On Interpretation

                                
  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.



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  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.



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  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.



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  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.



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  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.



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  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.



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  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.