another; but it is not, as in this case, the thing itself which has to be proved, nor yet that which has the same definition or is convertible with it.

The following difficulty applies both to a proof proceeding by division and to a syllogism based on definition. Why are the predicates of a definition not taken separately, as, in the sentence above ‘man is a biped animal,’ why should one not say ‘an animal’ and ‘biped’? The assumptions underlying the definition in no way demand that the attributes predicated should form a single expression; they might be stated separately, as one might call man both ‘musical’ and ‘capable of writing,’ not a ‘musical writer.’

CHAP. VII.

Whether the Essence can in any way be proved

Definition does not prove the essence of things, for, if it proved a thing’s essential nature, it would also prove that the thing exists. It does not however merely explain the meaning of words, for then every word we uttered would be a definition. The objects of definition and demonstration are entirely different, and neither gives knowledge of a thing’s essence.

How then is definition to prove the Substance or Nature of a subject? It will neither shew, as if demonstrating from admitted premises, that, when certain premises exist, something else must necessarily follow, nor will it shew, as induction shews from the evidence of particular instances, that everything must have a certain quality because nothing is without that quality; for induction does not prove the nature of a thing but only that the thing does or does not exist. What other method of demonstration then remains? It is surely impossible to demonstrate by an appeal to the senses, or by pointing at a thing with the finger.

Further, how is one to prove the essential nature of a thing? It is necessary, in order to learn the nature of Man or of anything else, to know that the subject in question exists; for no one can know the nature of the non-existent, but only what its name or other designation signifies, as when I say e.g. ‘Goatstag’; for the nature of a goatstag it is impossible to know. Moreover, though one may prove both the nature of a thing and that it exists, how can it be possible to do so by one and the same method? Definition and demonstration each prove one single thing; but ‘what man is,’ and ‘that man exists’ are two different questions.

Further we hold that the existence of anything must needs be proved by demonstration, with the exception of the essence. Existence as such is in no case identical with the essence, for ‘that which exists’ does not form a separate genus. Hence demonstration will only prove that the thing exists, not what it is. This may be seen in the separate sciences. E.g. the geometrician assumes the meaning of the word Triangle, but proves that Triangle exists. What is it then which definition will prove? Will it be the essence of triangle? In that case one would know by definition the essential nature of triangle without knowing whether triangle exists. This is impossible. It is also clear from the present system of definition that definitions do not prove the existence of a thing. Even if according to the definition, lines drawn from the centre to the circumference of the circle are equal, what proves the existence of lines or circle? Why is the thing defined a circle and nothing else? Why might one not call it bronze just as well as circle? If then definition must prove either the nature of the thing or the meaning of the name, if further the former be impossible, a definition would appear to be a phrase with the same meaning as the subject itself. This is untenable, for in the first place there would be definitions of things which are not substances and of things which do not exist at all, for even non-existing things may be denoted by a name. Further every phrase would in that case be a definition, for it is possible by means of a word to impose any name whatever on a thing, so that all of us would be talking in definitions, and the name Iliad would be a definition. Also no science could demonstrate that a particular name denoted a particular thing. Hence definition and syllogism are clearly not identical, and have not identical objects. Further definition does not demonstrate or prove anything, nor can one know the essential nature of a thing either by definition or demonstration.

CHAP. VIII.

How the Essence can be proved

When a thing is once known its essence and its cause are identified. The essence cannot be demonstrated, but before seeking for the cause one must know that the thing exists. Hence, though demonstration cannot give the essence, without it the essence could never be learned.

We must now consider which of our recent statements are well and which ill expressed; what consequently is the nature of definition, and whether it is possible to produce both a demonstration and a definition of a thing’s essential nature, or not. Now since, as we have said (Bk. II., Ch. 2), the knowledge of a thing’s nature is the same as knowledge of the cause of its nature, and the reason of this is that a cause exists for everything, this cause must be either the same as the subject itself or something different. If the latter, it must be either demonstrable or indemonstrable. If then it be other than the subject and also demonstrable, the cause must necessarily form the middle term of the demonstration, and the syllogism must be proved in the first figure, since that which is to be proved is a universal affirmative proposition.

Such is the only method of proving a thing’s essential nature by means of some other term, for in proofs of this sort the middle term also must be a substance, and one property of a thing is proved by means of another of its properties. Thus of two essential attributes of the same thing one may be proved, the other cannot (being taken as the cause or middle in the demonstration. That this method is not demonstration has been explained before, but it may be regarded as a dialectical proof of a thing’s essence.

