I think the approach you describe is valid but dangerous.

It's valid because occasionally (and maybe even frequently) you want to think about something that you cannot properly express in words and so cannot define precisely and unambiguously. Some people (e.g. Heidegger) basically create a new language to deal with that problem, but more often you try to define that je ne sais quoi through, to use a geometric analogy, multiple projections. Imagine that you want to think about a 6-dimensional manifold. Human minds, alas, are not well suited to thinking in six dimensions, so you need to construct some projections of that manifold into a 3-dimensional space which humans can deal with. You, of course, can construct many different projections and you will feel that some of them are more useful for capturing the character of that 6-dimensional thing, and some not so much. But other people may and probably will disagree about which projections are useful and which are not.

It's also dangerous for obvious reasons, starting with the well-know tale of the blind men and the elephant...