If we wanted to be more specific, we could tighten it up. — T Clark

But otherwise, we can use it as it is. With certain embarrassing difficulties on slippery slopes, admittedly.

What lots of people say only tells you what lots of people say. — Terrapin Station

Which, when you want to know about usage, is what you want to know.

And, otherwise of course, not. But I am interested in usage, so I am.

a situation where the idea of 'a heap of sand' has been an issue ! — fresco

Any "slippery slope" issue.

... is where, at any rate, 'a heap of sand' has seemed a pertinent analogy.

What if the tail end of such a distribution (of thresholds) reaches back to a single grain?
— bongo fury

Can you expand on that? — TheMadFool

By "threshold" I hoped to refer to what you were calling a "private definition of heap".

E.g., GMBA's 4-grains-or-more. From their observations about taking mean averages I guessed they were interested in a larger pattern or distribution of different individual thresholds, in order to reconcile their own sharp threshold with their own intuition of fuzziness. And I wondered whether this was likely to end up compromising their intuition of clarity, in the case of a single grain (your starting point).

Ok so far?

Sorry for not relating my comments directly to the OP. I was interested in that particular exchange between you, as an instance of the heap game, considered as a challenge to reconcile clarity with fuzziness. For which I am an enthusiast.

That makes sense but the definition of "heap" in this case would be private and others will probably disagree with you.
— TheMadFool

You're absolutely right. That's why I made no bones about it, and did not declare that my proposition is the ultimate answer. I came out straight away and said under what circumstances my opinion holds. — god must be atheist

But what about the big picture, a poll of judgements, or of individual thresholds? What if the tail end of such a distribution (of thresholds) reaches back to a single grain? From your observations about means, we guess that it will.

Then, for some enthusiasts at least, this play of the game is over. From their point of view, you won't play. You decline to agree that a single grain is absolutely not a heap. You admit that this grain is, in the current idiom, "on the spectrum" of (usage of) heap. Albeit at one far end of that spectrum. You've lost one of the two required (and puzzlingly opposed) intuitions that we are trying to reconcile.