Literature A-Z

Some of Aristotle's works

ANALYTIC

HISTORY OF ANIMALS

350 BC

POSTERIOR ANALYTICS

by Aristotle

translated by G. R. G. Mure

Book I

ALL instruction given or received by way of argument proceeds from

pre-existent knowledge. This becomes evident upon a survey of all

the species of such instruction. The mathematical sciences and all

other speculative disciplines are acquired in this way, and so are the

two forms of dialectical reasoning, syllogistic and inductive; for

each of these latter make use of old knowledge to impart new, the

syllogism assuming an audience that accepts its premisses, induction

exhibiting the universal as implicit in the clearly known

particular. Again, the persuasion exerted by rhetorical arguments is

in principle the same, since they use either example, a kind of

induction, or enthymeme, a form of syllogism.

The pre-existent knowledge required is of two kinds. In some cases

admission of the fact must be assumed, in others comprehension of

the meaning of the term used, and sometimes both assumptions are

essential. Thus, we assume that every predicate can be either truly

affirmed or truly denied of any subject, and that 'triangle' means

so and so; as regards 'unit' we have to make the double assumption

of the meaning of the word and the existence of the thing. The

reason is that these several objects are not equally obvious to us.

Recognition of a truth may in some cases contain as factors both

previous knowledge and also knowledge acquired simultaneously with

that recognition-knowledge, this latter, of the particulars actually

falling under the universal and therein already virtually known. For

example, the student knew beforehand that the angles of every triangle

are equal to two right angles; but it was only at the actual moment at

which he was being led on to recognize this as true in the instance

before him that he came to know 'this figure inscribed in the

semicircle' to be a triangle. For some things (viz. the singulars

finally reached which are not predicable of anything else as

subject) are only learnt in this way, i.e. there is here no

recognition through a middle of a minor term as subject to a major.

Before he was led on to recognition or before he actually drew a

conclusion, we should perhaps say that in a manner he knew, in a

manner not.

If he did not in an unqualified sense of the term know the existence

of this triangle, how could he know without qualification that its

angles were equal to two right angles? No: clearly he knows not

without qualification but only in the sense that he knows universally.

If this distinction is not drawn, we are faced with the dilemma in the

Meno: either a man will learn nothing or what he already knows; for we

cannot accept the solution which some people offer. A man is asked,

'Do you, or do you not, know that every pair is even?' He says he does

know it. The questioner then produces a particular pair, of the

existence, and so a fortiori of the evenness, of which he was unaware.

The solution which some people offer is to assert that they do not

know that every pair is even, but only that everything which they know

to be a pair is even: yet what they know to be even is that of which

they have demonstrated evenness, i.e. what they made the subject of

their premiss, viz. not merely every triangle or number which they

know to be such, but any and every number or triangle without

reservation. For no premiss is ever couched in the form 'every

number which you know to be such', or 'every rectilinear figure

which you know to be such': the predicate is always construed as

applicable to any and every instance of the thing. On the other

hand, I imagine there is nothing to prevent a man in one sense knowing

what he is learning, in another not knowing it. The strange thing

would be, not if in some sense he knew what he was learning, but if he

were to know it in that precise sense and manner in which he was

learning it.

We suppose ourselves to possess unqualified scientific knowledge

of a thing, as opposed to knowing it in the accidental way in which

the sophist knows, when we think that we know the cause on which the

fact depends, as the cause of that fact and of no other, and, further,

that the fact could not be other than it is. Now that scientific

knowing is something of this sort is evident-witness both those who

falsely claim it and those who actually possess it, since the former

merely imagine themselves to be, while the latter are also actually,

in the condition described. Consequently the proper object of

unqualified scientific knowledge is something which cannot be other

than it is.

There may be another manner of knowing as well-that will be

discussed later. What I now assert is that at all events we do know by

demonstration. By demonstration I mean a syllogism productive of

scientific knowledge, a syllogism, that is, the grasp of which is eo

ipso such knowledge. Assuming then that my thesis as to the nature

of scientific knowing is correct, the premisses of demonstrated

knowledge must be true, primary, immediate, better known than and

prior to the conclusion, which is further related to them as effect to

cause. Unless these conditions are satisfied, the basic truths will

not be 'appropriate' to the conclusion. Syllogism there may indeed

be without these conditions, but such syllogism, not being

productive of scientific knowledge, will not be demonstration. The

premisses must be true: for that which is non-existent cannot be

known-we cannot know, e.g. that the diagonal of a square is

commensurate with its side. The premisses must be primary and

indemonstrable; otherwise they will require demonstration in order

to be known, since to have knowledge, if it be not accidental

knowledge, of things which are demonstrable, means precisely to have a

demonstration of them. The premisses must be the causes of the

conclusion, better known than it, and prior to it; its causes, since

we possess scientific knowledge of a thing only when we know its

cause; prior, in order to be causes; antecedently known, this

antecedent knowledge being not our mere understanding of the

meaning, but knowledge of the fact as well. Now 'prior' and 'better

known' are ambiguous terms, for there is a difference between what

is prior and better known in the order of being and what is prior

and better known to man. I mean that objects nearer to sense are prior

and better known to man; objects without qualification prior and

better known are those further from sense. Now the most universal

causes are furthest from sense and particular causes are nearest to

sense, and they are thus exactly opposed to one another. In saying

that the premisses of demonstrated knowledge must be primary, I mean

that they must be the 'appropriate' basic truths, for I identify

primary premiss and basic truth. A 'basic truth' in a demonstration is

an immediate proposition. An immediate proposition is one which has no

other proposition prior to it. A proposition is either part of an

enunciation, i.e. it predicates a single attribute of a single

subject. If a proposition is dialectical, it assumes either part

indifferently; if it is demonstrative, it lays down one part to the

definite exclusion of the other because that part is true. The term

'enunciation' denotes either part of a contradiction indifferently.

A contradiction is an opposition which of its own nature excludes a

middle. The part of a contradiction which conjoins a predicate with

a subject is an affirmation; the part disjoining them is a negation. I

call an immediate basic truth of syllogism a 'thesis' when, though

it is not susceptible of proof by the teacher, yet ignorance of it

does not constitute a total bar to progress on the part of the

pupil: one which the pupil must know if he is to learn anything

whatever is an axiom. I call it an axiom because there are such truths

and we give them the name of axioms par excellence. If a thesis

assumes one part or the other of an enunciation, i.e. asserts either

the existence or the non-existence of a subject, it is a hypothesis;

if it does not so assert, it is a definition. Definition is a 'thesis'

or a 'laying something down', since the arithmetician lays it down

that to be a unit is to be quantitatively indivisible; but it is not a

hypothesis, for to define what a unit is is not the same as to

affirm its existence.

Now since the required ground of our knowledge-i.e. of our

conviction-of a fact is the possession of such a syllogism as we

call demonstration, and the ground of the syllogism is the facts

constituting its premisses, we must not only know the primary

premisses-some if not all of them-beforehand, but know them better

than the conclusion: for the cause of an attribute's inherence in a

subject always itself inheres in the subject more firmly than that

attribute; e.g. the cause of our loving anything is dearer to us

than the object of our love. So since the primary premisses are the

cause of our knowledge-i.e. of our conviction-it follows that we

know them better-that is, are more convinced of them-than their

consequences, precisely because of our knowledge of the latter is

the effect of our knowledge of the premisses. Now a man cannot believe

in anything more than in the things he knows, unless he has either

actual knowledge of it or something better than actual knowledge.

But we are faced with this paradox if a student whose belief rests

on demonstration has not prior knowledge; a man must believe in

some, if not in all, of the basic truths more than in the

conclusion. Moreover, if a man sets out to acquire the scientific

knowledge that comes through demonstration, he must not only have a

better knowledge of the basic truths and a firmer conviction of them

than of the connexion which is being demonstrated: more than this,

nothing must be more certain or better known to him than these basic

truths in their character as contradicting the fundamental premisses

which lead to the opposed and erroneous conclusion. For indeed the

conviction of pure science must be unshakable.

Some hold that, owing to the necessity of knowing the primary

premisses, there is no scientific knowledge. Others think there is,

but that all truths are demonstrable. Neither doctrine is either

true or a necessary deduction from the premisses. The first school,

assuming that there is no way of knowing other than by

demonstration, maintain that an infinite regress is involved, on the

ground that if behind the prior stands no primary, we could not know

the posterior through the prior (wherein they are right, for one

cannot traverse an infinite series): if on the other hand-they say-the

series terminates and there are primary premisses, yet these are

unknowable because incapable of demonstration, which according to them

is the only form of knowledge. And since thus one cannot know the

primary premisses, knowledge of the conclusions which follow from them

is not pure scientific knowledge nor properly knowing at all, but

rests on the mere supposition that the premisses are true. The other

party agree with them as regards knowing, holding that it is only

possible by demonstration, but they see no difficulty in holding

that all truths are demonstrated, on the ground that demonstration may

be circular and reciprocal.

Our own doctrine is that not all knowledge is demonstrative: on

the contrary, knowledge of the immediate premisses is independent of

demonstration. (The necessity of this is obvious; for since we must

know the prior premisses from which the demonstration is drawn, and

since the regress must end in immediate truths, those truths must be

indemonstrable.) Such, then, is our doctrine, and in addition we

maintain that besides scientific knowledge there is its originative

source which enables us to recognize the definitions.

Now demonstration must be based on premisses prior to and better

known than the conclusion; and the same things cannot simultaneously

be both prior and posterior to one another: so circular

demonstration is clearly not possible in the unqualified sense of

'demonstration', but only possible if 'demonstration' be extended to

include that other method of argument which rests on a distinction

between truths prior to us and truths without qualification prior,

i.e. the method by which induction produces knowledge. But if we

accept this extension of its meaning, our definition of unqualified

knowledge will prove faulty; for there seem to be two kinds of it.

Perhaps, however, the second form of demonstration, that which

proceeds from truths better known to us, is not demonstration in the

unqualified sense of the term.

The advocates of circular demonstration are not only faced with

the difficulty we have just stated: in addition their theory reduces

to the mere statement that if a thing exists, then it does exist-an

easy way of proving anything. That this is so can be clearly shown

by taking three terms, for to constitute the circle it makes no

difference whether many terms or few or even only two are taken.

Thus by direct proof, if A is, B must be; if B is, C must be;

therefore if A is, C must be. Since then-by the circular proof-if A

is, B must be, and if B is, A must be, A may be substituted for C

above. Then 'if B is, A must be'='if B is, C must be', which above

gave the conclusion 'if A is, C must be': but C and A have been

identified. Consequently the upholders of circular demonstration are

in the position of saying that if A is, A must be-a simple way of

proving anything. Moreover, even such circular demonstration is

impossible except in the case of attributes that imply one another,

viz. 'peculiar' properties.

Now, it has been shown that the positing of one thing-be it one

term or one premiss-never involves a necessary consequent: two

premisses constitute the first and smallest foundation for drawing a

conclusion at all and therefore a fortiori for the demonstrative

syllogism of science. If, then, A is implied in B and C, and B and C

are reciprocally implied in one another and in A, it is possible, as

has been shown in my writings on the syllogism, to prove all the

assumptions on which the original conclusion rested, by circular

demonstration in the first figure. But it has also been shown that

in the other figures either no conclusion is possible, or at least

none which proves both the original premisses. Propositions the

terms of which are not convertible cannot be circularly demonstrated

at all, and since convertible terms occur rarely in actual

demonstrations, it is clearly frivolous and impossible to say that

demonstration is reciprocal and that therefore everything can be

demonstrated.

Since the object of pure scientific knowledge cannot be other than

it is, the truth obtained by demonstrative knowledge will be

necessary. And since demonstrative knowledge is only present when we

have a demonstration, it follows that demonstration is an inference

from necessary premisses. So we must consider what are the premisses

of demonstration-i.e. what is their character: and as a preliminary,

let us define what we mean by an attribute 'true in every instance

of its subject', an 'essential' attribute, and a 'commensurate and

universal' attribute. I call 'true in every instance' what is truly

predicable of all instances-not of one to the exclusion of

others-and at all times, not at this or that time only; e.g. if animal

is truly predicable of every instance of man, then if it be true to

say 'this is a man', 'this is an animal' is also true, and if the

one be true now the other is true now. A corresponding account holds

if point is in every instance predicable as contained in line. There

is evidence for this in the fact that the objection we raise against a

proposition put to us as true in every instance is either an

instance in which, or an occasion on which, it is not true.

Essential attributes are (1) such as belong to their subject as

elements in its essential nature (e.g. line thus belongs to

triangle, point to line; for the very being or 'substance' of triangle

and line is composed of these elements, which are contained in the

formulae defining triangle and line): (2) such that, while they belong

to certain subjects, the subjects to which they belong are contained

in the attribute's own defining formula. Thus straight and curved

belong to line, odd and even, prime and compound, square and oblong,

to number; and also the formula defining any one of these attributes

contains its subject-e.g. line or number as the case may be.

Extending this classification to all other attributes, I distinguish

those that answer the above description as belonging essentially to

their respective subjects; whereas attributes related in neither of

these two ways to their subjects I call accidents or 'coincidents';

e.g. musical or white is a 'coincident' of animal.

Further (a) that is essential which is not predicated of a subject

other than itself: e.g. 'the walking [thing]' walks and is white in

virtue of being something else besides; whereas substance, in the

sense of whatever signifies a 'this somewhat', is not what it is in

virtue of being something else besides. Things, then, not predicated

of a subject I call essential; things predicated of a subject I call

accidental or 'coincidental'.

In another sense again (b) a thing consequentially connected with

anything is essential; one not so connected is 'coincidental'. An

example of the latter is 'While he was walking it lightened': the

lightning was not due to his walking; it was, we should say, a

coincidence. If, on the other hand, there is a consequential

connexion, the predication is essential; e.g. if a beast dies when its

throat is being cut, then its death is also essentially connected with

the cutting, because the cutting was the cause of death, not death a

'coincident' of the cutting.

So far then as concerns the sphere of connexions scientifically

known in the unqualified sense of that term, all attributes which

(within that sphere) are essential either in the sense that their

subjects are contained in them, or in the sense that they are

contained in their subjects, are necessary as well as

consequentially connected with their subjects. For it is impossible

for them not to inhere in their subjects either simply or in the

qualified sense that one or other of a pair of opposites must inhere

in the subject; e.g. in line must be either straightness or curvature,

in number either oddness or evenness. For within a single identical

genus the contrary of a given attribute is either its privative or its

contradictory; e.g. within number what is not odd is even, inasmuch as

within this sphere even is a necessary consequent of not-odd. So,

since any given predicate must be either affirmed or denied of any

subject, essential attributes must inhere in their subjects of

necessity.

Thus, then, we have established the distinction between the

attribute which is 'true in every instance' and the 'essential'

attribute.

I term 'commensurately universal' an attribute which belongs to

every instance of its subject, and to every instance essentially and

as such; from which it clearly follows that all commensurate

universals inhere necessarily in their subjects. The essential

attribute, and the attribute that belongs to its subject as such,

are identical. E.g. point and straight belong to line essentially, for

they belong to line as such; and triangle as such has two right

angles, for it is essentially equal to two right angles.

An attribute belongs commensurately and universally to a subject

when it can be shown to belong to any random instance of that

subject and when the subject is the first thing to which it can be

shown to belong. Thus, e.g. (1) the equality of its angles to two

right angles is not a commensurately universal attribute of figure.

For though it is possible to show that a figure has its angles equal

to two right angles, this attribute cannot be demonstrated of any

figure selected at haphazard, nor in demonstrating does one take a

figure at random-a square is a figure but its angles are not equal

to two right angles. On the other hand, any isosceles triangle has its

angles equal to two right angles, yet isosceles triangle is not the

primary subject of this attribute but triangle is prior. So whatever

can be shown to have its angles equal to two right angles, or to

possess any other attribute, in any random instance of itself and

primarily-that is the first subject to which the predicate in question

belongs commensurately and universally, and the demonstration, in

the essential sense, of any predicate is the proof of it as

belonging to this first subject commensurately and universally:

while the proof of it as belonging to the other subjects to which it

attaches is demonstration only in a secondary and unessential sense.

Nor again (2) is equality to two right angles a commensurately

universal attribute of isosceles; it is of wider application.

We must not fail to observe that we often fall into error because

our conclusion is not in fact primary and commensurately universal

in the sense in which we think we prove it so. We make this mistake

(1) when the subject is an individual or individuals above which there

is no universal to be found: (2) when the subjects belong to different

species and there is a higher universal, but it has no name: (3)

when the subject which the demonstrator takes as a whole is really

only a part of a larger whole; for then the demonstration will be true

of the individual instances within the part and will hold in every

instance of it, yet the demonstration will not be true of this subject

primarily and commensurately and universally. When a demonstration

is true of a subject primarily and commensurately and universally,

that is to be taken to mean that it is true of a given subject

primarily and as such. Case (3) may be thus exemplified. If a proof

were given that perpendiculars to the same line are parallel, it might

be supposed that lines thus perpendicular were the proper subject of

the demonstration because being parallel is true of every instance

of them. But it is not so, for the parallelism depends not on these

angles being equal to one another because each is a right angle, but

simply on their being equal to one another. An example of (1) would be

as follows: if isosceles were the only triangle, it would be thought

to have its angles equal to two right angles qua isosceles. An

instance of (2) would be the law that proportionals alternate.

Alternation used to be demonstrated separately of numbers, lines,

solids, and durations, though it could have been proved of them all by

a single demonstration. Because there was no single name to denote

that in which numbers, lengths, durations, and solids are identical,

and because they differed specifically from one another, this property

was proved of each of them separately. To-day, however, the proof is

commensurately universal, for they do not possess this attribute qua

lines or qua numbers, but qua manifesting this generic character which

they are postulated as possessing universally. Hence, even if one

prove of each kind of triangle that its angles are equal to two

right angles, whether by means of the same or different proofs; still,

as long as one treats separately equilateral, scalene, and

isosceles, one does not yet know, except sophistically, that

triangle has its angles equal to two right angles, nor does one yet

know that triangle has this property commensurately and universally,

even if there is no other species of triangle but these. For one

does not know that triangle as such has this property, nor even that

'all' triangles have it-unless 'all' means 'each taken singly': if

'all' means 'as a whole class', then, though there be none in which

one does not recognize this property, one does not know it of 'all

triangles'.

When, then, does our knowledge fail of commensurate universality,

and when it is unqualified knowledge? If triangle be identical in

essence with equilateral, i.e. with each or all equilaterals, then

clearly we have unqualified knowledge: if on the other hand it be not,

and the attribute belongs to equilateral qua triangle; then our

knowledge fails of commensurate universality. 'But', it will be asked,

'does this attribute belong to the subject of which it has been

demonstrated qua triangle or qua isosceles? What is the point at which

the subject. to which it belongs is primary? (i.e. to what subject can

it be demonstrated as belonging commensurately and universally?)'

Clearly this point is the first term in which it is found to inhere as

the elimination of inferior differentiae proceeds. Thus the angles

of a brazen isosceles triangle are equal to two right angles: but

eliminate brazen and isosceles and the attribute remains. 'But'-you

may say-'eliminate figure or limit, and the attribute vanishes.' True,

but figure and limit are not the first differentiae whose

elimination destroys the attribute. 'Then what is the first?' If it is

triangle, it will be in virtue of triangle that the attribute

belongs to all the other subjects of which it is predicable, and

triangle is the subject to which it can be demonstrated as belonging

commensurately and universally.

