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It's Impossible To Make An Un-title-able List

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7/22/2014 6:15:07 PM
Posted: 3 years ago
Just something I was thinking about recently. It seems like any list I try to make will always have all the elements having something in common. For example


You might say some of these items have nothing in common with the other things. Four is the only number, embezzlement is the only action. But they all have something in common. Pardon the absurdity for a second, but just to make a point, right now I'm eating supper watching a show with four main characters that has a joke about embezzlement and my cat is in the room. So a title

"Things I liked to think about while eating supper today."

would be a title for this list, because all of these things fit in that category. You might think that's a hack, because "things i like thinking about" could be literally anything. But we agree that I don't like thinking about rotting body organs while eating supper today, so the list doesn't include some things. What about simply the category "Things that can be thought of"? You might think that's a hack, but the item "unknown unknowns" does NOT fit on that list.

Why is it important to be able to exclude things from the list? Using a bit of basic set theory, let's define the list A as everything (suppose it is literally everything for the moment):

A = {1,2,3,4}

Suppose I can come up with a subgroup that meets the criteria of having one unifying quality, call that subgroup B = {1,2}. That means notB = {3,4}. What we can deduce from this is that if for every title you give me, I can give you an item NOT from the list, and the leftover thing that wasn't on that list shares something in common with at least one other item, then it is impossible to make an untitle-able list. If you can give me a title that I CAN'T NOT find something to go into the list (or in other words your title is so great it includes everything), then we can take the compliment of that title, and nothing fits under that title!

Still with me? OK. So if you have a set that includes literally every item ever in existence period, then you can have a true null set by taking the inverse of that set. Whatever the title of the null set is (I assume there can be no way to title a null set), there is only one such title. If you have one thing that shares nothing in common with anything else, then if you pair it with anything else you have an un-title-able list. So if you create a list that looks like:


for example, it would be an untitle-able list. But I don't have the title of the null set above, so it's not really on the list. It needs to be a real thing to be on the list, it can't just be a placeholder. I think you agree with me in that because I could just put 5 placeholders on the list, and placeholders have by definition nothing in common with anything else because it's a variable, not constant. The list that you make to submit to the challenge has to be a list of "constants" if that makes sense. I'm not touching lists with variables on them.

This was more or less a stream of consciousness and I'm not entirely sure that it can be cleaned up into something rigorous.

Basically my gut feeling is that if you can't meet either of the criteria below, then the title of the post is true. Or maybe just make a fool of me and beat the challenge easily.


So succinctly, the challenge is:

Come up with a list of items that can have no unifying title. Or come up with a title that can include any item I can come up with.