Aristotle
384-322 B.C.E. - Wrote in Greek
On Interpretation
Written 350 B.C.E
Translated by E. M. Edghill
On Interpretation
By Aristotle
Part 1
First we must define the terms 'noun' and 'verb', then the terms 'denial'
and 'affirmation', then 'proposition' and 'sentence.'
Spoken words are the symbols of mental experience and written words
are the symbols of spoken words. Just as all men have not the same writing,
so all men have not the same speech sounds, but the mental experiences,
which these directly symbolize, are the same for all, as also are those
things of which our experiences are the images. This matter has, however,
been discussed in my treatise about the soul, for it belongs to an investigation
distinct from that which lies before us.
As there are in the mind thoughts which do not involve truth or
falsity, and also those which must be either true or false, so it is in
speech. For truth and falsity imply combination and separation. Nouns and
verbs, provided nothing is added, are like thoughts without combination
or separation; 'man' and 'white', as isolated terms, are not yet either
true or false. In proof of this, consider the word 'goat-stag.' It has
significance, but there is no truth or falsity about it, unless 'is' or
'is not' is added, either in the present or in some other
tense.
Part 2
By a noun we mean a sound significant by convention, which has
no reference to time, and of which no part is significant apart from the
rest. In the noun 'Fairsteed,' the part 'steed' has no significance in
and by itself, as in the phrase 'fair steed.' Yet there is a difference
between simple and composite nouns; for in the former the part is in no
way significant, in the latter it contributes to the meaning of the whole,
although it has not an independent meaning. Thus in the word 'pirate-boat'
the word 'boat' has no meaning except as part of the whole
word.
The limitation 'by convention' was introduced because nothing is
by nature a noun or name-it is only so when it becomes a symbol; inarticulate
sounds, such as those which brutes produce, are significant, yet none of
these constitutes a noun.
The expression 'not-man' is not a noun. There is indeed no recognized
term by which we may denote such an expression, for it is not a sentence
or a denial. Let it then be called an indefinite noun.
The expressions 'of Philo', 'to Philo', and so on, constitute not
nouns, but cases of a noun. The definition of these cases of a noun is
in other respects the same as that of the noun proper, but, when coupled
with 'is', 'was', or will be', they do not, as they are, form a proposition
either true or false, and this the noun proper always does, under these
conditions. Take the words 'of Philo is' or 'of or 'of Philo is not'; these
words do not, as they stand, form either a true or a false
proposition.
Part 3
A verb is that which, in addition to its proper meaning, carries
with it the notion of time. No part of it has any independent meaning,
and it is a sign of something said of something else.
I will explain what I mean by saying that it carries with it the
notion of time. 'Health' is a noun, but 'is healthy' is a verb; for besides
its proper meaning it indicates the present existence of the state in
question.
Moreover, a verb is always a sign of something said of something
else, i.e. of something either predicable of or present in some other
thing.
Such expressions as 'is not-healthy', 'is not, ill', I do not describe
as verbs; for though they carry the additional note of time, and always
form a predicate, there is no specified name for this variety; but let
them be called indefinite verbs, since they apply equally well to that
which exists and to that which does not.
Similarly 'he was healthy', 'he will be healthy', are not verbs,
but tenses of a verb; the difference lies in the fact that the verb indicates
present time, while the tenses of the verb indicate those times which lie
outside the present.
Verbs in and by themselves are substantival and have significance,
for he who uses such expressions arrests the hearer's mind, and fixes his
attention; but they do not, as they stand, express any judgement, either
positive or negative. For neither are 'to be' and 'not to be' the participle
'being' significant of any fact, unless something is added; for they do
not themselves indicate anything, but imply a copulation, of which we cannot
form a conception apart from the things coupled.
Part 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 we separate one syllable of the word 'human'
from the other, it has no meaning; similarly in the word 'mouse', the part
'ouse' has no meaning in itself, but is merely a sound. In composite words,
indeed, the parts contribute to the meaning of the whole; yet, as has been
pointed out, they have not an independent meaning.
Every sentence has meaning, not as being the natural means by which
a physical faculty is realized, but, as we have said, by convention. Yet
every sentence is not a proposition; only such are propositions as have
in them either truth or falsity. Thus a prayer is a sentence, but is neither
true nor false.
Let us therefore dismiss all other types of sentence but the proposition,
for this last concerns our present inquiry, whereas the investigation of
the others belongs rather to the study of rhetoric or of
poetry.
Part 5
The first class of simple propositions is the simple affirmation,
the next, the simple denial; all others are only one by
conjunction.
Every proposition must contain a verb or the tense of a verb. The
phrase which defines the species 'man', if no verb in present, past, or
future time be added, is not a proposition. It may be asked how the expression
'a footed animal with two feet' can be called single; for it is not the
circumstance that the words follow in unbroken succession that effects
the unity. This inquiry, however, finds its place in an investigation foreign
to that before us.