Demonstrative knowledge must rest on necessary basic truths; for the

object of scientific knowledge cannot be other than it is. Now

attributes attaching essentially to their subjects attach

necessarily to them: for essential attributes are either elements in

the essential nature of their subjects, or contain their subjects as

elements in their own essential nature. (The pairs of opposites

which the latter class includes are necessary because one member or

the other necessarily inheres.) It follows from this that premisses of

the demonstrative syllogism must be connexions essential in the

sense explained: for all attributes must inhere essentially or else be

accidental, and accidental attributes are not necessary to their

subjects.

We must either state the case thus, or else premise that the

conclusion of demonstration is necessary and that a demonstrated

conclusion cannot be other than it is, and then infer that the

conclusion must be developed from necessary premisses. For though

you may reason from true premisses without demonstrating, yet if

your premisses are necessary you will assuredly demonstrate-in such

necessity you have at once a distinctive character of demonstration.

That demonstration proceeds from necessary premisses is also indicated

by the fact that the objection we raise against a professed

demonstration is that a premiss of it is not a necessary truth-whether

we think it altogether devoid of necessity, or at any rate so far as

our opponent's previous argument goes. This shows how naive it is to

suppose one's basic truths rightly chosen if one starts with a

proposition which is (1) popularly accepted and (2) true, such as

the sophists' assumption that to know is the same as to possess

knowledge. For (1) popular acceptance or rejection is no criterion

of a basic truth, which can only be the primary law of the genus

constituting the subject matter of the demonstration; and (2) not

all truth is 'appropriate'.

A further proof that the conclusion must be the development of

necessary premisses is as follows. Where demonstration is possible,

one who can give no account which includes the cause has no scientific

knowledge. If, then, we suppose a syllogism in which, though A

necessarily inheres in C, yet B, the middle term of the demonstration,

is not necessarily connected with A and C, then the man who argues

thus has no reasoned knowledge of the conclusion, since this

conclusion does not owe its necessity to the middle term; for though

the conclusion is necessary, the mediating link is a contingent

fact. Or again, if a man is without knowledge now, though he still

retains the steps of the argument, though there is no change in

himself or in the fact and no lapse of memory on his part; then

neither had he knowledge previously. But the mediating link, not being

necessary, may have perished in the interval; and if so, though

there be no change in him nor in the fact, and though he will still

retain the steps of the argument, yet he has not knowledge, and

therefore had not knowledge before. Even if the link has not

actually perished but is liable to perish, this situation is

possible and might occur. But such a condition cannot be knowledge.

When the conclusion is necessary, the middle through which it was

proved may yet quite easily be non-necessary. You can in fact infer

the necessary even from a non-necessary premiss, just as you can infer

the true from the not true. On the other hand, when the middle is

necessary the conclusion must be necessary; just as true premisses

always give a true conclusion. Thus, if A is necessarily predicated of

B and B of C, then A is necessarily predicated of C. But when the

conclusion is nonnecessary the middle cannot be necessary either.

Thus: let A be predicated non-necessarily of C but necessarily of B,

and let B be a necessary predicate of C; then A too will be a

necessary predicate of C, which by hypothesis it is not.

To sum up, then: demonstrative knowledge must be knowledge of a

necessary nexus, and therefore must clearly be obtained through a

necessary middle term; otherwise its possessor will know neither the

cause nor the fact that his conclusion is a necessary connexion.

Either he will mistake the non-necessary for the necessary and believe

the necessity of the conclusion without knowing it, or else he will

not even believe it-in which case he will be equally ignorant, whether

he actually infers the mere fact through middle terms or the

reasoned fact and from immediate premisses.

Of accidents that are not essential according to our definition of

essential there is no demonstrative knowledge; for since an

accident, in the sense in which I here speak of it, may also not

inhere, it is impossible to prove its inherence as a necessary

conclusion. A difficulty, however, might be raised as to why in

dialectic, if the conclusion is not a necessary connexion, such and

such determinate premisses should be proposed in order to deal with

such and such determinate problems. Would not the result be the same

if one asked any questions whatever and then merely stated one's

conclusion? The solution is that determinate questions have to be put,

not because the replies to them affirm facts which necessitate facts

affirmed by the conclusion, but because these answers are propositions

which if the answerer affirm, he must affirm the conclusion and affirm

it with truth if they are true.

Since it is just those attributes within every genus which are

essential and possessed by their respective subjects as such that

are necessary it is clear that both the conclusions and the

premisses of demonstrations which produce scientific knowledge are

essential. For accidents are not necessary: and, further, since

accidents are not necessary one does not necessarily have reasoned

knowledge of a conclusion drawn from them (this is so even if the

accidental premisses are invariable but not essential, as in proofs

through signs; for though the conclusion be actually essential, one

will not know it as essential nor know its reason); but to have

reasoned knowledge of a conclusion is to know it through its cause. We

may conclude that the middle must be consequentially connected with

the minor, and the major with the middle.

It follows that we cannot in demonstrating pass from one genus to

another. We cannot, for instance, prove geometrical truths by

arithmetic. For there are three elements in demonstration: (1) what is

proved, the conclusion-an attribute inhering essentially in a genus;

(2) the axioms, i.e. axioms which are premisses of demonstration;

(3) the subject-genus whose attributes, i.e. essential properties, are

revealed by the demonstration. The axioms which are premisses of

demonstration may be identical in two or more sciences: but in the

case of two different genera such as arithmetic and geometry you

cannot apply arithmetical demonstration to the properties of

magnitudes unless the magnitudes in question are numbers. How in

certain cases transference is possible I will explain later.

Arithmetical demonstration and the other sciences likewise

possess, each of them, their own genera; so that if the

demonstration is to pass from one sphere to another, the genus must be

either absolutely or to some extent the same. If this is not so,

transference is clearly impossible, because the extreme and the middle

terms must be drawn from the same genus: otherwise, as predicated,

they will not be essential and will thus be accidents. That is why

it cannot be proved by geometry that opposites fall under one science,

nor even that the product of two cubes is a cube. Nor can the

theorem of any one science be demonstrated by means of another

science, unless these theorems are related as subordinate to

superior (e.g. as optical theorems to geometry or harmonic theorems to

arithmetic). Geometry again cannot prove of lines any property which

they do not possess qua lines, i.e. in virtue of the fundamental

truths of their peculiar genus: it cannot show, for example, that

the straight line is the most beautiful of lines or the contrary of

the circle; for these qualities do not belong to lines in virtue of

their peculiar genus, but through some property which it shares with

other genera.

It is also clear that if the premisses from which the syllogism

proceeds are commensurately universal, the conclusion of such i.e.

in the unqualified sense-must also be eternal. Therefore no

attribute can be demonstrated nor known by strictly scientific

knowledge to inhere in perishable things. The proof can only be

accidental, because the attribute's connexion with its perishable

subject is not commensurately universal but temporary and special.

If such a demonstration is made, one premiss must be perishable and

not commensurately universal (perishable because only if it is

perishable will the conclusion be perishable; not commensurately

universal, because the predicate will be predicable of some

instances of the subject and not of others); so that the conclusion

can only be that a fact is true at the moment-not commensurately and

universally. The same is true of definitions, since a definition is

either a primary premiss or a conclusion of a demonstration, or else

only differs from a demonstration in the order of its terms.

Demonstration and science of merely frequent occurrences-e.g. of

eclipse as happening to the moon-are, as such, clearly eternal:

whereas so far as they are not eternal they are not fully

commensurate. Other subjects too have properties attaching to them

in the same way as eclipse attaches to the moon.

It is clear that if the conclusion is to show an attribute

inhering as such, nothing can be demonstrated except from its

'appropriate' basic truths. Consequently a proof even from true,

indemonstrable, and immediate premisses does not constitute knowledge.

Such proofs are like Bryson's method of squaring the circle; for

they operate by taking as their middle a common character-a character,

therefore, which the subject may share with another-and consequently

they apply equally to subjects different in kind. They therefore

afford knowledge of an attribute only as inhering accidentally, not as

belonging to its subject as such: otherwise they would not have been

applicable to another genus.

Our knowledge of any attribute's connexion with a subject is

accidental unless we know that connexion through the middle term in

virtue of which it inheres, and as an inference from basic premisses

essential and 'appropriate' to the subject-unless we know, e.g. the

property of possessing angles equal to two right angles as belonging

to that subject in which it inheres essentially, and as inferred

from basic premisses essential and 'appropriate' to that subject: so

that if that middle term also belongs essentially to the minor, the

middle must belong to the same kind as the major and minor terms.

The only exceptions to this rule are such cases as theorems in

harmonics which are demonstrable by arithmetic. Such theorems are

proved by the same middle terms as arithmetical properties, but with a

qualification-the fact falls under a separate science (for the subject

genus is separate), but the reasoned fact concerns the superior

science, to which the attributes essentially belong. Thus, even

these apparent exceptions show that no attribute is strictly

demonstrable except from its 'appropriate' basic truths, which,

however, in the case of these sciences have the requisite identity

of character.

It is no less evident that the peculiar basic truths of each

inhering attribute are indemonstrable; for basic truths from which

they might be deduced would be basic truths of all that is, and the

science to which they belonged would possess universal sovereignty.

This is so because he knows better whose knowledge is deduced from

higher causes, for his knowledge is from prior premisses when it

derives from causes themselves uncaused: hence, if he knows better

than others or best of all, his knowledge would be science in a higher

or the highest degree. But, as things are, demonstration is not

transferable to another genus, with such exceptions as we have

mentioned of the application of geometrical demonstrations to theorems

in mechanics or optics, or of arithmetical demonstrations to those

of harmonics.

It is hard to be sure whether one knows or not; for it is hard to be

sure whether one's knowledge is based on the basic truths

appropriate to each attribute-the differentia of true knowledge. We

think we have scientific knowledge if we have reasoned from true and

primary premisses. But that is not so: the conclusion must be

homogeneous with the basic facts of the science.

I call the basic truths of every genus those clements in it the

existence of which cannot be proved. As regards both these primary

truths and the attributes dependent on them the meaning of the name is

assumed. The fact of their existence as regards the primary truths

must be assumed; but it has to be proved of the remainder, the

attributes. Thus we assume the meaning alike of unity, straight, and

triangular; but while as regards unity and magnitude we assume also

the fact of their existence, in the case of the remainder proof is

required.

Of the basic truths used in the demonstrative sciences some are

peculiar to each science, and some are common, but common only in

the sense of analogous, being of use only in so far as they fall

within the genus constituting the province of the science in question.

Peculiar truths are, e.g. the definitions of line and straight;

common truths are such as 'take equals from equals and equals remain'.

Only so much of these common truths is required as falls within the

genus in question: for a truth of this kind will have the same force

even if not used generally but applied by the geometer only to

magnitudes, or by the arithmetician only to numbers. Also peculiar

to a science are the subjects the existence as well as the meaning

of which it assumes, and the essential attributes of which it

investigates, e.g. in arithmetic units, in geometry points and

lines. Both the existence and the meaning of the subjects are

assumed by these sciences; but of their essential attributes only

the meaning is assumed. For example arithmetic assumes the meaning

of odd and even, square and cube, geometry that of incommensurable, or

of deflection or verging of lines, whereas the existence of these

attributes is demonstrated by means of the axioms and from previous

conclusions as premisses. Astronomy too proceeds in the same way.

For indeed every demonstrative science has three elements: (1) that

which it posits, the subject genus whose essential attributes it

examines; (2) the so-called axioms, which are primary premisses of its

demonstration; (3) the attributes, the meaning of which it assumes.

Yet some sciences may very well pass over some of these elements; e.g.

we might not expressly posit the existence of the genus if its

existence were obvious (for instance, the existence of hot and cold is

more evident than that of number); or we might omit to assume

expressly the meaning of the attributes if it were well understood. In

the way the meaning of axioms, such as 'Take equals from equals and

equals remain', is well known and so not expressly assumed.

Nevertheless in the nature of the case the essential elements of

demonstration are three: the subject, the attributes, and the basic

premisses.

That which expresses necessary self-grounded fact, and which we must

necessarily believe, is distinct both from the hypotheses of a science

and from illegitimate postulate-I say 'must believe', because all

syllogism, and therefore a fortiori demonstration, is addressed not to

the spoken word, but to the discourse within the soul, and though we

can always raise objections to the spoken word, to the inward

discourse we cannot always object. That which is capable of proof

but assumed by the teacher without proof is, if the pupil believes and

accepts it, hypothesis, though only in a limited sense hypothesis-that

is, relatively to the pupil; if the pupil has no opinion or a contrary

opinion on the matter, the same assumption is an illegitimate

postulate. Therein lies the distinction between hypothesis and

illegitimate postulate: the latter is the contrary of the pupil's

opinion, demonstrable, but assumed and used without demonstration.

The definition-viz. those which are not expressed as statements that

anything is or is not-are not hypotheses: but it is in the premisses

of a science that its hypotheses are contained. Definitions require

only to be understood, and this is not hypothesis-unless it be

contended that the pupil's hearing is also an hypothesis required by

the teacher. Hypotheses, on the contrary, postulate facts on the being

of which depends the being of the fact inferred. Nor are the

geometer's hypotheses false, as some have held, urging that one must

not employ falsehood and that the geometer is uttering falsehood in

stating that the line which he draws is a foot long or straight,

when it is actually neither. The truth is that the geometer does not

draw any conclusion from the being of the particular line of which

he speaks, but from what his diagrams symbolize. A further distinction

is that all hypotheses and illegitimate postulates are either

universal or particular, whereas a definition is neither.

So demonstration does not necessarily imply the being of Forms nor a

One beside a Many, but it does necessarily imply the possibility of

truly predicating one of many; since without this possibility we

cannot save the universal, and if the universal goes, the middle

term goes witb. it, and so demonstration becomes impossible. We

conclude, then, that there must be a single identical term

unequivocally predicable of a number of individuals.

The law that it is impossible to affirm and deny simultaneously

the same predicate of the same subject is not expressly posited by any

demonstration except when the conclusion also has to be expressed in

that form; in which case the proof lays down as its major premiss that

the major is truly affirmed of the middle but falsely denied. It makes

no difference, however, if we add to the middle, or again to the minor

term, the corresponding negative. For grant a minor term of which it

is true to predicate man-even if it be also true to predicate

not-man of it--still grant simply that man is animal and not

not-animal, and the conclusion follows: for it will still be true to

say that Callias--even if it be also true to say that

not-Callias--is animal and not not-animal. The reason is that the

major term is predicable not only of the middle, but of something

other than the middle as well, being of wider application; so that the

conclusion is not affected even if the middle is extended to cover the

original middle term and also what is not the original middle term.

The law that every predicate can be either truly affirmed or truly

denied of every subject is posited by such demonstration as uses

reductio ad impossibile, and then not always universally, but so far

as it is requisite; within the limits, that is, of the genus-the

genus, I mean (as I have already explained), to which the man of

science applies his demonstrations. In virtue of the common elements

of demonstration-I mean the common axioms which are used as

premisses of demonstration, not the subjects nor the attributes

demonstrated as belonging to them-all the sciences have communion with

one another, and in communion with them all is dialectic and any

science which might attempt a universal proof of axioms such as the

law of excluded middle, the law that the subtraction of equals from

equals leaves equal remainders, or other axioms of the same kind.

Dialectic has no definite sphere of this kind, not being confined to a

single genus. Otherwise its method would not be interrogative; for the

interrogative method is barred to the demonstrator, who cannot use the

opposite facts to prove the same nexus. This was shown in my work on

the syllogism.

If a syllogistic question is equivalent to a proposition embodying

one of the two sides of a contradiction, and if each science has its

peculiar propositions from which its peculiar conclusion is developed,

then there is such a thing as a distinctively scientific question, and

it is the interrogative form of the premisses from which the

'appropriate' conclusion of each science is developed. Hence it is

clear that not every question will be relevant to geometry, nor to

medicine, nor to any other science: only those questions will be

geometrical which form premisses for the proof of the theorems of

geometry or of any other science, such as optics, which uses the

same basic truths as geometry. Of the other sciences the like is true.

Of these questions the geometer is bound to give his account, using

the basic truths of geometry in conjunction with his previous

conclusions; of the basic truths the geometer, as such, is not bound

to give any account. The like is true of the other sciences. There

is a limit, then, to the questions which we may put to each man of

science; nor is each man of science bound to answer all inquiries on

each several subject, but only such as fall within the defined field

of his own science. If, then, in controversy with a geometer qua

geometer the disputant confines himself to geometry and proves

anything from geometrical premisses, he is clearly to be applauded; if

he goes outside these he will be at fault, and obviously cannot even

refute the geometer except accidentally. One should therefore not

discuss geometry among those who are not geometers, for in such a

company an unsound argument will pass unnoticed. This is

correspondingly true in the other sciences.

Since there are 'geometrical' questions, does it follow that there

are also distinctively 'ungeometrical' questions? Further, in each

special science-geometry for instance-what kind of error is it that

may vitiate questions, and yet not exclude them from that science?

Again, is the erroneous conclusion one constructed from premisses

opposite to the true premisses, or is it formal fallacy though drawn

from geometrical premisses? Or, perhaps, the erroneous conclusion is

due to the drawing of premisses from another science; e.g. in a

geometrical controversy a musical question is distinctively

ungeometrical, whereas the notion that parallels meet is in one

sense geometrical, being ungeometrical in a different fashion: the

reason being that 'ungeometrical', like 'unrhythmical', is

equivocal, meaning in the one case not geometry at all, in the other

bad geometry? It is this error, i.e. error based on premisses of

this kind-'of' the science but false-that is the contrary of

science. In mathematics the formal fallacy is not so common, because

it is the middle term in which the ambiguity lies, since the major

is predicated of the whole of the middle and the middle of the whole

of the minor (the predicate of course never has the prefix 'all'); and

in mathematics one can, so to speak, see these middle terms with an

intellectual vision, while in dialectic the ambiguity may escape

detection. E.g. 'Is every circle a figure?' A diagram shows that

this is so, but the minor premiss 'Are epics circles?' is shown by the

diagram to be false.

If a proof has an inductive minor premiss, one should not bring an

'objection' against it. For since every premiss must be applicable

to a number of cases (otherwise it will not be true in every instance,

which, since the syllogism proceeds from universals, it must be), then

assuredly the same is true of an 'objection'; since premisses and

'objections' are so far the same that anything which can be validly

advanced as an 'objection' must be such that it could take the form of

a premiss, either demonstrative or dialectical. On the other hand,

arguments formally illogical do sometimes occur through taking as

middles mere attributes of the major and minor terms. An instance of

this is Caeneus' proof that fire increases in geometrical

proportion: 'Fire', he argues, 'increases rapidly, and so does

geometrical proportion'. There is no syllogism so, but there is a

syllogism if the most rapidly increasing proportion is geometrical and

the most rapidly increasing proportion is attributable to fire in

its motion. Sometimes, no doubt, it is impossible to reason from

premisses predicating mere attributes: but sometimes it is possible,

though the possibility is overlooked. If false premisses could never

give true conclusions 'resolution' would be easy, for premisses and

conclusion would in that case inevitably reciprocate. I might then

argue thus: let A be an existing fact; let the existence of A imply

such and such facts actually known to me to exist, which we may call

B. I can now, since they reciprocate, infer A from B.

Reciprocation of premisses and conclusion is more frequent in

mathematics, because mathematics takes definitions, but never an

accident, for its premisses-a second characteristic distinguishing

mathematical reasoning from dialectical disputations.

