F HISTORY

_THIRD PAPER_

In any classification of our intellectual domain which it is possible to
make on the basis of Principles now known to the Scientific world at
large, the most fundamental characteristic should be, the distinctive
separation of those departments of thought in which _Certainty_ is now
attainable, from those in which only varying degrees of Probability
exist, and the clear exhibition of that which is _positive and
demonstrable knowledge_, in the strict sense of the term, as
distinguished from that which is liable to be more or less fallible.
Although the precise point at which, in some cases, the proofs of
Probable Reasoning cease to be as convincing as those of Demonstration
cannot be readily apprehended, yet the essential nature of the two
_methods_ of proof is radically and inherently different, and is marked
by the most distinctive results. In the latter case, we have always
accuracy, precision, and certainty, _beyond the possibility of doubt_;
in the former, always the conviction that, how strong soever the array
of evidence may seem to be, in favor of a particular inference, there
still remains a possibility that the conclusion may be modified or
vitiated by the subsequent advancement of knowledge.

The Generalizations which respectively affirm that all the angles of a
triangle are equal to two right angles, or that the square of the
hypothenuse of a right-angled triangle is equal to the sum of the
squares of the other two sides, rest upon an entirely different basis of
proof from those upon which the Generalizations rest which respectively
assert that water is composed of certain chemical constituents combined
in certain proportions, or that the nerves are the instruments of
sensation and of motion. The former are irresistible conclusions of the
human mind, because, from the nature of the intellect, they cannot be
conceived of as being otherwise. The Laws of Thought are such, that we
are unable to think a triangle whose angles will _not_ be equal to two
right angles, or a right-angled one, the square of whose hypothenuse
will _not_ be equal to the squares of the other two sides. So long,
therefore, as man is constituted as he now is--unless the human
organization becomes radically changed, these geometrical Laws cannot be
conceived as being otherwise than as they are. All men must apprehend
them alike if they apprehend them at all. So long as man lives and
thinks they remain unalterable