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In the case of contraries, it is not always necessary that if one exists the other should also exist: for if all become healthy there will be health and no disease, and again, if everything turns white, there will be white, but no black. Again, since the fact that Socrates is ill is the contrary of the fact that Socrates is well, and two contrary conditions cannot both obtain in one and the same individual at the same time, both these contraries could not exist at once: for if that Socrates was well was a fact, then that Socrates was ill could not possibly be one.

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It is plain that contrary attributes must needs be present in subjects which belong to the same species or genus. Disease and health require as their subject the body of an animal; white and black require a body, without further qualification; justice and injustice require as their subject the human soul.

Moreover, it is necessary that pairs of contraries should in all cases either belong to the same genus or belong to contrary genera or be themselves genera. White and black belong to the same genus, colour; justice and injustice, to contrary genera, virtue and vice; while good and evil do not belong to genera, but are themselves actual genera, with terms under them.

12

There are four senses in which one thing can be said to be ‘prior’ to another. Primarily and most properly the term has reference to time: in this sense the word is used to indicate that one thing is older or more ancient than another, for the expressions ‘older’ and ‘more ancient’ imply greater length of time.

Secondly, one thing is said to be ‘prior’ to another when the sequence of their being cannot be reversed. In this sense ‘one’ is ‘prior’ to ‘two’.

For if ‘two’ exists, it follows directly that ‘one’ must exist, but if ‘one’ exists, it does not follow necessarily that ‘two’ exists: thus the sequence subsisting cannot be reversed. It is agreed, then, that when the sequence of two things cannot be reversed, then that one on which the other depends is called ‘prior’ to that other.

In the third place, the term ‘prior’ is used with reference to any order, as in the case of science and of oratory. For in sciences which use demonstration there is that which is prior and that which is posterior in order; in geometry, the elements are prior to the propositions; in reading and writing, the letters of the alphabet are prior to the syllables. Similarly, in the case of speeches, the exordium is prior in order to the narrative.

Besides these senses of the word, there is a fourth. That which is better and more honourable is said to have a natural priority. In common par-lance men speak of those whom they honour and love as ‘coming first’

with them. This sense of the word is perhaps the most far-fetched.

Such, then, are the different senses in which the term ‘prior’ is used.

Yet it would seem that besides those mentioned there is yet another.

For in those things, the being of each of which implies that of the other, that which is in any way the cause may reasonably be said to be by nature ‘prior’ to the effect. It is plain that there are instances of this. The 34

fact of the being of a man carries with it the truth of the proposition that he is, and the implication is reciprocal: for if a man is, the proposition wherein we allege that he is true, and conversely, if the proposition wherein we allege that he is true, then he is. The true proposition, however, is in no way the cause of the being of the man, but the fact of the man’s being does seem somehow to be the cause of the truth of the proposition, for the truth or falsity of the proposition depends on the fact of the man’s being or not being.

Thus the word ‘prior’ may be used in five senses.

13

The term ‘simultaneous’ is primarily and most appropriately applied to those things the genesis of the one of which is simultaneous with that of the other; for in such cases neither is prior or posterior to the other.

Such things are said to be simultaneous in point of time. Those things, again, are ‘simultaneous’ in point of nature, the being of each of which involves that of the other, while at the same time neither is the cause of the other’s being. This is the case with regard to the double and the half, for these are reciprocally dependent, since, if there is a double, there is also a half, and if there is a half, there is also a double, while at the same time neither is the cause of the being of the other.

Again, those species which are distinguished one from another and opposed one to another within the same genus are said to be

‘simultaneous’ in nature. I mean those species which are distinguished each from each by one and the same method of division. Thus the

‘winged’ species is simultaneous with the ‘terrestrial’ and the ‘water’

species. These are distinguished within the same genus, and are opposed each to each, for the genus ‘animal’ has the ‘winged’, the ‘terrestrial’, and the ‘water’ species, and no one of these is prior or posterior to another; on the contrary, all such things appear to be ‘simultaneous’ in nature.

Each of these also, the terrestrial, the winged, and the water species, can be divided again into subspecies. Those species, then, also will be

‘simultaneous’ point of nature, which, belonging to the same genus, are distinguished each from each by one and the same method of differentiation.

But genera are prior to species, for the sequence of their being cannot be reversed. If there is the species ‘water-animal’, there will be the genus

‘animal’, but granted the being of the genus ‘animal’, it does not follow necessarily that there will be the species ‘water-animal’.

35

Those things, therefore, are said to be ‘simultaneous’ in nature, the being of each of which involves that of the other, while at the same time neither is in any way the cause of the other’s being; those species, also, which are distinguished each from each and opposed within the same genus. Those things, moreover, are ‘simultaneous’ in the unqualified sense of the word which come into being at the same time.

14

There are six sorts of movement: generation, destruction, increase, diminution, alteration, and change of place.

