rectangle vs. square

[Arnold Zwicky]

On Jun 26, 2010, at 5:46 PM, 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.)

as *technical* terms.  but what about ordinary language?

> 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.)

maybe implicature would be at work for someone -- is there such a native speaker? -- who somehow learned the technical uses (of "ellipse" and "circle", of "rectangle" and "square") before the ordinary-language uses.  but for ordinary speakers, "circle" is not a special case of "ellipse", nor "square" a special case of "rectangle", period; that's the way you learn to talk when you learn to "talk geometry".

the technical uses don't have some sort of priority outside of context.  in fact, they're restricted to very special social contexts.

and the technical uses are wrenchings of the ordinary-language uses for special purposes.  compare other mathematical specializations of ordinary-language terms.

arnold

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