There's a sense in which definitions are arbitrary. Words are made by humans and no-one can stop me from calling red blue and blue red if I really want to. So when people ask questions like, "What is consciousness?" or "What is free-will?", it seems quite reasonable to respond, "Just pick a definition. These terms can be defined many different ways and it's completely your choice which one you choose to use".
This may appear to dissolve the question, however, I would suggest that such an answer often misunderstands what the asker is attempting. Typically the asker is concerned by more than the linguistic question, but also with attempting to understand the ontology or structure of reality. And it may be the case that this structure includes a substructure that naturally fits with our intuitions of what consciousness is or what freewill is or it may be the case, as per the standard LW view of these two cases, that such a structure doesn't exist.
What makes this especially confusing is that many people will conditionally accept the "it's arbitrary" answer when they are convinced that such a natural structure doesn't exist, while pointing out the natural structure otherwise. Here's an example. Let's suppose it was common knowledge that we all have souls. Then whenever someone asked about the definition of consciousness, we'd be tempted to point to the soul, just as whenever people ask about the definition of trees, we'd be tempted to talk about leaves and branches. The arguments for being able to use language arbitrarily and the fact that this isn't a perfectly well-specified definition remain. It's just that one definition suffices for 95% of cases, so we don't bring up that argument. But if instead it was common knowledge that there are no souls, it'd be much more likely they'd say that the definition is arbitrary. And by accepting answers to different questions depending on how things turn out, the intent behind the original question can easily be obscured.
Here are some possible interpretations of, "What is X?":
- What does term X intrinsically mean? (no intrinsic meaning exists)
- What natural structure (if any) corresponds to X?
- What are some useful interpretations of the term X?
- How is the term X used in society?
These kinds of discussions tend to work better if everyone is on the same page about what is being asked.
Note: Apparently, I actually had an old post on this topic here which I'd completely forgotten about.
I've also discovered that the philosophical term is natural kinds.