A science expands not by the interposition of fresh middle terms,

but by the apposition of fresh extreme terms. E.g. A is predicated

of B, B of C, C of D, and so indefinitely. Or the expansion may be

lateral: e.g. one major A, may be proved of two minors, C and E.

Thus let A represent number-a number or number taken

indeterminately; B determinate odd number; C any particular odd

number. We can then predicate A of C. Next let D represent determinate

even number, and E even number. Then A is predicable of E.

Knowledge of the fact differs from knowledge of the reasoned fact.

To begin with, they differ within the same science and in two ways:

(1) when the premisses of the syllogism are not immediate (for then

the proximate cause is not contained in them-a necessary condition

of knowledge of the reasoned fact): (2) when the premisses are

immediate, but instead of the cause the better known of the two

reciprocals is taken as the middle; for of two reciprocally predicable

terms the one which is not the cause may quite easily be the better

known and so become the middle term of the demonstration. Thus (2) (a)

you might prove as follows that the planets are near because they do

not twinkle: let C be the planets, B not twinkling, A proximity.

Then B is predicable of C; for the planets do not twinkle. But A is

also predicable of B, since that which does not twinkle is near--we

must take this truth as having been reached by induction or

sense-perception. Therefore A is a necessary predicate of C; so that

we have demonstrated that the planets are near. This syllogism,

then, proves not the reasoned fact but only the fact; since they are

not near because they do not twinkle, but, because they are near, do

not twinkle. The major and middle of the proof, however, may be

reversed, and then the demonstration will be of the reasoned fact.

Thus: let C be the planets, B proximity, A not twinkling. Then B is an

attribute of C, and A-not twinkling-of B. Consequently A is predicable

of C, and the syllogism proves the reasoned fact, since its middle

term is the proximate cause. Another example is the inference that the

moon is spherical from its manner of waxing. Thus: since that which so

waxes is spherical, and since the moon so waxes, clearly the moon is

spherical. Put in this form, the syllogism turns out to be proof of

the fact, but if the middle and major be reversed it is proof of the

reasoned fact; since the moon is not spherical because it waxes in a

certain manner, but waxes in such a manner because it is spherical.

(Let C be the moon, B spherical, and A waxing.) Again (b), in cases

where the cause and the effect are not reciprocal and the effect is

the better known, the fact is demonstrated but not the reasoned

fact. This also occurs (1) when the middle falls outside the major and

minor, for here too the strict cause is not given, and so the

demonstration is of the fact, not of the reasoned fact. For example,

the question 'Why does not a wall breathe?' might be answered,

'Because it is not an animal'; but that answer would not give the

strict cause, because if not being an animal causes the absence of

respiration, then being an animal should be the cause of

respiration, according to the rule that if the negation of causes

the non-inherence of y, the affirmation of x causes the inherence of

y; e.g. if the disproportion of the hot and cold elements is the cause

of ill health, their proportion is the cause of health; and

conversely, if the assertion of x causes the inherence of y, the

negation of x must cause y's non-inherence. But in the case given this

consequence does not result; for not every animal breathes. A

syllogism with this kind of cause takes place in the second figure.

Thus: let A be animal, B respiration, C wall. Then A is predicable

of all B (for all that breathes is animal), but of no C; and

consequently B is predicable of no C; that is, the wall does not

breathe. Such causes are like far-fetched explanations, which

precisely consist in making the cause too remote, as in Anacharsis'

account of why the Scythians have no flute-players; namely because

they have no vines.

Thus, then, do the syllogism of the fact and the syllogism of the

reasoned fact differ within one science and according to the

position of the middle terms. But there is another way too in which

the fact and the reasoned fact differ, and that is when they are

investigated respectively by different sciences. This occurs in the

case of problems related to one another as subordinate and superior,

as when optical problems are subordinated to geometry, mechanical

problems to stereometry, harmonic problems to arithmetic, the data

of observation to astronomy. (Some of these sciences bear almost the

same name; e.g. mathematical and nautical astronomy, mathematical

and acoustical harmonics.) Here it is the business of the empirical

observers to know the fact, of the mathematicians to know the reasoned

fact; for the latter are in possession of the demonstrations giving

the causes, and are often ignorant of the fact: just as we have

often a clear insight into a universal, but through lack of

observation are ignorant of some of its particular instances. These

connexions have a perceptible existence though they are manifestations

of forms. For the mathematical sciences concern forms: they do not

demonstrate properties of a substratum, since, even though the

geometrical subjects are predicable as properties of a perceptible

substratum, it is not as thus predicable that the mathematician

demonstrates properties of them. As optics is related to geometry,

so another science is related to optics, namely the theory of the

rainbow. Here knowledge of the fact is within the province of the

natural philosopher, knowledge of the reasoned fact within that of the

optician, either qua optician or qua mathematical optician. Many

sciences not standing in this mutual relation enter into it at points;

e.g. medicine and geometry: it is the physician's business to know

that circular wounds heal more slowly, the geometer's to know the

reason why.

Of all the figures the most scientific is the first. Thus, it is the

vehicle of the demonstrations of all the mathematical sciences, such

as arithmetic, geometry, and optics, and practically all of all

sciences that investigate causes: for the syllogism of the reasoned

fact is either exclusively or generally speaking and in most cases

in this figure-a second proof that this figure is the most scientific;

for grasp of a reasoned conclusion is the primary condition of

knowledge. Thirdly, the first is the only figure which enables us to

pursue knowledge of the essence of a thing. In the second figure no

affirmative conclusion is possible, and knowledge of a thing's essence

must be affirmative; while in the third figure the conclusion can be

affirmative, but cannot be universal, and essence must have a

universal character: e.g. man is not two-footed animal in any

qualified sense, but universally. Finally, the first figure has no

need of the others, while it is by means of the first that the other

two figures are developed, and have their intervals closepacked

until immediate premisses are reached.

Clearly, therefore, the first figure is the primary condition of

knowledge.

Just as an attribute A may (as we saw) be atomically connected

with a subject B, so its disconnexion may be atomic. I call 'atomic'

connexions or disconnexions which involve no intermediate term;

since in that case the connexion or disconnexion will not be

mediated by something other than the terms themselves. It follows that

if either A or B, or both A and B, have a genus, their disconnexion

cannot be primary. Thus: let C be the genus of A. Then, if C is not

the genus of B-for A may well have a genus which is not the genus of

B-there will be a syllogism proving A's disconnexion from B thus:

all A is C,

no B is C,

therefore no B is A.

Or if it is B which has a genus D, we have

all B is D,

no D is A,

therefore no B is A, by syllogism;

and the proof will be similar if both A and B have a genus. That the

genus of A need not be the genus of B and vice versa, is shown by

the existence of mutually exclusive coordinate series of

predication. If no term in the series ACD...is predicable of any

term in the series BEF...,and if G-a term in the former series-is

the genus of A, clearly G will not be the genus of B; since, if it

were, the series would not be mutually exclusive. So also if B has a

genus, it will not be the genus of A. If, on the other hand, neither A

nor B has a genus and A does not inhere in B, this disconnexion must

be atomic. If there be a middle term, one or other of them is bound to

have a genus, for the syllogism will be either in the first or the

second figure. If it is in the first, B will have a genus-for the

premiss containing it must be affirmative: if in the second, either

A or B indifferently, since syllogism is possible if either is

contained in a negative premiss, but not if both premisses are

negative.

Hence it is clear that one thing may be atomically disconnected from

another, and we have stated when and how this is possible.

Ignorance-defined not as the negation of knowledge but as a positive

state of mind-is error produced by inference.

(1) Let us first consider propositions asserting a predicate's

immediate connexion with or disconnexion from a subject. Here, it is

true, positive error may befall one in alternative ways; for it may

arise where one directly believes a connexion or disconnexion as

well as where one's belief is acquired by inference. The error,

however, that consists in a direct belief is without complication; but

the error resulting from inference-which here concerns us-takes many

forms. Thus, let A be atomically disconnected from all B: then the

conclusion inferred through a middle term C, that all B is A, will

be a case of error produced by syllogism. Now, two cases are possible.

Either (a) both premisses, or (b) one premiss only, may be false.

(a) If neither A is an attribute of any C nor C of any B, whereas

the contrary was posited in both cases, both premisses will be

false. (C may quite well be so related to A and B that C is neither

subordinate to A nor a universal attribute of B: for B, since A was

said to be primarily disconnected from B, cannot have a genus, and A

need not necessarily be a universal attribute of all things.

Consequently both premisses may be false.) On the other hand, (b)

one of the premisses may be true, though not either indifferently

but only the major A-C since, B having no genus, the premiss C-B

will always be false, while A-C may be true. This is the case if,

for example, A is related atomically to both C and B; because when the

same term is related atomically to more terms than one, neither of

those terms will belong to the other. It is, of course, equally the

case if A-C is not atomic.

Error of attribution, then, occurs through these causes and in

this form only-for we found that no syllogism of universal attribution

was possible in any figure but the first. On the other hand, an

error of non-attribution may occur either in the first or in the

second figure. Let us therefore first explain the various forms it

takes in the first figure and the character of the premisses in each

case.

atomically connected with both C and B, if it be then assumed that

no C is and all B is C, both premisses are false.

(d) It is also possible when one is false. This may be either

premiss indifferently. A-C may be true, C-B false-A-C true because A

is not an attribute of all things, C-B false because C, which never

has the attribute A, cannot be an attribute of B; for if C-B were

true, the premiss A-C would no longer be true, and besides if both

premisses were true, the conclusion would be true. Or again, C-B may

be true and A-C false; e.g. if both C and A contain B as genera, one

of them must be subordinate to the other, so that if the premiss takes

the form No C is A, it will be false. This makes it clear that whether

either or both premisses are false, the conclusion will equally be

false.

In the second figure the premisses cannot both be wholly false;

for if all B is A, no middle term can be with truth universally

affirmed of one extreme and universally denied of the other: but

premisses in which the middle is affirmed of one extreme and denied of

the other are the necessary condition if one is to get a valid

inference at all. Therefore if, taken in this way, they are wholly

false, their contraries conversely should be wholly true. But this

is impossible. On the other hand, there is nothing to prevent both

premisses being partially false; e.g. if actually some A is C and some

B is C, then if it is premised that all A is C and no B is C, both

premisses are false, yet partially, not wholly, false. The same is

true if the major is made negative instead of the minor. Or one

premiss may be wholly false, and it may be either of them. Thus,

supposing that actually an attribute of all A must also be an

attribute of all B, then if C is yet taken to be a universal attribute

of all but universally non-attributable to B, C-A will be true but C-B

false. Again, actually that which is an attribute of no B will not

be an attribute of all A either; for if it be an attribute of all A,

it will also be an attribute of all B, which is contrary to

supposition; but if C be nevertheless assumed to be a universal

attribute of A, but an attribute of no B, then the premiss C-B is true

but the major is false. The case is similar if the major is made the

negative premiss. For in fact what is an attribute of no A will not be

an attribute of any B either; and if it be yet assumed that C is

universally non-attributable to A, but a universal attribute of B, the

premiss C-A is true but the minor wholly false. Again, in fact it is

false to assume that that which is an attribute of all B is an

attribute of no A, for if it be an attribute of all B, it must be an

attribute of some A. If then C is nevertheless assumed to be an

attribute of all B but of no A, C-B will be true but C-A false.

It is thus clear that in the case of atomic propositions erroneous

inference will be possible not only when both premisses are false

but also when only one is false.

In the case of attributes not atomically connected with or

disconnected from their subjects, (a) (i) as long as the false

conclusion is inferred through the 'appropriate' middle, only the

major and not both premisses can be false. By 'appropriate middle' I

mean the middle term through which the contradictory-i.e. the

true-conclusion is inferrible. Thus, let A be attributable to B

through a middle term C: then, since to produce a conclusion the

premiss C-B must be taken affirmatively, it is clear that this premiss

must always be true, for its quality is not changed. But the major A-C

is false, for it is by a change in the quality of A-C that the

conclusion becomes its contradictory-i.e. true. Similarly (ii) if

the middle is taken from another series of predication; e.g. suppose D

to be not only contained within A as a part within its whole but

also predicable of all B. Then the premiss D-B must remain

unchanged, but the quality of A-D must be changed; so that D-B is

always true, A-D always false. Such error is practically identical

with that which is inferred through the 'appropriate' middle. On the

other hand, (b) if the conclusion is not inferred through the

'appropriate' middle-(i) when the middle is subordinate to A but is

predicable of no B, both premisses must be false, because if there

is to be a conclusion both must be posited as asserting the contrary

of what is actually the fact, and so posited both become false: e.g.

suppose that actually all D is A but no B is D; then if these

premisses are changed in quality, a conclusion will follow and both of

the new premisses will be false. When, however, (ii) the middle D is

not subordinate to A, A-D will be true, D-B false-A-D true because A

was not subordinate to D, D-B false because if it had been true, the

conclusion too would have been true; but it is ex hypothesi false.

When the erroneous inference is in the second figure, both premisses

cannot be entirely false; since if B is subordinate to A, there can be

no middle predicable of all of one extreme and of none of the other,

as was stated before. One premiss, however, may be false, and it may

be either of them. Thus, if C is actually an attribute of both A and

B, but is assumed to be an attribute of A only and not of B, C-A

will be true, C-B false: or again if C be assumed to be attributable

to B but to no A, C-B will be true, C-A false.

We have stated when and through what kinds of premisses error will

result in cases where the erroneous conclusion is negative. If the

conclusion is affirmative, (a) (i) it may be inferred through the

'appropriate' middle term. In this case both premisses cannot be false

since, as we said before, C-B must remain unchanged if there is to

be a conclusion, and consequently A-C, the quality of which is

changed, will always be false. This is equally true if (ii) the middle

is taken from another series of predication, as was stated to be the

case also with regard to negative error; for D-B must remain

unchanged, while the quality of A-D must be converted, and the type of

error is the same as before.

(b) The middle may be inappropriate. Then (i) if D is subordinate to

A, A-D will be true, but D-B false; since A may quite well be

predicable of several terms no one of which can be subordinated to

another. If, however, (ii) D is not subordinate to A, obviously A-D,

since it is affirmed, will always be false, while D-B may be either

true or false; for A may very well be an attribute of no D, whereas

all B is D, e.g. no science is animal, all music is science. Equally

well A may be an attribute of no D, and D of no B. It emerges, then,

that if the middle term is not subordinate to the major, not only both

premisses but either singly may be false.

Thus we have made it clear how many varieties of erroneous inference

are liable to happen and through what kinds of premisses they occur,

in the case both of immediate and of demonstrable truths.

It is also clear that the loss of any one of the senses entails

the loss of a corresponding portion of knowledge, and that, since we

learn either by induction or by demonstration, this knowledge cannot

be acquired. Thus demonstration develops from universals, induction

from particulars; but since it is possible to familiarize the pupil

with even the so-called mathematical abstractions only through

induction-i.e. only because each subject genus possesses, in virtue of

a determinate mathematical character, certain properties which can

be treated as separate even though they do not exist in isolation-it

is consequently impossible to come to grasp universals except

through induction. But induction is impossible for those who have

not sense-perception. For it is sense-perception alone which is

adequate for grasping the particulars: they cannot be objects of

scientific knowledge, because neither can universals give us knowledge

of them without induction, nor can we get it through induction without

sense-perception.

Every syllogism is effected by means of three terms. One kind of

syllogism serves to prove that A inheres in C by showing that A

inheres in B and B in C; the other is negative and one of its

premisses asserts one term of another, while the other denies one term

of another. It is clear, then, that these are the fundamentals and

so-called hypotheses of syllogism. Assume them as they have been

stated, and proof is bound to follow-proof that A inheres in C through

B, and again that A inheres in B through some other middle term, and

similarly that B inheres in C. If our reasoning aims at gaining

credence and so is merely dialectical, it is obvious that we have only

to see that our inference is based on premisses as credible as

possible: so that if a middle term between A and B is credible

though not real, one can reason through it and complete a

dialectical syllogism. If, however, one is aiming at truth, one must

be guided by the real connexions of subjects and attributes. Thus:

since there are attributes which are predicated of a subject

essentially or naturally and not coincidentally-not, that is, in the

sense in which we say 'That white (thing) is a man', which is not

the same mode of predication as when we say 'The man is white': the

man is white not because he is something else but because he is man,

but the white is man because 'being white' coincides with 'humanity'

within one substratum-therefore there are terms such as are

naturally subjects of predicates. Suppose, then, C such a term not

itself attributable to anything else as to a subject, but the

proximate subject of the attribute B--i.e. so that B-C is immediate;

suppose further E related immediately to F, and F to B. The first

question is, must this series terminate, or can it proceed to

infinity? The second question is as follows: Suppose nothing is

essentially predicated of A, but A is predicated primarily of H and of

no intermediate prior term, and suppose H similarly related to G and G

to B; then must this series also terminate, or can it too proceed to

infinity? There is this much difference between the questions: the

first is, is it possible to start from that which is not itself

attributable to anything else but is the subject of attributes, and

ascend to infinity? The second is the problem whether one can start

from that which is a predicate but not itself a subject of predicates,

and descend to infinity? A third question is, if the extreme terms are

fixed, can there be an infinity of middles? I mean this: suppose for

example that A inheres in C and B is intermediate between them, but

between B and A there are other middles, and between these again fresh

middles; can these proceed to infinity or can they not? This is the

equivalent of inquiring, do demonstrations proceed to infinity, i.e.

is everything demonstrable? Or do ultimate subject and primary

attribute limit one another?

I hold that the same questions arise with regard to negative

conclusions and premisses: viz. if A is attributable to no B, then

either this predication will be primary, or there will be an

intermediate term prior to B to which a is not attributable-G, let

us say, which is attributable to all B-and there may still be

another term H prior to G, which is attributable to all G. The same

questions arise, I say, because in these cases too either the series

of prior terms to which a is not attributable is infinite or it

terminates.

One cannot ask the same questions in the case of reciprocating

terms, since when subject and predicate are convertible there is

neither primary nor ultimate subject, seeing that all the

reciprocals qua subjects stand in the same relation to one another,

whether we say that the subject has an infinity of attributes or

that both subjects and attributes-and we raised the question in both

cases-are infinite in number. These questions then cannot be

asked-unless, indeed, the terms can reciprocate by two different

modes, by accidental predication in one relation and natural

predication in the other.

Now, it is clear that if the predications terminate in both the

upward and the downward direction (by 'upward' I mean the ascent to

the more universal, by 'downward' the descent to the more particular),

the middle terms cannot be infinite in number. For suppose that A is

predicated of F, and that the intermediates-call them BB'B"...-are

infinite, then clearly you might descend from and find one term

predicated of another ad infinitum, since you have an infinity of

terms between you and F; and equally, if you ascend from F, there

are infinite terms between you and A. It follows that if these

processes are impossible there cannot be an infinity of

intermediates between A and F. Nor is it of any effect to urge that

some terms of the series AB...F are contiguous so as to exclude

intermediates, while others cannot be taken into the argument at

all: whichever terms of the series B...I take, the number of

intermediates in the direction either of A or of F must be finite or

infinite: where the infinite series starts, whether from the first

term or from a later one, is of no moment, for the succeeding terms in

any case are infinite in number.

