  Weyl proposed a schema for symbolic construction of scientific representation
starting from subjective immediate experience, and moving toward the objective
ordered manifolds of possibilities due to "rational motives" of comprehending
the world in "the 'truly objective', exact, non-qualitative" way. Weyl's purely
infinitesimal geometry may be viewed as an application of the schema.Weyl
himself as well as various researchers have discussed the introduction of a
local coordinate system as an effort to bridge the chasm between the intuitive
and the mathematical continuum for this schema. I argue that the introduction
of a local coordinate system only explained the "exact, non-qualitative" aspect
of the "rational motives", and there is also a problem of how the
intersubjective constitution is possible. The latter was not explicitly
explained by Weyl, and corresponds to the "truly objective" aspect of "rational
motives". I argue that, a comprised intersubjective constitution could be
achieved by a strategy of introducing an additional structure to starting
points for theoretical constructions. The strategy might also provide an
explanation for gauge invariance in Weyl's unified field theory.
