The Basic Works of Aristotle (Modern Library Classics) (12 page)

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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.

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 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.
(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.

Now if this is the case,
(5)
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’ is merely equivalent to saying ‘man is walking’.

If then this rule is universal,
(10)
the contradictory of ‘it may be’ is ‘it 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.
(15)

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,
(20)
or that it is not by the addition of the verbs ‘be’ and ‘not be’, respectively, that positive and 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,
(25)
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,
(30)
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 ‘it cannot be’. Thus the propositions ‘it may be’ and ‘it may
not
be’ appear each to imply the other: for,
(35)
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.
[22a]

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’.
(5)

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.
(10)

We must consider the following pairs as contradictory propositions:

It may be.     
It cannot be.
It is contingent.     
It is not contingent.
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.
(15)
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.
(20)
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:
(25)

A.
It may be.
B.
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.
It may not be.
D.
It cannot not be.
 
It is contingent that it should not be.
 
It is not contingent that it should not be.
 
It is not impossible that it should not be.
 
It is impossible that it should not be.
 
It is not necessary that it should not be.
 
It is necessary that it should be.

Now the propositions ‘it is impossible that it should be’ and ‘it is not impossible that it should be’ are consequent upon the propositions ‘it may be’,
(30)
‘it is contingent’, and ‘it cannot be’, ‘it is not contingent’, the contradictories upon the contradictories. But there is inversion. The negative of the proposition ‘it is impossible’ is consequent upon
the proposition ‘it may be’ and the corresponding positive in the first case upon the negative in the second.
(35)
For ‘it is impossible’ is a positive proposition and ‘it is not impossible’ is negative.

We must investigate the relation subsisting between these propositions and those which predicate necessity. That there is a distinction is clear. In this case, contrary propositions follow respectively from contradictory propositions, and the contradictory propositions belong to separate sequences. For the proposition ‘it is not necessary that it should be’ is not the negative of ‘it is necessary that it should not be’, for both these propositions may be true of the same subject; for when it is necessary that a thing should not be, it is not necessary that it should be.
[22b]
The reason why the propositions predicating necessity do not follow in the same kind of sequence as the rest, lies in the fact that the proposition ‘it is impossible’ is equivalent, when used with a contrary subject, to the proposition ‘it is necessary’. For when it is impossible that a thing should be, it is necessary, not that it should be,
(5)
but that it should not be, and when it is impossible that a thing should not be, it is necessary that it should be. Thus, if the propositions predicating impossibility or non-impossibility follow without change of subject from those predicating possibility or non-possibility, those predicating necessity must follow with the contrary subject; for the propositions ‘it is impossible’ and ‘it is necessary’ are not equivalent, but, as has been said, inversely connected.

Yet perhaps it is impossible that the contradictory propositions predicating necessity should be thus arranged.
(10)
For when it is necessary that a thing should be, it is possible that it should be. (For if not, the opposite follows, since one or the other must follow; so, if it is not possible, it is impossible, and it is thus impossible that a thing should be, which must necessarily be; which is absurd.)

Yet from the proposition ‘it may be’ it follows that it is not impossible, and from that it follows that it is not necessary; it comes about therefore that the thing which must necessarily be need not be; which is absurd.
(15)
But again, the proposition ‘it is necessary that it should be’ does not follow from the proposition ‘it may be’, nor does the proposition ‘it is necessary that it should not be’. For the proposition ‘it may be’ implies a twofold possibility, while, if either of the two former propositions is true, the twofold possibility vanishes. For if a thing may be, it may also not be, but if it is necessary that it should be or that it should not be,
(20)
one of the two alternatives will be excluded. It remains, therefore, that the proposition ‘it is not necessary that it should not be’ follows from the proposition ‘it may be’. For this is true also of that which must necessarily be.

Moreover the proposition ‘it is not necessary that it should not be’ is the contradictory of that which follows from the proposition ‘it cannot be’; for ‘it cannot be’ is followed by ‘it is impossible that it should be’ and by ‘it is necessary that it should not be’,
(25)
and the contradictory of this is the proposition ‘it is not necessary that it should not be’. Thus in this case also contradictory propositions follow contradictory in the way indicated, and no logical impossibilities occur when they are thus arranged.

It may be questioned whether the proposition ‘it may be’ follows from the proposition ‘it is necessary that it should be’. If not,
(30)
the contradictory must follow, namely that it cannot be, or, if a man should maintain that this is not the contradictory, then the proposition ‘it may not be’.

Now both of these are false of that which necessarily is. At the same time, it is thought that if a thing may be cut it may also not be cut, if a thing may be it may also not be, and thus it would follow that a thing which must necessarily be may possibly not be; which is false.
(35)
It is evident, then, that it is not always the case that that which may be or may walk possesses also a potentiality in the other direction. There are exceptions. In the first place we must except those things which possess a potentiality not in accordance with a rational principle, as fire possesses the potentiality of giving out heat, that is, an irrational capacity. Those potentialities which involve a rational principle are potentialities of more than one result, that is, of contrary results; those that are irrational are not always thus constituted.
[23a]
As I have said, fire cannot both heat and not heat, neither has anything that is always actual any twofold potentiality. Yet some even of those potentialities which are irrational admit of opposite results.
(5)
However, thus much has been said to emphasize the truth that it is not every potentiality which admits of opposite results, even where the word is used always in the same sense.

But in some cases the word is used equivocally. For the term ‘possible’ is ambiguous, being used in the one case with reference to facts, to that which is actualized, as when a man is said to find walking possible because he is actually walking, and generally when a capacity is predicated because it is actually realized; in the other case,
(10)
with reference to a state in which realization is conditionally practicable, as when a man is said to find walking possible because under certain conditions he would walk. This last sort of potentiality belongs only to that which can be in motion, the former can exist also in the case of that which has not this power. Both of that which is walking and is actual, and of that which has the capacity though not necessarily
realized, it is true to say that it is not impossible that it should walk (or, in the other case, that it should be), but while we cannot predicate this latter kind of potentiality of that which is necessary in the unqualified sense of the word,
(15)
we can predicate the former.

Our conclusion, then, is this: that since the universal is consequent upon the particular, that which is necessary is also possible, though not in every sense in which the word may be used.

We may perhaps state that necessity and its absence are the initial principles of existence and non-existence, and that all else must be regarded as posterior to these.
(20)

It is plain from what has been said that that which is of necessity is actual. Thus, if that which is eternal is prior, actuality also is prior to potentiality. Some things are actualities without potentiality, namely, the primary substances; a second class consists of those things which are actual but also potential, whose actuality is in nature prior to their potentiality, though posterior in time; a third class comprises those things which are never actualized,
(25)
but are pure potentialities.

BOOK: The Basic Works of Aristotle (Modern Library Classics)
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