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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
|