Further, if in affirmative demonstration the series terminates in

both directions, clearly it will terminate too in negative

demonstration. Let us assume that we cannot proceed to infinity either

by ascending from the ultimate term (by 'ultimate term' I mean a

term such as was, not itself attributable to a subject but itself

the subject of attributes), or by descending towards an ultimate

from the primary term (by 'primary term' I mean a term predicable of a

subject but not itself a subject). If this assumption is justified,

the series will also terminate in the case of negation. For a negative

conclusion can be proved in all three figures. In the first figure

it is proved thus: no B is A, all C is B. In packing the interval

B-C we must reach immediate propositions--as is always the case with

the minor premiss--since B-C is affirmative. As regards the other

premiss it is plain that if the major term is denied of a term D prior

to B, D will have to be predicable of all B, and if the major is

denied of yet another term prior to D, this term must be predicable of

all D. Consequently, since the ascending series is finite, the descent

will also terminate and there will be a subject of which A is

primarily non-predicable. In the second figure the syllogism is, all A

is B, no C is B,..no C is A. If proof of this is required, plainly

it may be shown either in the first figure as above, in the second

as here, or in the third. The first figure has been discussed, and

we will proceed to display the second, proof by which will be as

follows: all B is D, no C is D..., since it is required that B

should be a subject of which a predicate is affirmed. Next, since D is

to be proved not to belong to C, then D has a further predicate

which is denied of C. Therefore, since the succession of predicates

affirmed of an ever higher universal terminates, the succession of

predicates denied terminates too.

The third figure shows it as follows: all B is A, some B is not C.

Therefore some A is not C. This premiss, i.e. C-B, will be proved

either in the same figure or in one of the two figures discussed

above. In the first and second figures the series terminates. If we

use the third figure, we shall take as premisses, all E is B, some E

is not C, and this premiss again will be proved by a similar

prosyllogism. But since it is assumed that the series of descending

subjects also terminates, plainly the series of more universal

non-predicables will terminate also. Even supposing that the proof

is not confined to one method, but employs them all and is now in

the first figure, now in the second or third-even so the regress

will terminate, for the methods are finite in number, and if finite

things are combined in a finite number of ways, the result must be

finite.

Thus it is plain that the regress of middles terminates in the

case of negative demonstration, if it does so also in the case of

affirmative demonstration. That in fact the regress terminates in both

these cases may be made clear by the following dialectical

considerations.

In the case of predicates constituting the essential nature of a

thing, it clearly terminates, seeing that if definition is possible,

or in other words, if essential form is knowable, and an infinite

series cannot be traversed, predicates constituting a thing's

essential nature must be finite in number. But as regards predicates

generally we have the following prefatory remarks to make. (1) We

can affirm without falsehood 'the white (thing) is walking', and

that big (thing) is a log'; or again, 'the log is big', and 'the man

walks'. But the affirmation differs in the two cases. When I affirm

'the white is a log', I mean that something which happens to be

white is a log-not that white is the substratum in which log

inheres, for it was not qua white or qua a species of white that the

white (thing) came to be a log, and the white (thing) is

consequently not a log except incidentally. On the other hand, when

I affirm 'the log is white', I do not mean that something else,

which happens also to be a log, is white (as I should if I said 'the

musician is white,' which would mean 'the man who happens also to be a

musician is white'); on the contrary, log is here the substratum-the

substratum which actually came to be white, and did so qua wood or qua

a species of wood and qua nothing else.

If we must lay down a rule, let us entitle the latter kind of

statement predication, and the former not predication at all, or not

strict but accidental predication. 'White' and 'log' will thus serve

as types respectively of predicate and subject.

We shall assume, then, that the predicate is invariably predicated

strictly and not accidentally of the subject, for on such

predication demonstrations depend for their force. It follows from

this that when a single attribute is predicated of a single subject,

the predicate must affirm of the subject either some element

constituting its essential nature, or that it is in some way

qualified, quantified, essentially related, active, passive, placed,

or dated.

(2) Predicates which signify substance signify that the subject is

identical with the predicate or with a species of the predicate.

Predicates not signifying substance which are predicated of a

subject not identical with themselves or with a species of

themselves are accidental or coincidental; e.g. white is a

coincident of man, seeing that man is not identical with white or a

species of white, but rather with animal, since man is identical

with a species of animal. These predicates which do not signify

substance must be predicates of some other subject, and nothing can be

white which is not also other than white. The Forms we can dispense

with, for they are mere sound without sense; and even if there are

such things, they are not relevant to our discussion, since

demonstrations are concerned with predicates such as we have defined.

(3) If A is a quality of B, B cannot be a quality of A-a quality

of a quality. Therefore A and B cannot be predicated reciprocally of

one another in strict predication: they can be affirmed without

falsehood of one another, but not genuinely predicated of each

other. For one alternative is that they should be substantially

predicated of one another, i.e. B would become the genus or

differentia of A-the predicate now become subject. But it has been

shown that in these substantial predications neither the ascending

predicates nor the descending subjects form an infinite series; e.g.

neither the series, man is biped, biped is animal, &c., nor the series

predicating animal of man, man of Callias, Callias of a further.

subject as an element of its essential nature, is infinite. For all

such substance is definable, and an infinite series cannot be

traversed in thought: consequently neither the ascent nor the

descent is infinite, since a substance whose predicates were

infinite would not be definable. Hence they will not be predicated

each as the genus of the other; for this would equate a genus with one

of its own species. Nor (the other alternative) can a quale be

reciprocally predicated of a quale, nor any term belonging to an

adjectival category of another such term, except by accidental

predication; for all such predicates are coincidents and are

predicated of substances. On the other hand-in proof of the

impossibility of an infinite ascending series-every predication

displays the subject as somehow qualified or quantified or as

characterized under one of the other adjectival categories, or else is

an element in its substantial nature: these latter are limited in

number, and the number of the widest kinds under which predications

fall is also limited, for every predication must exhibit its subject

as somehow qualified, quantified, essentially related, acting or

suffering, or in some place or at some time.

I assume first that predication implies a single subject and a

single attribute, and secondly that predicates which are not

substantial are not predicated of one another. We assume this

because such predicates are all coincidents, and though some are

essential coincidents, others of a different type, yet we maintain

that all of them alike are predicated of some substratum and that a

coincident is never a substratum-since we do not class as a coincident

anything which does not owe its designation to its being something

other than itself, but always hold that any coincident is predicated

of some substratum other than itself, and that another group of

coincidents may have a different substratum. Subject to these

assumptions then, neither the ascending nor the descending series of

predication in which a single attribute is predicated of a single

subject is infinite. For the subjects of which coincidents are

predicated are as many as the constitutive elements of each individual

substance, and these we have seen are not infinite in number, while in

the ascending series are contained those constitutive elements with

their coincidents-both of which are finite. We conclude that there

is a given subject (D) of which some attribute (C) is primarily

predicable; that there must be an attribute (B) primarily predicable

of the first attribute, and that the series must end with a term (A)

not predicable of any term prior to the last subject of which it was

predicated (B), and of which no term prior to it is predicable.

The argument we have given is one of the so-called proofs; an

alternative proof follows. Predicates so related to their subjects

that there are other predicates prior to them predicable of those

subjects are demonstrable; but of demonstrable propositions one cannot

have something better than knowledge, nor can one know them without

demonstration. Secondly, if a consequent is only known through an

antecedent (viz. premisses prior to it) and we neither know this

antecedent nor have something better than knowledge of it, then we

shall not have scientific knowledge of the consequent. Therefore, if

it is possible through demonstration to know anything without

qualification and not merely as dependent on the acceptance of certain

premisses-i.e. hypothetically-the series of intermediate

predications must terminate. If it does not terminate, and beyond

any predicate taken as higher than another there remains another still

higher, then every predicate is demonstrable. Consequently, since

these demonstrable predicates are infinite in number and therefore

cannot be traversed, we shall not know them by demonstration. If,

therefore, we have not something better than knowledge of them, we

cannot through demonstration have unqualified but only hypothetical

science of anything.

As dialectical proofs of our contention these may carry

conviction, but an analytic process will show more briefly that

neither the ascent nor the descent of predication can be infinite in

the demonstrative sciences which are the object of our

investigation. Demonstration proves the inherence of essential

attributes in things. Now attributes may be essential for two reasons:

either because they are elements in the essential nature of their

subjects, or because their subjects are elements in their essential

nature. An example of the latter is odd as an attribute of

number-though it is number's attribute, yet number itself is an

element in the definition of odd; of the former, multiplicity or the

indivisible, which are elements in the definition of number. In

neither kind of attribution can the terms be infinite. They are not

infinite where each is related to the term below it as odd is to

number, for this would mean the inherence in odd of another

attribute of odd in whose nature odd was an essential element: but

then number will be an ultimate subject of the whole infinite chain of

attributes, and be an element in the definition of each of them.

Hence, since an infinity of attributes such as contain their subject

in their definition cannot inhere in a single thing, the ascending

series is equally finite. Note, moreover, that all such attributes

must so inhere in the ultimate subject-e.g. its attributes in number

and number in them-as to be commensurate with the subject and not of

wider extent. Attributes which are essential elements in the nature of

their subjects are equally finite: otherwise definition would be

impossible. Hence, if all the attributes predicated are essential

and these cannot be infinite, the ascending series will terminate, and

consequently the descending series too.

If this is so, it follows that the intermediates between any two

terms are also always limited in number. An immediately obvious

consequence of this is that demonstrations necessarily involve basic

truths, and that the contention of some-referred to at the outset-that

all truths are demonstrable is mistaken. For if there are basic

truths, (a) not all truths are demonstrable, and (b) an infinite

regress is impossible; since if either (a) or (b) were not a fact,

it would mean that no interval was immediate and indivisible, but that

all intervals were divisible. This is true because a conclusion is

demonstrated by the interposition, not the apposition, of a fresh

term. If such interposition could continue to infinity there might

be an infinite number of terms between any two terms; but this is

impossible if both the ascending and descending series of

predication terminate; and of this fact, which before was shown

dialectically, analytic proof has now been given.

It is an evident corollary of these conclusions that if the same

attribute A inheres in two terms C and D predicable either not at all,

or not of all instances, of one another, it does not always belong

to them in virtue of a common middle term. Isosceles and scalene

possess the attribute of having their angles equal to two right angles

in virtue of a common middle; for they possess it in so far as they

are both a certain kind of figure, and not in so far as they differ

from one another. But this is not always the case: for, were it so, if

we take B as the common middle in virtue of which A inheres in C and

D, clearly B would inhere in C and D through a second common middle,

and this in turn would inhere in C and D through a third, so that

between two terms an infinity of intermediates would fall-an

impossibility. Thus it need not always be in virtue of a common middle

term that a single attribute inheres in several subjects, since

there must be immediate intervals. Yet if the attribute to be proved

common to two subjects is to be one of their essential attributes, the

middle terms involved must be within one subject genus and be

derived from the same group of immediate premisses; for we have seen

that processes of proof cannot pass from one genus to another.

It is also clear that when A inheres in B, this can be

demonstrated if there is a middle term. Further, the 'elements' of

such a conclusion are the premisses containing the middle in question,

and they are identical in number with the middle terms, seeing that

the immediate propositions-or at least such immediate propositions

as are universal-are the 'elements'. If, on the other hand, there is

no middle term, demonstration ceases to be possible: we are on the way

to the basic truths. Similarly if A does not inhere in B, this can

be demonstrated if there is a middle term or a term prior to B in

which A does not inhere: otherwise there is no demonstration and a

basic truth is reached. There are, moreover, as many 'elements' of the

demonstrated conclusion as there are middle terms, since it is

propositions containing these middle terms that are the basic

premisses on which the demonstration rests; and as there are some

indemonstrable basic truths asserting that 'this is that' or that

'this inheres in that', so there are others denying that 'this is

that' or that 'this inheres in that'-in fact some basic truths will

affirm and some will deny being.

When we are to prove a conclusion, we must take a primary

essential predicate-suppose it C-of the subject B, and then suppose

A similarly predicable of C. If we proceed in this manner, no

proposition or attribute which falls beyond A is admitted in the

proof: the interval is constantly condensed until subject and

predicate become indivisible, i.e. one. We have our unit when the

premiss becomes immediate, since the immediate premiss alone is a

single premiss in the unqualified sense of 'single'. And as in other

spheres the basic element is simple but not identical in all-in a

system of weight it is the mina, in music the quarter-tone, and so

on--so in syllogism the unit is an immediate premiss, and in the

knowledge that demonstration gives it is an intuition. In

syllogisms, then, which prove the inherence of an attribute, nothing

falls outside the major term. In the case of negative syllogisms on

the other hand, (1) in the first figure nothing falls outside the

major term whose inherence is in question; e.g. to prove through a

middle C that A does not inhere in B the premisses required are, all B

is C, no C is A. Then if it has to be proved that no C is A, a

middle must be found between and C; and this procedure will never

vary.

(2) If we have to show that E is not D by means of the premisses,

all D is C; no E, or not all E, is C; then the middle will never

fall beyond E, and E is the subject of which D is to be denied in

the conclusion.

(3) In the third figure the middle will never fall beyond the limits

of the subject and the attribute denied of it.

Since demonstrations may be either commensurately universal or

particular, and either affirmative or negative; the question arises,

which form is the better? And the same question may be put in regard

to so-called 'direct' demonstration and reductio ad impossibile. Let

us first examine the commensurately universal and the particular

forms, and when we have cleared up this problem proceed to discuss

'direct' demonstration and reductio ad impossibile.

The following considerations might lead some minds to prefer

particular demonstration.

(1) The superior demonstration is the demonstration which gives us

greater knowledge (for this is the ideal of demonstration), and we

have greater knowledge of a particular individual when we know it in

itself than when we know it through something else; e.g. we know

Coriscus the musician better when we know that Coriscus is musical

than when we know only that man is musical, and a like argument

holds in all other cases. But commensurately universal

demonstration, instead of proving that the subject itself actually

is x, proves only that something else is x- e.g. in attempting to

prove that isosceles is x, it proves not that isosceles but only that

triangle is x- whereas particular demonstration proves that the

subject itself is x. The demonstration, then, that a subject, as such,

possesses an attribute is superior. If this is so, and if the

particular rather than the commensurately universal forms

demonstrates, particular demonstration is superior.

(2) The universal has not a separate being over against groups of

singulars. Demonstration nevertheless creates the opinion that its

function is conditioned by something like this-some separate entity

belonging to the real world; that, for instance, of triangle or of

figure or number, over against particular triangles, figures, and

numbers. But demonstration which touches the real and will not mislead

is superior to that which moves among unrealities and is delusory. Now

commensurately universal demonstration is of the latter kind: if we

engage in it we find ourselves reasoning after a fashion well

illustrated by the argument that the proportionate is what answers

to the definition of some entity which is neither line, number, solid,

nor plane, but a proportionate apart from all these. Since, then, such

a proof is characteristically commensurate and universal, and less

touches reality than does particular demonstration, and creates a

false opinion, it will follow that commensurate and universal is

inferior to particular demonstration.

We may retort thus. (1) The first argument applies no more to

commensurate and universal than to particular demonstration. If

equality to two right angles is attributable to its subject not qua

isosceles but qua triangle, he who knows that isosceles possesses that

attribute knows the subject as qua itself possessing the attribute, to

a less degree than he who knows that triangle has that attribute. To

sum up the whole matter: if a subject is proved to possess qua

triangle an attribute which it does not in fact possess qua

triangle, that is not demonstration: but if it does possess it qua

triangle the rule applies that the greater knowledge is his who

knows the subject as possessing its attribute qua that in virtue of

which it actually does possess it. Since, then, triangle is the

wider term, and there is one identical definition of triangle-i.e. the

term is not equivocal-and since equality to two right angles belongs

to all triangles, it is isosceles qua triangle and not triangle qua

isosceles which has its angles so related. It follows that he who

knows a connexion universally has greater knowledge of it as it in

fact is than he who knows the particular; and the inference is that

commensurate and universal is superior to particular demonstration.

(2) If there is a single identical definition i.e. if the

commensurate universal is unequivocal-then the universal will

possess being not less but more than some of the particulars, inasmuch

as it is universals which comprise the imperishable, particulars

that tend to perish.

(3) Because the universal has a single meaning, we are not therefore

compelled to suppose that in these examples it has being as a

substance apart from its particulars-any more than we need make a

similar supposition in the other cases of unequivocal universal

predication, viz. where the predicate signifies not substance but

quality, essential relatedness, or action. If such a supposition is

entertained, the blame rests not with the demonstration but with the

hearer.

(4) Demonstration is syllogism that proves the cause, i.e. the

reasoned fact, and it is rather the commensurate universal than the

particular which is causative (as may be shown thus: that which

possesses an attribute through its own essential nature is itself

the cause of the inherence, and the commensurate universal is primary;

hence the commensurate universal is the cause). Consequently

commensurately universal demonstration is superior as more

especially proving the cause, that is the reasoned fact.

(5) Our search for the reason ceases, and we think that we know,

when the coming to be or existence of the fact before us is not due to

the coming to be or existence of some other fact, for the last step of

a search thus conducted is eo ipso the end and limit of the problem.

Thus: 'Why did he come?' 'To get the money-wherewith to pay a

debt-that he might thereby do what was right.' When in this regress we

can no longer find an efficient or final cause, we regard the last

step of it as the end of the coming-or being or coming to be-and we

regard ourselves as then only having full knowledge of the reason

why he came.

If, then, all causes and reasons are alike in this respect, and if

this is the means to full knowledge in the case of final causes such

as we have exemplified, it follows that in the case of the other

causes also full knowledge is attained when an attribute no longer

inheres because of something else. Thus, when we learn that exterior

angles are equal to four right angles because they are the exterior

angles of an isosceles, there still remains the question 'Why has

isosceles this attribute?' and its answer 'Because it is a triangle,

and a triangle has it because a triangle is a rectilinear figure.'

If rectilinear figure possesses the property for no further reason, at

this point we have full knowledge-but at this point our knowledge

has become commensurately universal, and so we conclude that

commensurately universal demonstration is superior.

(6) The more demonstration becomes particular the more it sinks into

an indeterminate manifold, while universal demonstration tends to

the simple and determinate. But objects so far as they are an

indeterminate manifold are unintelligible, so far as they are

determinate, intelligible: they are therefore intelligible rather in

so far as they are universal than in so far as they are particular.

From this it follows that universals are more demonstrable: but

since relative and correlative increase concomitantly, of the more

demonstrable there will be fuller demonstration. Hence the

commensurate and universal form, being more truly demonstration, is

the superior.

