That must be true, because otherwise language doesn't function. If words were entirely meaningless, there would be no difference between talking and nonverbal grunting—everything conveyed through context and inflection. That's obviously not the case; words do have meaning, and we've largely agreed on those meanings within languages. However, when I say "watermelon" and you say "watermelon", we're imagining different things. If I said "wow that box was as heavy as a watermelon", you might be confused if I look tired when saying it.
Watermelons aren't that heavy, you think. You're thinking of the personal watermelons you had every summer, that you bought to split with your family over a barbecue. You could carry them as a kid, they're small.
I'm thinking of the larger watermelons that my dad bought to cut into cubes and put in the fridge for a week's worth of lunch snacks. They were huge and took a while to break down. They shook the table when he set them down.
We said the same word, but we meant different things. The words had concrete definitions, but the exact meaning is something we assigned ourselves, which defines only our own perception of the word and all associated with it.
Now what do you picture when I say "rock?" What shape is it? Can you pick it up?
Which is bigger: "Huge", or "Giant"?
Which is worse: An "injury" or a "wound"?
Which is faster: A moment, or an instant?
Define the color teal. Now define grey.
Define "male" and "female".
Define "lesbian", "gay", "bisexual", "transgender," and "queer".
Define "pornography". Define "sex".
I'm sure you can. I'm sure someone can give me exact data that empirically proves their definition. You could point to a scientific or medical or geological database that gives a certain, absolute definition. And yet I can point to something which exists somewhere on the fringe of your definition. Do you expand your definition to include that fringe case, or rigidly insist that "words mean things" and insist we call that thing something else?
In one field, words lose meaning—anything can mean anything, and we're back to pointing and growling in context. In the other, we subdivide everything into increasingly smaller boxes, rigidly assigned words in a fractal of definitions.
Words mean things. Whatever "things" are.