The Lives and Opinions of Eminent PhilosophersDiogenes Laertius
Philosophy
The Lives and Opinions of Eminent Philosophers
Diogenes Laertius
Philosophers, Ancient -- Biography; Philosophy, Ancient
XLVIII. An axiom, is that thing which is true, or false, or perfect
in itself, being asserted, or denied positively, as far as depends
upon itself; as Chrysippus explains it in his Dialectic Definitions;
as for instance, “It is day,” “Dion is walking.” And it has received
the name of axiom, ἀξίωμα, because it is either maintained, ἀξιοῦται,
or repudiated. For the man who says, “It is day,” appears to maintain
the fact of its being day. If then it is day, the axiom put before one
is true; but if it is not day, the axiom is false. And an axiom, a
question, and an interrogation, differ from one another, and so does an
imperative proposition from one which is adjurative, or imprecatory,
or hypothetical, or appellative, or false. For that is an axiom which
we utter, when we affirm anything positively, which is either true or
false. And a question is a thing complete in itself, as also is an axiom,
but which requires an answer, as for instance, “Is it day?” Now this
is neither true nor false; but, as “It is day” is an axiom; so is, “Is
it day?” a question. But an interrogation, πύσμα, is a thing to which
it is not possible to make an answer symbolically, as in the case of a
question, ἐρώτημα, saying merely “Yes,” but we must reply, “He does live
in this place.”
The imperative proposition is a thing which we utter when we give an
order, as for instance this:—
Do you now go to the sweet stream of Inachus.[85]
…
The appellative proposition is one which is used in the case in which,
when a man says anything, he must address somebody, as for instance:—
Atrides, glorious king of men,
Most mighty Agamemnon.[86]
A false judgment is a proposition, which, while it has at the same time
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.”
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