6

consequences of his assumptions in the readiest
and speediest way. The logician does not care
much what the conclusions from this or that
system of assumptions may be. What he is
interested in is in dissecting the mathema-
tician's reasonings, in finding out what
their elementary steps are, and in showing what
positive facts about the real universe of things
and of thoughts it is from which the necessity
of the mathematician's reasonings and the
validity of other kinds of reasonings depend,
and exactly what the nature of that depen-
dence is. I have already pointed out that the
characters that make a system of symbols
good for logical [??mathematical] purposes are quite contrary to

consequences of his assumptions in the readiest
and speediest way. The logician does not care
much what the conclusions from this or that
system of assumptions may be. What he is
interested in is in dissecting the mathema-
tician's reasonings, in finding out what
their elementary steps are, and in showing what
positive facts about the real universe of things
and of thoughts it is from which the necessity
of the mathematician's reasonings and the
validity of other kinds of reasonings depend,
and exactly what the nature of that depen-
dence is. I have already pointed out that the
characters that make a system of symbols
good for [mathematical] purposes are quite contrary to