We call those propositions single which indicate a single fact,
or the conjunction of the parts of which results in unity: those propositions,
on the other hand, are separate and many in number, which indicate many
facts, or whose parts have no conjunction.
Let us, moreover, consent to call a noun or a verb an expression
only, and not a proposition, since it is not possible for a man to speak
in this way when he is expressing something, in such a way as to make a
statement, whether his utterance is an answer to a question or an act of
his own initiation.
To return: of propositions one kind is simple, i.e. that which
asserts or denies something of something, the other composite, i.e. that
which is compounded of simple propositions. A simple proposition is a statement,
with meaning, as to the presence of something in a subject or its absence,
in the present, past, or future, according to the divisions of
time.
Part 6
An affirmation is a positive assertion of something about something,
a denial a negative assertion.
Now it is possible both to affirm and to deny the presence of something
which is present or of something which is not, and since these same affirmations
and denials are possible with reference to those times which lie outside
the present, it would be possible to contradict any affirmation or denial.
Thus it is plain that every affirmation has an opposite denial, and similarly
every denial an opposite affirmation.
We will call such a pair of propositions a pair of contradictories.
Those positive and negative propositions are said to be contradictory which
have the same subject and predicate. The identity of subject and of predicate
must not be 'equivocal'. Indeed there are definitive qualifications besides
this, which we make to meet the casuistries of sophists.
Part 7
Some things are universal, others individual. By the term 'universal'
I mean that which is of such a nature as to be predicated of many subjects,
by 'individual' that which is not thus predicated. Thus 'man' is a universal,
'Callias' an individual.
Our propositions necessarily sometimes concern a universal subject,
sometimes an individual.
If, then, a man states a positive and a negative proposition of
universal character with regard to a universal, these two propositions
are 'contrary'. By the expression 'a proposition of universal character
with regard to a universal', such propositions as 'every man is white',
'no man is white' are meant. When, on the other hand, the positive and
negative propositions, though they have regard to a universal, are yet
not of universal character, they will not be contrary, albeit the meaning
intended is sometimes contrary. As instances of propositions made with
regard to a universal, but not of universal character, we may take the
'propositions 'man is white', 'man is not white'. 'Man' is a universal,
but the proposition is not made as of universal character; for the word
'every' does not make the subject a universal, but rather gives the proposition
a universal character. If, however, both predicate and subject are distributed,
the proposition thus constituted is contrary to truth; no affirmation will,
under such circumstances, be true. The proposition 'every man is every
animal' is an example of this type.
An affirmation is opposed to a denial in the sense which I denote
by the term 'contradictory', when, while the subject remains the same,
the affirmation is of universal character and the denial is not. The affirmation
'every man is white' is the contradictory of the denial 'not every man
is white', or again, the proposition 'no man is white' is the contradictory
of the proposition 'some men are white'. But propositions are opposed as
contraries when both the affirmation and the denial are universal, as in
the sentences 'every man is white', 'no man is white', 'every man is just',
'no man is just'.
We see that in a pair of this sort both propositions cannot be
true, but the contradictories of a pair of contraries can sometimes both
be true with reference to the same subject; for instance 'not every man
is white' and some men are white' are both true. Of such corresponding
positive and negative propositions as refer to universals and have a universal
character, one must be true and the other false. This is the case also
when the reference is to individuals, as in the propositions 'Socrates
is white', 'Socrates is not white'.
When, on the other hand, the reference is to universals, but the
propositions are not universal, it is not always the case that one is true
and the other false, for it is possible to state truly that man is white
and that man is not white and that man is beautiful and that man is not
beautiful; for if a man is deformed he is the reverse of beautiful, also
if he is progressing towards beauty he is not yet beautiful.
This statement might seem at first sight to carry with it a contradiction,
owing to the fact that the proposition 'man is not white' appears to be
equivalent to the proposition 'no man is white'. This, however, is not
the case, nor are they necessarily at the same time true or
false.
It is evident also that the denial corresponding to a single affirmation
is itself single; for the denial must deny just that which the affirmation
affirms concerning the same subject, and must correspond with the affirmation
both in the universal or particular character of the subject and in the
distributed or undistributed sense in which it is understood.
For instance, the affirmation 'Socrates is white' has its proper
denial in the proposition 'Socrates is not white'. If anything else be
negatively predicated of the subject or if anything else be the subject
though the predicate remain the same, the denial will not be the denial
proper to that affirmation, but on that is distinct.
The denial proper to the affirmation 'every man is white' is 'not
every man is white'; that proper to the affirmation 'some men are white'
is 'no man is white', while that proper to the affirmation 'man is white'
is 'man is not white'.
