ons which are, from
the nature of the human mind, inevitable. It is in the Mathematics, in
which the Deductive Method is rightly operative, that this kind of
Proof--Demonstration in the strict sense of the term--prevails. The
various branches of Mathematics have therefore been appropriately
denominated the _Exact_ Sciences, in contradistinction from those
domains of Thought whose Laws or Principles are liable to be somewhat
indefinite or uncertain; hence, called the _Inexact_ Sciences.

Exact Science--in its largest sense, that which extends to all domains
in which the proper Deductive Method has been or may hereafter be
rightly employed--is therefore a _system or series of truths relating to
the whole Universe, or to some department of it, consecutively and
necessarily resulting from, and dependent upon, each other, in a
definite chain or series; and resting primarily upon some fundamental
truth or truths so simple and self-evident, that, when clearly stated,
all men must, by the natural constitution of the human mind, perceive
them and recognize them as true. Demonstration is the pointing out of
the definite links in the chain or series by which we go from
fundamental truths, clearly perceived and irresistible, up to the
particular truth in question_.

Thus far in the history of Science, Mathematics, as a whole, has ranked
as the only Exact Science; being the only department of intellectual
activity, all of whose Laws or Principles are established on a basis of
_undeniable certainty_. If, however, theories of Cosmogony and
considerations of Cosmography be excluded from the field of Astronomy,
this Science consists almost wholly of the application of the Laws of
Mathematics to the movements of the celestial bodies. Restricting
Astronomy proper to this domain, where, as a _Science_, it strictly
belongs, and setting aside its merely descriptive and conjectural
features, as hardly an integral part of the Science itself, we have
another Exact Science in addition to Mathematics.

Of still another domain, that of Physics, Professor Silliman says, 'all
its phenomena are dependent on a limited number of general laws ...
which may be represented by numbers and algebraic symbols; and these
condensed _formulae_ enable us to conduct investigations with the
certainty and precision of pure Mathematics.'

The various branches of Physics have not hitherto been ranked as Exact
Sciences, because, as in Astronomy, unsubstantiated the