  Arguably, this conceptual tension between boundaries understood as lower-dimensional entities and boundaries understood as thin layers reflects an irreducible ambiguity in ordinary speech (Stroll 1979, 1988).  And, arguably, it is only the first conception that gives rise to the puzzles outlined in the foregoing sections; bulky boundaries can be treated as ordinary, extended parts of the bodies they bound. Yet a general theory of boundaries should have something to say about the second conception as well — and more generally about the interaction between the mathematical idealization associated with the former conception and the physical, cognitive, and philosophical significance of the latter (Galton 2007).