Comment by joggery | Hacker News Reader

Comment by joggery | Hacker News Reader

I like to consider the difference between 'one','a couple','a few','several','many'. e.g 1,2,3-6,5-12,10+ respectively.

>Vagueness isn’t a problem about logic; it’s a problem about knowledge.

I think it's more to do with context. 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.

The confusion arises from the fact that 'a grain' is considered to be well-defined without context and that language refers to it directly. Thus we lament that we can't adequately define 'heap'. Whereas in fact all language is metaphorical and indirect, and definitions can't rescue us from this. So even the label 'a grain' is fuzzy if you look deeply and scientifically enough.

>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.

>All language is metaphorical and indirect, and definitions can't rescue us from this.

I think that overstates the problem. Just don't use 'heap' in a context where greater precision is needed; there are alternatives.

Ok here goes.

A heap is more than three.

You can't have a heap if the objects aren't stacked, and stacking nonrectangular objects generally requires 4 if you want it to be a stable heap. 3 as the base, 1 on top.

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