It is evident in all but one case that all these sorts of movement are distinct each from each. Generation is distinct from destruction, increase and change of place from diminution, and so on. But in the case of alteration it may be argued that the process necessarily implies one or other of the other five sorts of motion. This is not true, for we may say that all affections, or nearly all, produce in us an alteration which is distinct from all other sorts of motion, for that which is affected need not suffer either increase or diminution or any of the other sorts of motion. Thus alteration is a distinct sort of motion; for, if it were not, the thing altered would not only be altered, but would forthwith necessarily suffer increase or diminution or some one of the other sorts of motion in addition; which as a matter of fact is not the case. Similarly that which was undergoing the process of increase or was subject to some other sort of motion would, if alteration were not a distinct form of motion, necessarily be subject to alteration also. But there are some things which undergo increase but yet not alteration. The square, for instance, if a gnomon is applied to it, undergoes increase but not alteration, and so it is with all other figures of this sort. Alteration and increase, therefore, are distinct.

Speaking generally, rest is the contrary of motion. But the different forms of motion have their own contraries in other forms; thus destruction is the contrary of generation, diminution of increase, rest in a place, of change of place. As for this last, change in the reverse direction would seem to be most truly its contrary; thus motion upwards is the contrary of motion downwards and vice versa.

In the case of that sort of motion which yet remains, of those that have been enumerated, it is not easy to state what is its contrary. It appears to have no contrary, unless one should define the contrary here also either as ‘rest in its quality’ or as ‘change in the direction of the contrary quality’, just as we defined the contrary of change of place either as rest in a place or as change in the reverse direction. For a thing is altered when 36

change of quality takes place; therefore either rest in its quality or change in the direction of the contrary may be called the contrary of this qualitative form of motion. In this way becoming white is the contrary of becoming black; there is alteration in the contrary direction, since a change of a qualitative nature takes place.

15

The term ‘to have’ is used in various senses. In the first place it is used with reference to habit or disposition or any other quality, for we are said to ‘have’ a piece of knowledge or a virtue. Then, again, it has reference to quantity, as, for instance, in the case of a man’s height; for he is said to ‘have’ a height of three or four cubits. It is used, moreover, with regard to apparel, a man being said to ‘have’ a coat or tunic; or in respect of something which we have on a part of ourselves, as a ring on the hand: or in respect of something which is a part of us, as hand or foot.

The term refers also to content, as in the case of a vessel and wheat, or of a jar and wine; a jar is said to ‘have’ wine, and a corn-measure wheat.

The expression in such cases has reference to content. Or it refers to that which has been acquired; we are said to ‘have’ a house or a field. A man is also said to ‘have’ a wife, and a wife a husband, and this appears to be the most remote meaning of the term, for by the use of it we mean simply that the husband lives with the wife.

Other senses of the word might perhaps be found, but the most ordinary ones have all been enumerated.

37

On Interpretation

Translated by E. M. Edghill

1

First we must define the terms ‘noun’ and ‘verb’, then the terms

‘denial’ and ‘affirmation’, then ‘proposition’ and ‘sentence.’

Spoken words are the symbols of mental experience and written words are the symbols of spoken words. Just as all men have not the same writing, so all men have not the same speech sounds, but the mental experiences, which these directly symbolize, are the same for all, as also are those things of which our experiences are the images. This matter has, however, been discussed in my treatise about the soul, for it belongs to an investigation distinct from that which lies before us.

As there are in the mind thoughts which do not involve truth or falsity, and also those which must be either true or false, so it is in speech.

For truth and falsity imply combination and separation. Nouns and verbs, provided nothing is added, are like thoughts without combination or separation; ‘man’ and ‘white’, as isolated terms, are not yet either true or false. In proof of this, consider the word ‘goat-stag.’ It has significance, but there is no truth or falsity about it, unless ‘is’ or ‘is not’ is added, either in the present or in some other tense.

2

By a noun we mean a sound significant by convention, which has no reference to time, and of which no part is significant apart from the rest.

In the noun ‘Fairsteed,’ the part ‘steed’ has no significance in and by itself, as in the phrase ‘fair steed.’ Yet there is a difference between simple and composite nouns; for in the former the part is in no way significant, in the latter it contributes to the meaning of the whole, although it has not an independent meaning. Thus in the word ‘pirate-boat’ the word

‘boat’ has no meaning except as part of the whole word.

The limitation ‘by convention’ was introduced because nothing is by nature a noun or name-it is only so when it becomes a symbol; inarticulate sounds, such as those which brutes produce, are significant, yet none of these constitutes a noun.

The expression ‘not-man’ is not a noun. There is indeed no recognized term by which we may denote such an expression, for it is not a sentence or a denial. Let it then be called an indefinite noun.

38

The expressions ‘of Philo’, ‘to Philo’, and so on, constitute not nouns, but cases of a noun. The definition of these cases of a noun is in other respects the same as that of the noun proper, but, when coupled with ‘is’,

‘was’, or will be’, they do not, as they are, form a proposition either true or false, and this the noun proper always does, under these conditions.

Take the words ‘of Philo is’ or ‘of or ‘of Philo is not’; these words do not, as they stand, form either a true or a false proposition.

