"Do words exist somewhere, true, pure, fixed in meaning, waiting to be used"

I don't think so. But I think when we talk about, for example, an idea, there is some consensus that we are talking about a mental model of the way something works, the way something could work, or the way something has worked previously. (For sufficiently large definitions of something.) And if I asked you whether or not a fact was the same as an idea, you would agree that it was not. So our collective agreement on what the word means doesn't differ from the dictionary definition because it comes from some platonic ideal, but rather the definition in the dictionary is wrong because of a quirk in the way dictionaries are made.

"Objectively... funny? As in, if the entire human race disappeared and no other beings capable of abstract thought existed, certain things would have the qualities of funny?"

All humor comes from something being novel or broken relative to a set of existing mental models. When I say something can be objectively funny, what I mean is that something can be objectively novel or broken in relation to an existing mental model, whether or not anyone else realizes it.

So, can something be funny independently of humans?

Imagine if you will something being novel or broken relative to a mental model that no one actually holds. Is this funny? Clearly it can't be subjectively funny to anyone, because the humor is relative to a belief that no person holds. But can it be objectively funny, in sort of a mathematical sense? I don't see why not.

"All humor comes from something being novel or broken relative to a set of existing mental models. When I say something can be objectively funny, what I mean is that something can be objectively novel or broken in relation to an existing mental model, whether or not anyone else realizes it."

So you're saying that something can be objective subject to its relationship with something else. Isn't that subjective?

"I don't see why not."

Well. Going along with your definition before, the one regarding that study, you need to realize that there is no way of quantifying the unexpected. Take Monty Python. They and their fans showed that you can take something unexpected and, by repeating it, make it more expected and therefore less funny, subjectively, over time. So the joke is subjective in terms of who it appeals to.

Now, you couldn't quantify something like the humorous value inherent in the Spanish Inquisition Sketch, and here's why. The primary punch line relies on the knowledge of the fact that "I didn't expect the bloody Spanish Inquisition" is a snippy, commonplace response to somebody's becoming overreacted to something. In order for "Nobody expects the Spanish Inquisition!" to be funny, you need to understand a) the perception that the preceding dialogue is indeed snippy, b) the understanding that the lead-up line is a gross exaggeration, and c) the knowledge of what the Spanish Inquisition was, and why they are, in fact, unexpected.

The problem is that all three of these things are subjective. You said it yourself: animals wouldn't find it funny. And the reason for that is that our humor is largely based on notions about our society. They're only funny subjectively within our society. Without the society, there is no humor inherent in many of these things. That also explains why infants laugh so much at funny noises. When you're young, these things are entirely unexpected. The older and more sophisticated you get, the more you come to expect from things and the harder it gets to produce a funny response. And people evolve their responses at different speeds. I don't laugh at very many jokes anymore, because between dedicated study and a set of rude friends, I've heard an incredible variety of jokes and humorous situations. The comedic shows I watch tend to be the ones that are more focused on craftsmanship rather than on the unexpected. When I do find a new type of humor, my response is delightedly juvenile - and usually, my responses to other forms of humor are lessened. This is all entirely subjective. You can't define it. You can monitor it, as that study did, but that's something different entirely.

"So you're saying that something can be objective subject to its relationship with something else. Isn't that subjective?"

Two is larger subjective to its relationship with one, but two is objectively larger than one.

First off, "two is objectively larger" is silly. If you're comparing two to one, then there's subjectivity involved. Rather, your argument is like saying two is objectively large, period. That's something that you can't do.

But humor isn't as harshly defined as the number system is. Rather, defining humor like that would be like saying "the sound of the word 'two' is objectively greater than the sound of the word 'one'." Once you say that, you need to define what those sounds actually mean, determine the numeric value of each, and then make the comparison. Until you do all those things - and all of those things require subjectivity within the confines of a language - then the sound of the word "two" has no meaning. The concept of two is objective, because mathematics deals only with objectivity. But humor doesn't have such harsh definitions, none of it is objective, and you can't limit it in a way that makes it objective.

Similarly, the word "humor" can mean both "response to something funny" and "state of mind." That's what makes "objective humor" kind of hard.