A Mark Stivers cartoon of 5/21/11 (found via Funny Times):
This is an ambiguity in context, discussed in this blog here:
If you order a hot dog in an eating establishment, you’ll automatically get the sausage in a bun. But if you go to a grocery store to buy hot dogs, they don’t come with buns; these you have to buy separately.
So strictly speaking, hotdog-1 + bun = hotdog-2 (and we can’t conclude that bun = 0, even conceding the ambiguity of + and =).
(Hamburger works the same way.)
A related ambiguity, from the posting linked to above:
If you go to an Olneyville N.Y. System place and order a wiener roll, you expect to get a roll (or bun) with a wiener in it, a wiener in a roll. On the other hand, if you go to a grocery story and WIENER ROLLS are on the shopping list, you’ll be looking for just the buns, and if you want some sort of hot-dog-oid items to put in those buns, that’s a separate trip to a different aisle.
So wiener roll is ambiguous, with the appropriate meaning determined by context.
June 17, 2012 at 9:36 am |
An exchange on Facebook:
It’s hard to disentangle this discussion, since it’s not clear what the expression hotdog stands for. If the elements of the group are two, HOTDOG and BUN, then HOTDOG + HOTDOG must be an element, either HOTDOG (in which case + is idempotent, and that’s fine) or BUN, but in either case the results require a non-standard interpretation of +.
The alternative is that the elements of the group are hotdogs and buns, in which case hotdog-x + bun-y is a hotdog, either hotdog-x (in which case bun-y is a zero) or hotdog-z (different from hotdog-x); hotdog-z is at least consistent with the intended interpretation of +. But then what are hotdog-x + hotdog-x and hotdog-x + hotdog-z? This is where the mind starts boggling.
Group theory is not a good place to go.
June 17, 2012 at 12:21 pm |
Evidently definite anaphora is not sensitive to the “ambiguity” of “hotdog”. “I bought hotdogs at the market and served them to my kids” has the most probably interpretation that the “them” refers to hotdogs-with-buns and the antecedent “hotdog” refers to hogdogs-without-buns. I imagine one could find other similar instances where the name of a dish is taken from its principle ingredient.
June 18, 2012 at 6:55 am |
I’m inclined to say “them” refers to the hotdogs without buns, and it is inferred (but not stated) that they are served in buns, simply because that’s the most common serving method and no serving method is indicated. Still, it’s an inference, and what’s directly stated is only that the meat was served.