And how are we attempting to define a sandwich (with or without a hot dog)? Are we comparing it with an ideal Platonic sandwich (something that partakes of the form we can think of as sandwichness)?
Are we defining it functionally, in terms of how it’s used, or are we thinking of its composition? Can we pinpoint the exact moment that it goes from being not a sandwich but just a collection of ingredients to having the Gestalt of a sandwich? And how far can it depart from that standard and still be a sandwich? Do we call anything we can sit on a chair just because a chair is something we sit on?
Is an ice cream sandwich a sandwich? How about an Oreo?
And when does it stop being a sandwich? When, for example, the bun and the hot dog don’t come out even, and your last bite is just bread because the hot dog is all gone, is what’s left in your hand still a sandwich or not?
How do you know when you have half a sandwich?
Are we looking for a dictionary definition that places “sandwich” in a certain class and then distinguishes it from other members of its class? Or are we perhaps interested in the common usage of the term, and if so, then common in what population? and during what time period?
(A single dictionary definition doesn’t necessarily constitute an authority. If I were seriously questing after this word, I’d want to see half a dozen, including the OED, Merriam-Webster, and at least one foreign language dictionary; in this case, probably not Latin or Greek, but German would do.)
The more we think about words, the more surprising it is that we can manage to say anything at all.