3

A verb is that which, in addition to its proper meaning, carries with it the notion of time. No part of it has any independent meaning, and it is a sign of something said of something else.

I will explain what I mean by saying that it carries with it the notion of time. ‘Health’ is a noun, but ‘is healthy’ is a verb; for besides its proper meaning it indicates the present existence of the state in question.

Moreover, a verb is always a sign of something said of something else, i.e. of something either predicable of or present in some other thing.

Such expressions as ‘is not-healthy’, ‘is not, ill’, I do not describe as verbs; for though they carry the additional note of time, and always form a predicate, there is no specified name for this variety; but let them be called indefinite verbs, since they apply equally well to that which exists and to that which does not.

Similarly ‘he was healthy’, ‘he will be healthy’, are not verbs, but tenses of a verb; the difference lies in the fact that the verb indicates present time, while the tenses of the verb indicate those times which lie outside the present.

Verbs in and by themselves are substantival and have significance, for he who uses such expressions arrests the hearer’s mind, and fixes his attention; but they do not, as they stand, express any judgement, either positive or negative. For neither are ‘to be’ and ‘not to be’ the participle

‘being’ significant of any fact, unless something is added; for they do not themselves indicate anything, but imply a copulation, of which we cannot form a conception apart from the things coupled.

4

A sentence is a significant portion of speech, some parts of which have an independent meaning, that is to say, as an utterance, though not as the expression of any positive judgement. Let me explain. The word

‘human’ has meaning, but does not constitute a proposition, either 39

positive or negative. It is only when other words are added that the whole will form an affirmation or denial. But if we separate one syllable of the word ‘human’ from the other, it has no meaning; similarly in the word ‘mouse’, the part ‘ouse’ has no meaning in itself, but is merely a sound. In composite words, indeed, the parts contribute to the meaning of the whole; yet, as has been pointed out, they have not an independent meaning.

Every sentence has meaning, not as being the natural means by which a physical faculty is realized, but, as we have said, by convention. Yet every sentence is not a proposition; only such are propositions as have in them either truth or falsity. Thus a prayer is a sentence, but is neither true nor false.

Let us therefore dismiss all other types of sentence but the proposition, for this last concerns our present inquiry, whereas the investigation of the others belongs rather to the study of rhetoric or of poetry.

5

The first class of simple propositions is the simple affirmation, the next, the simple denial; all others are only one by conjunction.

Every proposition must contain a verb or the tense of a verb. The phrase which defines the species ‘man’, if no verb in present, past, or future time be added, is not a proposition. It may be asked how the expression ‘a footed animal with two feet’ can be called single; for it is not the circumstance that the words follow in unbroken succession that effects the unity. This inquiry, however, finds its place in an investigation foreign to that before us.

We call those propositions single which indicate a single fact, or the conjunction of the parts of which results in unity: those propositions, on the other hand, are separate and many in number, which indicate many facts, or whose parts have no conjunction.

Let us, moreover, consent to call a noun or a verb an expression only, and not a proposition, since it is not possible for a man to speak in this way when he is expressing something, in such a way as to make a statement, whether his utterance is an answer to a question or an act of his own initiation.

To return: of propositions one kind is simple, i.e. that which asserts or denies something of something, the other composite, i.e. that which is compounded of simple propositions. A simple proposition is a statement, with meaning, as to the presence of something in a subject or its absence, in the present, past, or future, according to the divisions of time.

40

6

An affirmation is a positive assertion of something about something, a denial a negative assertion.

Now it is possible both to affirm and to deny the presence of something which is present or of something which is not, and since these same affirmations and denials are possible with reference to those times which lie outside the present, it would be possible to contradict any affirmation or denial. Thus it is plain that every affirmation has an opposite denial, and similarly every denial an opposite affirmation.

We will call such a pair of propositions a pair of contradictories. Those positive and negative propositions are said to be contradictory which have the same subject and predicate. The identity of subject and of predicate must not be ‘equivocal’. Indeed there are definitive qualifications besides this, which we make to meet the casuistries of sophists.

7

Some things are universal, others individual. By the term ‘universal’ I mean that which is of such a nature as to be predicated of many subjects, by ‘individual’ that which is not thus predicated. Thus ‘man’ is a universal, ‘Callias’ an individual.

Our propositions necessarily sometimes concern a universal subject, sometimes an individual.

If, then, a man states a positive and a negative proposition of universal character with regard to a universal, these two propositions are

‘contrary’. By the expression ‘a proposition of universal character with regard to a universal’, such propositions as ‘every man is white’, ‘no man is white’ are meant. When, on the other hand, the positive and negative propositions, though they have regard to a universal, are yet not of universal character, they will not be contrary, albeit the meaning intended is sometimes contrary. As instances of propositions made with regard to a universal, but not of universal character, we may take the ‘propositions

‘man is white’, ‘man is not white’. ‘Man’ is a universal, but the proposition is not made as of universal character; for the word ‘every’ does not make the subject a universal, but rather gives the proposition a universal character. If, however, both predicate and subject are distributed, the proposition thus constituted is contrary to truth; no affirmation will, under such circumstances, be true. The proposition ‘every man is every animal’ is an example of this type.