We will now repeat our former statements concerning the way in which demonstration is concerned with the essence of subjects. Just as we begin to seek for the cause of a thing only when we are acquainted with the fact of a thing’s existence, while sometimes (though the cause cannot be learned before the fact) both fact and cause are learned simultaneously, so the essential form clearly cannot be learned without a previous knowledge that the thing exists. It is impossible to know what a thing is without knowing whether it exists. The latter fact we know sometimes from the accidental qualities of the thing itself, sometimes because we are acquainted with some of its essential attributes. To take an example of the second; we know that thunder exists from the noise in the clouds; that an eclipse exists from the interception of light; that man exists, because we know that an animal of a particular kind exists; that soul exists, because we know something to exist which moves itself. In every case where we know a thing only from its accidental qualities, we are necessarily ignorant of its essential nature, for, properly speaking, we do not know that it exists; and to search for a thing’s essential nature without even knowing that the thing exists is to search for a nonentity. But the process is easier when we know something of the subject’s essential nature. Thus the better the knowledge we have of the thing’s existence the more easily may we learn its essence. The following may stand as a first example of those cases where the knowledge of a thing’s existence gives us part of its essence. Let Eclipse be A. Moon C. Interposition of the earth B. To seek whether the moon is eclipsed or not is equivalent to enquiring whether B really exists or not, and that is the same as enquiring whether B is the cause of A. If that be the case, we say that B also exists. As a second example, take the question ‘with which of these two contradictory majors does the definition of triangle agree:—a triangle has its angles equal to two right angles; no triangle has its angles equal to two right angles’? If the premises are immediate truths we learn the fact and the cause of the quality simultaneously. If no demonstration be possible we know the fact but not the cause. Let C be the moon; A, eclipse; B, the impossibility of there being a shadow at full moon when nothing visible interposes. If then B (inability to cast a shadow when nothing interposes between us and the moon) be true of C, while A (being eclipsed) is true of B, the fact of an eclipse is evident, but the cause is not yet known. Thus we know that there is such a thing as an eclipse but not what its nature is.

When it is clear that A is true of B, to seek for the reason why it is true of B is the same thing as seeking for the nature of B, whether this be an exclusion of light, a turning away of the moon or an extinction of its light. Here then is the cause of the major term, in this case A, that is to say an eclipse is caused by an exclusion of light by the earth. As another example take the question, what is thunder? A quenching of fire in a cloud. Why does it thunder? Because fire is quenched in a cloud. Let cloud be C; Thunder A; Quenching of fire B. Now B is true of C, the cloud, for fire is quenched in the cloud; A, the noise, is true of B. Thus B is the cause of the major term A. If the middle term here given be included under another middle term the definition will be a prior one. We have then shewn how the nature of a thing is attained to and becomes known, and it follows that there can be no syllogism or demonstration proving a thing’s nature, though this may become clear as a result of syllogism and demonstration. Thus we cannot know a thing’s nature without demonstration, in cases where the cause is outside the thing; and yet it cannot itself be demonstrated, as we remarked in our previous statement of difficulties.

CHAP. IX.

What Essences can and what cannot be proved

When the Cause of the thing and the thing itself are identical, no demonstration is possible; for we have then reached ultimate principles, the nature of which must be assumed. When the Cause is outside the thing the Cause may be used as a middle term in the demonstration.

Some things have, others have not a cause outside themselves. It is clear therefore that of a thing’s essential qualities some are ultimate and primary, the existence and nature of which must either be assumed by hypothesis or made clear in some other way than by demonstration. The arithmetician proceeds in this way, assuming both the nature of unity and also that it exists. In the case of things which have a middle term, things the cause of whose substance is something outside themselves, there may be a demonstration, as we have said, this cause being taken as a middle term, although the underlying essence of the thing is not demonstrated.

CHAP. X.

The nature and forms of Definition

A definition which gives the real nature of a thing also gives its cause, and thus differs only in form from demonstration. There are three classes of definition: (1) An indemonstrable explanation of the essence of a thing; (2) Definitions which resemble a syllogism concerning a thing’s essence; (3) A conclusion of an essential demonstration.

