Plato, like Francis Bacon, took a review of the sciences of his
time: he enumerates arithmetic and plane geometry, treated as
collections of abstract and permanent truths; solid geometry, which
he “notes as deficient” in his time, although in fact he and his
school were in possession of the doctrine of the “five regular
solids;” astronomy, in which he demands a science which should
be elevated above the mere knowledge of phenomena. The visible
appearances of the heavens only suggest the problems with which
true astronomy deals; as beautiful geometrical diagrams do not
prove, but only suggest geometrical propositions. Finally, Plato
notices the subject of harmonics, in which he requires a science
which shall deal with truths more exact than the ear can establish,
as in astronomy he requires truths more exact than the eye can
assure us of.
In a subsequent paper Plato speaks of _Dialectic_ as a still
higher element of a philosophical education, fitted to lead men
to the knowledge of real existences and of the supreme good. Here
he describes dialectic by its objects and purpose. In other places
dialectic is spoken of as a method or process of analysis; as in
the _Phædrus_, where Socrates describes a good dialectician as one
who can divide a subject according to its natural members, and not
miss the joint, like a bad carver. Xenophon says that Socrates
derived _dialectic_ from a term implying to _divide a subject into
parts_, which Mr. Grote thinks unsatisfactory as an etymology, but
which has indicated a practical connection in the Socratic school.
The result seems to be that Plato did not establish any method of
analysis of a subject as his dialectic; but he conceived that the
analytical habits formed by the comprehensive study of the exact
sciences, and sharpened by the practice of dialogue, would lead his
students to the knowledge of first principles.--_Dr. Whewell._