Quotations by Plato


Let no one ignorant of Mathematics enter here.
[Said to have been above the doorway of his Academy.]

He who can properly define and divide is to be considered a god.

The ludicrous state of solid geometry made me pass over this branch. Republic, VII, 528.

He is unworthy of the name of man who is ignorant of the fact that the diagonal of a square is incommensurable with its side.

Mathematics is like draughts [checkers] in being suitable for the young, not too difficult, amusing, and without peril to the state.

The knowledge of which geometry aims is the knowledge of the eternal.
Republic, VII, 52.

I have hardly ever known a mathematician who was capable of reasoning.
Quoted in N Rose Mathematical Maxims and Minims (Raleigh N C 1988).

There still remain three studies suitable for free man. Arithmetic is one of them.
Quoted in J R Newman, The World of Mathematics (New York 1956).

[Of the five Platonic solids]
So their combinations with themselves and with each other give rise to endless complexities, which anyone who is to give a likely account of reality must survey.
The Timaeus

[The Earth is] like one of those balls made of twelve pieces of skin.
Theatetus

He who can properly define and divide is to be considered a god.
Quoted in F Bacon, Novum Organum

I can show you that the art of calculation has to do with odd and even numbers in their numerical relations to themselves and to each other.
Charmides

... arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number, and rebelling against the introduction of visible or tngible objects into the argument.
The Republic

... those who have a natural talent for calculation are generally quick-witted at every other kind of knowledge; and even the dull, if they have had an arithmetical training, although they may derive no other advantage from it, always become much quicker than they would have been.
The Republic

... arithmetic is a kind of knowledge in which the best natures should be trained, and which must not be given up.
The Republic

...no intelligent man will ever be so bold as to put into language those things which his reason has contemplated.

A wise man speaks because he has something to say; a fool because he has to say something.
Quoted in Des MacHale, Wisdom (London, 2002).

Let early education be a sort of amusement. You will then be better able to find out the natural bent.
Quoted in Des MacHale, Wisdom (London, 2002).

One of the penalties for refusing to participate in politics is that you end up being governed by your inferiors.
Quoted in Des MacHale, Wisdom (London, 2002).

Our love for our children springs from the soul's greatest yearning for immortality.
Quoted in Des MacHale, Wisdom (London, 2002).

The greatest penalty of evil-doing is to grow into the likeness of a bad man.
Quoted in Des MacHale, Wisdom (London, 2002).


JOC/EFR February 2006

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