4

is that they cannot hold clearly before their minds
intricate relations between objects that are almost
exactly alike except in respect to abstract relations.
But when I ask one of those gentlement to give me an
example of a necessary reasoning that he considers is not
to be mathematical, it turns out to be one of those that
are most readily amenible to mathematical repre-
sentation, differing only from the reasoning he cannot
grasp in its extreme simplicity. But that which con-
clusively stamps all necessary reasoning as mathe-
matical is that in such reasoning, it makes not
the slightest difference whether the premises
express observed facts (as strictly speaking, they seldom do)
or whether they describe wholly imaginary states of
things. The conclusion follows as necessarily concern-