We have shown further that a single denial is contradictorily opposite
to a single affirmation and we have explained which these are; we have
also stated that contrary are distinct from contradictory propositions
and which the contrary are; also that with regard to a pair of opposite
propositions it is not always the case that one is true and the other false.
We have pointed out, moreover, what the reason of this is and under what
circumstances the truth of the one involves the falsity of the
other.
Part 8
An affirmation or denial is single, if it indicates some one fact
about some one subject; it matters not whether the subject is universal
and whether the statement has a universal character, or whether this is
not so. Such single propositions are: 'every man is white', 'not every
man is white';'man is white','man is not white'; 'no man is white', 'some
men are white'; provided the word 'white' has one meaning. If, on the other
hand, one word has two meanings which do not combine to form one, the affirmation
is not single. For instance, if a man should establish the symbol 'garment'
as significant both of a horse and of a man, the proposition 'garment is
white' would not be a single affirmation, nor its opposite a single denial.
For it is equivalent to the proposition 'horse and man are white', which,
again, is equivalent to the two propositions 'horse is white', 'man is
white'. If, then, these two propositions have more than a single significance,
and do not form a single proposition, it is plain that the first proposition
either has more than one significance or else has none; for a particular
man is not a horse.
This, then, is another instance of those propositions of which
both the positive and the negative forms may be true or false
simultaneously.
Part 9
In the case of that which is or which has taken place, propositions,
whether positive or negative, must be true or false. Again, in the case
of a pair of contradictories, either when the subject is universal and
the propositions are of a universal character, or when it is individual,
as has been said,' one of the two must be true and the other false; whereas
when the subject is universal, but the propositions are not of a universal
character, there is no such necessity. We have discussed this type also
in a previous chapter.
When the subject, however, is individual, and that which is predicated
of it relates to the future, the case is altered. For if all propositions
whether positive or negative are either true or false, then any given predicate
must either belong to the subject or not, so that if one man affirms that
an event of a given character will take place and another denies it, it
is plain that the statement of the one will correspond with reality and
that of the other will not. For the predicate cannot both belong and not
belong to the subject at one and the same time with regard to the
future.
Thus, if it is true to say that a thing is white, it must necessarily
be white; if the reverse proposition is true, it will of necessity not
be white. Again, if it is white, the proposition stating that it is white
was true; if it is not white, the proposition to the opposite effect was
true. And if it is not white, the man who states that it is making a false
statement; and if the man who states that it is white is making a false
statement, it follows that it is not white. It may therefore be argued
that it is necessary that affirmations or denials must be either true or
false.
Now if this be so, nothing is or takes place fortuitously, either
in the present or in the future, and there are no real alternatives; everything
takes place of necessity and is fixed. For either he that affirms that
it will take place or he that denies this is in correspondence with fact,
whereas if things did not take place of necessity, an event might just
as easily not happen as happen; for the meaning of the word 'fortuitous'
with regard to present or future events is that reality is so constituted
that it may issue in either of two opposite directions. Again, if a thing
is white now, it was true before to say that it would be white, so that
of anything that has taken place it was always true to say 'it is' or 'it
will be'. But if it was always true to say that a thing is or will be,
it is not possible that it should not be or not be about to be, and when
a thing cannot not come to be, it is impossible that it should not come
to be, and when it is impossible that it should not come to be, it must
come to be. All, then, that is about to be must of necessity take place.
It results from this that nothing is uncertain or fortuitous, for if it
were fortuitous it would not be necessary.
Again, to say that neither the affirmation nor the denial is true,
maintaining, let us say, that an event neither will take place nor will
not take place, is to take up a position impossible to defend. In the first
place, though facts should prove the one proposition false, the opposite
would still be untrue. Secondly, if it was true to say that a thing was
both white and large, both these qualities must necessarily belong to it;
and if they will belong to it the next day, they must necessarily belong
to it the next day. But if an event is neither to take place nor not to
take place the next day, the element of chance will be eliminated. For
example, it would be necessary that a sea-fight should neither take place
nor fail to take place on the next day.
These awkward results and others of the same kind follow, if it
is an irrefragable law that of every pair of contradictory propositions,
whether they have regard to universals and are stated as universally applicable,
or whether they have regard to individuals, one must be true and the other
false, and that there are no real alternatives, but that all that is or
takes place is the outcome of necessity. There would be no need to deliberate
or to take trouble, on the supposition that if we should adopt a certain
course, a certain result would follow, while, if we did not, the result
would not follow. For a man may predict an event ten thousand years beforehand,
and another may predict the reverse; that which was truly predicted at
the moment in the past will of necessity take place in the fullness of
time.
