#philosophicaldigression

Doesn't vagueness have some, or at least one, sharp boundary condition even if it's fuzzy? For example, one grain of sand isn't a heap ("a disorderly collection of objects placed haphazardly on top of each other") while two grains of sand seems unclear if it is. Therefore, one gain of sand is a sharp boundary for 'heap,' namely that it isn't a heap.

The lesson takes lower boundaries of ambiguities like 'some' and says it has a sharp boundary and vague concepts like 'heap' as having a fuzzy boundary, but thinking of what would constitute a lower boundary for 'heap' seems like it would be a sharp boundary in the same way as 'some' has a sharp boundary. For upper boundaries, this distinction between sharp boundaries and fuzzy boundaries might be different and I think probably is. Yet, in this lesson alone, given the two examples, lower boundaries between the two aren't exactly different in the way it's making it out to be .

Well at least we know it's not something on our end, with our accounts, and they need to fix it. Hopefully soon it will be resolved.