Since definition is, as we have said, the expression of a thing’s essence, it is clear that one kind of definition may give the meaning of the name, or of some other expression having the force of a name:—e.g. the definition of the meaning of ‘nature of triangularity as such.’ On learning that the thing corresponding to the name exists we enquire why it exists, for it is difficult to grasp the cause of a thing when we do not know previously that the thing exists. The reason of this difficulty has been mentioned before (II, c. 8), namely that we do not know whether a thing exists or not except accidentally.

An expression may have unity in two ways; either from a union of the separate parts (in the manner in which the whole Iliad is a unity), or from predicating an attribute of the subject essentially, not accidentally. Thus one form of definition is that which gives the meaning of a word, as mentioned above. Another explains the reason why a thing is. Hence the former explains signification but proves nothing, while the latter clearly gives a kind of demonstration of the subject’s essence, and differs from demonstration only in form. Thus there is a difference between saying, ‘Why does it thunder?’ and ‘What is thunder?’ To the former one would answer, ‘because fire is quenched in the clouds’; to the question, ‘What is thunder?’ ‘Thunder is the noise of fire being quenched in the clouds.’ Thus the same thought is expressed in two different ways; the former answer containing all the parts of a demonstration, the latter being stated as a definition.

Further there may be a definition of thunder, as ‘a noise in the clouds,’ which forms only the conclusion of the demonstration of the essence of thunder. Lastly the definition of ultimate terms is an indemonstrable proposition stating the essence of the subject. Consequently definition is either (1) An indemonstrable expression of the thing’s essence, or (2) A syllogism expressing its essence, differing only in form from demonstration, or (3) The conclusion of a demonstration which states the subject’s essence. What has been said is enough to shew how far a thing’s essence is demonstrable, how far the reverse; also what things admit of demonstration and what do not, in what senses ‘definition’ is used, and in what ways it does or does not prove a thing’s essence, and in what cases this can be done; lastly the relations of definition to demonstration have been given, and it has been shewn how far the two may have the same object.

CHAP. XI.

The kinds of Causes used in Demonstration

To know a thing is to know its cause; and the Causes, each of which may be used as a middle term in demonstration, are (1) The substantial or Formal cause; (2) The necessary conditions of a thing, or Material cause; (3)That which gave the first impulse to a thing, or Efficient cause; (4) That for the sake of which a thing is done, or Final cause.

Necessity is of two kinds: (1) Obedience to natural impulse; (2) Obedience to external compulsion.

We suppose ourselves to have scientific knowledge of a thing when we have learned its cause. The causes are four in number. First, the essential conception of things; Second, the conditions from which the phenomena necessarily follow. Third, that which gave the first impulse to the thing. Fourth, that for the sake of which the thing happens. All these causes may serve as middle terms. The material cause cannot be demonstrated by means of one premise only, there must be at least two, and that can only happen when one middle term is added. When this is done a conclusion must necessarily follow. This may be made clear from the following example; ‘Why is the angle in a semicircle a right angle? or, under what conditions is it a right angle?’

Let A be right angle, B the half of two right angles, C the angle in a semicircle. Now B is the cause of A, right angle, being predicable of C, the angle in a semicircle; for this latter is equal to A, and C is equal to B, for it also is a half of two right angles. As then B is a half of two right angles A is predicable of C, that is the angle in a semicircle is a right angle. This cause is however the same as the formal cause, which gives the definition of ‘right angle.’ Further it has been proved that the formal cause may be used as a middle term.

As another example take the question, ‘for what reason were the Athenians engaged in the Persian war?’ or, ‘What was the cause of the Athenians being attacked?’ ‘Because they assaulted Sardes together with the Eretrians’; for it was that which gave the first impulse. Now let A represent ‘War’; B, ‘making the first assault’; C, ‘the Athenians.’ Here B, making the first assault, is true of C, the Athenians, and A, war, is true of B, for men fight against those who have done the first wrong. Hence A, being attacked, is true of B, those who did the first wrong, and B is true of C, the Athenians, for they were the aggressors. Hence in this case also the middle term is a cause, namely the efficient cause. As an instance of the final cause take the question: ‘For what reason is he walking?’ ‘In order that he may keep well.’ ‘What is the object of a house?’ ‘The preservation of furniture.’ Thus, the purpose of the former is ‘keeping well,’ of the latter ‘preserving furniture.’ [There is no difference between the cause which makes him walk after supper and the final cause of his walking]. Let C represent ‘a walk after supper,’ B ‘food not remaining undigested,’ A ‘keeping well.’ Let it be assumed as an attribute of walking after supper that it prevents food remaining undigested at the entrance to the stomach, and that the absence of this latter produces health. Now food not remaining undigested is considered to be an attribute of C, walking; and A, health, of B. What then is the reason why A, the final cause, is an attribute of C? Clearly it is B (food not remaining undigested), and B is in a manner the cause of A, for it is through it that A will be explained.

