aries. People even use small integers in 'vague' ways, as when a
&gt; recipe calls for '3 or 4  grains of salt', and it doesnt really
&gt; matter if you put in, say, 5, but it does matter if you put in 5000.
&gt; 

   I completely agree that people use vague concepts in language,
and often do so intentionally.   But it seems the comments above
are drifting very far from the question of how vagueness affects the
heap paradox, and how to formalize it.  I believe that there are
many vague concepts that can be 