special sciences, such as mathematics, for example. Of the general
tendency there can be no question. The only problem is: Why does this
tendency exist?

68. LOGIC AND PHILOSOPHY.--Let us contrast the science of arithmetic
with logic; and let us notice, regarding it, the following points:--

It is, like logic, a _general_ science, in that the things treated of
in many sciences may be numbered. It considers only a certain aspect
of the things.

Now, that things may be counted, added together, subtracted, etc., is
guaranteed by the experience of the plain man; and the methods of
determining the numerical relations of things are gradually developed
before his eyes, beginning with operations of great simplicity.
Moreover, verification is possible, and within certain limits
verification by direct inspection.

To this we may add, that there has gradually been built up a fine
system of unambiguous symbols, and it is possible for a man to know
just what he is dealing with.

Thus, a certain beaten path has been attained, and a man may travel
this very well without having forced on his attention the problems of
reflective thought. The knowledge of numbers with which he starts is
sufficient equipment with which to undertake the journey. That one is
on the right road is proved by the results one obtains. As a rule,
disputes can be settled by well-tried mathematical methods.

There is, then, a common agreement as to initial assumptions and