Further, it makes no difference whether people have or have not
actually made the contradictory statements. For it is manifest that the
circumstances are not influenced by the fact of an affirmation or denial
on the part of anyone. For events will not take place or fail to take place
because it was stated that they would or would not take place, nor is this
any more the case if the prediction dates back ten thousand years or any
other space of time. Wherefore, if through all time the nature of things
was so constituted that a prediction about an event was true, then through
all time it was necessary that that should find fulfillment; and with regard
to all events, circumstances have always been such that their occurrence
is a matter of necessity. For that of which someone has said truly that
it will be, cannot fail to take place; and of that which takes place, it
was always true to say that it would be.
Yet this view leads to an impossible conclusion; for we see that
both deliberation and action are causative with regard to the future, and
that, to speak more generally, in those things which are not continuously
actual there is potentiality in either direction. Such things may either
be or not be; events also therefore may either take place or not take place.
There are many obvious instances of this. It is possible that this coat
may be cut in half, and yet it may not be cut in half, but wear out first.
In the same way, it is possible that it should not be cut in half; unless
this were so, it would not be possible that it should wear out first. So
it is therefore with all other events which possess this kind of potentiality.
It is therefore plain that it is not of necessity that everything is or
takes place; but in some instances there are real alternatives, in which
case the affirmation is no more true and no more false than the denial;
while some exhibit a predisposition and general tendency in one direction
or the other, and yet can issue in the opposite direction by
exception.
Now that which is must needs be when it is, and that which is not
must needs not be when it is not. Yet it cannot be said without qualification
that all existence and non-existence is the outcome of necessity. For there
is a difference between saying that that which is, when it is, must needs
be, and simply saying that all that is must needs be, and similarly in
the case of that which is not. In the case, also, of two contradictory
propositions this holds good. Everything must either be or not be, whether
in the present or in the future, but it is not always possible to distinguish
and state determinately which of these alternatives must necessarily come
about.
Let me illustrate. A sea-fight must either take place to-morrow
or not, but it is not necessary that it should take place to-morrow, neither
is it necessary that it should not take place, yet it is necessary that
it either should or should not take place to-morrow. Since propositions
correspond with facts, it is evident that when in future events there is
a real alternative, and a potentiality in contrary directions, the corresponding
affirmation and denial have the same character.
This is the case with regard to that which is not always existent
or not always nonexistent. One of the two propositions in such instances
must be true and the other false, but we cannot say determinately that
this or that is false, but must leave the alternative undecided. One may
indeed be more likely to be true than the other, but it cannot be either
actually true or actually false. It is therefore plain that it is not necessary
that of an affirmation and a denial one should be true and the other false.
For in the case of that which exists potentially, but not actually, the
rule which applies to that which exists actually does not hold good. The
case is rather as we have indicated.
Part 10
An affirmation is the statement of a fact with regard to a subject,
and this subject is either a noun or that which has no name; the subject
and predicate in an affirmation must each denote a single thing. I have
already explained' what is meant by a noun and by that which has no name;
for I stated that the expression 'not-man' was not a noun, in the proper
sense of the word, but an indefinite noun, denoting as it does in a certain
sense a single thing. Similarly the expression 'does not enjoy health'
is not a verb proper, but an indefinite verb. Every affirmation, then,
and every denial, will consist of a noun and a verb, either definite or
indefinite.
There can be no affirmation or denial without a verb; for the expressions
'is', 'will be', 'was', 'is coming to be', and the like are verbs according
to our definition, since besides their specific meaning they convey the
notion of time. Thus the primary affirmation and denial are 'as follows:
'man is', 'man is not'. Next to these, there are the propositions: 'not-man
is', 'not-man is not'. Again we have the propositions: 'every man is, 'every
man is not', 'all that is not-man is', 'all that is not-man is not'. The
same classification holds good with regard to such periods of time as lie
outside the present.
When the verb 'is' is used as a third element in the sentence,
there can be positive and negative propositions of two sorts. Thus in the
sentence 'man is just' the verb 'is' is used as a third element, call it
verb or noun, which you will. Four propositions, therefore, instead of
two can be formed with these materials. Two of the four, as regards their
affirmation and denial, correspond in their logical sequence with the propositions
which deal with a condition of privation; the other two do not correspond
with these.
I mean that the verb 'is' is added either to the term 'just' or
to the term 'not-just', and two negative propositions are formed in the
same way. Thus we have the four propositions. Reference to the subjoined
table will make matters clear:
A. Affirmation B. Denial Man is just Man
is not just \ / X / \ D. Denial
C. Affirmation Man is not not-just Man is not-just
Here 'is' and 'is not' are added either to 'just' or to 'not-just'. This
then is the proper scheme for these propositions, as has been said in the
Analytics. The same rule holds good, if the subject is distributed. Thus
we have the table:
A'. Affirmation B'. Denial Every man is
just Not every man is just \ / X D'. Denial
/ \ C'. Affirmation
Not every man is not-just Every man is not-just Yet here it
is not possible, in the same way as in the former case, that the propositions
joined in the table by a diagonal line should both be true; though under
certain circumstances this is the case.
