ples, and also a third, which
is compounded out of them; but I fear that I am ridiculously clumsy at
these processes of division and enumeration.

PROTARCHUS: What do you mean, my good friend?

SOCRATES: I say that a fourth class is still wanted.

PROTARCHUS: What will that be?

SOCRATES: Find the cause of the third or compound, and add this as a
fourth class to the three others.

PROTARCHUS: And would you like to have a fifth class or cause of
resolution as well as a cause of composition?

SOCRATES: Not, I think, at present; but if I want a fifth at some future
time you shall allow me to have it.

PROTARCHUS: Certainly.

SOCRATES: Let us begin with the first three; and as we find two out of
the three greatly divided and dispersed, let us endeavour to reunite
them, and see how in each of them there is a one and many.

PROTARCHUS: If you would explain to me a little more about them, perhaps
I might be able to follow you.

SOCRATES: Well, the two classes are the same which I mentioned before,
one the finite, and the other the infinite; I will first show that the
infinite is in a certain sense many, and the finite may be hereafter
discussed.

PROTARCHUS: I agree.

SOCRATES: And now consider well; for the question to which I invite your
attention is difficult and controverted. When you speak of hotter and
colder, can you conceive any limit in those qualities? Does not the more
and less, which dwells in their very nature, prevent their having any
end? for if they had an end, the more and less would themselves have an
end.

PROTARCHUS: That is most true.

SOCRATES: Ever, as we say, into the hotter and the colder there enters a
more and a less.

PROTARCHUS: Yes.

SOCRATES: Then, says the argument, there is never any end of them, and
being endless they must also be infinite.

PROTARCHUS: Yes, Socrates, that is exceedingly true.

SOCRATES: Yes, my dear Protarchus, and your answer reminds me that such
an expression as 'exceedingly,' which you have just uttered, and also
the term 'gently,' have the same significance as more or less; for
whenever they occur they do not allow of the existence of quantity--they
are always introducing degrees into actions, instituting a comparison
of a more or a less excessive or a more or a less gentle, and at each
creation of more or less, quantity disappears. For, as I was just now
saying, if quantity and measure did not disappear, but were allowed to
intrude in the sphere