Recently, in a Q&A session, some coworkers asked me the singular question of our age: is a hot dog a sandwich?
If you're not familiar with this pop-philosophy question, let me google it for you: to quote a 2015 article on the subject, “The debate over hot dogs’ sandwich status has raged for so long on the internet that asking someone whether he or she believes a hot dog to be a sandwich has itself become something of a web-wide in-joke”.
Internet people have entertained deep debates about the status of hot dogs, even coining words for their factions, like “seamists” and “fillingists”. Some have even argued that the answer “exemplifies how the government manipulates consumer interests to reap the largest possible profit for itself.” Goodness, internet people!
In the heat of the moment, I gave some relatively hemming answer like “it depends on what the definition of is is ...”. But as good questions tend to do, it stuck in my background processor overnight. I've worked out a better answer, which I am 110% confident can resolve this dispute across the entire internets, for ever and ever, amen.
Hot dogs are NOT sandwiches; lemme 'splain why.
Let’s set a little groundwork. What we’re debating here is not mere surface wordplay. The strings of characters “hot dog” and “sandwich” are arbitrary labels. In Spanish, the labels would be different (“pancho” and “emparedado”); esa no es la pregunta.
The actual question here is about the abstract categories that underlie our use of the words. As I’m using the word here, "categories" are definitions that collect some set of instances under common criteria. They’re the boundaries of our conceptual sets, our tools of perception for essences in the world .
If you think of categories as sets, this question has a more complex possible layout of answers:
(a) No sandwich is a hot dog, and no hot dog is a sandwich; they're disjoint
(b) Some sandwiches are hot dogs, and vice versa; they intersect
(c) Every hot dog is s sandwich, and vice versa; they're the same
(d) Every hot dog is a sandwich, but some sandwiches are not hot dogs
(e) Every sandwich is a hot dog, but some hot dogs are not sandwiches
With these options, it’s clear that the debate is really between (a), (b), and (d). Even the most deranged of fillingists would agree that a PB&J sandwich is not a hot dog, so (c) and (e) are out.
But that still leaves us in a pickle; which of the remaining three are right? That depends entirely on how we draw the categories, of course.
I’m operating from a particular view of categories, which I explain a bit more in the article "categories are predicates". In a nutshell, categories aren’t eternal, indivisible truths; they instead consist of rules. These rules are like little classifier functions, identifying whether something is a member of the category or not. Rules can be abstract (like "sandwiches must include fillings between bread"). But they can also be prototype-based (like "this is a sandwich, but that is not").
And, sadly for those who would like an ultimate answer to this question, a category’s rules are fundamentally arbitrary. Categories are epichoric (local to a place or time), and they evolve alongside the other ways you make sense of the world, like language. Their boundaries are fuzzy and implicit, not formal and explicit. There’s no official arbiter of the true category of “hot dog” (the existence of a “National Council On Hot Dogs And Sausages” notwithstanding). Different groups of people, and even different individuals, carry around a different sense of the boundaries, like so:
In fact, even a single brain will draw these boundaries differently over time, as it incorporates more examples that reinforce one or another view. A child who’s repeatedly told “That’s not a sandwich, it’s a hot dog” will internalize this categorization rule, even if there’s no logical basis for it. An adult brain, too, is still soaking in examples; say you happened to drive past this billboard every day on the way to work:
Over time, even if you didn’t notice it, it might tip the scales of your wet neural net towards the “hot dogs are inside the sandwich circle” interpretation.
Outside the rigorous bounds of mathematics, the best we can collectively do at the “true” delineation of a category is the popular vote ; there’s no underlying truth other than the aggregation of all our individual category detectors. There’s no category police, nor could there be, since categorization is a fundamental function of language, and language isn’t under any centralized control. (Well, except for French, but they also don't have jokes.)
"Let Me Tell You Why This Joke Is Funny!"
In the time-honored tradition of philosophers, I will now squeeze every ounce of joy out of this joke. (If you'd prefer to continue to enjoy the magic, this would be a fine place to stop reading.)
Why are things are funny, in general? Because they violate your expectations. In this case, the violated expectation is that it’s obvious what a sandwich is and is not. We expect our category for “sandwich” to be as simple and mundane as ... well, as sandwiches themselves are.
But surprise! The category is actually more nuanced than that; it doesn’t follow strict rules you could write down (like “bread wrapped around non-bread food”). Instead, it's more prototype-based: a sandwich is something that matches the 10,000 examples of things you’ve called sandwiches in the past. You could factor out commonalities from those past prototypes, but that’s not how your sandwich classifier works by default. You're more like a neural net that can tell kitteh from doggo; life has trained you with a reliable “is this a sandwich” classifier, based on the behavior of everyone around you.
But when forced to introspect about how this classifier works, we're stumped. Put on the spot, our powers of post-hoc rationalization kick in; our conscious minds grope around for a reason (“Why didn’t I categorize a hot dog as a sandwich?”). And the answers come back as clever fabricated rules, like “sandwiches don’t have seams” or “hot dogs have toppings”. 
And so the mirth of this topic is precisely because it voids our expectations. When you stare into the sandwich void, you must confront the uncomfortable truth that categories are messy. They act like terrible spaghetti code, rather than elegant mathematical proofs. When someone points out that our post-hoc rules about sandwich definition should theoretically include something we know damn well isn’t a sandwich, that’s ... well, funny.
As "Exhibit A", I give you The Cube Rule, which groups foods by the geometry of their containing starch. The moment you've bought into the beauty of this elegant and appealingly mathematical scheme, you're immediately confronted with the horrifying and hilarious implications of this choice:
It's a work of comedic genius, in which pizza is a type of toast, and corndogs are calzones. As useful as the geometrical grouping might be for telling us something essential about starch containment shapes, the real reason it's funny is because it drives home the point that none of these category names are apt.
Ipso Facto Taco
So herein lies the actual answer to the question, which I'm confident will lay the matter to rest. The humor of suggesting that hot dogs are sandwiches (or that sushi is toast, pop tarts are ravioli, etc.), is itself the proof that they are no such thing. The only “truth” of a category’s correctness is its robustness in a population of humans, and if all the humans chuckle and post about it on Twitter, you've got your answer.
QED: hot dogs are not sandwiches because it’s funny to suggest that they are.
The harder you laugh, internet, the more right I am.
You may now return to enjoying jokes, rather than crushing them.
 I’m using the word “category” here in more or less the same sense that Douglas Hofstadter would use it in his works, like Surfaces and Essences. As opposed to, say, the way a mathematician might use it in category theory.
 If you wanted to actually get a vote on the hot dog question, I suspect you’d have to be psychology-experiment-sneaky to get an accurate count, because as soon as you’ve activated this as a funny question, people would take a stance that’s more about their level of contrarian-ness than their actual in-built category boundary; you’d have to do something like flashing pictures of food in various situations, and have people rapidly press a categorization button, or something like that.
 This is a subject that’s covered exceptionally well in a fantastic recent book from Kevin Simler and Robin Hanson, The Elephant In The Brain; highly recommended.