The Lives and Opinions of Eminent Philosophers
the appearance of a real judgment, loses this character by the addition,
and under the influence of, some particle, as for instance:
The Parthenon at least is beautiful.
How like the herdsman is to Priam’s sons.
There is also the dubitative proposition, which differs from the
judgment, inasmuch as it is always uttered in the form of a doubt; as for
instance:—
Are not, then, grief and life two kindred states?[87]
But questions, and interrogations, and things like these, are neither
true nor false, while judgments and propositions are necessarily one or
the other.
Now of axioms, some are simple, and others are not simple; as
Chrysippus, and Archedemus, and Athenodorus, and Antipater, and Crinis,
agree in dividing them. Those are simple, which consist of an axiom
or proposition, which is not ambiguous, (or of several axioms, or
propositions of the same character,) as for instance the sentence, “It is
day.” And those are not simple, which consist of an axiom or proposition
which is ambiguous, or of several axioms or propositions of that
character. Of an axiom, or proposition, which is ambiguous, as “If it is
day;” of several axioms, or propositions of that character, as, “If it is
day, it is light.”
And simple propositions are divided into the affirmative, the negative,
the privative, the categorical, the definite, and the indefinite; those
which are not simple, are divided into the combined, and the adjunctive,
the connected and the disjunctive, and the causal and the augmentative,
and the diminutive. That is an affirmative proposition, “It is not day.”
And the species of this is doubly affirmative. That again is doubly
affirmative, which is affirmative of an affirmative, as for instance, “It
is not not day;” for this amounts to, “It is day.” That is a negative
proposition, which consists of a negative particle and a categorem, as
for instance, “No one is walking.” That is a privative proposition which
consists of a privative particle and an axiom according to power, as
“This man is inhuman.” That is a categorical proposition, which consists
of a nominative case and a categorem, as for instance, “Dion is walking.”
That is a definite proposition, which consists of a demonstrative
nominative case and a categorem, as for instance, “This man is walking.”
That is an indefinite one which consists of an indefinite particle, or
of indefinite particles, as for instance, “Somebody is walking,” “He is
moving.”
Of propositions which are not simple, the combined proposition is, as
Chrysippus states, in his Dialectics, and Diogenes, too, in his Dialectic
Art; that which is held together by the copulative conjunction “if.”
And this conjunction professes that the second member of the sentence
follows the first, as for instance, “If it is day, it is light.” That
which is adjunctive is, as Crinis states in his Dialectic Art, an axiom
which is made to depend on the conjunction “since” (ἐπεὶ), beginning
with an axiom and ending in an axiom, as for instance, “Since it is
day, it is light.” And this conjunction professes both that the second
portion of the proposition follows the first, and the first is true.
That is a connected proposition which is connected by some copulative
conjunctions, as for instance, “It both is day, and it is light.” That
is a disjunctive proposition which is disconnected by the disjunctive
conjunction, “or” (ἤτοι), as for instance, “It is either day or night.”
And this proposition professes that one or other of these propositions
is false. That is a causal proposition which is connected by the word,
“because;” as for instance, “Because it is day, it is light.” For the
first is, as it were, the cause of the second. That is an augmentative
proposition, which explains the greater, which is construed with an
augmentative particle, and which is placed between the two members of
the proposition, as for instance, “It is rather day than night.” The
diminutive proposition is, in every respect, the exact contrary of the
preceding one; as for instance, “It is less night than day.” Again, at
times, axioms or propositions are opposed to one another in respect of
their truth and falsehood, when one is an express denial of the other; as
for instance, “It is day,” and, “It is not day.”
Again, a conjunctive proposition is correct, when it is such that the
opposite of the conclusion is contradictory of the premiss; as for
instance, the proposition, “If it is day, it is light,” is true; for,
“It is not light,” which is the opposite to the conclusion expressed, is
contradictory to the premiss, “It is day.” And a conjunctive proposition
is incorrect, when it is such that the opposite of the conclusion is not
inconsistent with the premiss, as for instance, “If it is day, Dion is
walking.” For the fact that Dion is not walking, is not contradictory of
the premiss, “It is day.”
An adjunctive proposition is correct, which begins with a true premiss,
and ends in a consequence which follows of necessity, as for instance,
“Since it is day, the sun is above the earth.” But it is incorrect when
it either begins with a false premiss, or ends with a consequence which
does not follow properly; as for instance, “Since it is night, Dion is
walking,” for this may be said in the day-time.
A causal proposition is correct, when it begins with a true premiss, and
ends in a consequence which necessarily follows from it, but yet does
not have its premiss reciprocally consequent upon its conclusion; as for
instance, “Because it is day, it is light.” For the fact of its being
light, is a necessary consequence of its being day; but the fact of its
being day, is not necessarily a consequence of its being light. A causal
proposition is incorrect, which either begins with a false premiss, or
ends with a conclusion that does not follow from it, or which has a
premiss which does not correspond to the conclusion; as for instance,
“Because it is night, Dion is walking.”
