Ordinary language is all right.
One could divide humanity into two classes:
those who master a metaphor, and those who hold by a formula.
Those with a bent for both are too few, they do not comprise a class.
—Of course, expressions are yours, or mine, or ours—'owned', per 'other minds' jargon. So students expressing their thoughts in writing would have to be able to believe that what they were doing was theirs. Both before and after they submit an assignment for a grade. What does it take to believe that—to come to be a person who can believe that about what they write, say? And, to believe it there, then, after a dozen or so years in that institution, a school?
We have almost no idea how to teach students about the expression of philosophy. When communication is the guiding concept of our crude writing pedagogy, whatever we say about clarity and rigor will not be enough to make students understand what we want of them, or of clarity and rigor. Writing is a way in which our thought appears to, for, others (and for ourselves). It has an element of Offenbarung to it: it's how our thoughts come out into the open. What was private is disclosed, made public, published to the world. —This sort of act, event, of exposure to the public is understood in other forms of culture (conversation, the arts, journalism, political life, scientific research) as staged in a certain way, as properly taking place at certain boundaries somehow between public and private (the role and its performance, not the actor and her life; the story, not the storyteller; the office, not the officeholder; arguments, not homines; the book and its readers) or if privately then as taking place between those whose privacies have been opened directly to each other by choice, out of curiosity, in trust. Often the spaces and places for these events are themselves public, shared, or private. —But there seems to me to be something off in the whole way we frame what the philosophy student is doing, when writing or when doing all the things that prepare for it and surround it. Listening, reading, talking, revising, presenting. We render these distinctions between private and public unavailable: at best, situate them too far off in the distance, beyond professionally-guarded checkpoints. Or too far out into the life or the world philosophy is supposed to matter to.
Communication is for orders, and reports, and relationships (the first and last of which philosophy wants little to do with). Expression takes place in a wider circle of others (as philosophy aims to reach). On some conceptions, even communication is a nuisance: a complex form of signaling would be preferable—if only a notation could be devised…
Philosophers speak in alls and nevers, musts and ifs.
Heidegger's hermeneutic is top-down, Cavell's, ground-up.
We read the weather as volatile, time as fleeting, when we should just as often note the obdurate stasis of clouded days and constant temperatures, the inert bulk of times, skies, which need hardly a week to make us feel that things have always been this way, that this is how it is.
We recall the sun and recall our nights on different occasions, in different circumstances.