The Basic Works of Aristotle (Modern Library Classics) Page 8

  (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.

  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.

  12. (1) Propositions concerning possibility, impossibility, contingency, and necessity.

  (2) Determination of the proper contradictories of such propositions.

  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.

  14. Discussion as to whether a contrary affirmation or a denial is the proper contrary of an affirmation, either universal or particular.

  DE INTERPRETATIONE

  (On Interpretation)

  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 all men have not the same writing, (5) 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, (10) 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’, (15) 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, (20) 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, (25) 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. (30) 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.

  The expressions ‘of Philo’, ‘to Philo’, and so on, constitute not nouns, but cases of a noun. [16b] 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 a true or a false proposition. (5)

  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, (10) 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, (15) 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 substantial and have significance, for he who uses such expressions arrests the hearer’s mind, (20) 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 apart from the things coupled. (25)

  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. (30) 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,1 they have not an independent meaning.

  [17a] 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, (5) for this last concerns our present inquiry, whereas the investigation of the others belongs rather to the study of rhetoric or of poetry.2

  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. (10) 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, (15) 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 pos
sible 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, (20) 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 An affirmation is a positive assertion of something about something, (25) 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. (35) 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. (40)

  Our propositions necessarily sometimes concern a universal subject, sometimes an individual. [17b]

  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’, (5) 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’. (10) ‘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. (15)

  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 subject; for instance ‘not every man is white’ and ‘some men are white’ are both true. (25) 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, (30) 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, (35) 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. [18a]

  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 ‘some men are white’ is ‘no man is white’, (5) 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. (10) 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’, (15) ‘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, (20) 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. (25)

  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, (30) as has been said,3 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.4

  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, (35) 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 ano
ther 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.

  [18b] 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 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, (5) 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, (10) 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. (15) 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.