Ludwig, I’ll take these in order.
On preconditions and contexts, you’re right that something can be a precondition of one practice without being a precondition of every practice. That’s where the layered picture of hinges comes in. The deepest hinges, object persistence, experiential continuity, are preconditions of any practice whatsoever. But more local hinges can hold fast in some contexts and not others. “No one has been to the moon” functioned as a hinge until it didn’t. So not all preconditions are universal, but that doesn’t undermine the concept. It means hinges sit at different depths.
On Godel, I’ve described this parallel as mostly structural in the past, but I think it’s more than that. Godel’s result is mathematical epistemology. He showed that formal systems can’t fully justify themselves from within. There are truths the system relies on but can’t prove using its own resources. Witt showed the same thing about epistemic practices. They rest on something non-epistemic that they can’t internally secure. Both are epistemological results about the limits of internal justification, arrived at through different methods in different domains. Godel proved formally what Witt showed grammatically. The conclusion is the same, viz., no system of justification is completely self-contained.
Is philosophy as a special context? This is an interesting point. I don’t think Witt is ruling out philosophical discourse. He’s diagnosing what goes wrong when it tries to treat framework conditions as propositions within the framework. OC 37 makes this clear. The difficulty the realist and idealist are responding to is real. Their first expressions of it, though, land in the wrong place, and investigation is needed to find the right point of attack. That’s philosophy working, not philosophy being dismissed. What misfires isn’t the investigation. It’s the attempt to assert or deny hinges as though they were empirical claims.
I agree with your name example. What makes “I am L.W.” certain is the ongoing practice, not the baptismal event. The certainty is maintained in the use.
On philosophical discussions as language games: what makes something a language-game is that it has criteria for correctness internal to the practice. Measuring, calculating, reporting all have this. Philosophical assertions like “There are physical objects” don’t have conditions of success within a functioning practice. They’re moves that look like they belong to a game but don’t connect to anything that could count as getting it right or wrong. That’s what Witt means by language going on holiday.
On hinges being liminal and connected, I think you’re right that hinges aren’t isolated. They’re what makes the movement of empirical propositions possible, so there is a relationship. The hinge doesn’t swing, but the door couldn’t swing without it. The connection is real. But it’s enabling, not inferential. The hinge doesn’t participate in the logical space of the propositions it supports. It makes that space possible.