This may also be expressed as follows: ‘Why is B an attribute of A?’ ‘Because being in such a condition as that denoted by B constitutes keeping well.’ The matter would be made still more clear if we substituted the notion of final cause for that of efficient cause in this example1 . The origins of a thing will appear in an inverted order in connection with the efficient cause to that in which they appear in the final cause syllogism, for in the former case the middle term or efficient cause must precede the phenomenon, while in the case of the final cause the minor term C is in point of time earlier, the final cause itself (A) coming last in time.

It is possible for a thing to have a final cause and yet to be necessary; e.g. Why does light pass through a lantern? Because that which consists of the smallest parts necessarily passes through the larger apertures. Thus light is produced because it passes through the lantern in this particular way, and it also has a final cause—namely to prevent us from stumbling.

As then a thing which has a final cause and is necessary can exist, so also such a thing can come into existence. For instance, suppose thunder to arise both because there must necessarily be hissings and roarings when fire is quenched and also, as the Pythagoreans hold, in order to menace those in Tartarus and inspire them with dread. Most instances are of this kind, especially things which are or have been produced by natural laws, for nature works in some cases with a definite purpose, in others of necessity.

Necessity itself has two aspects, one kind being that which obeys nature or a natural impulse, another that which acts under compulsion and contrary to its own impulse. Thus a stone moves both upwards and downwards ‘of necessity,’ though not owing to the same kind of necessary. With regard to the results of intellectual processes some things are never produced by accident, but with some end in view (as House or Statue), others from chance (as Health, or Deliverance from danger). The final cause is of the greatest importance in the case of contingent matters, when the origin of the phenomenon is not fortuitous, and the object aimed at, whether natural or artificial, is something good. Nothing however which comes about by chance can have any definite object.

CHAP. XII.

On the Causes of events which exist, are in process, have happened, or will happen

The Cause is the same for past, existing, proceeding and future occurrences, and is always the middle term. It may be simultaneous with or anterior to its effect. In circular demonstrations causes may be inferred from their effects and vice versâ. Probable effects have probable causes.

The same cause as that which produces existing things applies also to things which are in process, have happened and will happen, for in all these cases the middle term is the cause. Existing things, however, require an existing cause, things in process a like cause, things past a past cause, things future a future cause. For instance, to the question ‘Why did an eclipse take place?’ the answer is ‘because the earth was interposing.’ It will take place because the earth will interpose: it does take place because the earth does interpose. Again: What is ice? It may be assumed that it is frozen water. Let C represent Water; A Frozen; B the middle term or cause, namely a total failure of heat. Now B is true of C, and A, frozen, of B. Hence, Ice is being produced when B is in process, has been produced when B has taken place, and will be produced when it does take place. Thus this kind of cause and its effect occur together when they occur at all, they are in process together, do exist, will exist and have existed simultaneously.

In cases, however, where cause and effect are not simultaneous, it may be asked whether, as would appear to be the case, some things are the causes of others which immediately follow them. E.g. Can one thing in process be the cause of another’s being in process; is it a future cause which produces a future effect, or a past cause a past effect? Now one may deduce a cause from the effects which have followed it, and in this case the starting point lies in the past. On the other hand one cannot draw an inference from the cause concerning the effect, e. g. that because such a thing has happened some particular effect must have followed. So too with future events. Whether the time intervening between cause and effect be indefinite or definite one cannot say that ‘because this has happened, such and such an effect must also have occurred.’ In the interval between the cause and the effect it would be incorrect to say that the latter had occurred, though the cause had already appeared. The same argument applies to future events. When one thing has happened another thing is not necessarily about to happen. The cause or middle term ought to belong to the same genus as the effect, being, in the case of past events, past, of future events, future, of events in process, in process also, of existing events, existing; but past and future cannot be homogeneous in this way. Further, the interval between cause and effect cannot be indefinite nor, until the effect is produced, can it be definite, for during the whole of that interval it would be false to say that the effect exists.

