We must never forget that every rule is shattered whenever any single
element of the situation is unknown, and that happens very easily and
frequently. Suppose that I did not have full knowledge of the nature of
water, and walked on terra firma to the edge of some quiet, calm pool.
When now I presume: water has a body, it has a definite density, it has
consistency, weight, etc., I will also presume that I may go on walking
over its surface just as over the surface of the earth,--and that,
simply because I am ignorant of its fluidity and its specific gravity.
Liebman[137] summarizes the situation as follows. The causal nexus, the
existential and objective relation between lightning and thunder, the
firing of powder and the explosion, are altogether different from the
logical nexus, i.e. the mere conceptual connection between antecedent
and consequent in deduction. This constitutes the well known kernel of
Humian skepticism. We must keep in mind clearly that we never can know
with certainty whether we are in possession of all the determining
factors of a phenomenon, and hence we must adhere to the only
unexceptionable rule: _Be careful about making rules that admit of no
exceptions_. There is still another objection to discuss, i.e. the
mathematical exception to Humian skepticism. It might be held that
inasmuch as the science of justice is closely related in many ways to
mathematics, it may permit of propositions a priori. Leibnitz already
had said, “The mathematicians count with numbers, the lawyers with
ideas,--fundamentally both do the same thing.” If the relationship were
really so close, general skepticism about phenomenal sciences could not
be applied to the legal disciplines. But we nowadays deal not with
concepts merely, and in spite of all obstruction, Leibnitz’s time has
passed and the realities of our profession, indeed its most important
object, the human being itself, constitute an integrating part of our
studies. And the question may be still further raised whether
mathematics is really so exempt from skepticism. The work of Gauss,
Lobatschewski, Bolyai, Lambert, would make the answer negative.
Let us, for once, consider what significance mathematical postulates
have. When Pythagoras discovered his proposition in such a way that he
first drew a right-angled triangle and then built a square on each of
the sides, and finally measured the area of each and compared them, he
must at first have got the notion that that also might be merely
accidental. If he had made the construction 10 or 100 times with various
triangles and these had resulted always identically, only then might he
have been justified in saying that he had apparently discovered a
theorem. But then his process was just as thoroughly experiential as
that of a scientist who says that a bird has never yet been observed to
give birth to living young, and that hence all birds lay eggs.
Public-domain text, read in full here on John Shaqi.
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