We have thus set out two pairs of opposite propositions; there
are moreover two other pairs, if a term be conjoined with 'not-man', the
latter forming a kind of subject. Thus:
A." B." Not-man is just
Not-man is not just \ / -
X
D." / \ C." Not-man is not not-just
Not-man is not-just
This is an exhaustive enumeration of all the pairs of opposite
propositions that can possibly be framed. This last group should remain
distinct from those which preceded it, since it employs as its subject
the expression 'not-man'.
When the verb 'is' does not fit the structure of the sentence (for
instance, when the verbs 'walks', 'enjoys health' are used), that scheme
applies, which applied when the word 'is' was added.
Thus we have the propositions: 'every man enjoys health', 'every
man does-not-enjoy-health', 'all that is not-man enjoys health', 'all that
is not-man does-not-enjoy-health'. We must not in these propositions use
the expression 'not every man'. The negative must be attached to the word
'man', for the word 'every' does not give to the subject a universal significance,
but implies that, as a subject, it is distributed. This is plain from the
following pairs: 'man enjoys health', 'man does not enjoy health'; 'not-man
enjoys health', 'not man does not enjoy health'. These propositions differ
from the former in being indefinite and not universal in character. Thus
the adjectives 'every' and no additional significance except that the subject,
whether in a positive or in a negative sentence, is distributed. The rest
of the sentence, therefore, will in each case be the
same.
Since the contrary of the proposition 'every animal is just' is
'no animal is just', it is plain that these two propositions will never
both be true at the same time or with reference to the same subject. Sometimes,
however, the contradictories of these contraries will both be true, as
in the instance before us: the propositions 'not every animal is just'
and 'some animals are just' are both true.
Further, the proposition 'no man is just' follows from the proposition
'every man is not just' and the proposition 'not every man is not just',
which is the opposite of 'every man is not-just', follows from the proposition
'some men are just'; for if this be true, there must be some just
men.
It is evident, also, that when the subject is individual, if a
question is asked and the negative answer is the true one, a certain positive
proposition is also true. Thus, if the question were asked Socrates wise?'
and the negative answer were the true one, the positive inference 'Then
Socrates is unwise' is correct. But no such inference is correct in the
case of universals, but rather a negative proposition. For instance, if
to the question 'Is every man wise?' the answer is 'no', the inference
'Then every man is unwise' is false. But under these circumstances the
inference 'Not every man is wise' is correct. This last is the contradictory,
the former the contrary. Negative expressions, which consist of an indefinite
noun or predicate, such as 'not-man' or 'not-just', may seem to be denials
containing neither noun nor verb in the proper sense of the words. But
they are not. For a denial must always be either true or false, and he
that uses the expression 'not man', if nothing more be added, is not nearer
but rather further from making a true or a false statement than he who
uses the expression 'man'.
The propositions 'everything that is not man is just', and the
contradictory of this, are not equivalent to any of the other propositions;
on the other hand, the proposition 'everything that is not man is not just'
is equivalent to the proposition 'nothing that is not man is
just'.
The conversion of the position of subject and predicate in a sentence
involves no difference in its meaning. Thus we say 'man is white' and 'white
is man'. If these were not equivalent, there would be more than one contradictory
to the same proposition, whereas it has been demonstrated' that each proposition
has one proper contradictory and one only. For of the proposition 'man
is white' the appropriate contradictory is 'man is not white', and of the
proposition 'white is man', if its meaning be different, the contradictory
will either be 'white is not not-man' or 'white is not man'. Now the former
of these is the contradictory of the proposition 'white is not-man', and
the latter of these is the contradictory of the proposition 'man is white';
thus there will be two contradictories to one proposition.
It is evident, therefore, that the inversion of the relative position
of subject and predicate does not affect the sense of affirmations and
denials.
On Interpretation
By Aristotle
Part 11
There is no unity about an affirmation or denial which, either positively
or negatively, predicates one thing of many subjects, or many things of
the same subject, unless that which is indicated by the many is really
some one thing. do not apply this word 'one' to those things which, though
they have a single recognized name, yet do not combine to form a unity.
Thus, man may be an animal, and biped, and domesticated, but these three
predicates combine to form a unity. On the other hand, the predicates 'white',
'man', and 'walking' do not thus combine. Neither, therefore, if these
three form the subject of an affirmation, nor if they form its predicate,
is there any unity about that affirmation. In both cases the unity is linguistic,
but not real.
