23

19

Everything depends, in logic, upon formulating
precise definitions. Now what precisely do
we mean by saying that one collection is at
least as small as another. The best definitions are those
which express how the truth or falsity of the
term defined will affect what we can do in the future.
To say that a thing is soft is to say that it can easily
be scratched. To say that is is hard is to say that it never
will easily be scratched, unless it turns soft. The relation
of greater and less was first defined in this fashion by
the Catholic logician Bolzano in his posthumous work
which appeared in 1851. He said a collection, say that of
the As is at least as small as another collection