rectangle vs. square

[Garson O'Toole]

Laurence Horn
> This context brings out the likelihood of
> exclusive readings in which the implicature
> becomes part of the meaning.  "What's the
> difference between a finger and a thumb?"
> "What's the difference between a lion and a
> lioness?"  "What's the difference between a goose
> and a gander?"  "What's the difference between
> gays and lesbians?" or even "What's the
> difference between cats and kittens?"
> etc.--doesn't prove that there aren't other
> contexts that bring out the fact that ganders
> *are* geese, thumbs *are* fingers, kittens *are*
> cats, etc

I certainly agree that the issue is complex and context is important.
Consider the following example in the domain of architecture. The
writer assumes that the set of rectangular objects includes squares.
Therefore he or she must explicitly rule out the inclusion of squares.

[1] ... what Pliny tells us is that the building was rectangular (but
not square), that it was surrounded by a colonnade of thirty-six
columns, ...

The parenthetical remark "(but not square)" would be redundant if the
speaker thought that the set of rectangles already excluded squares.
Here are another two examples:

[2] Lumber is used that has rectangular, but not square, cross
section, and is always oriented so that the longer dimension is
parallel to the load (ie, usually is vertical).

[3] This room was rectangular, but not square with the sepulchral
chamber, as it lay 25° east of north ; …

Perhaps these are not ordinary speakers/writers. I did trawl through
the massive Google Books database to find these examples. It is also
easy to find examples like the following:

[4] Not only is the cross equal-armed, but the official flag of
Switzerland is unusual in being a perfect square (not a rectangle),
further accentuating the symmetry.

This statement would be incoherent if the speaker thought that the set
of squares was a subset of the set of rectangles. It would be similar
to saying "The animal is a poodle (not a dog)."

Garson

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