41

An affirmation is opposed to a denial in the sense which I denote by the term ‘contradictory’, when, while the subject remains the same, the affirmation is of universal character and the denial is not. The affirmation ‘every man is white’ is the contradictory of the denial ‘not every man is white’, or again, the proposition ‘no man is white’ is the contradictory of the proposition ‘some men are white’. But propositions are opposed as contraries when both the affirmation and the denial are universal, as in the sentences ‘every man is white’, ‘no man is white’, ‘every man is just’, ‘no man is just’.

We see that in a pair of this sort both propositions cannot be true, but the contradictories of a pair of contraries can sometimes both be true with reference to the same subject; for instance ‘not every man is white’

and some men are white’ are both true. Of such corresponding positive and negative propositions as refer to universals and have a universal character, one must be true and the other false. This is the case also when the reference is to individuals, as in the propositions ‘Socrates is white’,

‘Socrates is not white’.

When, on the other hand, the reference is to universals, but the propositions are not universal, it is not always the case that one is true and the other false, for it is possible to state truly that man is white and that man is not white and that man is beautiful and that man is not beautiful; for if a man is deformed he is the reverse of beautiful, also if he is progressing towards beauty he is not yet beautiful.

This statement might seem at first sight to carry with it a contradiction, owing to the fact that the proposition ‘man is not white’ appears to be equivalent to the proposition ‘no man is white’. This, however, is not the case, nor are they necessarily at the same time true or false.

It is evident also that the denial corresponding to a single affirmation is itself single; for the denial must deny just that which the affirmation affirms concerning the same subject, and must correspond with the affirmation both in the universal or particular character of the subject and in the distributed or undistributed sense in which it is understood.

For instance, the affirmation ‘Socrates is white’ has its proper denial in the proposition ‘Socrates is not white’. If anything else be negatively predicated of the subject or if anything else be the subject though the predicate remain the same, the denial will not be the denial proper to that affirmation, but on that is distinct.

The denial proper to the affirmation ‘every man is white’ is ‘not every man is white’; that proper to the affirmation ‘some men are white’ is ‘no 42

man is white’, while that proper to the affirmation ‘man is white’ is ‘man is not white’.

We have shown further that a single denial is contradictorily opposite to a single affirmation and we have explained which these are; we have also stated that contrary are distinct from contradictory propositions and which the contrary are; also that with regard to a pair of opposite propositions it is not always the case that one is true and the other false. We have pointed out, moreover, what the reason of this is and under what circumstances the truth of the one involves the falsity of the other.

8

An affirmation or denial is single, if it indicates some one fact about some one subject; it matters not whether the subject is universal and whether the statement has a universal character, or whether this is not so. Such single propositions are: ‘every man is white’, ‘not every man is white’;’man is white’,’man is not white’; ‘no man is white’, ‘some men are white’; provided the word ‘white’ has one meaning. If, on the other hand, one word has two meanings which do not combine to form one, the affirmation is not single. For instance, if a man should establish the symbol ‘garment’ as significant both of a horse and of a man, the proposition ‘garment is white’ would not be a single affirmation, nor its opposite a single denial. For it is equivalent to the proposition ‘horse and man are white’, which, again, is equivalent to the two propositions ‘horse is white’, ‘man is white’. If, then, these two propositions have more than a single significance, and do not form a single proposition, it is plain that the first proposition either has more than one significance or else has none; for a particular man is not a horse.

This, then, is another instance of those propositions of which both the positive and the negative forms may be true or false simultaneously.

9

In the case of that which is or which has taken place, propositions, whether positive or negative, must be true or false. Again, in the case of a pair of contradictories, either when the subject is universal and the propositions are of a universal character, or when it is individual, as has been said,’ one of the two must be true and the other false; whereas when the subject is universal, but the propositions are not of a universal character, there is no such necessity. We have discussed this type also in a previous chapter.

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When the subject, however, is individual, and that which is predicated of it relates to the future, the case is altered. For if all propositions whether positive or negative are either true or false, then any given predicate must either belong to the subject or not, so that if one man affirms that an event of a given character will take place and another denies it, it is plain that the statement of the one will correspond with reality and that of the other will not. For the predicate cannot both belong and not belong to the subject at one and the same time with regard to the future.

Thus, if it is true to say that a thing is white, it must necessarily be white; if the reverse proposition is true, it will of necessity not be white.

Again, if it is white, the proposition stating that it is white was true; if it is not white, the proposition to the opposite effect was true. And if it is not white, the man who states that it is making a false statement; and if the man who states that it is white is making a false statement, it follows that it is not white. It may therefore be argued that it is necessary that affirmations or denials must be either true or false.

