# The Works of Aristotle/On Interpretation

| Ch. 1. | (1) The spoken word is a symbol of thought. |
| Ch. 1 | (2) Isolated thoughts or expressions are neither true or false. |
| Ch. 1 | (3) Truth and falsehood are only attributable to certain combinations of thoughts or of words. |
| Ch. 2. | (1) Definition of a noun. |
| Ch. 2 | (2) Simple and composite nouns. |
| Ch. 2 | (3) Indefinite nouns. |
| Ch. 2 | (4) Cases of an noun. |
| Ch. 3. | (1) Definition of a verb. |
| Ch. 3 | (2) Indefinite verbs. |
| Ch. 3 | (3) Tenses of a verb. |
| Ch. 3 | (4) Verbal nouns and adjectives. |
| Ch. 4. | Definition of a sentence. |
| Ch. 5. | Simple and compound propositions. |
| Ch. 6. | Contradictory propositions. |
| Ch. 7. | (1) Universal, indefinite, and particular affirmations and denials. |
| Ch. 7 | (2) Contrary as opposed to contradictory propositions. |
| Ch. 7 | (3) In contrary propositions, of which the subject is universal or particular, the truth of the one proposition implies the falsity of the other, but this is not the case in indefinite propositions. |
| Ch. 8. | Definition of single propositions. |
| Ch. 9. | Propositions which refer to rpesent or past time must be either true or false: propositions which refer to future time must be either true or false, but it is not determined which must be true and which false. |
| Ch. 10. | (1) Diagrammatic arrangement of pairs of affirmations and denials, (a) without the complement of the verb 'to be', (b) with the complement of the verb 'to be', (c) with an indefinite noun for subject. |
| (2) | The right position of the negative. |
| (3) | Contraries can never be both true, but subcontraries may both be true. |
| (4) | In particular propositions, if the affirmative is false, the contrary is true; in universal propositions, if the affirmative is false, the contradictory is true. |
| (5) | Propositions consisting of an indefinite noun and an indefinite verb are not denials. |
| (6) | The relation to other propositions of those which have an indefinite noun as subject. |
| (7) | The transposition of nouns and verbs makes no difference to the sense of the proposition. |
| Ch. 11. | (1) Some seemingly simple propositions are really compound. |
| (2) | Similarly some dialectical questions are really compound. |
| (3) | The nature of a dialectical question. |
| (4) | When two simple propositions having the same subject are true, it is not necessarily the case that the proposition resulting from the combination of the predicates is true. |
| (5) | A plurality of predicates which individually belong to the same subject can only be combined to form a simple proposition when they are essentially predicable of the subject, and when one is not implicit in another. |
| (6) | A compound predicate cannot be resolved into simple predicates when the compound predicate has within it a contradiction in terms, or when one of the predicates is used in a secondary sense. |
| Ch. 12. | (1) Propositions concerning possibility, impossibility, contingency, and necessity. |
| (2) | Determination of the proper contradictories of such propositions. |
| Ch. 13. | (1) Scheme to show the relation subsisting between such propositions. |
| (2) | Illogical character of this scheme proved. |
| (3) | Revised scheme. |
| (4) | That which is said to be possible may be (a) always actual, (b) sometimes actual and sometimes not, (c) never actual. |
| Ch. 14. | Discussion as to whether a contrary affirmation or a denial is the proper contrary of an affirmation, either universal or particular. |
1 16a 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 $^5$ 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 $^{10}$ false, so it is in speech. For truth and falsity imply combination and separation. Nouns and verbs, provided no thing is added, are like thoughts without combination or separation; 'man' and 'white', as isolated terms, are not $^{15}$ 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 $^{20}$ 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 $^{25}$ 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.
$^{30}$ 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 e called an indefinite noun.
The expressions 'of Philo', 'to Philo', and so on, constitute 16b 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 Philo is not'; these words do not, as they stand, form either $^5$ 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.
$^{10}$ 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 $^5$ 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 $^{20}$ 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' and 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 $^{25}$ 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 positive or negative. It is only when other words are added that the whole will form an affirmation or denial. But if $^{30}$ 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 17a 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.
​$^5$ 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.
$^{10}$ 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.
$^{15}$ 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.
$^{20}$ 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.
6 $^{25}$ 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. $^{30}$ 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 $^{35}$ 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' $^{40}$ an individual.
17b 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 $^5$ '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' $^{10}$ 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, $^{15}$ be true. The proposition every man is every animal is an example of this type.
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'. $^{20}$ 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 $^{25}$ 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 $^{30}$ 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 $^{35}$ 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 18a 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 one that is distinct.
