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, (20) 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 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. (25)
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, (30) 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 before-hand, 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. (35)
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. [19a] 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 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 place, (5) 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 or not be; events also therefore may either take place or not take place. (10) 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, (15) 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 tendency in one direction or the other, (20) 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. (25) 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. (30) 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 non-existent. (35) 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. [19b] 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, (5) 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 explained5 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 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 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’, (15) ‘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, (20) 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. (25) Thus we have the four propositions. Reference to the sub-joined table will make matters clear:
Here ‘is’ and ‘is not’ are added either to ‘just’ or to ‘not-just’. This then is the proper scheme for these propositions, (30) as has been said in the Analytics.6 The same rule holds good, if the subject is distributed. Thus we have the table:
Yet here it is not possible, (35) 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:
[20a] 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’, ‘enjo
ys health’ are used), that scheme applies, which applied when the word ‘is’ was added.
Thus we have the propositions: ‘every man enjoys health’, (5) ‘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, (10) 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’ have 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. (15)
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.
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’, (20) 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 ‘Is Socrates wise?’ and the negative answer were the true one, (25) 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. (30) 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, (35) 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’. (40)
The conversion of the position of subject and predicate in a sentence involves no difference in its meaning. [20b] 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 demonstrated7 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’, (5) 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, (10) therefore, that the inversion of the relative position of subject and predicate does not affect the sense of affirmations and denials.
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.
I do not apply this word ‘one’ to those things which, (15) 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, (20) 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. (25) For as I have explained in the Topics,8 the 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. (30) 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, (35) 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 white man and so on indefinitely. (40) Or, again, we may combine the predicates ‘musical’, ‘white’, and ‘walking’, and these may be combined many times. [21a] 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 a man states unconditionally that predicates can always be combined, (5) 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’. (10) 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, (15) 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 an
imal-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. (20)
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, (25) 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.
Thus, in the case of those predications which have within them no contradiction when the nouns are expanded into definitions, (30) 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, (35) 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’ in 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’. [21b] 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.
The Basic Works of Aristotle (Modern Library Classics) Page 9