(7) Demonstration which teaches two things is preferable to

demonstration which teaches only one. He who possesses

commensurately universal demonstration knows the particular as well,

but he who possesses particular demonstration does not know the

universal. So that this is an additional reason for preferring

commensurately universal demonstration. And there is yet this

further argument:

(8) Proof becomes more and more proof of the commensurate

universal as its middle term approaches nearer to the basic truth, and

nothing is so near as the immediate premiss which is itself the

basic truth. If, then, proof from the basic truth is more accurate

than proof not so derived, demonstration which depends more closely on

it is more accurate than demonstration which is less closely

dependent. But commensurately universal demonstration is characterized

by this closer dependence, and is therefore superior. Thus, if A had

to be proved to inhere in D, and the middles were B and C, B being the

higher term would render the demonstration which it mediated the

more universal.

Some of these arguments, however, are dialectical. The clearest

indication of the precedence of commensurately universal demonstration

is as follows: if of two propositions, a prior and a posterior, we

have a grasp of the prior, we have a kind of knowledge-a potential

grasp-of the posterior as well. For example, if one knows that the

angles of all triangles are equal to two right angles, one knows in

a sense-potentially-that the isosceles' angles also are equal to two

right angles, even if one does not know that the isosceles is a

triangle; but to grasp this posterior proposition is by no means to

know the commensurate universal either potentially or actually.

Moreover, commensurately universal demonstration is through and

through intelligible; particular demonstration issues in

sense-perception.

The preceding arguments constitute our defence of the superiority of

commensurately universal to particular demonstration. That affirmative

demonstration excels negative may be shown as follows.

(1) We may assume the superiority ceteris paribus of the

demonstration which derives from fewer postulates or hypotheses-in

short from fewer premisses; for, given that all these are equally well

known, where they are fewer knowledge will be more speedily

acquired, and that is a desideratum. The argument implied in our

contention that demonstration from fewer assumptions is superior may

be set out in universal form as follows. Assuming that in both cases

alike the middle terms are known, and that middles which are prior are

better known than such as are posterior, we may suppose two

demonstrations of the inherence of A in E, the one proving it

through the middles B, C and D, the other through F and G. Then A-D is

known to the same degree as A-E (in the second proof), but A-D is

better known than and prior to A-E (in the first proof); since A-E

is proved through A-D, and the ground is more certain than the

conclusion.

Hence demonstration by fewer premisses is ceteris paribus

superior. Now both affirmative and negative demonstration operate

through three terms and two premisses, but whereas the former

assumes only that something is, the latter assumes both that something

is and that something else is not, and thus operating through more

kinds of premiss is inferior.

(2) It has been proved that no conclusion follows if both

premisses are negative, but that one must be negative, the other

affirmative. So we are compelled to lay down the following

additional rule: as the demonstration expands, the affirmative

premisses must increase in number, but there cannot be more than one

negative premiss in each complete proof. Thus, suppose no B is A,

and all C is B. Then if both the premisses are to be again expanded, a

middle must be interposed. Let us interpose D between A and B, and E

between B and C. Then clearly E is affirmatively related to B and C,

while D is affirmatively related to B but negatively to A; for all B

is D, but there must be no D which is A. Thus there proves to be a

single negative premiss, A-D. In the further prosyllogisms too it is

the same, because in the terms of an affirmative syllogism the

middle is always related affirmatively to both extremes; in a negative

syllogism it must be negatively related only to one of them, and so

this negation comes to be a single negative premiss, the other

premisses being affirmative. If, then, that through which a truth is

proved is a better known and more certain truth, and if the negative

proposition is proved through the affirmative and not vice versa,

affirmative demonstration, being prior and better known and more

certain, will be superior.

(3) The basic truth of demonstrative syllogism is the universal

immediate premiss, and the universal premiss asserts in affirmative

demonstration and in negative denies: and the affirmative

proposition is prior to and better known than the negative (since

affirmation explains denial and is prior to denial, just as being is

prior to not-being). It follows that the basic premiss of

affirmative demonstration is superior to that of negative

demonstration, and the demonstration which uses superior basic

premisses is superior.

(4) Affirmative demonstration is more of the nature of a basic

form of proof, because it is a sine qua non of negative demonstration.

Since affirmative demonstration is superior to negative, it is

clearly superior also to reductio ad impossibile. We must first make

certain what is the difference between negative demonstration and

reductio ad impossibile. Let us suppose that no B is A, and that all C

is B: the conclusion necessarily follows that no C is A. If these

premisses are assumed, therefore, the negative demonstration that no C

is A is direct. Reductio ad impossibile, on the other hand, proceeds

as follows. Supposing we are to prove that does not inhere in B, we

have to assume that it does inhere, and further that B inheres in C,

with the resulting inference that A inheres in C. This we have to

suppose a known and admitted impossibility; and we then infer that A

cannot inhere in B. Thus if the inherence of B in C is not questioned,

A's inherence in B is impossible.

The order of the terms is the same in both proofs: they differ

according to which of the negative propositions is the better known,

the one denying A of B or the one denying A of C. When the falsity

of the conclusion is the better known, we use reductio ad

impossible; when the major premiss of the syllogism is the more

obvious, we use direct demonstration. All the same the proposition

denying A of B is, in the order of being, prior to that denying A of

C; for premisses are prior to the conclusion which follows from

them, and 'no C is A' is the conclusion, 'no B is A' one of its

premisses. For the destructive result of reductio ad impossibile is

not a proper conclusion, nor are its antecedents proper premisses.

On the contrary: the constituents of syllogism are premisses related

to one another as whole to part or part to whole, whereas the

premisses A-C and A-B are not thus related to one another. Now the

superior demonstration is that which proceeds from better known and

prior premisses, and while both these forms depend for credence on the

not-being of something, yet the source of the one is prior to that

of the other. Therefore negative demonstration will have an

unqualified superiority to reductio ad impossibile, and affirmative

demonstration, being superior to negative, will consequently be

superior also to reductio ad impossibile.

The science which is knowledge at once of the fact and of the

reasoned fact, not of the fact by itself without the reasoned fact, is

the more exact and the prior science.

A science such as arithmetic, which is not a science of properties

qua inhering in a substratum, is more exact than and prior to a

science like harmonics, which is a science of pr,operties inhering

in a substratum; and similarly a science like arithmetic, which is

constituted of fewer basic elements, is more exact than and prior to

geometry, which requires additional elements. What I mean by

'additional elements' is this: a unit is substance without position,

while a point is substance with position; the latter contains an

additional element.

A single science is one whose domain is a single genus, viz. all the

subjects constituted out of the primary entities of the genus-i.e. the

parts of this total subject-and their essential properties.

One science differs from another when their basic truths have

neither a common source nor are derived those of the one science

from those the other. This is verified when we reach the

indemonstrable premisses of a science, for they must be within one

genus with its conclusions: and this again is verified if the

conclusions proved by means of them fall within one genus-i.e. are

homogeneous.

One can have several demonstrations of the same connexion not only

by taking from the same series of predication middles which are

other than the immediately cohering term e.g. by taking C, D, and F

severally to prove A-B--but also by taking a middle from another

series. Thus let A be change, D alteration of a property, B feeling

pleasure, and G relaxation. We can then without falsehood predicate

D of B and A of D, for he who is pleased suffers alteration of a

property, and that which alters a property changes. Again, we can

predicate A of G without falsehood, and G of B; for to feel pleasure

is to relax, and to relax is to change. So the conclusion can be drawn

through middles which are different, i.e. not in the same series-yet

not so that neither of these middles is predicable of the other, for

they must both be attributable to some one subject.

A further point worth investigating is how many ways of proving

the same conclusion can be obtained by varying the figure,

There is no knowledge by demonstration of chance conjunctions; for

chance conjunctions exist neither by necessity nor as general

connexions but comprise what comes to be as something distinct from

these. Now demonstration is concerned only with one or other of

these two; for all reasoning proceeds from necessary or general

premisses, the conclusion being necessary if the premisses are

necessary and general if the premisses are general. Consequently, if

chance conjunctions are neither general nor necessary, they are not

demonstrable.

Scientific knowledge is not possible through the act of

perception. Even if perception as a faculty is of 'the such' and not

merely of a 'this somewhat', yet one must at any rate actually

perceive a 'this somewhat', and at a definite present place and

time: but that which is commensurately universal and true in all cases

one cannot perceive, since it is not 'this' and it is not 'now'; if it

were, it would not be commensurately universal-the term we apply to

what is always and everywhere. Seeing, therefore, that

demonstrations are commensurately universal and universals

imperceptible, we clearly cannot obtain scientific knowledge by the

act of perception: nay, it is obvious that even if it were possible to

perceive that a triangle has its angles equal to two right angles,

we should still be looking for a demonstration-we should not (as

some say) possess knowledge of it; for perception must be of a

particular, whereas scientific knowledge involves the recognition of

the commensurate universal. So if we were on the moon, and saw the

earth shutting out the sun's light, we should not know the cause of

the eclipse: we should perceive the present fact of the eclipse, but

not the reasoned fact at all, since the act of perception is not of

the commensurate universal. I do not, of course, deny that by watching

the frequent recurrence of this event we might, after tracking the

commensurate universal, possess a demonstration, for the

commensurate universal is elicited from the several groups of

singulars.

The commensurate universal is precious because it makes clear the

cause; so that in the case of facts like these which have a cause

other than themselves universal knowledge is more precious than

sense-perceptions and than intuition. (As regards primary truths there

is of course a different account to be given.) Hence it is clear

that knowledge of things demonstrable cannot be acquired by

perception, unless the term perception is applied to the possession of

scientific knowledge through demonstration. Nevertheless certain

points do arise with regard to connexions to be proved which are

referred for their explanation to a failure in sense-perception: there

are cases when an act of vision would terminate our inquiry, not

because in seeing we should be knowing, but because we should have

elicited the universal from seeing; if, for example, we saw the

pores in the glass and the light passing through, the reason of the

kindling would be clear to us because we should at the same time see

it in each instance and intuit that it must be so in all instances.

All syllogisms cannot have the same basic truths. This may be

shown first of all by the following dialectical considerations. (1)

Some syllogisms are true and some false: for though a true inference

is possible from false premisses, yet this occurs once only-I mean

if A for instance, is truly predicable of C, but B, the middle, is

false, both A-B and B-C being false; nevertheless, if middles are

taken to prove these premisses, they will be false because every

conclusion which is a falsehood has false premisses, while true

conclusions have true premisses, and false and true differ in kind.

Then again, (2) falsehoods are not all derived from a single identical

set of principles: there are falsehoods which are the contraries of

one another and cannot coexist, e.g. 'justice is injustice', and

'justice is cowardice'; 'man is horse', and 'man is ox'; 'the equal is

greater', and 'the equal is less.' From established principles we

may argue the case as follows, confining-ourselves therefore to true

conclusions. Not even all these are inferred from the same basic

truths; many of them in fact have basic truths which differ

generically and are not transferable; units, for instance, which are

without position, cannot take the place of points, which have

position. The transferred terms could only fit in as middle terms or

as major or minor terms, or else have some of the other terms

between them, others outside them.

Nor can any of the common axioms-such, I mean, as the law of

excluded middle-serve as premisses for the proof of all conclusions.

For the kinds of being are different, and some attributes attach to

quanta and some to qualia only; and proof is achieved by means of

the common axioms taken in conjunction with these several kinds and

their attributes.

Again, it is not true that the basic truths are much fewer than

the conclusions, for the basic truths are the premisses, and the

premisses are formed by the apposition of a fresh extreme term or

the interposition of a fresh middle. Moreover, the number of

conclusions is indefinite, though the number of middle terms is

finite; and lastly some of the basic truths are necessary, others

variable.

Looking at it in this way we see that, since the number of

conclusions is indefinite, the basic truths cannot be identical or

limited in number. If, on the other hand, identity is used in

another sense, and it is said, e.g. 'these and no other are the

fundamental truths of geometry, these the fundamentals of calculation,

these again of medicine'; would the statement mean anything except

that the sciences have basic truths? To call them identical because

they are self-identical is absurd, since everything can be

identified with everything in that sense of identity. Nor again can

the contention that all conclusions have the same basic truths mean

that from the mass of all possible premisses any conclusion may be

drawn. That would be exceedingly naive, for it is not the case in

the clearly evident mathematical sciences, nor is it possible in

analysis, since it is the immediate premisses which are the basic

truths, and a fresh conclusion is only formed by the addition of a new

immediate premiss: but if it be admitted that it is these primary

immediate premisses which are basic truths, each subject-genus will

provide one basic truth. If, however, it is not argued that from the

mass of all possible premisses any conclusion may be proved, nor yet

admitted that basic truths differ so as to be generically different

for each science, it remains to consider the possibility that, while

the basic truths of all knowledge are within one genus, special

premisses are required to prove special conclusions. But that this

cannot be the case has been shown by our proof that the basic truths

of things generically different themselves differ generically. For

fundamental truths are of two kinds, those which are premisses of

demonstration and the subject-genus; and though the former are common,

the latter-number, for instance, and magnitude-are peculiar.

Scientific knowledge and its object differ from opinion and the

object of opinion in that scientific knowledge is commensurately

universal and proceeds by necessary connexions, and that which is

necessary cannot be otherwise. So though there are things which are

true and real and yet can be otherwise, scientific knowledge clearly

does not concern them: if it did, things which can be otherwise

would be incapable of being otherwise. Nor are they any concern of

rational intuition-by rational intuition I mean an originative

source of scientific knowledge-nor of indemonstrable knowledge,

which is the grasping of the immediate premiss. Since then rational

intuition, science, and opinion, and what is revealed by these

terms, are the only things that can be 'true', it follows that it is

opinion that is concerned with that which may be true or false, and

can be otherwise: opinion in fact is the grasp of a premiss which is

immediate but not necessary. This view also fits the observed facts,

for opinion is unstable, and so is the kind of being we have described

as its object. Besides, when a man thinks a truth incapable of being

otherwise he always thinks that he knows it, never that he opines

it. He thinks that he opines when he thinks that a connexion, though

actually so, may quite easily be otherwise; for he believes that

such is the proper object of opinion, while the necessary is the

object of knowledge.

In what sense, then, can the same thing be the object of both

opinion and knowledge? And if any one chooses to maintain that all

that he knows he can also opine, why should not opinion be

knowledge? For he that knows and he that opines will follow the same

train of thought through the same middle terms until the immediate

premisses are reached; because it is possible to opine not only the

fact but also the reasoned fact, and the reason is the middle term; so

that, since the former knows, he that opines also has knowledge.

The truth perhaps is that if a man grasp truths that cannot be other

than they are, in the way in which he grasps the definitions through

which demonstrations take place, he will have not opinion but

knowledge: if on the other hand he apprehends these attributes as

inhering in their subjects, but not in virtue of the subjects'

substance and essential nature possesses opinion and not genuine

knowledge; and his opinion, if obtained through immediate premisses,

will be both of the fact and of the reasoned fact; if not so obtained,

of the fact alone. The object of opinion and knowledge is not quite

identical; it is only in a sense identical, just as the object of true

and false opinion is in a sense identical. The sense in which some

maintain that true and false opinion can have the same object leads

them to embrace many strange doctrines, particularly the doctrine that

what a man opines falsely he does not opine at all. There are really

many senses of 'identical', and in one sense the object of true and

false opinion can be the same, in another it cannot. Thus, to have a

true opinion that the diagonal is commensurate with the side would

be absurd: but because the diagonal with which they are both concerned

is the same, the two opinions have objects so far the same: on the

other hand, as regards their essential definable nature these

objects differ. The identity of the objects of knowledge and opinion

is similar. Knowledge is the apprehension of, e.g. the attribute

'animal' as incapable of being otherwise, opinion the apprehension

of 'animal' as capable of being otherwise-e.g. the apprehension that

animal is an element in the essential nature of man is knowledge;

the apprehension of animal as predicable of man but not as an

element in man's essential nature is opinion: man is the subject in

both judgements, but the mode of inherence differs.

This also shows that one cannot opine and know the same thing

simultaneously; for then one would apprehend the same thing as both

capable and incapable of being otherwise-an impossibility. Knowledge

and opinion of the same thing can co-exist in two different people

in the sense we have explained, but not simultaneously in the same

person. That would involve a man's simultaneously apprehending, e.g.

(1) that man is essentially animal-i.e. cannot be other than

animal-and (2) that man is not essentially animal, that is, we may

assume, may be other than animal.

Further consideration of modes of thinking and their distribution

under the heads of discursive thought, intuition, science, art,

practical wisdom, and metaphysical thinking, belongs rather partly

to natural science, partly to moral philosophy.

Quick wit is a faculty of hitting upon the middle term

instantaneously. It would be exemplified by a man who saw that the

moon has her bright side always turned towards the sun, and quickly

grasped the cause of this, namely that she borrows her light from him;

or observed somebody in conversation with a man of wealth and

divined that he was borrowing money, or that the friendship of these

people sprang from a common enmity. In all these instances he has seen

the major and minor terms and then grasped the causes, the middle

terms.

Let A represent 'bright side turned sunward', B 'lighted from the

sun', C the moon. Then B, 'lighted from the sun' is predicable of C,

the moon, and A, 'having her bright side towards the source of her

light', is predicable of B. So A is predicable of C through B.

Book II

THE kinds of question we ask are as many as the kinds of things

which we know. They are in fact four:-(1) whether the connexion of

an attribute with a thing is a fact, (2) what is the reason of the

connexion, (3) whether a thing exists, (4) What is the nature of the

thing. Thus, when our question concerns a complex of thing and

attribute and we ask whether the thing is thus or otherwise

qualified-whether, e.g. the sun suffers eclipse or not-then we are

asking as to the fact of a connexion. That our inquiry ceases with the

discovery that the sun does suffer eclipse is an indication of this;

and if we know from the start that the sun suffers eclipse, we do

not inquire whether it does so or not. On the other hand, when we know

the fact we ask the reason; as, for example, when we know that the sun

is being eclipsed and that an earthquake is in progress, it is the

reason of eclipse or earthquake into which we inquire.

Where a complex is concerned, then, those are the two questions we

ask; but for some objects of inquiry we have a different kind of

question to ask, such as whether there is or is not a centaur or a

God. (By 'is or is not' I mean 'is or is not, without further

qualification'; as opposed to 'is or is not [e.g.] white'.) On the

other hand, when we have ascertained the thing's existence, we inquire

as to its nature, asking, for instance, 'what, then, is God?' or 'what

is man?'.

These, then, are the four kinds of question we ask, and it is in the

answers to these questions that our knowledge consists.

Now when we ask whether a connexion is a fact, or whether a thing

without qualification is, we are really asking whether the connexion

or the thing has a 'middle'; and when we have ascertained either

that the connexion is a fact or that the thing is-i.e. ascertained

either the partial or the unqualified being of the thing-and are

proceeding to ask the reason of the connexion or the nature of the

thing, then we are asking what the 'middle' is.

(By distinguishing the fact of the connexion and the existence of

the thing as respectively the partial and the unqualified being of the

thing, I mean that if we ask 'does the moon suffer eclipse?', or 'does

the moon wax?', the question concerns a part of the thing's being; for

what we are asking in such questions is whether a thing is this or

that, i.e. has or has not this or that attribute: whereas, if we ask

whether the moon or night exists, the question concerns the

unqualified being of a thing.)