Now if this be so, nothing is or takes place fortuitously, either in the present or in the future, and there are no real alternatives; everything takes place of necessity and is fixed. For either he that affirms that it will take place or he that denies this is in correspondence with fact, whereas if things did not take place of necessity, an event might just as easily not happen as happen; for the meaning of the word ‘fortuitous’ with regard to present or future events is that reality is so constituted that it may issue in either of two opposite directions. Again, if a thing is white now, it was true before to say that it would be white, so that of anything that has taken place it was always true to say ‘it is’ or ‘it will be’. But if it was always true to say that a thing is or will be, it is not possible that it should not be or not be about to be, and when a thing cannot not come to be, it is impossible that it should not come to be, and when it is impossible that it should not come to be, it must come to be. All, then, that is about to be must of necessity take place. It results from this that nothing is uncertain or fortuitous, for if it were fortuitous it would not be necessary.

Again, to say that neither the affirmation nor the denial is true, maintaining, let us say, that an event neither will take place nor will not take place, is to take up a position impossible to defend. In the first place, though facts should prove the one proposition false, the opposite would still be untrue. Secondly, if it was true to say that a thing was both white and large, both these qualities must necessarily belong to it; and if they will belong to it the next day, they must necessarily belong to it the next day. But if an event is neither to take place nor not to take place the next 44

day, the element of chance will be eliminated. For example, it would be necessary that a sea-fight should neither take place nor fail to take place on the next day.

These awkward results and others of the same kind follow, if it is an irrefragable law that of every pair of contradictory propositions, whether they have regard to universals and are stated as universally applicable, or whether they have regard to individuals, one must be true and the other false, and that there are no real alternatives, but that all that is or takes place is the outcome of necessity. There would be no need to deliberate or to take trouble, on the supposition that if we should adopt a certain course, a certain result would follow, while, if we did not, the result would not follow. For a man may predict an event ten thousand years beforehand, and another may predict the reverse; that which was truly predicted at the moment in the past will of necessity take place in the fullness of time.

Further, it makes no difference whether people have or have not actually made the contradictory statements. For it is manifest that the circumstances are not influenced by the fact of an affirmation or denial on the part of anyone. For events will not take place or fail to take place because it was stated that they would or would not take place, nor is this any more the case if the prediction dates back ten thousand years or any other space of time. Wherefore, if through all time the nature of things was so constituted that a prediction about an event was true, then through all time it was necessary that that should find fulfillment; and with regard to all events, circumstances have always been such that their occurrence is a matter of necessity. For that of which someone has said truly that it will be, cannot fail to take place; and of that which takes place, it was always true to say that it would be.

Yet this view leads to an impossible conclusion; for we see that both deliberation and action are causative with regard to the future, and that, to speak more generally, in those things which are not continuously actual there is potentiality in either direction. Such things may either be or not be; events also therefore may either take place or not take place.

There are many obvious instances of this. It is possible that this coat may be cut in half, and yet it may not be cut in half, but wear out first. In the same way, it is possible that it should not be cut in half; unless this were so, it would not be possible that it should wear out first. So it is therefore with all other events which possess this kind of potentiality. It is therefore plain that it is not of necessity that everything is or takes place; but in some instances there are real alternatives, in which case the 45

affirmation is no more true and no more false than the denial; while some exhibit a predisposition and general tendency in one direction or the other, and yet can issue in the opposite direction by exception.

Now that which is must needs be when it is, and that which is not must needs not be when it is not. Yet it cannot be said without qualification that all existence and non-existence is the outcome of necessity. For there is a difference between saying that that which is, when it is, must needs be, and simply saying that all that is must needs be, and similarly in the case of that which is not. In the case, also, of two contradictory propositions this holds good. Everything must either be or not be, whether in the present or in the future, but it is not always possible to distinguish and state determinately which of these alternatives must necessarily come about.

Let me illustrate. A sea-fight must either take place to-morrow or not, but it is not necessary that it should take place to-morrow, neither is it necessary that it should not take place, yet it is necessary that it either should or should not take place to-morrow. Since propositions correspond with facts, it is evident that when in future events there is a real alternative, and a potentiality in contrary directions, the corresponding affirmation and denial have the same character.

This is the case with regard to that which is not always existent or not always nonexistent. One of the two propositions in such instances must be true and the other false, but we cannot say determinately that this or that is false, but must leave the alternative undecided. One may indeed be more likely to be true than the other, but it cannot be either actually true or actually false. It is therefore plain that it is not necessary that of an affirmation and a denial one should be true and the other false. For in the case of that which exists potentially, but not actually, the rule which applies to that which exists actually does not hold good. The case is rather as we have indicated.

10

An affirmation is the statement of a fact with regard to a subject, and this subject is either a noun or that which has no name; the subject and predicate in an affirmation must each denote a single thing. I have already explained’ what is meant by a noun and by that which has no name; for I stated that the expression ‘not-man’ was not a noun, in the proper sense of the word, but an indefinite noun, denoting as it does in a certain sense a single thing. Similarly the expression ‘does not enjoy health’ is not a verb proper, but an indefinite verb. Every affirmation, 46

then, and every denial, will consist of a noun and a verb, either definite or indefinite.