Here we ought to examine the meaning of ‘Uniformity of Nature,’ owing to which a thing when it has once happened is inclined to happen again. But is it not clear that what is in process is not a continuation of that which is past, that one past event is not a continuation of another, and that everything which is past is an ultimate and indivisible, past events being in fact no more contiguous to one another than are points, both of which are indivisible? The same reasoning shews that the present is not merely a continuation of the past, for an event in process is divisible, a past event indivisible. An event in process really bears the same relation to a past event as a line bears to a point.

Infinite past events go to make up that which is now in process. These subjects must, however, be discussed more clearly in the general treatment of Motion (Cf. Phys. Bk. vi). With regard to the manner in which the middle can be the cause when the result is continuous, this much may suffice. In these cases also the primary term and the middle must both be ultimates. For instance, suppose A to have taken place because C has taken place1 , C however coming later than A. Now the starting point is C, because it is nearer to the present moment, which forms the starting point in time. Now C has taken place if D has taken place; and when D has taken place A must previously have taken place. The cause of this is C, for when D has taken place it is necessary that C should have taken place, and when C has taken place, it is necessary that A should have done so before. If the middle term be thus expressed it might be asked whether the process must sometime reach an ultimate and terminate, or whether a middle term would always appear and so produce an infinite regress, for as was said a past event is not a continuation of another past event. Yet one must begin with the middle term and with the present moment as a primary point of departure. The same is true of future events: for if it be true to say that the effect D will be, it must be a previous truth that the cause A will be. The cause of this is C, for if D will be, C will be previously, but if C will be A will be previously. Thus in these cases also an infinite subdivision is possible, for future events likewise are not bound together in perfect continuity, and in the case of them also an ultimate starting point must be assumed.

The same thing applies to matters of production. E.g. If a house has been built the stones must have been cut and have existed. What is the reason of this? Because, for a house to be built, a foundation must have been laid. If so, stones must have existed previously. Similarly, if there is to be a house, walls also must exist beforehand. This too is proved by means of the same middle term, namely, that a foundation must be laid before the house can be built.

We see with regards to matters in process that production is effected in a circular manner, and we observe that this may happen when the major and minor and also the middle terms are each of them consequences of the other, and it is then that Conversion takes place. Now we proved at the outset (Pr. An. II. 5–7) that causes and effects may be proved circularly, and that is the meaning of the circular process. In the case of matters of production the method may be regarded as follows. When the earth has been moistened vapours must arise. When that happens a cloud is produced. From the cloud comes rain, and as a result of the rain the earth must be moistened. Hence the process has returned to its starting point, and when any one of the terms is present another follows, when that is present a third follows, and when the third is present the first recurs again.

Some events in process are universal, for they exist or come into existence always and in every instance; others are not invariable but Probable. E.g. Not every man can grow a beard, but this is usually so. In such cases the middle term also must be of ordinary application. If A be predicated of B universally, and B of C universally also, then A must be predicated as invariable attribute of C, always present in every instance of it (for so we may paraphrase the expressions ‘universal,’ ‘distributive,’ and ‘eternal’). Our hypothesis was, however, that the attribute was only ordinarily present in the subject, and therefore the middle term B must be probable also. It follows then that things which exist or come into existence ordinarily but not invariably must also possess certain ultimate starting points or first principles.

CHAP. 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 some1 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.

CHAP. XIV.

On the discovery of Questions for Demonstration

To express questions for demonstration in a fitting manner a subject must be selected to which the quality to be demonstrated primarily belongs.

In order to find questions for solution we must make a selection from various partitions and divisions, taking care that a common generic notion lies at the base of all subordinate divisions, and assuming that all belong to a common genus. E.g. If Animals be the subject of investigation, we must first lay down what attributes are common to every animal. When this is done we should find what are the attributes of the first subdivision after the genus. Thus, if the subject be a bird, we should find the qualities possessed by every bird, and we must continue thus with the attributes of each lower term in the series. We shall then clearly be able to give the reason why the species included in the common genus possess such and such attributes; e.g. the reason why Man or Horse, as species of Animal, possess particular attributes. Let A be animal, B the attributes of every animal, C, D, E, particular species of animal. Now it is clear why B is an attribute of D, namely because of A, and it will similarly belong to the other species of animal. The same reasoning applies to other instances.