We conclude that in all our inquiries we are asking either whether

there is a 'middle' or what the 'middle' is: for the 'middle' here

is precisely the cause, and it is the cause that we seek in all our

inquiries. Thus, 'Does the moon suffer eclipse?' means 'Is there or is

there not a cause producing eclipse of the moon?', and when we have

learnt that there is, our next question is, 'What, then, is this

cause? for the cause through which a thing is-not is this or that,

i.e. has this or that attribute, but without qualification is-and

the cause through which it is-not is without qualification, but is

this or that as having some essential attribute or some accident-are

both alike the middle'. By that which is without qualification I

mean the subject, e.g. moon or earth or sun or triangle; by that which

a subject is (in the partial sense) I mean a property, e.g. eclipse,

equality or inequality, interposition or non-interposition. For in all

these examples it is clear that the nature of the thing and the reason

of the fact are identical: the question 'What is eclipse?' and its

answer 'The privation of the moon's light by the interposition of

the earth' are identical with the question 'What is the reason of

eclipse?' or 'Why does the moon suffer eclipse?' and the reply

'Because of the failure of light through the earth's shutting it out'.

Again, for 'What is a concord? A commensurate numerical ratio of a

high and a low note', we may substitute 'What ratio makes a high and a

low note concordant? Their relation according to a commensurate

numerical ratio.' 'Are the high and the low note concordant?' is

equivalent to 'Is their ratio commensurate?'; and when we find that it

is commensurate, we ask 'What, then, is their ratio?'.

Cases in which the 'middle' is sensible show that the object of

our inquiry is always the 'middle': we inquire, because we have not

perceived it, whether there is or is not a 'middle' causing, e.g. an

eclipse. On the other hand, if we were on the moon we should not be

inquiring either as to the fact or the reason, but both fact and

reason would be obvious simultaneously. For the act of perception

would have enabled us to know the universal too; since, the present

fact of an eclipse being evident, perception would then at the same

time give us the present fact of the earth's screening the sun's

light, and from this would arise the universal.

Thus, as we maintain, to know a thing's nature is to know the reason

why it is; and this is equally true of things in so far as they are

said without qualification to he as opposed to being possessed of some

attribute, and in so far as they are said to be possessed of some

attribute such as equal to right angles, or greater or less.

It is clear, then, that all questions are a search for a 'middle'.

Let us now state how essential nature is revealed and in what way it

can be reduced to demonstration; what definition is, and what things

are definable. And let us first discuss certain difficulties which

these questions raise, beginning what we have to say with a point most

intimately connected with our immediately preceding remarks, namely

the doubt that might be felt as to whether or not it is possible to

know the same thing in the same relation, both by definition and by

demonstration. It might, I mean, be urged that definition is held to

concern essential nature and is in every case universal and

affirmative; whereas, on the other hand, some conclusions are negative

and some are not universal; e.g. all in the second figure are

negative, none in the third are universal. And again, not even all

affirmative conclusions in the first figure are definable, e.g. 'every

triangle has its angles equal to two right angles'. An argument

proving this difference between demonstration and definition is that

to have scientific knowledge of the demonstrable is identical with

possessing a demonstration of it: hence if demonstration of such

conclusions as these is possible, there clearly cannot also be

definition of them. If there could, one might know such a conclusion

also in virtue of its definition without possessing the

demonstration of it; for there is nothing to stop our having the one

without the other.

Induction too will sufficiently convince us of this difference;

for never yet by defining anything-essential attribute or accident-did

we get knowledge of it. Again, if to define is to acquire knowledge of

a substance, at any rate such attributes are not substances.

It is evident, then, that not everything demonstrable can be

defined. What then? Can everything definable be demonstrated, or

not? There is one of our previous arguments which covers this too.

Of a single thing qua single there is a single scientific knowledge.

Hence, since to know the demonstrable scientifically is to possess the

demonstration of it, an impossible consequence will follow:-possession

of its definition without its demonstration will give knowledge of the

demonstrable.

Moreover, the basic premisses of demonstrations are definitions, and

it has already been shown that these will be found indemonstrable;

either the basic premisses will be demonstrable and will depend on

prior premisses, and the regress will be endless; or the primary

truths will be indemonstrable definitions.

But if the definable and the demonstrable are not wholly the same,

may they yet be partially the same? Or is that impossible, because

there can be no demonstration of the definable? There can be none,

because definition is of the essential nature or being of something,

and all demonstrations evidently posit and assume the essential

nature-mathematical demonstrations, for example, the nature of unity

and the odd, and all the other sciences likewise. Moreover, every

demonstration proves a predicate of a subject as attaching or as not

attaching to it, but in definition one thing is not predicated of

another; we do not, e.g. predicate animal of biped nor biped of

animal, nor yet figure of plane-plane not being figure nor figure

plane. Again, to prove essential nature is not the same as to prove

the fact of a connexion. Now definition reveals essential nature,

demonstration reveals that a given attribute attaches or does not

attach to a given subject; but different things require different

demonstrations-unless the one demonstration is related to the other as

part to whole. I add this because if all triangles have been proved to

possess angles equal to two right angles, then this attribute has been

proved to attach to isosceles; for isosceles is a part of which all

triangles constitute the whole. But in the case before us the fact and

the essential nature are not so related to one another, since the

one is not a part of the other.

So it emerges that not all the definable is demonstrable nor all the

demonstrable definable; and we may draw the general conclusion that

there is no identical object of which it is possible to possess both a

definition and a demonstration. It follows obviously that definition

and demonstration are neither identical nor contained either within

the other: if they were, their objects would be related either as

identical or as whole and part.

So much, then, for the first stage of our problem. The next step

is to raise the question whether syllogism-i.e. demonstration-of the

definable nature is possible or, as our recent argument assumed,

impossible.

We might argue it impossible on the following grounds:-(a) syllogism

proves an attribute of a subject through the middle term; on the other

hand (b) its definable nature is both 'peculiar' to a subject and

predicated of it as belonging to its essence. But in that case (1) the

subject, its definition, and the middle term connecting them must be

reciprocally predicable of one another; for if A is to C, obviously

A is 'peculiar' to B and B to C-in fact all three terms are 'peculiar'

to one another: and further (2) if A inheres in the essence of all B

and B is predicated universally of all C as belonging to C's

essence, A also must be predicated of C as belonging to its essence.

If one does not take this relation as thus duplicated-if, that is, A

is predicated as being of the essence of B, but B is not of the

essence of the subjects of which it is predicated-A will not

necessarily be predicated of C as belonging to its essence. So both

premisses will predicate essence, and consequently B also will be

predicated of C as its essence. Since, therefore, both premisses do

predicate essence-i.e. definable form-C's definable form will appear

in the middle term before the conclusion is drawn.

We may generalize by supposing that it is possible to prove the

essential nature of man. Let C be man, A man's essential

nature--two-footed animal, or aught else it may be. Then, if we are to

syllogize, A must be predicated of all B. But this premiss will be

mediated by a fresh definition, which consequently will also be the

essential nature of man. Therefore the argument assumes what it has to

prove, since B too is the essential nature of man. It is, however, the

case in which there are only the two premisses-i.e. in which the

premisses are primary and immediate-which we ought to investigate,

because it best illustrates the point under discussion.

Thus they who prove the essential nature of soul or man or

anything else through reciprocating terms beg the question. It would

be begging the question, for example, to contend that the soul is that

which causes its own life, and that what causes its own life is a

self-moving number; for one would have to postulate that the soul is a

self-moving number in the sense of being identical with it. For if A

is predicable as a mere consequent of B and B of C, A will not on that

account be the definable form of C: A will merely be what it was

true to say of C. Even if A is predicated of all B inasmuch as B is

identical with a species of A, still it will not follow: being an

animal is predicated of being a man-since it is true that in all

instances to be human is to be animal, just as it is also true that

every man is an animal-but not as identical with being man.

We conclude, then, that unless one takes both the premisses as

predicating essence, one cannot infer that A is the definable form and

essence of C: but if one does so take them, in assuming B one will

have assumed, before drawing the conclusion, what the definable form

of C is; so that there has been no inference, for one has begged the

question.

Nor, as was said in my formal logic, is the method of division a

process of inference at all, since at no point does the

characterization of the subject follow necessarily from the

premising of certain other facts: division demonstrates as little as

does induction. For in a genuine demonstration the conclusion must not

be put as a question nor depend on a concession, but must follow

necessarily from its premisses, even if the respondent deny it. The

definer asks 'Is man animal or inanimate?' and then assumes-he has not

inferred-that man is animal. Next, when presented with an exhaustive

division of animal into terrestrial and aquatic, he assumes that man

is terrestrial. Moreover, that man is the complete formula,

terrestrial-animal, does not follow necessarily from the premisses:

this too is an assumption, and equally an assumption whether the

division comprises many differentiae or few. (Indeed as this method of

division is used by those who proceed by it, even truths that can be

inferred actually fail to appear as such.) For why should not the

whole of this formula be true of man, and yet not exhibit his

essential nature or definable form? Again, what guarantee is there

against an unessential addition, or against the omission of the

final or of an intermediate determinant of the substantial being?

The champion of division might here urge that though these lapses do

occur, yet we can solve that difficulty if all the attributes we

assume are constituents of the definable form, and if, postulating the

genus, we produce by division the requisite uninterrupted sequence

of terms, and omit nothing; and that indeed we cannot fail to fulfil

these conditions if what is to be divided falls whole into the

division at each stage, and none of it is omitted; and that this-the

dividendum-must without further question be (ultimately) incapable

of fresh specific division. Nevertheless, we reply, division does

not involve inference; if it gives knowledge, it gives it in another

way. Nor is there any absurdity in this: induction, perhaps, is not

demonstration any more than is division, et it does make evident

some truth. Yet to state a definition reached by division is not to

state a conclusion: as, when conclusions are drawn without their

appropriate middles, the alleged necessity by which the inference

follows from the premisses is open to a question as to the reason

for it, so definitions reached by division invite the same question.

Thus to the question 'What is the essential nature of man?' the

divider replies 'Animal, mortal, footed, biped, wingless'; and when at

each step he is asked 'Why?', he will say, and, as he thinks, proves

by division, that all animal is mortal or immortal: but such a formula

taken in its entirety is not definition; so that even if division does

demonstrate its formula, definition at any rate does not turn out to

be a conclusion of inference.

Can we nevertheless actually demonstrate what a thing essentially

and substantially is, but hypothetically, i.e. by premising (1) that

its definable form is constituted by the 'peculiar' attributes of

its essential nature; (2) that such and such are the only attributes

of its essential nature, and that the complete synthesis of them is

peculiar to the thing; and thus-since in this synthesis consists the

being of the thing-obtaining our conclusion? Or is the truth that,

since proof must be through the middle term, the definable form is

once more assumed in this minor premiss too?

Further, just as in syllogizing we do not premise what syllogistic

inference is (since the premisses from which we conclude must be

related as whole and part), so the definable form must not fall within

the syllogism but remain outside the premisses posited. It is only

against a doubt as to its having been a syllogistic inference at all

that we have to defend our argument as conforming to the definition of

syllogism. It is only when some one doubts whether the conclusion

proved is the definable form that we have to defend it as conforming

to the definition of definable form which we assumed. Hence

syllogistic inference must be possible even without the express

statement of what syllogism is or what definable form is.

The following type of hypothetical proof also begs the question.

If evil is definable as the divisible, and the definition of a thing's

contrary-if it has one the contrary of the thing's definition; then,

if good is the contrary of evil and the indivisible of the

divisible, we conclude that to be good is essentially to be

indivisible. The question is begged because definable form is

assumed as a premiss, and as a premiss which is to prove definable

form. 'But not the same definable form', you may object. That I admit,

for in demonstrations also we premise that 'this' is predicable of

'that'; but in this premiss the term we assert of the minor is neither

the major itself nor a term identical in definition, or convertible,

with the major.

Again, both proof by division and the syllogism just described are

open to the question why man should be animal-biped-terrestrial and

not merely animal and terrestrial, since what they premise does not

ensure that the predicates shall constitute a genuine unity and not

merely belong to a single subject as do musical and grammatical when

predicated of the same man.

How then by definition shall we prove substance or essential nature?

We cannot show it as a fresh fact necessarily following from the

assumption of premisses admitted to be facts-the method of

demonstration: we may not proceed as by induction to establish a

universal on the evidence of groups of particulars which offer no

exception, because induction proves not what the essential nature of a

thing is but that it has or has not some attribute. Therefore, since

presumably one cannot prove essential nature by an appeal to sense

perception or by pointing with the finger, what other method remains?

To put it another way: how shall we by definition prove essential

nature? He who knows what human-or any other-nature is, must know also

that man exists; for no one knows the nature of what does not

exist-one can know the meaning of the phrase or name 'goat-stag' but

not what the essential nature of a goat-stag is. But further, if

definition can prove what is the essential nature of a thing, can it

also prove that it exists? And how will it prove them both by the same

process, since definition exhibits one single thing and

demonstration another single thing, and what human nature is and the

fact that man exists are not the same thing? Then too we hold that

it is by demonstration that the being of everything must be

proved-unless indeed to be were its essence; and, since being is not a

genus, it is not the essence of anything. Hence the being of

anything as fact is matter for demonstration; and this is the actual

procedure of the sciences, for the geometer assumes the meaning of the

word triangle, but that it is possessed of some attribute he proves.

What is it, then, that we shall prove in defining essential nature?

Triangle? In that case a man will know by definition what a thing's

nature is without knowing whether it exists. But that is impossible.

Moreover it is clear, if we consider the methods of defining

actually in use, that definition does not prove that the thing defined

exists: since even if there does actually exist something which is

equidistant from a centre, yet why should the thing named in the

definition exist? Why, in other words, should this be the formula

defining circle? One might equally well call it the definition of

mountain copper. For definitions do not carry a further guarantee that

the thing defined can exist or that it is what they claim to define:

one can always ask why.

Since, therefore, to define is to prove either a thing's essential

nature or the meaning of its name, we may conclude that definition, if

it in no sense proves essential nature, is a set of words signifying

precisely what a name signifies. But that were a strange

consequence; for (1) both what is not substance and what does not

exist at all would be definable, since even non-existents can be

signified by a name: (2) all sets of words or sentences would be

definitions, since any kind of sentence could be given a name; so that

we should all be talking in definitions, and even the Iliad would be a

definition: (3) no demonstration can prove that any particular name

means any particular thing: neither, therefore, do definitions, in

addition to revealing the meaning of a name, also reveal that the name

has this meaning. It appears then from these considerations that

neither definition and syllogism nor their objects are identical,

and further that definition neither demonstrates nor proves

anything, and that knowledge of essential nature is not to be obtained

either by definition or by demonstration.

We must now start afresh and consider which of these conclusions are

sound and which are not, and what is the nature of definition, and

whether essential nature is in any sense demonstrable and definable or

in none.

Now to know its essential nature is, as we said, the same as to know

the cause of a thing's existence, and the proof of this depends on the

fact that a thing must have a cause. Moreover, this cause is either

identical with the essential nature of the thing or distinct from

it; and if its cause is distinct from it, the essential nature of

the thing is either demonstrable or indemonstrable. Consequently, if

the cause is distinct from the thing's essential nature and

demonstration is possible, the cause must be the middle term, and, the

conclusion proved being universal and affirmative, the proof is in the

first figure. So the method just examined of proving it through

another essential nature would be one way of proving essential nature,

because a conclusion containing essential nature must be inferred

through a middle which is an essential nature just as a 'peculiar'

property must be inferred through a middle which is a 'peculiar'

property; so that of the two definable natures of a single thing

this method will prove one and not the other.

Now it was said before that this method could not amount to

demonstration of essential nature-it is actually a dialectical proof

of it-so let us begin again and explain by what method it can be

demonstrated. When we are aware of a fact we seek its reason, and

though sometimes the fact and the reason dawn on us simultaneously,

yet we cannot apprehend the reason a moment sooner than the fact;

and clearly in just the same way we cannot apprehend a thing's

definable form without apprehending that it exists, since while we are

ignorant whether it exists we cannot know its essential nature.

Moreover we are aware whether a thing exists or not sometimes

through apprehending an element in its character, and sometimes

accidentally, as, for example, when we are aware of thunder as a noise

in the clouds, of eclipse as a privation of light, or of man as some

species of animal, or of the soul as a self-moving thing. As often

as we have accidental knowledge that the thing exists, we must be in a

wholly negative state as regards awareness of its essential nature;

for we have not got genuine knowledge even of its existence, and to

search for a thing's essential nature when we are unaware that it

exists is to search for nothing. On the other hand, whenever we

apprehend an element in the thing's character there is less

difficulty. Thus it follows that the degree of our knowledge of a

thing's essential nature is determined by the sense in which we are

aware that it exists. Let us then take the following as our first

instance of being aware of an element in the essential nature. Let A

be eclipse, C the moon, B the earth's acting as a screen. Now to ask

whether the moon is eclipsed or not is to ask whether or not B has

occurred. But that is precisely the same as asking whether A has a

defining condition; and if this condition actually exists, we assert

that A also actually exists. Or again we may ask which side of a

contradiction the defining condition necessitates: does it make the

angles of a triangle equal or not equal to two right angles? When we

have found the answer, if the premisses are immediate, we know fact

and reason together; if they are not immediate, we know the fact

without the reason, as in the following example: let C be the moon,

A eclipse, B the fact that the moon fails to produce shadows though

she is full and though no visible body intervenes between us and

her. Then if B, failure to produce shadows in spite of the absence

of an intervening body, is attributable A to C, and eclipse, is

attributable to B, it is clear that the moon is eclipsed, but the

reason why is not yet clear, and we know that eclipse exists, but we

do not know what its essential nature is. But when it is clear that

A is attributable to C and we proceed to ask the reason of this

fact, we are inquiring what is the nature of B: is it the earth's

acting as a screen, or the moon's rotation or her extinction? But B is

the definition of the other term, viz. in these examples, of the major

term A; for eclipse is constituted by the earth acting as a screen.

Thus, (1) 'What is thunder?' 'The quenching of fire in cloud', and (2)

'Why does it thunder?' 'Because fire is quenched in the cloud', are

equivalent. Let C be cloud, A thunder, B the quenching of fire. Then B

is attributable to C, cloud, since fire is quenched in it; and A,

noise, is attributable to B; and B is assuredly the definition of

the major term A. If there be a further mediating cause of B, it

will be one of the remaining partial definitions of A.

We have stated then how essential nature is discovered and becomes

known, and we see that, while there is no syllogism-i.e. no

demonstrative syllogism-of essential nature, yet it is through

syllogism, viz. demonstrative syllogism, that essential nature is

exhibited. So we conclude that neither can the essential nature of

anything which has a cause distinct from itself be known without

demonstration, nor can it be demonstrated; and this is what we

contended in our preliminary discussions.

Now while some things have a cause distinct from themselves,

others have not. Hence it is evident that there are essential

natures which are immediate, that is are basic premisses; and of these

not only that they are but also what they are must be assumed or

revealed in some other way. This too is the actual procedure of the

arithmetician, who assumes both the nature and the existence of

unit. On the other hand, it is possible (in the manner explained) to

exhibit through demonstration the essential nature of things which

have a 'middle', i.e. a cause of their substantial being other than

that being itself; but we do not thereby demonstrate it.

