Should hinge propositions be taken as given/factual for a language game to make sense ? I'm just going to do a general post because I just don't have the energy to respond to all of you.
Much of the problem probably stems from the different ways we view beliefs. My contention is that beliefs can function quite apart from language (Wittgenstein's showing), i.e., we can observe beliefs in non-linguistic actions (even in animals). And, epistemological language-games (knowing, justification and truth), in terms of hinge's or bedrock beliefs, come later as language develops.
If we think of very primitive language-games (for e.g. W.'s example at the beginning of the PI), I think it follows, again, necessarily, that epistemology, and all the concepts involved (even truth), will not, and cannot obtain, until the conceptual framework develops. So, bedrock or hinge beliefs at their core, i.e., because of how they come about as part of the framework or backdrop of reality, have a status that excludes them from all epistemological talk (including truth - OC 204, 205, 206).
All epistemological talk (as arguments against my position), even truth, is always after the fact, we tend to bring it into the conversation as though its always been there. Even in young children, who learn what it means to know only later in their language talk, have these primitive beliefs long before they develop the concepts involved in epistemology.
Now some of you might argue that it doesn't matter that the concepts of justification and truth come later, that doesn't, in itself, negate the truth of these bedrock beliefs. If this, however, was true, then it would seem to follow that it wouldn't negate our use of justification either, or it wouldn't negate Moore's use of the concept know within the the context Moore is using the word.
One of the key features W. points out about Moorean propositions is that when seen against their negation (e.g. "I don't know this is a hand.") it's not clear what their sense is (OC 4). After all if we're not sure of the very backdrop of reality, then how can you be sure of the very words used to talk about such things (W.). It also seems clear to me that truth (as an epistemological function) has the same problem, viz., if Moore had said, as he held up his hand, "It's true that I have a hand," it would have the identical problem that Moore's use of know has, especially since knowing entails truth. Again, consider the negation, "It's not true that I have hands," this proposition also lacks sense in the same way.
One last point, W. pointed out through examples that Moore's use of "I know..." can have a sense in other settings or language-games, but this use is different from the use as a hinge, which is the use Moore is being criticized for. The same is true when speaking of bedrock or hinge beliefs when it comes to truth, in a bedrock setting, they are neither true nor false. However, in other settings or language-game, they can be true or false. I think to fail to acknowledge this is to fail to understand W. point about hinges, or as I like to refer to them, bedrock beliefs.