)
6.33 We do not have an a priori belief in a law of conservation, but rather
a priori knowledge of the possibility of a logical form.
6.34 All such propositions, including the principle of sufficient reason,
tile laws of continuity in nature and of least effort in nature, etc. etc.--
all these are a priori insights about the forms in which the propositions
of science can be cast.
6.341 Newtonian mechanics, for example, imposes a unified form on the
description of the world. Let us imagine a white surface with irregular
black spots on it. We then say that whatever kind of picture these make, I
can always approximate as closely as I wish to the description of it by
covering the surface with a sufficiently fine square mesh, and then saying
of every square whether it is black or white. In this way I shall have
imposed a unified form on the description of the surface. The form is
optional, since I could have achieved the same result by using a net with a
triangular or hexagonal mesh. Possibly the use of a triangular mesh would
have made the description simpler: that is to say, it might be that we
could describe the surface more accurately with a coarse triangular mesh
than with a fine square mesh (or conversely), and so on. The different nets
correspond to different systems for describing the world. Mechanics
determines one form of description of the world by saying that all
propositions used in the description of the world must be obtained in a
given way from a given set of propositions--the axioms of mechanics.
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