Since definition is said to be the statement of a thing's nature,

obviously one kind of definition will be a statement of the meaning of

the name, or of an equivalent nominal formula. A definition in this

sense tells you, e.g. the meaning of the phrase 'triangular

character'. When we are aware that triangle exists, we inquire the

reason why it exists. But it is difficult thus to learn the definition

of things the existence of which we do not genuinely know-the cause of

this difficulty being, as we said before, that we only know

accidentally whether or not the thing exists. Moreover, a statement

may be a unity in either of two ways, by conjunction, like the

Iliad, or because it exhibits a single predicate as inhering not

accidentally in a single subject.

That then is one way of defining definition. Another kind of

definition is a formula exhibiting the cause of a thing's existence.

Thus the former signifies without proving, but the latter will clearly

be a quasi-demonstration of essential nature, differing from

demonstration in the arrangement of its terms. For there is a

difference between stating why it thunders, and stating what is the

essential nature of thunder; since the first statement will be

'Because fire is quenched in the clouds', while the statement of

what the nature of thunder is will be 'The noise of fire being

quenched in the clouds'. Thus the same statement takes a different

form: in one form it is continuous demonstration, in the other

definition. Again, thunder can be defined as noise in the clouds,

which is the conclusion of the demonstration embodying essential

nature. On the other hand the definition of immediates is an

indemonstrable positing of essential nature.

We conclude then that definition is (a) an indemonstrable

statement of essential nature, or (b) a syllogism of essential

nature differing from demonstration in grammatical form, or (c) the

conclusion of a demonstration giving essential nature.

Our discussion has therefore made plain (1) in what sense and of

what things the essential nature is demonstrable, and in what sense

and of what things it is not; (2) what are the various meanings of the

term definition, and in what sense and of what things it proves the

essential nature, and in what sense and of what things it does not;

(3) what is the relation of definition to demonstration, and how far

the same thing is both definable and demonstrable and how far it is

not.

We think we have scientific knowledge when we know the cause, and

there are four causes: (1) the definable form, (2) an antecedent which

necessitates a consequent, (3) the efficient cause, (4) the final

cause. Hence each of these can be the middle term of a proof, for

(a) though the inference from antecedent to necessary consequent

does not hold if only one premiss is assumed-two is the

minimum-still when there are two it holds on condition that they

have a single common middle term. So it is from the assumption of this

single middle term that the conclusion follows necessarily. The

following example will also show this. Why is the angle in a

semicircle a right angle?-or from what assumption does it follow

that it is a right angle? Thus, let A be right angle, B the half of

two right angles, C the angle in a semicircle. Then B is the cause

in virtue of which A, right angle, is attributable to C, the angle

in a semicircle, since B=A and the other, viz. C,=B, for C is half

of two right angles. Therefore it is the assumption of B, the half

of two right angles, from which it follows that A is attributable to

C, i.e. that the angle in a semicircle is a right angle. Moreover, B

is identical with (b) the defining form of A, since it is what A's

definition signifies. Moreover, the formal cause has already been

shown to be the middle. (c) 'Why did the Athenians become involved

in the Persian war?' means 'What cause originated the waging of war

against the Athenians?' and the answer is, 'Because they raided Sardis

with the Eretrians', since this originated the war. Let A be war, B

unprovoked raiding, C the Athenians. Then B, unprovoked raiding, is

true of C, the Athenians, and A is true of B, since men make war on

the unjust aggressor. So A, having war waged upon them, is true of

B, the initial aggressors, and B is true of C, the Athenians, who were

the aggressors. Hence here too the cause-in this case the efficient

cause-is the middle term. (d) This is no less true where the cause

is the final cause. E.g. why does one take a walk after supper? For

the sake of one's health. Why does a house exist? For the preservation

of one's goods. The end in view is in the one case health, in the

other preservation. To ask the reason why one must walk after supper

is precisely to ask to what end one must do it. Let C be walking after

supper, B the non-regurgitation of food, A health. Then let walking

after supper possess the property of preventing food from rising to

the orifice of the stomach, and let this condition be healthy; since

it seems that B, the non-regurgitation of food, is attributable to

C, taking a walk, and that A, health, is attributable to B. What,

then, is the cause through which A, the final cause, inheres in C?

It is B, the non-regurgitation of food; but B is a kind of

definition of A, for A will be explained by it. Why is B the cause

of A's belonging to C? Because to be in a condition such as B is to be

in health. The definitions must be transposed, and then the detail

will become clearer. Incidentally, here the order of coming to be is

the reverse of what it is in proof through the efficient cause: in the

efficient order the middle term must come to be first, whereas in

the teleological order the minor, C, must first take place, and the

end in view comes last in time.

The same thing may exist for an end and be necessitated as well. For

example, light shines through a lantern (1) because that which consists

of relatively small particles necessarily passes through pores larger

than those particles-assuming that light does issue by penetration-

and (2) for an end, namely to save us from stumbling. If then, a

thing can exist through two causes, can it come to be through two

causes-as for instance if thunder be a hiss and a roar necessarily

produced by the quenching of fire, and also designed, as the

Pythagoreans say, for a threat to terrify those that lie in Tartarus?

Indeed, there are very many such cases, mostly among the processes

and products of the natural world; for nature, in different senses

of the term 'nature', produces now for an end, now by necessity.

Necessity too is of two kinds. It may work in accordance with a

thing's natural tendency, or by constraint and in opposition to it;

as, for instance, by necessity a stone is borne both upwards and

downwards, but not by the same necessity.

Of the products of man's intelligence some are never due to chance

or necessity but always to an end, as for example a house or a statue;

others, such as health or safety, may result from chance as well.

It is mostly in cases where the issue is indeterminate (though

only where the production does not originate in chance, and the end is

consequently good), that a result is due to an end, and this is true

alike in nature or in art. By chance, on the other hand, nothing comes

to be for an end.

The effect may be still coming to be, or its occurrence may be past

or future, yet the cause will be the same as when it is actually

existent-for it is the middle which is the cause-except that if the

effect actually exists the cause is actually existent, if it is coming

to be so is the cause, if its occurrence is past the cause is past, if

future the cause is future. For example, the moon was eclipsed because

the earth intervened, is becoming eclipsed because the earth is in

process of intervening, will be eclipsed because the earth will

intervene, is eclipsed because the earth intervenes.

To take a second example: assuming that the definition of ice is

solidified water, let C be water, A solidified, B the middle, which is

the cause, namely total failure of heat. Then B is attributed to C,

and A, solidification, to B: ice when B is occurring, has formed

when B has occurred, and will form when B shall occur.

This sort of cause, then, and its effect come to be simultaneously

when they are in process of becoming, and exist simultaneously when

they actually exist; and the same holds good when they are past and

when they are future. But what of cases where they are not

simultaneous? Can causes and effects different from one another

form, as they seem to us to form, a continuous succession, a past

effect resulting from a past cause different from itself, a future

effect from a future cause different from it, and an effect which is

coming-to-be from a cause different from and prior to it? Now on

this theory it is from the posterior event that we reason (and this

though these later events actually have their source of origin in

previous events--a fact which shows that also when the effect is

coming-to-be we still reason from the posterior event), and from the

event we cannot reason (we cannot argue that because an event A has

occurred, therefore an event B has occurred subsequently to A but

still in the past-and the same holds good if the occurrence is

future)-cannot reason because, be the time interval definite or

indefinite, it will never be possible to infer that because it is true

to say that A occurred, therefore it is true to say that B, the

subsequent event, occurred; for in the interval between the events,

though A has already occurred, the latter statement will be false. And

the same argument applies also to future events; i.e. one cannot infer

from an event which occurred in the past that a future event will

occur. The reason of this is that the middle must be homogeneous, past

when the extremes are past, future when they are future, coming to

be when they are coming-to-be, actually existent when they are

actually existent; and there cannot be a middle term homogeneous

with extremes respectively past and future. And it is a further

difficulty in this theory that the time interval can be neither

indefinite nor definite, since during it the inference will be

false. We have also to inquire what it is that holds events together

so that the coming-to-be now occurring in actual things follows upon a

past event. It is evident, we may suggest, that a past event and a

present process cannot be 'contiguous', for not even two past events

can be 'contiguous'. For past events are limits and atomic; so just as

points are not 'contiguous' neither are past events, since both are

indivisible. For the same reason a past event and a present process

cannot be 'contiguous', for the process is divisible, the event

indivisible. Thus the relation of present process to past event is

analogous to that of line to point, since a process contains an

infinity of past events. These questions, however, must receive a more

explicit treatment in our general theory of change.

The following must suffice as an account of the manner in which

the middle would be identical with the cause on the supposition that

coming-to-be is a series of consecutive events: for in the terms of

such a series too the middle and major terms must form an immediate

premiss; e.g. we argue that, since C has occurred, therefore A

occurred: and C's occurrence was posterior, A's prior; but C is the

source of the inference because it is nearer to the present moment,

and the starting-point of time is the present. We next argue that,

since D has occurred, therefore C occurred. Then we conclude that,

since D has occurred, therefore A must have occurred; and the cause is

C, for since D has occurred C must have occurred, and since C has

occurred A must previously have occurred.

If we get our middle term in this way, will the series terminate

in an immediate premiss, or since, as we said, no two events are

'contiguous', will a fresh middle term always intervene because

there is an infinity of middles? No: though no two events are

'contiguous', yet we must start from a premiss consisting of a

middle and the present event as major. The like is true of future

events too, since if it is true to say that D will exist, it must be a

prior truth to say that A will exist, and the cause of this conclusion

is C; for if D will exist, C will exist prior to D, and if C will

exist, A will exist prior to it. And here too the same infinite

divisibility might be urged, since future events are not 'contiguous'.

But here too an immediate basic premiss must be assumed. And in the

world of fact this is so: if a house has been built, then blocks

must have been quarried and shaped. The reason is that a house

having been built necessitates a foundation having been laid, and if a

foundation has been laid blocks must have been shaped beforehand.

Again, if a house will be built, blocks will similarly be shaped

beforehand; and proof is through the middle in the same way, for the

foundation will exist before the house.

Now we observe in Nature a certain kind of circular process of

coming-to-be; and this is possible only if the middle and extreme

terms are reciprocal, since conversion is conditioned by reciprocity

in the terms of the proof. This-the convertibility of conclusions

and premisses-has been proved in our early chapters, and the

circular process is an instance of this. In actual fact it is

exemplified thus: when the earth had been moistened an exhalation

was bound to rise, and when an exhalation had risen cloud was bound to

form, and from the formation of cloud rain necessarily resulted and by

the fall of rain the earth was necessarily moistened: but this was the

starting-point, so that a circle is completed; for posit any one of

the terms and another follows from it, and from that another, and from

that again the first.

Some occurrences are universal (for they are, or come-to-be what

they are, always and in ever case); others again are not always what

they are but only as a general rule: for instance, not every man can

grow a beard, but it is the general rule. In the case of such

connexions the middle term too must be a general rule. For if A is

predicated universally of B and B of C, A too must be predicated

always and in every instance of C, since to hold in every instance and

always is of the nature of the universal. But we have assumed a

connexion which is a general rule; consequently the middle term B must

also be a general rule. So connexions which embody a general rule-i.e.

which exist or come to be as a general rule-will also derive from

immediate basic premisses.

We have already explained how essential nature is set out in the

terms of a demonstration, and the sense in which it is or is not

demonstrable or definable; so let us now discuss the method to be

adopted in tracing the elements predicated as constituting the

definable form.

Now of the attributes which inhere always in each several thing

there are some which are wider in extent than it but not wider than

its genus (by attributes of wider extent mean all such as are

universal attributes of each several subject, but in their application

are not confined to that subject). while an attribute may inhere in

every triad, yet also in a subject not a triad-as being inheres in

triad but also in subjects not numbers at all-odd on the other hand is

an attribute inhering in every triad and of wider application

(inhering as it does also in pentad), but which does not extend beyond

the genus of triad; for pentad is a number, but nothing outside number

is odd. It is such attributes which we have to select, up to the exact

point at which they are severally of wider extent than the subject but

collectively coextensive with it; for this synthesis must be the

substance of the thing. For example every triad possesses the

attributes number, odd, and prime in both senses, i.e. not only as

possessing no divisors, but also as not being a sum of numbers.

This, then, is precisely what triad is, viz. a number, odd, and

prime in the former and also the latter sense of the term: for these

attributes taken severally apply, the first two to all odd numbers,

the last to the dyad also as well as to the triad, but, taken

collectively, to no other subject. Now since we have shown above' that

attributes predicated as belonging to the essential nature are

necessary and that universals are necessary, and since the

attributes which we select as inhering in triad, or in any other

subject whose attributes we select in this way, are predicated as

belonging to its essential nature, triad will thus possess these

attributes necessarily. Further, that the synthesis of them

constitutes the substance of triad is shown by the following argument.

If it is not identical with the being of triad, it must be related

to triad as a genus named or nameless. It will then be of wider extent

than triad-assuming that wider potential extent is the character of

a genus. If on the other hand this synthesis is applicable to no

subject other than the individual triads, it will be identical with

the being of triad, because we make the further assumption that the

substance of each subject is the predication of elements in its

essential nature down to the last differentia characterizing the

individuals. It follows that any other synthesis thus exhibited will

likewise be identical with the being of the subject.

The author of a hand-book on a subject that is a generic whole

should divide the genus into its first infimae species-number e.g.

into triad and dyad-and then endeavour to seize their definitions by

the method we have described-the definition, for example, of

straight line or circle or right angle. After that, having established

what the category is to which the subaltern genus belongs-quantity

or quality, for instance-he should examine the properties 'peculiar'

to the species, working through the proximate common differentiae.

He should proceed thus because the attributes of the genera compounded

of the infimae species will be clearly given by the definitions of the

species; since the basic element of them all is the definition, i.e.

the simple infirma species, and the attributes inhere essentially in

the simple infimae species, in the genera only in virtue of these.

Divisions according to differentiae are a useful accessory to this

method. What force they have as proofs we did, indeed, explain

above, but that merely towards collecting the essential nature they

may be of use we will proceed to show. They might, indeed, seem to

be of no use at all, but rather to assume everything at the start

and to be no better than an initial assumption made without

division. But, in fact, the order in which the attributes are

predicated does make a difference--it matters whether we say

animal-tame-biped, or biped-animal-tame. For if every definable

thing consists of two elements and 'animal-tame' forms a unity, and

again out of this and the further differentia man (or whatever else is

the unity under construction) is constituted, then the elements we

assume have necessarily been reached by division. Again, division is

the only possible method of avoiding the omission of any element of

the essential nature. Thus, if the primary genus is assumed and we

then take one of the lower divisions, the dividendum will not fall

whole into this division: e.g. it is not all animal which is either

whole-winged or split-winged but all winged animal, for it is winged

animal to which this differentiation belongs. The primary

differentiation of animal is that within which all animal falls. The

like is true of every other genus, whether outside animal or a

subaltern genus of animal; e.g. the primary differentiation of bird is

that within which falls every bird, of fish that within which falls

every fish. So, if we proceed in this way, we can be sure that nothing

has been omitted: by any other method one is bound to omit something

without knowing it.

To define and divide one need not know the whole of existence. Yet

some hold it impossible to know the differentiae distinguishing each

thing from every single other thing without knowing every single other

thing; and one cannot, they say, know each thing without knowing its

differentiae, since everything is identical with that from which it

does not differ, and other than that from which it differs. Now

first of all this is a fallacy: not every differentia precludes

identity, since many differentiae inhere in things specifically

identical, though not in the substance of these nor essentially.

Secondly, when one has taken one's differing pair of opposites and

assumed that the two sides exhaust the genus, and that the subject one

seeks to define is present in one or other of them, and one has

further verified its presence in one of them; then it does not

matter whether or not one knows all the other subjects of which the

differentiae are also predicated. For it is obvious that when by

this process one reaches subjects incapable of further differentiation

one will possess the formula defining the substance. Moreover, to

postulate that the division exhausts the genus is not illegitimate

if the opposites exclude a middle; since if it is the differentia of

that genus, anything contained in the genus must lie on one of the two

sides.

In establishing a definition by division one should keep three

objects in view: (1) the admission only of elements in the definable

form, (2) the arrangement of these in the right order, (3) the

omission of no such elements. The first is feasible because one can

establish genus and differentia through the topic of the genus, just

as one can conclude the inherence of an accident through the topic

of the accident. The right order will be achieved if the right term is

assumed as primary, and this will be ensured if the term selected is

predicable of all the others but not all they of it; since there

must be one such term. Having assumed this we at once proceed in the

same way with the lower terms; for our second term will be the first

of the remainder, our third the first of those which follow the second

in a 'contiguous' series, since when the higher term is excluded, that

term of the remainder which is 'contiguous' to it will be primary, and

so on. Our procedure makes it clear that no elements in the

definable form have been omitted: we have taken the differentia that

comes first in the order of division, pointing out that animal, e.g.

is divisible exhaustively into A and B, and that the subject accepts

one of the two as its predicate. Next we have taken the differentia of

the whole thus reached, and shown that the whole we finally reach is

not further divisible-i.e. that as soon as we have taken the last

differentia to form the concrete totality, this totality admits of

no division into species. For it is clear that there is no superfluous

addition, since all these terms we have selected are elements in the

definable form; and nothing lacking, since any omission would have

to be a genus or a differentia. Now the primary term is a genus, and

this term taken in conjunction with its differentiae is a genus:

moreover the differentiae are all included, because there is now no

further differentia; if there were, the final concrete would admit

of division into species, which, we said, is not the case.

To resume our account of the right method of investigation: We

must start by observing a set of similar-i.e. specifically

identical-individuals, and consider what element they have in

common. We must then apply the same process to another set of

individuals which belong to one species and are generically but not

specifically identical with the former set. When we have established

what the common element is in all members of this second species,

and likewise in members of further species, we should again consider

whether the results established possess any identity, and persevere

until we reach a single formula, since this will be the definition

of the thing. But if we reach not one formula but two or more,

evidently the definiendum cannot be one thing but must be more than

one. I may illustrate my meaning as follows. If we were inquiring what

the essential nature of pride is, we should examine instances of proud

men we know of to see what, as such, they have in common; e.g. if

Alcibiades was proud, or Achilles and Ajax were proud, we should

find on inquiring what they all had in common, that it was intolerance

of insult; it was this which drove Alcibiades to war, Achilles

wrath, and Ajax to suicide. We should next examine other cases,

Lysander, for example, or Socrates, and then if these have in common

indifference alike to good and ill fortune, I take these two results

and inquire what common element have equanimity amid the

vicissitudes of life and impatience of dishonour. If they have none,

there will be two genera of pride. Besides, every definition is always

universal and commensurate: the physician does not prescribe what is

healthy for a single eye, but for all eyes or for a determinate

species of eye. It is also easier by this method to define the

single species than the universal, and that is why our procedure

should be from the several species to the universal genera-this for

the further reason too that equivocation is less readily detected in

genera than in infimae species. Indeed, perspicuity is essential in

definitions, just as inferential movement is the minimum required in

demonstrations; and we shall attain perspicuity if we can collect

separately the definition of each species through the group of

singulars which we have established e.g. the definition of

similarity not unqualified but restricted to colours and to figures;

the definition of acuteness, but only of sound-and so proceed to the

common universal with a careful avoidance of equivocation. We may

add that if dialectical disputation must not employ metaphors, clearly

metaphors and metaphorical expressions are precluded in definition:

otherwise dialectic would involve metaphors.

