I could still call certain things heaps even if I had a sharp definition of a heap.
Sorry, what I meant was, “Heaps as they are currently defined can be said to exist because of vagueness in the definition of what precisely makes something a heap.” They can also be said to not exist because of vagueness in the definition of what precisely makes something a heap. However, it is extremely difficult if not impossible for any definition to have absolutely no ambiguity at all, and even if that was possible, language can still be considered a social construct in the sense that linguistic terms are constructed socially. Vague terms have an extra layer of social construction though, because rather than just giving a term to a phenomenon, they also introduce a simplification. This makes the constructed aspect more obvious. I guess I didn’t word my above quote very well, since I didn’t mention that the social construction of all language itself is also enough to make “heaps” a social construct.
Not that they are necessarily using multiple definitions, but the common definitions themselves do not specify an exact range in quantity in which a cluster of things could be considered a heap. Two people could disagree about whether something is a heap despite using the same vague definition of “heap”. They may be comparing the candidate heap relative to things that they have experienced being called heaps in the past. I suppose you could still treat this as being a difference in their personal definitions of “heap”. However, I don’t think that if pressed to define “heap”, that people would be likely to state an explicit quantity range. They would most likely give vague qualitative definitions. The same person may even use inconsistent definitions at different times or forget to include certain aspects that they would consider to be important defining characteristics. People don’t normally think in terms of definitions when classifying things. They usually just classify based on what feels correct, and definitions are after-the-fact attempted explanations of their classifications.
Doesn’t the introduction of a simplification itself give a term some vagueness, because then you don’t know the details of the relevant characteristic, just a qualitative judgment? For “heaps”, the simplification is one that keeps the exact quantity obscured while providing a qualitative description instead. Even if you had a different quantity term that, unlike “heap”, didn’t have fuzzy boundaries, it could still be considered vague in a different sense if multiple quantities could fulfill its definition (assuming an exact quantity really did exist in reality). It would certainly at least be considered somewhat ambiguous. For example, the category “integers” has seemingly clear boundaries, but calling an unknown number an integer is still vague if it doesn’t express all the relevant information.
Yes, terms can be vague in that way too.