290 
PLATO 
regard to them either to themselves or any one else, but treat 
them.as manifest to every one; basing themselves on these 
hypotheses, they proceed at once to go through the rest of 
the argument till they arrive, with general assent, at the 
particular conclusion to which their inquiry was directed. 
Further you know that they make use of visible figures and 
argue about them, but in doing so they are not thinking of 
these figures but of the things which they represent; thus 
it is the absolute square and the absolute diameter which is 
the object of their argument, not the diameter which they 
draw; and similarly, in other cases, the things which they 
actually model or draw, and which may also have their images 
in shadows or in water, are themselves in turn used as 
images, the object of the inquirer being to see their abso 
lute counterparts which cannot be seen otherwise than by 
thought.’ 1 
(/3) The two intellectual methods. 
Plato distinguishes two processes: both begin from hypo 
theses. The one method cannot get above these hypotheses, 
but, treating them as if they were first principles, builds upon 
them and, with the aid of diagrams or images, arrives at 
conclusions: this is the method of geometry and mathematics 
in general. The other method treats the hypotheses as being 
really hypotheses and nothing more, but uses them as stepping- 
stones for mounting higher and higher until the principle 
of all things is reached, a principle about which there is 
nothing hypothetical; when this is reached, it is possible to 
descend again, by steps each connected with the preceding 
step, to the conclusion, a process which has no need of any 
sensible images but deals in ideals only and ends in them 2 ; 
this method, which rises above and puts an end to hypotheses, 
and reaches the first principle in this way, is the dialectical 
method. For want of this, geometry and the other sciences 
which in some sort lay hold of truth are comparable to one 
dreaming about truth, nor can they have a waking sight of 
it so long as they treat their hypotheses as immovable 
truths, and are unable to give any account or explanation 
of them. 3 
1 Republic, vi. 510 c-E. 2 lb. vi. 510 B 511 A-c. 
3 lb. vii. 538 b e.