From the Beginning to Plato

426 GLOSSARY
Platonic: pertaining to Plato.
Platonism, Platonist: the doctrines of a range of schools of thought owing
their inspiration to the work of Plato, including the
Middle Platonist and Neoplatonist schools of the first
to sixth centuries AD. (See also ‘Neoplatonism’.)
Pertaining to Platonism; an adherent of Platonism.
pre-Socratic: pertaining to the philosophers of the sixth and fifth
centuries BC. Strictly speaking, the term is
inaccurate, since a number of those philosophers,
including Anaxagoras, Democritus and the sophists,
were contemporaries of Socrates.
proportion (analogia): an expression of the form ‘a is to b as c is to
d’ (a:b :: c:d). See also ‘mean’.
Protagorean: pertaining to Protagoras, the fifth-century BC sophist.
protreptic: a method whose aim is to encourage the reader or
hearer to seek wisdom.
prudential paradox: the view maintained by Socrates in Plato’s early
dialogues that no one ever intentionally acts contrary
Pythagoreanism,
Pythagorean:
to his or her own good.
the religious and philosophical doctines and
communal life-style traditionally said to have been
initiated by Pythagoras (sixth century BC). Pertaining
to Pythagoreanism; an adherent of Pythagoreanism.
production of a square equal in area to a given figure.
quadrature
(tetragōnismos) of a figure:
ratio (logos): a loosely defined term for the relation of one
magnitude to another; if a is to b as c is to d, then a is
said to have the same ratio to b as c has to d.
rational (rhētos) and In Book X of Euclid’s Elements, the terms are defined
irrational (alogos): for straight lines relative to a given straight line l in
such a way that a straight line is called rational if it is
commensurable (q.v.) with l or if the square with it as
side is commensurable with the square with side l;
otherwise the line is called irrational. This means that,
for example, the diagonal of the square with side l is
irrational. The ancient terms closest to the modern
mathematical terms ‘rational’ and ‘irrational’ are
‘commensurable’ and ‘incommensurable’, but even
in their case one has to note differences in style and
content between ancient and modern mathematics.
realist: see ‘nominalist’.
recollection (anamnēsis): Plato’s belief, expressed in the Phaedo, that we are
born with latent knowledge of the Forms (q.v.)
acquired before birth, and that we can recover this