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Written 350 B.C.E
Translated by E. M. Edghill
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
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
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
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
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
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.
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
The first class of simple propositions is the simple affirmation,
the next, the simple denial; all others are only one by
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
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.
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
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
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
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
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
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
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
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
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.
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
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
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 \ / -
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
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
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
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