If therefore the dialectical question is a request for an answer,
i.e. either for the admission of a premiss or for the admission of one
of two contradictories-and the premiss is itself always one of two contradictories-the
answer to such a question as contains the above predicates cannot be a
single proposition. For as I have explained in the Topics, question is
not a single one, even if the answer asked for is true.
At the same time it is plain that a question of the form 'what
is it?' is not a dialectical question, for a dialectical questioner must
by the form of his question give his opponent the chance of announcing
one of two alternatives, whichever he wishes. He must therefore put the
question into a more definite form, and inquire, e.g.. whether man has
such and such a characteristic or not.
Some combinations of predicates are such that the separate predicates
unite to form a single predicate. Let us consider under what conditions
this is and is not possible. We may either state in two separate propositions
that man is an animal and that man is a biped, or we may combine the two,
and state that man is an animal with two feet. Similarly we may use 'man'
and 'white' as separate predicates, or unite them into one. Yet if a man
is a shoemaker and is also good, we cannot construct a composite proposition
and say that he is a good shoemaker. For if, whenever two separate predicates
truly belong to a subject, it follows that the predicate resulting from
their combination also truly belongs to the subject, many absurd results
ensue. For instance, a man is man and white. Therefore, if predicates may
always be combined, he is a white man. Again, if the predicate 'white'
belongs to him, then the combination of that predicate with the former
composite predicate will be permissible. Thus it will be right to say that
he is a white man so on indefinitely. Or, again, we may combine the predicates
'musical', 'white', and 'walking', and these may be combined many times.
Similarly we may say that Socrates is Socrates and a man, and that therefore
he is the man Socrates, or that Socrates is a man and a biped, and that
therefore he is a two-footed man. Thus it is manifest that if man states
unconditionally that predicates can always be combined, many absurd consequences
ensue.
We will now explain what ought to be laid down.
Those predicates, and terms forming the subject of predication, which
are accidental either to the same subject or to one another, do not combine
to form a unity. Take the proposition 'man is white of complexion and musical'.
Whiteness and being musical do not coalesce to form a unity, for they belong
only accidentally to the same subject. Nor yet, if it were true to say
that that which is white is musical, would the terms 'musical' and 'white'
form a unity, for it is only incidentally that that which is musical is
white; the combination of the two will, therefore, not form a
unity.
Thus, again, whereas, if a man is both good and a shoemaker, we
cannot combine the two propositions and say simply that he is a good shoemaker,
we are, at the same time, able to combine the predicates 'animal' and 'biped'
and say that a man is an animal with two feet, for these predicates are
not accidental.
Those predicates, again, cannot form a unity, of which the one
is implicit in the other: thus we cannot combine the predicate 'white'
again and again with that which already contains the notion 'white', nor
is it right to call a man an animal-man or a two-footed man; for the notions
'animal' and 'biped' are implicit in the word 'man'. On the other hand,
it is possible to predicate a term simply of any one instance, and to say
that some one particular man is a man or that some one white man is a white
man.
Yet this is not always possible: indeed, when in the adjunct there
is some opposite which involves a contradiction, the predication of the
simple term is impossible. Thus it is not right to call a dead man a man.
When, however, this is not the case, it is not impossible.
Yet the facts of the case might rather be stated thus: when some
such opposite elements are present, resolution is never possible, but when
they are not present, resolution is nevertheless not always possible. Take
the proposition 'Homer is so-and-so', say 'a poet'; does it follow that
Homer is, or does it not? The verb 'is' is here used of Homer only incidentally,
the proposition being that Homer is a poet, not that he is, in the independent
sense of the word.
Thus, in the case of those predications which have within them
no contradiction when the nouns are expanded into definitions, and wherein
the predicates belong to the subject in their own proper sense and not
in any indirect way, the individual may be the subject of the simple propositions
as well as of the composite. But in the case of that which is not, it is
not true to say that because it is the object of opinion, it is; for the
opinion held about it is that it is not, not that it
is.
Part 12
As these distinctions have been made, we must consider the mutual
relation of those affirmations and denials which assert or deny possibility
or contingency, impossibility or necessity: for the subject is not without
difficulty.
We admit that of composite expressions those are contradictory
each to each which have the verb 'to be' its positive and negative form
respectively. Thus the contradictory of the proposition 'man is' is 'man
is not', not 'not-man is', and the contradictory of 'man is white' is 'man
is not white', not 'man is not-white'. For otherwise, since either the
positive or the negative proposition is true of any subject, it will turn
out true to say that a piece of wood is a man that is not
white.
