I think what I mean by "Aha, this the meaning of the word flooble" is: "I use the word flooble in everyday life, and I feel comfortable with it. But until now I've never been able to 'play Taboo' with it. Now I can give a substantive definition of how I use it. This will be useful if I need to unpack my utterances for other people (or, conceivably, computers). Also, when people near me in 'language space' use the word flooble, we can compare definitions and possibly dissolve arguments."
So "the meaning" here isn't a definition of the word (all must bow to the mighty power of the definition), but a location of my language along the 'flooble-meaning' axis. To put it another way, the meaning that we "feel" is the one in our (individual) heads. Of course the word has little power if you can't use it for communication --- although we shouldn't underestimate its use in the internal monologue.
In all this, I realise other people may be located at other places along the "meaning-meaning" axis, and mean something else by "Aha, this is the meaning of..." but Doug S., in the comment you link, says:
I've come up with what is, to me, a satisfactory definition of "art"...
which is a more unpacked version of "meaning" than I usually manage.
The second point I want to make is about words being "wrong" --- saying "fish" and meaning to include dolphins, for example.
In a sense, I'm using the top of the post to argue with the bottom of it.
Wondering how to define a word means you're looking at the problem the wrong way—searching for the mysterious essence of what is, in fact, a communication signal.
vs
You come up with a list of things that feel similar, and take a guess at why this is so. But when you finally discover what they really have in common, it may turn out that your guess was wrong. It may even turn out that your list was wrong.
We have two different uses of words here. Firstly, you have a communication signal, which means "When I say this word, I trust that it conjures a picture in your head which is broadly similar to mine." --- so, for example, you can say "go to the shops and get some fish" to your partner, and you know that they'll bring back, not just fish, but the right kind of fish --- or maybe the shop had no fish, so they got crab, or chicken. Of course, they wouldn't argue that they'd brought home fish, but the mental picture painted by the word was sufficient that you are happy with their purchase.
Secondly, you have an academic, informational label, which means "Things whose properties are generally correlated for some underlying reason, so that observations of a large set of these things carry evidence about all of these things." "Is a trout a fish? It has scales and gills, this is good evidence, so we'll accept that it's likely to be a fish. Therefore we guess that it lays eggs." Again, there is an underlying cultural assumption, but the scientific literature makes this explicit. We can actually test whether a dolphin is a (biological) fish, by looking at the properties written in the textbook.
These two uses of words are related, of course, but they are different. In the first case, all you can say about the "meaning" of the word is the dictionary-writer's approach --- roughly how are people using the word? Can we form a better indication of what they mean by it than a list? A use of the word can "fail" in the sense that the idea in the speaker's head hasn't been transmitted to the listener, but apportioning blame in this case is pretty pointless. If we must (in order to avoid the problem in the future, for example), I put the onus on the speaker to ensure that they use words which are appropriate to their current milieu and on the listener to use the milieu to interpret the words. If you have gone back in time and say "I eat fish" and someone presents you with unwanted dolphin-meat, that was your error. If they have come to the present (their future) and say "dolphins are my favourite fish", it's reasonable to update their vocabulary. In either case, adapting the outliers to the population is a reasonably low-cost way of doing business.
In the second use of a word, an authority really has defined the word to mean something, and a use of it can be "wrong" by not matching the definition. We can also ask "is the authority's definition helpful?" which I think is where you're going with "dolphins aren't fish, even if everyone thinks they are". If the textbooks define "fish" in such a way to include dolphins, and then we determine that dolphins don't fit into the same categories as other fish, it's worth taking them out of the category to avoid future confusion.
As a final remark, consider the use of the word "dairy [products]". A good way to start an argument is to ask if this classification includes eggs. (This is pertinent to me, since I'm allergic to both milk and eggs. I want to make sure people don't give me butter, so I say "no dairy products", and then I either say "or eggs" or "including eggs". Experience has shown that neither of these phrasings will avoid an argument.)
