5

ing the imaginary state of things as it would if that
state of things had been observed. This, indeed, is pre-
cisely what the necessity of such reasoning con-
sists in. For the purposes of the reasoning, therefore, the
premisses are mere assumptions. If they happen to
be more, it has nothing to do with the reasoning. Now
the only science which deals with pure assumptions
regardless of their real truth is mathematics. That is,
on the whole, the best definition of mathematics. All necessary
reasonings, therefore, are pieces of mathematics.

The only reason I do not agree with Dedekind
in making mathematics a branch of logic
is that logic is not a science of pure assump-
tions but is a study of positive truth. The
mathematician seeks only to trace out the