The denial proper to the affirmation 'every man is white' is not 'every man is white'; that proper to the affirmation $^5$ 'some men are white' is 'no 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 $^{10}$ 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 $^{15}$ 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 $^{20}$ 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 $^{25}$ 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 $^{30}$ 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.
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 $^{35}$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 18bnecessarily 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 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, $^5$ 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 $^{10}$ 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, $^{15}$ 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 $^{20}$ 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 day, the element of chance will be eliminated. For example, it would be necessary that a sea-fight should neither $^{25}$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 $^{30}$ 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 $^{35}$ 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 19a 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 prediction should find fulfilment; 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 $^5$ 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 a potentiality in either direction. Such things may either be $^{10}$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 $^{15}$ 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 affirmation is no more true and no more false than the denial; while some exhibit a predisposition and general $^{20}$ 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 ​not be said without qualification that all existence and non-existence is the outcome of necessity. For there is a $^{25}$ 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.
$^{30}$ 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.
$^{35}$ This is the case with regard to that which is not always existent or not always non-existent. 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 19b 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 $^5$ 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, then, and every denial, $^{10}$ 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 be sides 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: $^{15}$ '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 $^{20}$ '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 $^{25}$ 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:
Here 'is' and 'is not' are added either to 'just' or to 'not-just'. $^{30}$ 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:
$^{35}$ 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; ​Page:Works of Aristotle - vol. 1, ed. Ross - 1928 (djvu, worksofaristotle01arisuoft).djvu/75 ​Page:Works of Aristotle - vol. 1, ed. Ross - 1928 (djvu, worksofaristotle01arisuoft).djvu/76 ​Page:Works of Aristotle - vol. 1, ed. Ross - 1928 (djvu, worksofaristotle01arisuoft).djvu/77 ​Page:Works of Aristotle - vol. 1, ed. Ross - 1928 (djvu, worksofaristotle01arisuoft).djvu/78 ​Page:Works of Aristotle - vol. 1, ed. Ross - 1928 (djvu, worksofaristotle01arisuoft).djvu/79 ​Page:Works of Aristotle - vol. 1, ed. Ross - 1928 (djvu, worksofaristotle01arisuoft).djvu/80 ​Page:Works of Aristotle - vol. 1, ed. Ross - 1928 (djvu, worksofaristotle01arisuoft).djvu/81 ​Page:Works of Aristotle - vol. 1, ed. Ross - 1928 (djvu, worksofaristotle01arisuoft).djvu/82 ​Page:Works of Aristotle - vol. 1, ed. Ross - 1928 (djvu, worksofaristotle01arisuoft).djvu/83 ​Page:Works of Aristotle - vol. 1, ed. Ross - 1928 (djvu, worksofaristotle01arisuoft).djvu/84 ​Page:Works of Aristotle - vol. 1, ed. Ross - 1928 (djvu, worksofaristotle01arisuoft).djvu/85 ​Page:Works of Aristotle - vol. 1, ed. Ross - 1928 (djvu, worksofaristotle01arisuoft).djvu/86 ​Page:Works of Aristotle - vol. 1, ed. Ross - 1928 (djvu, worksofaristotle01arisuoft).djvu/87 ​Page:Works of Aristotle - vol. 1, ed. Ross - 1928 (djvu, worksofaristotle01arisuoft).djvu/88 ​Page:Works of Aristotle - vol. 1, ed. Ross - 1928 (djvu, worksofaristotle01arisuoft).djvu/89 ​Page:Works of Aristotle - vol. 1, ed. Ross - 1928 (djvu, worksofaristotle01arisuoft).djvu/90
* ↑ Great difficulty has been found in discovering any passage of the De Anima to which this can refer. Maier is probably right in holding that this sentence should come after the next two (after ἀληθές, l. 13), and refers to De An. 430a 26-8.
* ↑ i.e. as in the case of a chemical compound, so in that of compound words, the elements, being amalgamated into one whole, cease to have their own particular character and significance.
* ↑ Omit ὅτι…μὴ ὄντος, ll. 32, 33, with A, B, and Waitz. These oords have probably been introduced from b 15.
* ↑ The words 'to be' and 'not to be' are here regarded in their strictly copulative sense.
* ↑ Omit κατὰ συνθήκην in l. 26 with B, C, Amm., Boeth., and Waitz.
* ↑ Omit ἢ ἀπόφασις in l. 28 with B, C, Amm., and Waitz.
* ↑ Cf. 16a 22-26.
* ↑ Cf. Poet. 1456b 11.
* ↑ Cf. Met. Ζ. 12, H.6. Read οὐ…ἔσται l. 14 in brackets, with a comma following.
* ↑ Read a comma after ἕκαστον l. 1, a colon after ἕκαστον l. 3, and place λέγω…οὐδεὶς ἄνθρωπος λευκός, ll. 5, 6, in brackets, followed by a colon. Bonitz has thus cleared up the construction of the sentence.