The one comes to you and says:
Just because there's a word "art" doesn't mean that it has a meaning, floating out there in the void, which you can discover by finding the right definition.
It feels that way, but it is not so.
Wondering how to define a word means you're looking at the problem the wrong way—searching for the mysterious essence of what is, in fact, a communication signal.
Now, there is a real challenge which a rationalist may legitimately attack, but the challenge is not to find a satisfactory definition of a word. The real challenge can be played as a single-player game, without speaking aloud. The challenge is figuring out which things are similar to each other—which things are clustered together—and sometimes, which things have a common cause.
If you define "eluctromugnetism" to include lightning, include compasses, exclude light, and include Mesmer's "animal magnetism" (what we now call hypnosis), then you will have some trouble asking "How does electromugnetism work?" You have lumped together things which do not belong together, and excluded others that would be needed to complete a set. (This example is historically plausible; Mesmer came before Faraday.)
We could say that electromugnetism is a wrong word, a boundary in thingspace that loops around and swerves through the clusters, a cut that fails to carve reality along its natural joints.
Figuring where to cut reality in order to carve along the joints—this is the problem worthy of a rationalist. It is what people should be trying to do, when they set out in search of the floating essence of a word.
And make no mistake: it is a scientific challenge to realize that you need a single word to describe breathing and fire. So do not think to consult the dictionary editors, for that is not their job.
What is "art"? But there is no essence of the word, floating in the void.
Perhaps you come to me with a long list of the things that you call "art" and "not art":
And you say to me: "It feels intuitive to me to draw this boundary, but I don't know why—can you find me an intension that matches this extension? Can you give me a simple description of this boundary?"
So I reply: "I think it has to do with admiration of craftsmanship: work going in and wonder coming out. What the included items have in common is the similar aesthetic emotions that they inspire, and the deliberate human effort that went into them with the intent of producing such an emotion."
Is this helpful, or is it just cheating at Taboo? I would argue that the list of which human emotions are or are not aesthetic is far more compact than the list of everything that is or isn't art. You might be able to see those emotions lighting up an fMRI scan—I say this by way of emphasizing that emotions are not ethereal.
But of course my definition of art is not the real point. The real point is that you could well dispute either the intension or the extension of my definition.
You could say, "Aesthetic emotion is not what these things have in common; what they have in common is an intent to inspire any complex emotion for the sake of inspiring it." That would be disputing my intension, my attempt to draw a curve through the data points. You would say, "Your equation may roughly fit those points, but it is not the true generating distribution."
Or you could dispute my extension by saying, "Some of these things do belong together—I can see what you're getting at—but the Python language shouldn't be on the list, and Modern Art should be." (This would mark you as a gullible philistine, but you could argue it.) Here, the presumption is that there is indeed an underlying curve that generates this apparent list of similar and dissimilar things—that there is a rhyme and reason, even though you haven't said yet where it comes from—but I have unwittingly lost the rhythm and included some data points from a different generator.
Long before you know what it is that electricity and magnetism have in common, you might still suspect—based on surface appearances—that "animal magnetism" does not belong on the list.
Once upon a time it was thought that the word "fish" included dolphins. Now you could play the oh-so-clever arguer, and say, "The list: {Salmon, guppies, sharks, dolphins, trout} is just a list—you can't say that a list is wrong. I can prove in set theory that this list exists. So my definition of fish, which is simply this extensional list, cannot possibly be 'wrong' as you claim."
Or you could stop playing nitwit games and admit that dolphins don't belong on the fish list.
You come up with a list of things that feel similar, and take a guess at why this is so. But when you finally discover what they really have in common, it may turn out that your guess was wrong. It may even turn out that your list was wrong.
You cannot hide behind a comforting shield of correct-by-definition. Both extensional definitions and intensional definitions can be wrong, can fail to carve reality at the joints.
Categorizing is a guessing endeavor, in which you can make mistakes; so it's wise to be able to admit, from a theoretical standpoint, that your definition-guesses can be "mistaken".