It's probably annoying the way I oversimplify things, but you reminded me of something I read somewhere.

Some Jazz musician was asked to define Jazz.

He couldn't really, his answer was something like: 'I don't know. But I'll know when I hear it'.

To add something to the discussion directly: thinking requires vocabulary. Vocabulary is the currency of thought.

You can usually express an idea with a few thoughts, or many. The audience, and amount of details chosen should always be kept in mind. Writing helps you to remember vocabulary and word choice when expressing ideas.