used out of school. The problems dealt with may be only problems of
science: problems, that is, which would occur to one already initiated
in the science of the subject. Our attention may be devoted to getting
skill in technical manipulation without reference to the connection of
laboratory exercises with a problem belonging to subject matter. There
is sometimes a ritual of laboratory instruction as well as of heathen
religion. 1 It has been mentioned, incidentally, that scientific
statements, or logical form, implies the use of signs or symbols.
The statement applies, of course, to all use of language. But in the
vernacular, the mind proceeds directly from the symbol to the thing
signified. Association with familiar material is so close that the mind
does not pause upon the sign. The signs are intended only to stand for
things and acts. But scientific terminology has an additional use. It is
designed, as we have seen, not to stand for the things directly in their
practical use in experience, but for the things placed in a cognitive
system. Ultimately, of course, they denote the things of our common
sense acquaintance. But immediately they do not designate them in their
common context, but translated into terms of scientific inquiry. Atoms,
molecules, chemical formulae, the mathematical propositions in the study
of physics--all these have primarily an intellectual value and only
indirectly an empirical value. They represent instruments for
the carrying on of science. As in the case of other tools, their
significance can be learned only by use. We cannot procure understanding
of their meaning by pointing to things, but only by pointing to their
work when they are employed as part of the technique of knowledge. Even
the circle, square, etc., of geometry exhibit a difference from the
squares and circles of familiar acquaintance, and the further one
proceeds in mathematical science the greater the remoteness from the
everyday empirical thing. Qualities which do not count for the pursuit
of knowledge about spatial relations are left out; those which are
important for this purpose are accentuated. If one carries his study
far enough, he will find even the properties which are significant for
spatial knowledge giving way to those which facilitate knowledge of
other things--perhaps a knowledge of the general relations of number.
There will be nothing in the conceptual definitions even to suggest
spatial form, size, or direction