IX 
PLATO 
It is in the Seventh Book of the Republic that we find 
the most general statement of the attitude of Plato towards 
mathematics. Plato regarded mathematics in its four branches, 
arithmetic, geometry, stereometry and astronomy, as the first 
essential in the training of philosophers and of those who 
should rule his ideal State ; ‘ let no one destitute of geometry 
enter my doors ’, said the inscription over the door of his 
school. There could be no better evidence of the supreme 
importance which he attached to the mathematical sciences. 
What Plato emphasizes throughout when speaking of mathe 
matics is its value for the training of the mind; its practical 
utility is of no account in comparison. Thus arithmetic must 
be pursued for the sake of knowledge, not for any practical 
ends such as its use in trade 1 ; the real science of arithmetic 
has nothing to do with actions, its object is knowledge. 2 
A very little geometry and arithmetical calculation suffices 
for the commander of an army; it is the higher and more 
advanced portions which tend to lift the mind on high and 
to enable it ultimately to see the final aim of philosophy, 
the idea of the Good 3 ; the value of the two sciences consists 
in the fact that they draw the soul towards truth and create 
the philosophic attitude of mind, lifting on high the things 
which our ordinary habit would keep down. 4 
The extent to which Plato insisted on the purely theoretical 
character of the mathematical sciences is illustrated by his 
peculiar views about the two subjects which the ordinary 
person would regard as having, at least, an important practical 
side, namely astronomy and music. According to Plato, true 
astronomy is not concerned with the movements of the visible 
1 Rep. vii. 525 c, n. 
3 Rep. 526 n, e. 
2 Politicus 258 n. 
4 Ih. 527 b.