There can be no affirmation or denial without a verb; for the expressions ‘is’, ‘will be’, ‘was’, ‘is coming to be’, and the like are verbs according to our definition, since besides their specific meaning they convey the notion of time. Thus the primary affirmation and denial are ‘as follows: ‘man is’, ‘man is not’. Next to these, there are the propositions:

‘not-man is’, ‘not-man is not’. Again we have the propositions: ‘every man is, ‘every man is not’, ‘all that is not-man is’, ‘all that is not-man is not’. The same classification holds good with regard to such periods of time as lie outside the present.

When the verb ‘is’ is used as a third element in the sentence, there can be positive and negative propositions of two sorts. Thus in the sentence

‘man is just’ the verb ‘is’ is used as a third element, call it verb or noun, which you will. Four propositions, therefore, instead of two can be formed with these materials. Two of the four, as regards their affirmation and denial, correspond in their logical sequence with the propositions which deal with a condition of privation; the other two do not correspond with these.

I mean that the verb ‘is’ is added either to the term ‘just’ or to the term

‘not-just’, and two negative propositions are formed in the same way.

Thus we have the four propositions. Reference to the subjoined table will make matters clear:

<

tbody>

A. Affirmation. Man is just

B. Denial. Man is not just

\

/

/

\

D. Denial. Man is not not-just C. Affirmation. Man is not-just Here ‘is’ and ‘is not’ are added either to ‘just’ or to ‘not-just’. This then is the proper scheme for these propositions, as has been said in the Analytics. The same rule holds good, if the subject is distributed. Thus we have the table:

<

tbody>

A'. Affirmation. Every man is just B'. Denial. Not every man is just

\

/

/

\

47

D'. Denial. Not every man is not- C'. Affirmation. Every man is not-just

just.

Yet here it is not possible, in the same way as in the former case, that the propositions joined in the table by a diagonal line should both be true; though under certain circumstances this is the case.

We have thus set out two pairs of opposite propositions; there are moreover two other pairs, if a term be conjoined with ‘not-man’, the latter forming a kind of subject. Thus:

<

tbody>

A". Not-man is just.

B". Not-man is not just

\

/

/

\

D". Not-man is not not-just. C". Not-man is not-just.

This is an exhaustive enumeration of all the pairs of opposite propositions that can possibly be framed. This last group should remain distinct from those which preceded it, since it employs as its subject the expression ‘not-man’.

When the verb ‘is’ does not fit the structure of the sentence (for instance, when the verbs ‘walks’, ‘enjoys health’ are used), that scheme applies, which applied when the word ‘is’ was added.

Thus we have the propositions: ‘every man enjoys health’, ‘every man does-not-enjoy-health’, ‘all that is not-man enjoys health’, ‘all that is not-man does-not-enjoy-health’. We must not in these propositions use the expression ‘not every man’. The negative must be attached to the word

‘man’, for the word ‘every’ does not give to the subject a universal significance, but implies that, as a subject, it is distributed. This is plain from the following pairs: ‘man enjoys health’, ‘man does not enjoy health’;

‘not-man enjoys health’, ‘not man does not enjoy health’. These propositions differ from the former in being indefinite and not universal in character. Thus the adjectives ‘every’ and no additional significance except that the subject, whether in a positive or in a negative sentence, is distributed. The rest of the sentence, therefore, will in each case be the same.

Since the contrary of the proposition ‘every animal is just’ is ‘no animal is just’, it is plain that these two propositions will never both be true at the same time or with reference to the same subject. Sometimes, however, the contradictories of these contraries will both be true, as in the instance before us: the propositions ‘not every animal is just’ and

‘some animals are just’ are both true.

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Further, the proposition ‘no man is just’ follows from the proposition

‘every man is not just’ and the proposition ‘not every man is not just’, which is the opposite of ‘every man is not-just’, follows from the proposition ‘some men are just’; for if this be true, there must be some just men.

It is evident, also, that when the subject is individual, if a question is asked and the negative answer is the true one, a certain positive proposition is also true. Thus, if the question were asked Socrates wise?’ and the negative answer were the true one, the positive inference ‘Then Socrates is unwise’ is correct. But no such inference is correct in the case of universals, but rather a negative proposition. For instance, if to the question

‘Is every man wise?’ the answer is ‘no’, the inference ‘Then every man is unwise’ is false. But under these circumstances the inference ‘Not every man is wise’ is correct. This last is the contradictory, the former the contrary. Negative expressions, which consist of an indefinite noun or predicate, such as ‘not-man’ or ‘not-just’, may seem to be denials containing neither noun nor verb in the proper sense of the words. But they are not.

For a denial must always be either true or false, and he that uses the expression ‘not man’, if nothing more be added, is not nearer but rather further from making a true or a false statement than he who uses the expression ‘man’.

The propositions ‘everything that is not man is just’, and the contradictory of this, are not equivalent to any of the other propositions; on the other hand, the proposition ‘everything that is not man is not just’ is equivalent to the proposition ‘nothing that is not man is just’.

The conversion of the position of subject and predicate in a sentence involves no difference in its meaning. Thus we say ‘man is white’ and

‘white is man’. If these were not equivalent, there would be more than one contradictory to the same proposition, whereas it has been demonstrated’ that each proposition has one proper contradictory and one only.