Now if this is the case, in those propositions which do not contain
the verb 'to be' the verb which takes its place will exercise the same
function. Thus the contradictory of 'man walks' is 'man does not walk',
not 'not-man walks'; for to say 'man walks' merely equivalent to saying
'man is walking'.
If then this rule is universal, the contradictory of 'it may be'
is may not be', not 'it cannot be'.
Now it appears that the same thing both may and may not be; for
instance, everything that may be cut or may walk may also escape cutting
and refrain from walking; and the reason is that those things that have
potentiality in this sense are not always actual. In such cases, both the
positive and the negative propositions will be true; for that which is
capable of walking or of being seen has also a potentiality in the opposite
direction.
But since it is impossible that contradictory propositions should
both be true of the same subject, it follows that' it may not be' is not
the contradictory of 'it may be'. For it is a logical consequence of what
we have said, either that the same predicate can be both applicable and
inapplicable to one and the same subject at the same time, or that it is
not by the addition of the verbs 'be' and 'not be', respectively, that
positive and negative propositions are formed. If the former of these alternatives
must be rejected, we must choose the latter.
The contradictory, then, of 'it may be' is 'it cannot be'. The
same rule applies to the proposition 'it is contingent that it should be';
the contradictory of this is 'it is not contingent that it should be'.
The similar propositions, such as 'it is necessary' and 'it is impossible',
may be dealt with in the same manner. For it comes about that just as in
the former instances the verbs 'is' and 'is not' were added to the subject-matter
of the sentence 'white' and 'man', so here 'that it should be' and 'that
it should not be' are the subject-matter and 'is possible', 'is contingent',
are added. These indicate that a certain thing is or is not possible, just
as in the former instances 'is' and 'is not' indicated that certain things
were or were not the case.
The contradictory, then, of 'it may not be' is not 'it cannot be',
but 'it cannot not be', and the contradictory of 'it may be' is not 'it
may not be', but cannot be'. Thus the propositions 'it may be' and 'it
may not be' appear each to imply the other: for, since these two propositions
are not contradictory, the same thing both may and may not be. But the
propositions 'it may be' and 'it cannot be' can never be true of the same
subject at the same time, for they are contradictory. Nor can the propositions
'it may not be' and 'it cannot not be' be at once true of the same
subject.
The propositions which have to do with necessity are governed by
the same principle. The contradictory of 'it is necessary that it should
be', is not 'it is necessary that it should not be,' but 'it is not necessary
that it should be', and the contradictory of 'it is necessary that it should
not be' is 'it is not necessary that it should not be'.
Again, the contradictory of 'it is impossible that it should be'
is not 'it is impossible that it should not be' but 'it is not impossible
that it should be', and the contradictory of 'it is impossible that it
should not be' is 'it is not impossible that it should not
be'.
To generalize, we must, as has been stated, define the clauses
'that it should be' and 'that it should not be' as the subject-matter of
the propositions, and in making these terms into affirmations and denials
we must combine them with 'that it should be' and 'that it should not be'
respectively.
We must consider the following pairs as contradictory
propositions:
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.
Part 13
Logical sequences follow in due course when we have arranged the
propositions thus. From the proposition 'it may be' it follows that it
is contingent, and the relation is reciprocal. It follows also that it
is not impossible and not necessary.
From the proposition 'it may not be' or 'it is contingent that
it should not be' it follows that it is not necessary that it should not
be and that it is not impossible that it should not be. From the proposition
'it cannot be' or 'it is not contingent' it follows that it is necessary
that it should not be and that it is impossible that it should be. From
the proposition 'it cannot not be' or 'it is not contingent that it should
not be' it follows that it is necessary that it should be and that it is
impossible that it should not be.
Let us consider these statements by the help of a
table:
A. B.
It may be. It cannot be.
It is contingent. It is not contingent.
It is not impossible It is impossible that
it
that it should be. should be.
It is not necessary It is necessary that
it
that it should be. should not be.
C. D.
It may not be. It cannot not be.
It is contingent that it It is not contingent
that
should not be. it should not
be.
It is not impossible It is impossible thatit
that it should not be. should not be.
It is not necessary that It is necessary that
it
it should not be. 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', '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. 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. 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, 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. 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. 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, 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', 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, 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.
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. 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. 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, 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, 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.
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, but are pure potentialities.
Part 14
The question arises whether an affirmation finds its contrary in
a denial or in another affirmation; whether the proposition 'every man
is just' finds its contrary in the proposition 'no man is just', or in
the proposition 'every man is unjust'. Take the propositions 'Callias is
just', 'Callias is not just', 'Callias is unjust'; we have to discover
which of these form contraries.
Now if the spoken word corresponds with the judgement of the mind,
and if, in thought, that judgement is the contrary of another, which pronounces
a contrary fact, in the way, for instance, in which the judgement 'every
man is just' pronounces a contrary to that pronounced by the judgement
'every man is unjust', the same must needs hold good with regard to spoken
affirmations.