Hitherto we have spoken of cases where custom has sanctioned the application of the common class names to the particular species, but we should not limit ourselves to these. If anything else be seen to be an attribute of several things but to have no common generic name, we should take it for examination and look what are its attributes or of what it is an attribute. Thus, the possession of a ruminating stomach is a commonattribute of horned animals, as well as the possession of front teeth in one jaw only. We must then enquire what animals have the attribute of being horned. It will then be clear why the attribute mentioned belongs to these animals. It will belong to them because they have horns.1 Another method consists in the observation of analogies. No single designation for instance exists for the spine of a fish, the pounce of a cuttle and ordinary bone, and yet all these parts have common qualities, as if their nature were the same in each case.

CHAP. XV.

How far the same Middle Term is employed for demonstrating different Questions

Questions for demonstration are the same when they use the same middle term. Questions may be generically the same and specifically different.

Questions for solution are the same, first from having the same middle term (as for instance all questions which can be solved by the common middle term ‘reactionary influence,’) and of these some are generically identical while possessing certain specific differences, whether of object or only of method. Take the three questions ‘What produces an Echo?’ ‘Why are objects reflected?’ ‘What causes a Rainbow?’ All these are generically one, for all involve refraction, but they differ specifically. In other cases questions differ in that the middle term of the one is subordinate to that of the other. Thus, ‘Why is the current of the Nile stronger at the end of the month?’

‘Because the end of the month is more rainy.’

‘Why then is the end of the month more rainy?’

‘Because the moon is waning.’

These two questions stand to one another in the second of the above relations.

CHAP. XVI.

On inferring the Cause from the Effect

When the Cause is known the effect also must be known, but in consequence of the Plurality of causes an effect may be known without the exact cause being known.

A difficulty might be raised in connection with the Cause and its result as to whether, when the effect is present, the cause must also be present; for instance whether, supposing leaves to fall from the tree or the moon to be eclipsed, the cause of the fall, or of the eclipse, is likewise present. It may be assumed that the cause of the former is the possession of broad leaves, that of the eclipse the interposition of the earth, for even if it be not so something else will be the cause of the phenomena. Now if the cause be present the effect must also be present; e.g. if the earth be interposing the moon is being eclipsed, if the tree have broad leaves it is deciduous. An objection might here be raised that if this were so, the cause and effect would be simultaneous, and each of them might be proved from the other. Thus: let A represent the quality of shedding leaves, B broad-leaved, C vine. Now, if A be true of B (since every broad-leaved tree is deciduous), and also B of C (since every vine has broad leaves), then A is true of C, and every vine is proved to be deciduous. The cause of this is B, which is here the middle term. It may also be demonstrated conversely that the vine has broad leaves from the fact of its being deciduous. Thus, let D be broad-leaved, E deciduous, F vine. Now E is true of F (for every vine is deciduous), and D of E (for every deciduous tree is broad-leaved). Therefore every vine is broad-leaved, and the cause of it is that it is deciduous. On the other hand these qualities cannot be the causes of one another, since the cause is prior to that of which it is the cause. Thus supposing the interposition of the earth to be the cause of an eclipse, then the eclipse cannot be the cause of the interposition of the earth. If then the demonstration of the cause give the reason of a thing, while the demonstration which does not explain the cause gives only the fact, this latter demonstration may suffice to inform us that the earth interposes between sun and moon, but not why it interposes. That the eclipse is not the cause of the interposition of the earth, but this latter of the eclipse, is obvious, for the interposition of the earth is an element in the definition of eclipse, and it is therefore clear that the latter is demonstrable by means of the former, not vice versa.

Can there be several causes of the same thing?

Since the same thing can be immediately predicated of several subjects, let A be immediately predicable of B, and also immediately predicable of another subject C, and again B and C of D and E. Here A will be predicable of D and E, and the cause of this will, in the case of D be B, in that of E it will be C. Hence when the cause is present the thing caused must also be present, but when the thing caused is present it is not necessary for every separate cause one may select to be present. Some cause must indeed be present, but not every cause. Again if the subject proposed be a universal one, not only must the cause be something universal but also that of which it is the cause. Thus ‘shedding leaves’ is a universal attribute of a whole genus, though this may include subordinate species, being applicable either to plants in general or to particular kinds of plants. Hence in these cases the middle term and the effect must be co-extensive and convertible. Take for instance the question ‘Why do trees lose their leaves?’ If the reason be that the sap is dried up, whenever the tree sheds its leaves this drying up must occur, and if it occur in tree and nothing but tree, that tree must shed its leaves.

CHAP. XVII.