For of the proposition ‘man is white’ the appropriate contradictory is

‘man is not white’, and of the proposition ‘white is man’, if its meaning be different, the contradictory will either be ‘white is not not-man’ or

‘white is not man’. Now the former of these is the contradictory of the proposition ‘white is not-man’, and the latter of these is the contradictory of the proposition ‘man is white’; thus there will be two contradictories to one proposition.

It is evident, therefore, that the inversion of the relative position of subject and predicate does not affect the sense of affirmations and denials.

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11

There is no unity about an affirmation or denial which, either positively or negatively, predicates one thing of many subjects, or many things of the same subject, unless that which is indicated by the many is really some one thing. do not apply this word ‘one’ to those things which, though they have a single recognized name, yet do not combine to form a unity. Thus, man may be an animal, and biped, and domesticated, but these three predicates combine to form a unity. On the other hand, the predicates ‘white’, ‘man’, and ‘walking’ do not thus combine.

Neither, therefore, if these three form the subject of an affirmation, nor if they form its predicate, is there any unity about that affirmation. In both cases the unity is linguistic, but not real.

If therefore the dialectical question is a request for an answer, i.e.

either for the admission of a premiss or for the admission of one of two contradictories-and

the

premiss

is

itself

always

one

of

two

contradictories-the answer to such a question as contains the above predicates cannot be a single proposition. For as I have explained in the Topics, question is not a single one, even if the answer asked for is true.

At the same time it is plain that a question of the form ‘what is it?’ is not a dialectical question, for a dialectical questioner must by the form of his question give his opponent the chance of announcing one of two alternatives, whichever he wishes. He must therefore put the question into a more definite form, and inquire, e.g.. whether man has such and such a characteristic or not.

Some combinations of predicates are such that the separate predicates unite to form a single predicate. Let us consider under what conditions this is and is not possible. We may either state in two separate propositions that man is an animal and that man is a biped, or we may combine the two, and state that man is an animal with two feet. Similarly we may use ‘man’ and ‘white’ as separate predicates, or unite them into one. Yet if a man is a shoemaker and is also good, we cannot construct a composite proposition and say that he is a good shoemaker. For if, whenever two separate predicates truly belong to a subject, it follows that the predicate resulting from their combination also truly belongs to the subject, many absurd results ensue. For instance, a man is man and white. Therefore, if predicates may always be combined, he is a white man. Again, if the predicate ‘white’ belongs to him, then the combination of that predicate with the former composite predicate will be permissible. Thus it will be right to say that he is a white man so on indefinitely. Or, again, we may combine the predicates ‘musical’, ‘white’, and ‘walking’, and these 50

may be combined many times. Similarly we may say that Socrates is Socrates and a man, and that therefore he is the man Socrates, or that Socrates is a man and a biped, and that therefore he is a two-footed man.

Thus it is manifest that if man states unconditionally that predicates can always be combined, many absurd consequences ensue.

We will now explain what ought to be laid down.

Those predicates, and terms forming the subject of predication, which are accidental either to the same subject or to one another, do not combine to form a unity. Take the proposition ‘man is white of complexion and musical’. Whiteness and being musical do not coalesce to form a unity, for they belong only accidentally to the same subject. Nor yet, if it were true to say that that which is white is musical, would the terms

‘musical’ and ‘white’ form a unity, for it is only incidentally that that which is musical is white; the combination of the two will, therefore, not form a unity.

Thus, again, whereas, if a man is both good and a shoemaker, we cannot combine the two propositions and say simply that he is a good shoemaker, we are, at the same time, able to combine the predicates ‘animal’

and ‘biped’ and say that a man is an animal with two feet, for these predicates are not accidental.

Those predicates, again, cannot form a unity, of which the one is implicit in the other: thus we cannot combine the predicate ‘white’ again and again with that which already contains the notion ‘white’, nor is it right to call a man an animal-man or a two-footed man; for the notions

‘animal’ and ‘biped’ are implicit in the word ‘man’. On the other hand, it is possible to predicate a term simply of any one instance, and to say that some one particular man is a man or that some one white man is a white man.

Yet this is not always possible: indeed, when in the adjunct there is some opposite which involves a contradiction, the predication of the simple term is impossible. Thus it is not right to call a dead man a man.

When, however, this is not the case, it is not impossible.

Yet the facts of the case might rather be stated thus: when some such opposite elements are present, resolution is never possible, but when they are not present, resolution is nevertheless not always possible. Take the proposition ‘Homer is so-and-so’, say ‘a poet’; does it follow that Homer is, or does it not? The verb ‘is’ is here used of Homer only incidentally, the proposition being that Homer is a poet, not that he is, in the independent sense of the word.

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Thus, in the case of those predications which have within them no contradiction when the nouns are expanded into definitions, and wherein the predicates belong to the subject in their own proper sense and not in any indirect way, the individual may be the subject of the simple propositions as well as of the composite. But in the case of that which is not, it is not true to say that because it is the object of opinion, it is; for the opinion held about it is that it is not, not that it is.

