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.
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.
