tablish their connection with the
lowest, most fundamental, and self-evident truths, and in this manner
become competent to advance step by step from undeniable first truths to
those equally undeniable. In Mathematics, in Astronomy, and in Physics,
we are able to do this. We _know_ the Laws or Principles of these
Sciences, therefore, so far as we have developed the Sciences
themselves. We know the relations of the various Laws within the range
of each Science, and the relations of the different Sciences with each
other. We can advance, within their boundaries, from the simplest and
most positive verities, such as the whole is equal to all its parts--a
self-evident truth, which it is impossible to conceive as being
otherwise than as here stated--up to the most intricate ulterior Facts
of the universe, by Inferences which are as irresistible to the mind as
the axioms with which we started. In no other domains of Thought can
this be done by any methods now in vogue. In no other realms, therefore,
are complete precision and infallibility attainable. It is this which
constitutes the peculiar character of these three Sciences, and
distinguishes them radically from all others.

The whole body of our authoritative and irrevocably determinate
intellectual acquisitions lies, therefore, at the present time, so far
as is commonly known, within the range of Mathematics, Astronomy, and
Physics. These are in strictness the only _Sciences_ which we possess;
and the only domains in which _knowledge_, in the proper sense of the
term, is attainable. In passing their boundaries, we leave the regions
of positive _certitude_, and come into the domain where Conjecture,
varying from the strongest presumption to mere plausibility, is the
highest proof. Laws or Principles are yet undiscovered there, and in
their place we find Generalizations--Suppositive or Proximate
Laws--which are in process of proof, or already established by such
evidence as the Inductive Method can array, and which carry the
conviction of their correctness with varying degrees of force, to larger
or smaller classes of investigators.

These three branches of knowledge are unquestionably entitled to the
designation of _Positive_ Sciences; and to no others can it with justice
be accorded. To apply the name of _Science_ to domains in which real
knowledge is not attainable, is, in some sense, an abuse of terms. To
denominate _Positive Sciences_, domains which are not strictly