Reference by description is inherently ambiguous
¥Ordinary discourse is full of ambiguities which are rarely noted, because they have no practical importance, but which are rendered vivid by trying to agree about Ôcommon senseÕ well enough to write it down in a formal notation. My favorite example (apologies to those who have heard it before) was a disagreement about whether or not a fitted carpet was ÔinÕ an office or Ôpart ofÕ the office.
¥Two competent, intelligent adult native speakers of English each discovered, to their mutual amazement, that another could believe such an obviously false claim. Over an hour of discussion it gradually emerged, by a process of induction from many examples, that they understood the meaning of ÔofficeÕ differently: for one it meant, roughly, an inhabitable place; for the other, something like a volume of space defined by the architectural walls.
¥These two people never knew, until this event, that they had different mental meanings for ÔofficeÕ (in fact, more generally, for ÔroomÕ). Presumably this was possible because they had never previously engaged in a communicative act in which their conceptual differences made any difference to the communication: but note that each had, in fact, been understanding the English word ÔofficeÕ differently. So ÔofficeÕ and ÔroomÕ, in this instance, are ambiguous. Probably every word in English is ambiguous.