A proposition is persuasive, which leads to the assent of the mind, as
for instance, “If she brought him forth, she is his mother.” But still
this is a falsehood, for a hen is not the mother of an egg. Again, there
are some propositions which are possible, and some which are impossible;
and some which are necessary, and some which are not necessary. That is
possible, which is capable of being true, since external circumstances
are no hindrance to its being true; as for instance, “Diocles lives.” And
that is impossible which is not capable of being true; as for instance,
“The earth flies.” That is necessary which, being true, is not capable
of being false; or perhaps is intrinsically capable of being false,
but still has external circumstances which hinder its being false, as
for instance, “Virtue profits a man.” That again, is not necessary,
which is true, but which has a capacity of being false, though external
circumstances offer no hindrance to either alternative; as for instance,
“Dion walks.”
That is a reasonable or probable proposition, which has a great
preponderance of opportunities in favour of its being true; as for
instance, “I shall be alive to-morrow.” And there are other different
kinds of propositions and conversions of them, from true to false, and
re-conversions again; concerning which we must speak at some length.
XLIX. An argument, as Crinis says, is that which is composed of a lemma
or major premiss, an assumption or minor premiss, and a conclusion; as
for instance this, “If it is day, it is light;” “But it is day, therefore
it is light.” For the lemma, or major premiss, is, “If it is day, it is
light.” The assumption, or minor premiss, is, “It is day.” The conclusion
follows, “Therefore it is light.” The mode of a proposition is, as it
were, a figure of an argument, as for instance, such as this, “If it is
the first, it is the second; but it is the first, therefore it is the
second.”
A conditional syllogism is that which is composed of both the preceding
arguments; as for instance, “If Plato is alive, Plato breathes; but the
first fact is so, therefore so is the second.” And this conditional
syllogism has been introduced for the sake, in long and complex
sentences, of not being forced to repeat the assumption, as it was a long
one, and also the conclusion; but of being able, instead, to content
one’s self with summing it up briefly thus, “The first case put is true,
therefore so is the second.”
Of arguments, some are conclusive, others are inconclusive. Those are
inconclusive which are such, that the opposite of the conclusion drawn
in them is not necessarily incompatible with the connection of the
premisses. As for instance, such arguments as these, “If it is day, it
is light; but it is day, therefore, Dion is walking.” But of conclusive
arguments, some are called properly by the kindred name conclusions,
and some are called syllogistic arguments. Those then are syllogistic
which are either such as do not admit of demonstration, or such as are
brought to an indemonstrable conclusion, according to some one or more
propositions; such for instance as the following: “If Dion walks, then
Dion is in motion.” Those are conclusive, which infer their conclusion
specially, and not syllogistically; such for instance, as this, “The
proposition it is both day and night is false. Now it is day; therefore,
it is not night.”
Those again, are unsyllogistic arguments which have an air of
probability about them, and a resemblance to syllogistic ones, but
which still do not lead to the deduction of proper conclusions. As for
instance, “If Dion is a horse, Dion is an animal; but Dion is not a
horse, therefore, Dion is not an animal.”
Again, of arguments, some are true, and some are false. Those are true
which deduce a conclusion from true premisses, as, for instance, “If
virtue profits, then vice injures.” And those are false which have
some falsehood in their premisses, or which are inconclusive; as, for
instance, “If it is day, it is light; but it is day, therefore, Dion is
alive.”
There are also arguments which are possible, and others which are
impossible; some likewise which are necessary, and others which are not
necessary. There are too, some which are not demonstrated from their not
standing in need of demonstration, and these are laid down differently
by different people; but Chrysippus enumerates five kinds, which serve
as the foundation for every kind of argument; and which are assumed in
conclusive arguments properly so called, and in syllogisms, and in modes.
The first kind that is not demonstrated, is that in which the whole
argument consists of a conjunctive and an antecedent; and in which
the first term repeats itself so as to form a sort of conjunctive
proposition, and to bring forward as the conclusion the last term. As,
for instance, “If the first be true, so is the second; but the first
is true, therefore, so is the second.” The second kind that is not
demonstrated, is that which, by means of the conjunctive and the opposite
of the conclusion, has a conclusion opposite to the first premiss. As,
for instance, “If it be day, it is light; but it is night, therefore it
is not day.” For here the assumption arises from the opposite of the
conclusion, and the conclusion from the opposite of the first term.
The third kind that is not demonstrative, is that which, by a negative
combination, and by one of the terms in the proposition, produces the
contradictory of the remainder; as, for instance, “Plato is not dead and
alive at the same time but Plato is dead; therefore, Plato is not alive.”
The fourth kind that is not demonstrative, is that which, by means of a
disjunctive, and one of those terms which are in the disjunctive, has
a conclusion opposite to what remains; as, for instance, “It is either