But if, in thought, it is not the judgement which pronounces a
contrary fact that is the contrary of another, then one affirmation will
not find its contrary in another, but rather in the corresponding denial.
We must therefore consider which true judgement is the contrary of the
false, that which forms the denial of the false judgement or that which
affirms the contrary fact.
Let me illustrate. There is a true judgement concerning that which
is good, that it is good; another, a false judgement, that it is not good;
and a third, which is distinct, that it is bad. Which of these two is contrary
to the true? And if they are one and the same, which mode of expression
forms the contrary?
It is an error to suppose that judgements are to be defined as
contrary in virtue of the fact that they have contrary subjects; for the
judgement concerning a good thing, that it is good, and that concerning
a bad thing, that it is bad, may be one and the same, and whether they
are so or not, they both represent the truth. Yet the subjects here are
contrary. But judgements are not contrary because they have contrary subjects,
but because they are to the contrary effect.
Now if we take the judgement that that which is good is good, and
another that it is not good, and if there are at the same time other attributes,
which do not and cannot belong to the good, we must nevertheless refuse
to treat as the contraries of the true judgement those which opine that
some other attribute subsists which does not subsist, as also those that
opine that some other attribute does not subsist which does subsist, for
both these classes of judgement are of unlimited content.
Those judgements must rather be termed contrary to the true judgements,
in which error is present. Now these judgements are those which are concerned
with the starting points of generation, and generation is the passing from
one extreme to its opposite; therefore error is a like
transition.
Now that which is good is both good and not bad. The first quality
is part of its essence, the second accidental; for it is by accident that
it is not bad. But if that true judgement is most really true, which concerns
the subject's intrinsic nature, then that false judgement likewise is most
really false, which concerns its intrinsic nature. Now the judgement that
that is good is not good is a false judgement concerning its intrinsic
nature, the judgement that it is bad is one concerning that which is accidental.
Thus the judgement which denies the true judgement is more really false
than that which positively asserts the presence of the contrary quality.
But it is the man who forms that judgement which is contrary to the true
who is most thoroughly deceived, for contraries are among the things which
differ most widely within the same class. If then of the two judgements
one is contrary to the true judgement, but that which is contradictory
is the more truly contrary, then the latter, it seems, is the real contrary.
The judgement that that which is good is bad is composite. For presumably
the man who forms that judgement must at the same time understand that
that which is good is not good.
Further, the contradictory is either always the contrary or never;
therefore, if it must necessarily be so in all other cases, our conclusion
in the case just dealt with would seem to be correct. Now where terms have
no contrary, that judgement is false, which forms the negative of the true;
for instance, he who thinks a man is not a man forms a false judgement.
If then in these cases the negative is the contrary, then the principle
is universal in its application.
Again, the judgement that that which is not good is not good is
parallel with the judgement that that which is good is good. Besides these
there is the judgement that that which is good is not good, parallel with
the judgement that that that is not good is good. Let us consider, therefore,
what would form the contrary of the true judgement that that which is not
good is not good. The judgement that it is bad would, of course, fail to
meet the case, since two true judgements are never contrary and this judgement
might be true at the same time as that with which it is connected. For
since some things which are not good are bad, both judgements may be true.
Nor is the judgement that it is not bad the contrary, for this too might
be true, since both qualities might be predicated of the same subject.
It remains, therefore, that of the judgement concerning that which is not
good, that it is not good, the contrary judgement is that it is good; for
this is false. In the same way, moreover, the judgement concerning that
which is good, that it is not good, is the contrary of the judgement that
it is good.
It is evident that it will make no difference if we universalize
the positive judgement, for the universal negative judgement will form
the contrary. For instance, the contrary of the judgement that everything
that is good is good is that nothing that is good is good. For the judgement
that that which is good is good, if the subject be understood in a universal
sense, is equivalent to the judgement that whatever is good is good, and
this is identical with the judgement that everything that is good is good.
We may deal similarly with judgements concerning that which is not
good.
If therefore this is the rule with judgements, and if spoken affirmations
and denials are judgements expressed in words, it is plain that the universal
denial is the contrary of the affirmation about the same subject. Thus
the propositions 'everything good is good', 'every man is good', have for
their contraries the propositions 'nothing good is good', 'no man is good'.
The contradictory propositions, on the other hand, are 'not everything
good is good', 'not every man is good'.
It is evident, also, that neither true judgements nor true propositions
can be contrary the one to the other. For whereas, when two propositions
are true, a man may state both at the same time without inconsistency,
contrary propositions are those which state contrary conditions, and contrary
conditions cannot subsist at one and the same time in the same
subject.
THE END
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