Whether there can be several causes of the same thing

In a demonstration of the cause, no effect can be regarded as the outcome of several causes, for in such a demonstration things are regarded in the light of essentials and not of accidents. Here the middle term is the definition of the major.

Is it possible that it should not be the same cause which produces a like effect in all the subjects included in the minor term, but that another cause should exist, or is that impossible? If the cause has been demonstrated to be essential and not a mere external sign or accidental cause it is impossible that there should be more than one cause, for the middle term is the cause of the minor. Otherwise it is possible. One may indeed consider the effect and the subject in which it is produced from the point of view of their accidental attributes, but these cases are not to be looked on as scientific problems. If the cause be not made to depend on accidental attributes the middle term will be of like kind with the subjects themselves, but if the latter are one only from an applied use of the common name the middle term can only be employed with like restrictions, while if the subjects be all included under the same genus the middle will be so also. Thus, suppose that one had to state the cause of reciprocal proportion. The cause of this differs in the case of lines and in that of numbers, and yet is in both connections the same in so far as it depends on a certain law of increase. The same argument applies to all such instances. There is however a difference between the cause which makes one colour resemble another and that which makes one figure resemble another, for in these two cases ‘resemblance’ bears a two-fold meaning. In connection with figures it consists in having an equal number of sides and equal angles, in the case of colours that they convey a similar sensation to the senses or something of the kind. Things which are analogously identical will also have an analogous middle term.

The reason of this is that the cause, the effect and the snbject in which the effect is produced correspond to one another. If one take particular species as subjects the term in which the cause produces the effect will be more comprehensive than any one of the subjects. Thus the quality of having the external angles equal to four right angles is more comprehensive than triangle or square, but the quality is co-extensive with all angular figures taken together. So too all figures which have their external angles equal to four right angles are included under the same middle term.

As the middle term contains the definition of the major, all scientific knowledge is based on definition. For instance, shedding leaves is a quality both of vines and figs, but is more comprehensive than either of them. Yet it is not more comprehensive than all deciduous species of trees but co-extensive with them. If one take the primary middle term (broad-leaved) it will contain the definition of this quality of shedding leaves. This term will serve as middle term both in questions concerning vines and figs and will shew that all vines and figs possess the quality of having broad leaves. The middle term or cause through which broad-leaved trees are deciduous is that the sap dries up, or something of the kind. In what then does this quality of shedding leaves consist? In having the sap dried up at the junction of stalk and stem.

We will answer enquiries as to the mode in which cause and effect can follow each other by this example. Let A be true of all B, and B be true of all D, but be more comprehensive. Then B will be universally predicable of D. By ‘universal,’ I here denote a predicate which is not convertible with its subject, while ‘primary universal’ is a predicate with which the separate individual subjects are not convertible, though the whole subject is convertible and co-extensive with that predicate.

In the above instance B is the cause why A is predicable of the various subjects D; A therefore must be more comprehensive than B; otherwise why should B be the cause rather than A? If A be predicable of all the subjects E, these latter taken together form a single concept distinct from B. Otherwise how could one say that everything which is E is also A, but that not everything which is A is also E? For why should not the cause be, for instance, that every D is A? Then the various subjects E will form a single concept which must also be considered, and may be denoted by C.

Thus it is possible for several causes to produce the same effect; but not when the subjects in which the effect is produced are specifically the same. For instance, the cause of long life in quadrupeds may be the absence of gall, in birds dryness of constitution, or something else. If however we do not at once attain some ultimate proposition, and if the middle term be found to be not one but many, then the causes also must be many.

CHAP. XVIII.

Which is the prior cause, that which is nearer the particular, or the more universal?

Particular effects are produced by causes which lie nearer to the particular than to the universal.

Which middle term produces effects in individual subjects? Is it the middle term which stands first on reckoning from the universal, or the middle which stands next to the particular? Clearly the middle terms nearest to the subjects in which the effect is produced, since it is those middle terms which are the cause of the major term falling under the universal law; e.g. C is the cause of B being true of D. Now C is the cause why A is predicable of D, B the cause why A predicable of C; that A is predicable of B is due to B alone and to no further cause.

CHAP. XIX.

On the attainment of Primary Principles

Concerning the faculty which acquires knowledge of the ultimate principles of demonstration. These principles cannot be innate, but are derived from repeated sense perceptions which produce memory and experience, the germ of unity or generalisation in the mind. Thus primary principles are derived from induction, and as they are indemonstrable they cannot be learned by Science, but by Pure Reason (νον̂ς) which is the Principle of Science.