* ↑ An image should appear at this position in the text. If you are able to provide it, see Wikisource:Image guidelines and Help:Adding images for guidance.
* ↑ Strictly 'one of which has a universal character'.
* ↑ By the words ἀληθὴς ἢ ψευδής, as Waitz explains, Aristotle means ἀντίφασις, τὴν μὲν ἀεὶ ἔ χουσα ἀληθῆ, τὴν δὲ ψευδῆ. The subcontraries, that is, contradictories of the contraries, may both be true. Cf. 17b 31.
* ↑ Omit οὐδὲ ἀπόφασις μία in l. 19 with B, Amm., and Waitz.
* ↑ Aristotle means that if you start with a universal proposition (A or E) and take the corresponding negation (by which he means O or I), one must be true and the other false.
* ↑ Cf. 17b 26-9.
* ↑ Cf. 17b 29-37.
* ↑ In this chapter, as Pacius points out, Aristotle deals with four possible theories as to contradictory propositions concerning the future: (i) that both are true; this he refutes, 18a 34-9, by implication; (2) that one is true and the other false determinately; this he deals with at length; (3) that both are false; this he dismisses, 18b 16-25; (4) that one is true and the other false, indeterminately; this last he commends, 19a 23-b 4.
* ↑ In 18a 34, 38 Bekker reads καί, but it seems better to adhere to the reading ἤ, which is that of B, C, Amm., and Waitz, since the phrase occurs in a 29, b 4 in the same sense; i.e. propositions, whether positive or negative.
* ↑ sc. 'ex hypothesi: and thus the Law of Excluded Middle would be violated.
* ↑ Or: 'if it was true to say that they would belong to it'; and below: 'if it was true to say that an event…'. Possibly Pacius is right in his contention that ἀληθὴς ἦν εἰπεῖν ὅτι should be understood after εἰ δέ.
* ↑ 18b 23 read ὑπάρξειν εἰς αὔριον with A, B, Amm., and Waitz.
* ↑ sc. 'and thus this suggestion does not prove any amendment on the first'.
* ↑ sc. 'on our hypothesis'.
* ↑ sc. 'on our hypothesis'.
* ↑ Bonitz has pointed out that ὁπῶμεν l. 7–τοιαίτην l. 18 is parenthetical, φανερόν beginning the apodosis of the main sentence.
* ↑ sc. ἀφωρισμένως 'determinately'.
* ↑ 16a 19, 30.
* ↑ Waitz argues that the use of the word προσκατηγορεῖται implies that the verb 'to be' is not here regarded as a copula, i.e. that the sentence ἐστὶ δίκαιος ἄνθρωπος should be translated 'there is a just man'. As a matter of fact, however, when interpreted as strictly indefinite, the proposition 'man is just' means exactly the same as the proposition 'there is a just man'. An objection to Waitz's contention is that Aristotle expressly refuses to define the function of ἐστί, but calls it ὄνομα ἢ ῥῆμα. It is difficult to see why it should not be defined as ῥῆμα, if it were being used in its independent sense. Besides this, in the form of proposition adopted by Waitz 'just man' is one term; the whole therefore consists not of three elements, but of two.
* ↑ Four propositions, not four pairs of propositions. The objection to Grote's rendering lies in the fact that while he translates τέτταρα here as 'four pairs', he makes τὰ μὲν δύο mean one pair (i.e. the second pair of the first quaternion) and τὰ δὲ δύο another single pair (i.e. the second pair of the second quarternion, of which οὐκ ἄνθρωπος is the subject).
* ↑ In the subjoined table to which Aristotle refers, D follows from A and B from C and the sequence is the same as it would be if 'unjust' were substituted for 'not-just'.
* ↑ Let c represent the proposition 'man is injust' and d the propotion 'man is not unjust'. D and C correspond with d and c, A and B do not.
* ↑ 19b 25-30. Waitz reads ἀνθρώπῳ for δικαίῳ and οὐκ ἀνθρώπῳ for οὐ ἀνθρώπῳ and maintains that in both cases δικαίῳ is understood before ἀνθρώπῳ and that has in some MSS. caused the easier reading δικαίῳ, οὐ δικαίῳ to supplant the true. The omission of δικαίῳ between οὐ and ἀνθρώπῳ is obviously impossible, and there is no other way of taking the words, should that reading be adopted. To those, however, who consider ἐστί to be the copula in all these propositions, there can be no question as to the reading, δικαίῳ and οὐ δικαίῳ being necessary to the argument.
* ↑ Analytica Prioria, 51b 36‒52a 17.
* ↑ D' and B' may both be true.
Footnotes