12

As these distinctions have been made, we must consider the mutual relation of those affirmations and denials which assert or deny possibility or contingency, impossibility or necessity: for the subject is not without difficulty.

We admit that of composite expressions those are contradictory each to each which have the verb ‘to be’ its positive and negative form respectively. Thus the contradictory of the proposition ‘man is’ is ‘man is not’, not ‘not-man is’, and the contradictory of ‘man is white’ is ‘man is not white’, not ‘man is not-white’. For otherwise, since either the positive or the negative proposition is true of any subject, it will turn out true to say that a piece of wood is a man that is not white.

Now if this is the case, in those propositions which do not contain the verb ‘to be’ the verb which takes its place will exercise the same function.

Thus the contradictory of ‘man walks’ is ‘man does not walk’, not ‘not-man walks’; for to say ‘man walks’ merely equivalent to saying ‘man is walking’.

If then this rule is universal, the contradictory of ‘it may be’ is may not be’, not ‘it cannot be’.

Now it appears that the same thing both may and may not be; for instance, everything that may be cut or may walk may also escape cutting and refrain from walking; and the reason is that those things that have potentiality in this sense are not always actual. In such cases, both the positive and the negative propositions will be true; for that which is capable of walking or of being seen has also a potentiality in the opposite direction.

But since it is impossible that contradictory propositions should both be true of the same subject, it follows that’ it may not be’ is not the contradictory of ‘it may be’. For it is a logical consequence of what we have said, either that the same predicate can be both applicable and inapplicable to one and the same subject at the same time, or that it is not by the addition of the verbs ‘be’ and ‘not be’, respectively, that positive and 52

negative propositions are formed. If the former of these alternatives must be rejected, we must choose the latter.

The contradictory, then, of ‘it may be’ is ‘it cannot be’. The same rule applies to the proposition ‘it is contingent that it should be’; the contradictory of this is ‘it is not contingent that it should be’. The similar propositions, such as ‘it is necessary’ and ‘it is impossible’, may be dealt with in the same manner. For it comes about that just as in the former instances the verbs ‘is’ and ‘is not’ were added to the subject-matter of the sentence ‘white’ and ‘man’, so here ‘that it should be’ and ‘that it should not be’ are the subject-matter and ‘is possible’, ‘is contingent’, are added.

These indicate that a certain thing is or is not possible, just as in the former instances ‘is’ and ‘is not’ indicated that certain things were or were not the case.

The contradictory, then, of ‘it may not be’ is not ‘it cannot be’, but ‘it cannot not be’, and the contradictory of ‘it may be’ is not ‘it may not be’, but cannot be’. Thus the propositions ‘it may be’ and ‘it may not be’ appear each to imply the other: for, since these two propositions are not contradictory, the same thing both may and may not be. But the propositions ‘it may be’ and ‘it cannot be’ can never be true of the same subject at the same time, for they are contradictory. Nor can the propositions ‘it may not be’ and ‘it cannot not be’ be at once true of the same subject.

The propositions which have to do with necessity are governed by the same principle. The contradictory of ‘it is necessary that it should be’, is not ‘it is necessary that it should not be,’ but ‘it is not necessary that it should be’, and the contradictory of ‘it is necessary that it should not be’

is ‘it is not necessary that it should not be’.

Again, the contradictory of ‘it is impossible that it should be’ is not ‘it is impossible that it should not be’ but ‘it is not impossible that it should be’, and the contradictory of ‘it is impossible that it should not be’ is ‘it is not impossible that it should not be’.

To generalize, we must, as has been stated, define the clauses ‘that it should be’ and ‘that it should not be’ as the subject-matter of the propositions, and in making these terms into affirmations and denials we must combine them with ‘that it should be’ and ‘that it should not be’

respectively.

We must consider the following pairs as contradictory propositions:

<

tbody>

It may be.

It cannot be.

It is contingent. It is not contingent.

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It is impossible. It is not impossible.

It is necessary. It is not necessary.

It is true.

It is not true.

13

Logical sequences follow in due course when we have arranged the propositions thus. From the proposition ‘it may be’ it follows that it is contingent, and the relation is reciprocal. It follows also that it is not impossible and not necessary.

From the proposition ‘it may not be’ or ‘it is contingent that it should not be’ it follows that it is not necessary that it should not be and that it is not impossible that it should not be. From the proposition ‘it cannot be’

or ‘it is not contingent’ it follows that it is necessary that it should not be and that it is impossible that it should be. From the proposition ‘it cannot not be’ or ‘it is not contingent that it should not be’ it follows that it is necessary that it should be and that it is impossible that it should not be.

Let us consider these statements by the help of a table:

<

tbody>

A.

B.

It may be.

It cannot be.

It is contingent.

It is not contingent.

It is not impossible that it should be. It is impossible that it should be.

It is not necessary that it should be. It is necessary that it should not be.

C.

D.

It may not be.

It cannot not be.

It is not contingent that it should

It is contingent that it should not be. not be.

It is not impossible that it should It is impossible that it should not not be.