We have now shewn what syllogism and demonstration are, and how they are effected; and we have also discussed demonstrative knowledge, for that is the same thing as demonstration. We shall understand the primary principles, both as regards the method of their acquisition and the habit of mind which acquires them, if we first settle certain difficulties connected with the subject. It has already (I. c. 2) been stated that it is possible to acquire scientific knowledge by means of demonstration without first explaining the primary and ultimate principles. A question might however be raised as to whether the knowledge of the ultimate principles is or is not the same as demonstrable knowledge, and whether either of them constitutes a science or not, whether there can be a science only of the one class, while some other faculty cognizes the other; likewise whether faculties for attaining primary principles are produced in us without being innate, or whether they are innate and have remained unnoticed.

It would be absurd to say that we already naturally possess these principles, as then we should have a form of knowledge more accurate than demonstration, of which however we remained in ignorance.

On the other hand if we acquire these principles without having had them before, how can we learn and understand anything when no previous knowledge existed? That as we said when dealing with demonstration (I. c. 1) would be impossible. It is clear then that we cannot already possess knowledge of this kind, nor can it be produced in us if we are unable to recognize the principles and have no faculty for acquiring them. We must therefore possess some such undeveloped faculty, but not of such a nature as to be superior to the principles themselves in point of accuracy. This faculty indeed is clearly possessed by all animals, for all have an innate critical faculty which is called Sense-perception. When possessed of this some animals become capable of retaining perceptions, others do not. Those which do not retain perception can have no knowledge outside their separate acts of perception, either none at all or none concerning the object which they are incapable of retaining. The other class, in which perceptions are retained, though also perceiving by means of the senses, still preserve a representation of their perceptions in the mind1 . As these latter multiply a further distinction may be remarked in them. Some beings attain to a concept as a result of the retention of these perceptions, others never do. From perception then, as we hold, memory results, and from repeated recollections of the same phenomenon comes experience, for memories which are numerically many form but a single experience.

Next, from experience, or from the entire universal which is retained in the soul, the single unit apart from the manifold of sense, which is identical in all particular cases, comes the elementary principle of art and science; if the concern be with production, of art, if with reality, of science. The faculties do not exist distinct in the mind, nor do they result from higher states of consciousness, but from sense-perception. Thus, when one side gives way in battle, if a single man rally, another rallies also and then a third, until the original order has been restored. Now the soul’s nature is such that a similar process is capable of taking place in it also. We will now state again what has been said with some obscurity just now. When one of the atoms of sense has taken its stand in the soul a first universal idea forms therein, for one may perceive particulars by means of an action of the senses, but perception is concerned with the universal, not with the particular man Callias. Then the remaining particulars halt, and the process continues until indivisible and universal ideas are formed. Thus as a result of the perception of such and such animals the general idea of Animal is formed, and this latter serves to form yet wider conceptions.

It is clear that the most primary knowledge is attained by means of Induction, for it is through induction that sense-perception produces the universal in the mind. Now there are different modes of thought by means of which we attain to truth, and some of them are always infallible, while others, as Opinion and Calculation, admit of error. On the other hand Science and Reason are always true, and there is no further class of faculties, save Reason, which surpasses Science in exactness. Since then the principles of demonstration are better known than the demonstrations themselves, and since all scientific knowledge implies conclusion, the principles cannot be the objects of Science. Since further, nothing admits of greater truth than Science except Reason, this latter would seem to be the faculty which has the primary principles as its objects. The above argument will serve to shew that demonstration cannot be its own principle, so that science also cannot be its own principle. If then we have no true form of thought (other than science) except Reason, Reason would seem to be the principle of scientific knowledge. Reason is thus the principle of the principles, and bears the same relation to science as the latter does to all other truths.

[1 ]I.e. the efficient cause is demonstrated by means of the final cause. In full the syllogism would be:—A (keeping well, the final cause) accompanies good digestion (B). But C (the efficient cause) produces A; therefore C produces B.

[1 ]E. g. the foundations of a house may be known to have been laid when the house is seen, though the latter came into existence after the former.

[1 ]Viz. Speusippus (Diog. Laert., IV, § 5).

[1 ]Cf. Arist. de Part. Anim., III, 2.

[1 ]Reading αἰσθανομένοις with the Clarendon Press Edition. A better reading is μὴ αἰσθανομένοις: ‘Even at a time when the senses convey no such perceptions.’