In order to formulate the connexions we wish to prove we have to

select our analyses and divisions. The method of selection consists in

laying down the common genus of all our subjects of investigation-if

e.g. they are animals, we lay down what the properties are which

inhere in every animal. These established, we next lay down the

properties essentially connected with the first of the remaining

classes-e.g. if this first subgenus is bird, the essential

properties of every bird-and so on, always characterizing the

proximate subgenus. This will clearly at once enable us to say in

virtue of what character the subgenera-man, e.g. or horse-possess

their properties. Let A be animal, B the properties of every animal, C

D E various species of animal. Then it is clear in virtue of what

character B inheres in D-namely A-and that it inheres in C and E for

the same reason: and throughout the remaining subgenera always the

same rule applies.

We are now taking our examples from the traditional class-names, but

we must not confine ourselves to considering these. We must collect

any other common character which we observe, and then consider with

what species it is connected and what.properties belong to it. For

example, as the common properties of horned animals we collect the

possession of a third stomach and only one row of teeth. Then since it

is clear in virtue of what character they possess these

attributes-namely their horned character-the next question is, to what

species does the possession of horns attach?

Yet a further method of selection is by analogy: for we cannot

find a single identical name to give to a squid's pounce, a fish's

spine, and an animal's bone, although these too possess common

properties as if there were a single osseous nature.

Some connexions that require proof are identical in that they

possess an identical 'middle' e.g. a whole group might be proved

through 'reciprocal replacement'-and of these one class are

identical in genus, namely all those whose difference consists in

their concerning different subjects or in their mode of manifestation.

This latter class may be exemplified by the questions as to the causes

respectively of echo, of reflection, and of the rainbow: the

connexions to be proved which these questions embody are identical

generically, because all three are forms of repercussion; but

specifically they are different.

Other connexions that require proof only differ in that the 'middle'

of the one is subordinate to the 'middle' of the other. For example:

Why does the Nile rise towards the end of the month? Because towards

its close the month is more stormy. Why is the month more stormy

towards its close? Because the moon is waning. Here the one cause is

subordinate to the other.

The question might be raised with regard to cause and effect whether

when the effect is present the cause also is present; whether, for

instance, if a plant sheds its leaves or the moon is eclipsed, there

is present also the cause of the eclipse or of the fall of the

leaves-the possession of broad leaves, let us say, in the latter case,

in the former the earth's interposition. For, one might argue, if this

cause is not present, these phenomena will have some other cause: if

it is present, its effect will be at once implied by it-the eclipse by

the earth's interposition, the fall of the leaves by the possession of

broad leaves; but if so, they will be logically coincident and each

capable of proof through the other. Let me illustrate: Let A be

deciduous character, B the possession of broad leaves, C vine. Now

if A inheres in B (for every broad-leaved plant is deciduous), and B

in C (every vine possessing broad leaves); then A inheres in C

(every vine is deciduous), and the middle term B is the cause. But

we can also demonstrate that the vine has broad leaves because it is

deciduous. Thus, let D be broad-leaved, E deciduous, F vine. Then E

inheres in F (since every vine is deciduous), and D in E (for every

deciduous plant has broad leaves): therefore every vine has broad

leaves, and the cause is its deciduous character. If, however, they

cannot each be the cause of the other (for cause is prior to effect,

and the earth's interposition is the cause of the moon's eclipse and

not the eclipse of the interposition)-if, then, demonstration

through the cause is of the reasoned fact and demonstration not

through the cause is of the bare fact, one who knows it through the

eclipse knows the fact of the earth's interposition but not the

reasoned fact. Moreover, that the eclipse is not the cause of the

interposition, but the interposition of the eclipse, is obvious

because the interposition is an element in the definition of

eclipse, which shows that the eclipse is known through the

interposition and not vice versa.

On the other hand, can a single effect have more than one cause? One

might argue as follows: if the same attribute is predicable of more

than one thing as its primary subject, let B be a primary subject in

which A inheres, and C another primary subject of A, and D and E

primary subjects of B and C respectively. A will then inhere in D

and E, and B will be the cause of A's inherence in D, C of A's

inherence in E. The presence of the cause thus necessitates that of

the effect, but the presence of the effect necessitates the presence

not of all that may cause it but only of a cause which yet need not be

the whole cause. We may, however, suggest that if the connexion to

be proved is always universal and commensurate, not only will the

cause be a whole but also the effect will be universal and

commensurate. For instance, deciduous character will belong

exclusively to a subject which is a whole, and, if this whole has

species, universally and commensurately to those species-i.e. either

to all species of plant or to a single species. So in these

universal and commensurate connexions the 'middle' and its effect must

reciprocate, i.e. be convertible. Supposing, for example, that the

reason why trees are deciduous is the coagulation of sap, then if a

tree is deciduous, coagulation must be present, and if coagulation

is present-not in any subject but in a tree-then that tree must be

deciduous.

Can the cause of an identical effect be not identical in every

instance of the effect but different? Or is that impossible? Perhaps

it is impossible if the effect is demonstrated as essential and not as

inhering in virtue of a symptom or an accident-because the middle is

then the definition of the major term-though possible if the

demonstration is not essential. Now it is possible to consider the

effect and its subject as an accidental conjunction, though such

conjunctions would not be regarded as connexions demanding

scientific proof. But if they are accepted as such, the middle will

correspond to the extremes, and be equivocal if they are equivocal,

generically one if they are generically one. Take the question why

proportionals alternate. The cause when they are lines, and when

they are numbers, is both different and identical; different in so far

as lines are lines and not numbers, identical as involving a given

determinate increment. In all proportionals this is so. Again, the

cause of likeness between colour and colour is other than that between

figure and figure; for likeness here is equivocal, meaning perhaps

in the latter case equality of the ratios of the sides and equality of

the angles, in the case of colours identity of the act of perceiving

them, or something else of the sort. Again, connexions requiring proof

which are identical by analogy middles also analogous.

The truth is that cause, effect, and subject are reciprocally

predicable in the following way. If the species are taken severally,

the effect is wider than the subject (e.g. the possession of

external angles equal to four right angles is an attribute wider

than triangle or are), but it is coextensive with the species taken

collectively (in this instance with all figures whose external

angles are equal to four right angles). And the middle likewise

reciprocates, for the middle is a definition of the major; which is

incidentally the reason why all the sciences are built up through

definition.

We may illustrate as follows. Deciduous is a universal attribute

of vine, and is at the same time of wider extent than vine; and of

fig, and is of wider extent than fig: but it is not wider than but

coextensive with the totality of the species. Then if you take the

middle which is proximate, it is a definition of deciduous. I say

that, because you will first reach a middle next the subject, and a

premiss asserting it of the whole subject, and after that a middle-the

coagulation of sap or something of the sort-proving the connexion of

the first middle with the major: but it is the coagulation of sap at

the junction of leaf-stalk and stem which defines deciduous.

If an explanation in formal terms of the inter-relation of cause and

effect is demanded, we shall offer the following. Let A be an

attribute of all B, and B of every species of D, but so that both A

and B are wider than their respective subjects. Then B will be a

universal attribute of each species of D (since I call such an

attribute universal even if it is not commensurate, and I call an

attribute primary universal if it is commensurate, not with each

species severally but with their totality), and it extends beyond each

of them taken separately.

Thus, B is the cause of A's inherence in the species of D:

consequently A must be of wider extent than B; otherwise why should

B be the cause of A's inherence in D any more than A the cause of

B's inherence in D? Now if A is an attribute of all the species of

E, all the species of E will be united by possessing some common cause

other than B: otherwise how shall we be able to say that A is

predicable of all of which E is predicable, while E is not

predicable of all of which A can be predicated? I mean how can there

fail to be some special cause of A's inherence in E, as there was of

A's inherence in all the species of D? Then are the species of E, too,

united by possessing some common cause? This cause we must look for.

Let us call it C.

We conclude, then, that the same effect may have more than one

cause, but not in subjects specifically identical. For instance, the

cause of longevity in quadrupeds is lack of bile, in birds a dry

constitution-or certainly something different.

If immediate premisses are not reached at once, and there is not

merely one middle but several middles, i.e. several causes; is the

cause of the property's inherence in the several species the middle

which is proximate to the primary universal, or the middle which is

proximate to the species? Clearly the cause is that nearest to each

species severally in which it is manifested, for that is the cause

of the subject's falling under the universal. To illustrate

formally: C is the cause of B's inherence in D; hence C is the cause

of A's inherence in D, B of A's inherence in C, while the cause of A's

inherence in B is B itself.

As regards syllogism and demonstration, the definition of, and the

conditions required to produce each of them, are now clear, and with

that also the definition of, and the conditions required to produce,

demonstrative knowledge, since it is the same as demonstration. As

to the basic premisses, how they become known and what is the

developed state of knowledge of them is made clear by raising some

preliminary problems.

We have already said that scientific knowledge through demonstration

is impossible unless a man knows the primary immediate premisses.

But there are questions which might be raised in respect of the

apprehension of these immediate premisses: one might not only ask

whether it is of the same kind as the apprehension of the conclusions,

but also whether there is or is not scientific knowledge of both; or

scientific knowledge of the latter, and of the former a different kind

of knowledge; and, further, whether the developed states of

knowledge are not innate but come to be in us, or are innate but at

first unnoticed. Now it is strange if we possess them from birth;

for it means that we possess apprehensions more accurate than

demonstration and fail to notice them. If on the other hand we acquire

them and do not previously possess them, how could we apprehend and

learn without a basis of pre-existent knowledge? For that is

impossible, as we used to find in the case of demonstration. So it

emerges that neither can we possess them from birth, nor can they come

to be in us if we are without knowledge of them to the extent of

having no such developed state at all. Therefore we must possess a

capacity of some sort, but not such as to rank higher in accuracy than

these developed states. And this at least is an obvious characteristic

of all animals, for they possess a congenital discriminative

capacity which is called sense-perception. But though sense-perception

is innate in all animals, in some the sense-impression comes to

persist, in others it does not. So animals in which this persistence

does not come to be have either no knowledge at all outside the act of

perceiving, or no knowledge of objects of which no impression

persists; animals in which it does come into being have perception and

can continue to retain the sense-impression in the soul: and when such

persistence is frequently repeated a further distinction at once

arises between those which out of the persistence of such

sense-impressions develop a power of systematizing them and those

which do not. So out of sense-perception comes to be what we call

memory, and out of frequently repeated memories of the same thing

develops experience; for a number of memories constitute a single

experience. From experience again-i.e. from the universal now

stabilized in its entirety within the soul, the one beside the many

which is a single identity within them all-originate the skill of

the craftsman and the knowledge of the man of science, skill in the

sphere of coming to be and science in the sphere of being.

We conclude that these states of knowledge are neither innate in a

determinate form, nor developed from other higher states of knowledge,

but from sense-perception. It is like a rout in battle stopped by

first one man making a stand and then another, until the original

formation has been restored. The soul is so constituted as to be

capable of this process.

Let us now restate the account given already, though with

insufficient clearness. When one of a number of logically

indiscriminable particulars has made a stand, the earliest universal

is present in the soul: for though the act of sense-perception is of

the particular, its content is universal-is man, for example, not

the man Callias. A fresh stand is made among these rudimentary

universals, and the process does not cease until the indivisible

concepts, the true universals, are established: e.g. such and such a

species of animal is a step towards the genus animal, which by the

same process is a step towards a further generalization.

Thus it is clear that we must get to know the primary premisses by

induction; for the method by which even sense-perception implants

the universal is inductive. Now of the thinking states by which we

grasp truth, some are unfailingly true, others admit of error-opinion,

for instance, and calculation, whereas scientific knowing and

intuition are always true: further, no other kind of thought except

intuition is more accurate than scientific knowledge, whereas

primary premisses are more knowable than demonstrations, and all

scientific knowledge is discursive. From these considerations it

follows that there will be no scientific knowledge of the primary

premisses, and since except intuition nothing can be truer than

scientific knowledge, it will be intuition that apprehends the primary

premisses-a result which also follows from the fact that demonstration

cannot be the originative source of demonstration, nor,

consequently, scientific knowledge of scientific knowledge.If,

therefore, it is the only other kind of true thinking except

scientific knowing, intuition will be the originative source of

scientific knowledge. And the originative source of science grasps the

original basic premiss, while science as a whole is similarly

related as originative source to the whole body of fact.

-THE END-

350 BC

HISTORY OF ANIMALS

by Aristotle

translated by D'Arcy Wentworth Thompson

Book I

OF the parts of animals some are simple: to wit, all such as

divide into parts uniform with themselves, as flesh into flesh; others

are composite, such as divide into parts not uniform with

themselves, as, for instance, the hand does not divide into hands

nor the face into faces.

And of such as these, some are called not parts merely, but limbs

or members. Such are those parts that, while entire in themselves,

have within themselves other diverse parts: as for instance, the head,

foot, hand, the arm as a whole, the chest; for these are all in

themselves entire parts, and there are other diverse parts belonging

to them.

All those parts that do not subdivide into parts uniform with

themselves are composed of parts that do so subdivide, for instance,

hand is composed of flesh, sinews, and bones. Of animals, some

resemble one another in all their parts, while others have parts

wherein they differ. Sometimes the parts are identical in form or

species, as, for instance, one man's nose or eye resembles another

man's nose or eye, flesh flesh, and bone bone; and in like manner with

a horse, and with all other animals which we reckon to be of one and

the same species: for as the whole is to the whole, so each to each

are the parts severally. In other cases the parts are identical,

save only for a difference in the way of excess or defect, as is the

case in such animals as are of one and the same genus. By 'genus' I

mean, for instance, Bird or Fish, for each of these is subject to

difference in respect of its genus, and there are many species of

fishes and of birds.

Within the limits of genera, most of the parts as a rule

exhibit differences through contrast of the property or accident, such

as colour and shape, to which they are subject: in that some are

more and some in a less degree the subject of the same property or

accident; and also in the way of multitude or fewness, magnitude or

parvitude, in short in the way of excess or defect. Thus in some the

texture of the flesh is soft, in others firm; some have a long bill,

others a short one; some have abundance of feathers, others have

only a small quantity. It happens further that some have parts that

others have not: for instance, some have spurs and others not, some

have crests and others not; but as a general rule, most parts and

those that go to make up the bulk of the body are either identical

with one another, or differ from one another in the way of contrast

and of excess and defect. For 'the more' and 'the less' may be

represented as 'excess' or 'defect'.

Once again, we may have to do with animals whose parts are

neither identical in form nor yet identical save for differences in

the way of excess or defect: but they are the same only in the way

of analogy, as, for instance, bone is only analogous to fish-bone,

nail to hoof, hand to claw, and scale to feather; for what the feather

is in a bird, the scale is in a fish.

The parts, then, which animals severally possess are diverse

from, or identical with, one another in the fashion above described.

And they are so furthermore in the way of local disposition: for

many animals have identical organs that differ in position; for

instance, some have teats in the breast, others close to the thighs.

Of the substances that are composed of parts uniform (or

homogeneous) with themselves, some are soft and moist, others are

dry and solid. The soft and moist are such either absolutely or so

long as they are in their natural conditions, as, for instance, blood,

serum, lard, suet, marrow, sperm, gall, milk in such as have it

flesh and the like; and also, in a different way, the superfluities,

as phlegm and the excretions of the belly and the bladder. The dry and

solid are such as sinew, skin, vein, hair, bone, gristle, nail, horn

(a term which as applied to the part involves an ambiguity, since

the whole also by virtue of its form is designated horn), and such

parts as present an analogy to these.

Animals differ from one another in their modes of subsistence,

in their actions, in their habits, and in their parts. Concerning

these differences we shall first speak in broad and general terms, and

subsequently we shall treat of the same with close reference to each

particular genus.

Differences are manifested in modes of subsistence, in habits, in

actions performed. For instance, some animals live in water and others

on land. And of those that live in water some do so in one way, and

some in another: that is to say, some live and feed in the water, take

in and emit water, and cannot live if deprived of water, as is the

case with the great majority of fishes; others get their food and

spend their days in the water, but do not take in water but air, nor

do they bring forth in the water. Many of these creatures are

furnished with feet, as the otter, the beaver, and the crocodile; some

are furnished with wings, as the diver and the grebe; some are

destitute of feet, as the water-snake. Some creatures get their living

in the water and cannot exist outside it: but for all that do not take

in either air or water, as, for instance, the sea-nettle and the

oyster. And of creatures that live in the water some live in the

sea, some in rivers, some in lakes, and some in marshes, as the frog

and the newt.

Of animals that live on dry land some take in air and emit it,

which phenomena are termed 'inhalation' and 'exhalation'; as, for

instance, man and all such land animals as are furnished with lungs.

Others, again, do not inhale air, yet live and find their sustenance

on dry land; as, for instance, the wasp, the bee, and all other

insects. And by 'insects' I mean such creatures as have nicks or

notches on their bodies, either on their bellies or on both backs

and bellies.

And of land animals many, as has been said, derive their

subsistence from the water; but of creatures that live in and inhale

water not a single one derives its subsistence from dry land.

Some animals at first live in water, and by and by change their

shape and live out of water, as is the case with river worms, for

out of these the gadfly develops.

Furthermore, some animals are stationary, and some are erratic.

Stationary animals are found in water, but no such creature is found

on dry land. In the water are many creatures that live in close

adhesion to an external object, as is the case with several kinds of

oyster. And, by the way, the sponge appears to be endowed with a

certain sensibility: as a proof of which it is alleged that the

difficulty in detaching it from its moorings is increased if the

movement to detach it be not covertly applied.

Other creatures adhere at one time to an object and detach

themselves from it at other times, as is the case with a species of

the so-called sea-nettle; for some of these creatures seek their

food in the night-time loose and unattached.

Many creatures are unattached but motionless, as is the case with

oysters and the so-called holothuria. Some can swim, as, for instance,

fishes, molluscs, and crustaceans, such as the crawfish. But some of

these last move by walking, as the crab, for it is the nature of the

creature, though it lives in water, to move by walking.

Of land animals some are furnished with wings, such as birds

and bees, and these are so furnished in different ways one from

another; others are furnished with feet. Of the animals that are

furnished with feet some walk, some creep, and some wriggle. But no

creature is able only to move by flying, as the fish is able only to

swim, for the animals with leathern wings can walk; the bat has feet

and the seal has imperfect feet.

Some birds have feet of little power, and are therefore called

Apodes. This little bird is powerful on the wing; and, as a rule,

birds that resemble it are weak-footed and strong winged, such as

the swallow and the drepanis or (?) Alpine swift; for all these

birds resemble one another in their habits and in their plumage, and

may easily be mistaken one for another. (The apus is to be seen at all

seasons, but the drepanis only after rainy weather in summer; for this

is the time when it is seen and captured, though, as a general rule,

it is a rare bird.)

Again, some animals move by walking on the ground as well as by

swimming in water.

Furthermore, the following differences are manifest in their

modes of living and in their actions. Some are gregarious, some are

solitary, whether they be furnished with feet or wings or be fitted

for a life in the water; and some partake of both characters, the

solitary and the gregarious. And of the gregarious, some are