rectangle vs. square

[Laurence Horn]

At 7:46 PM -0500 6/26/10, Jim Parish wrote:
>Dan Goncharoff wrote:
>>  Second, what would be the justification for using "ellipse" when describing
>>  a circle, or rectangle for square? It may be correct, but it's not
>>  informative.
>
>Precisely the point. *As terms* "ellipse"
>includes "circle", and "rectangle" includes
>"square". (Trust me on this: I'm a professional
>mathematician, specializing in geometry.)
>But to use "ellipse", referring to a circle, is
>misleading; by the usual conventions of
>conversational implicature, the failure to use
>the more specific term invites the hearer to
>conclude that the more specific term does not
>apply. In other words, *semantically* the
>word "rectangle" applies to squares, but
>*pragmatically* it almost never will. (I might
>use
>it that way, but mathematical language deliberately defies the conventions of
>implicature.)
>
>Jim Parish
>
As a pragmaticist (who's been worrying about this
stuff since '72) and a non-mathematician, I
wholeheartedly concur.

At 7:32 PM -0400 6/26/10, Garson O'Toole wrote:
>Here is another example. Formally every circle is also an ellipse. The
>set of all circles is a subset of the set of all ellipses. But the
>informal use of these terms is different, e.g.:
>
>http://wiki.answers.com/Q/What_is_the_difference_between_a_circle_and_a_ellipse
>
>What is the difference between a circle and a ellipse?
>Basically a circle has a constant radius throughout and an ellipse does not.

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.  (A modern example, at least for a
while, was Macs vs. PCs, but my impression is
that now "PC" semantically excludes Macs, and not
only in the commercials for the latter.) Another
context that favors contrast rather than
inclusion is that of metalinguistic negation:
"That's not a ___, it's a _____".  This is often
used to suggest something like "It's not
sufficient to call that a ___, you can more
perspicuously call it a ____"  (as in the old
Volkswagen commercial's claim "It's not a car,
it's a VW").

(There was a nice paper on these kinds of cases
in the Journal of Semantics, 1985, but Günther
Rohdenburg called something like "Dogs, bitches,
and other creatures" that went through a lot of
these cases--shoes/sandals, children/babies, and
so on.)

The examples above (including square/rectangle)
involve narrowing, but broadening can produce the
same effects, especially in cases of genericide:
"guys" (including or excluding women?),
"band-aid" (including or excluding Curad
strips?), "kleenex" (including or excluding other
brands of tissues?)  YMMV, of course.  And I'm
*not* inviting Ron to launch another round of our
Great (but Inconclusive) Debate on name brands
and generics; I'm talking about ordinary language
use, not the law.  The fact of the matter can
shift in any of these cases, but like Jim, I'm
not convinced that it has (semantically) in the
case of rectangle/square the way I believe it has
with "PC".

LH

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