[woodandsteel]

>The transition from 'a grain' to 'a pile' to 'a heap' where those terms are actually useful is normally clear in the context of whatever problem we're trying to solve.

That's the position of pragmatist philosophers, the existential-phenomenologists and the analytic philosophers influenced by the later Wittgenstein.

In Western philosophy, there are two competing ideas about the metaphysical status of basic concepts. According to one, as in Platonism, dualism, and materialism, concepts concerning the real world are perfect, like mathematical ideas. In the other view, concepts are the products of the great complexities of human living, and so are inherently vague, complex, and contextual. In the last century or so, I would say the later idea has been winning out, though many philosphers still hold the former one.