Hinges and Fundamentals

The truth of a hinge is a logical consequence of the playability of the game, because denial of the hinge undermines the game. It is only in a practical (a matter of practice) sense that the game depends upon the hinge. The ground for the hinge is the playability of the game, and not vice versa.

The argument is a modus tollens, not a modus ponens: If the hinge was false, then we could not speak (this way) - we can speak (this way), therefore the hinge is true.

In OC Wittgenstein cannot explain the reliability of the hinges:

470:

"Why is there no doubt that I am called L.W.? It does not seem at all like something that one could establish at once beyond doubt. One would not think that it is one of the indubitable truths.

[Here there is still a big gap in my thinking. And I doubt whether it will be filled now.]"

Then in 474:

"This game proves its worth. That may be the cause of its being played, but it is not the ground."

But to give a ground is to make a move in the game. To ask whether the game has a ground is to ask, if it is to ask anything, whether the game might not be playable if there were no ground. However, the game must be playable because we cannot say that it is not. The absence of a ground would demonstrate the absence of need for a ground, if it demonstrated anything - if the game can be playable without a ground, then grounds are not required for this kind of conclusion.

And since any prospective ground could only be articulated within the game, the ground could not be more reliable than the general possibility of giving grounds. We cannot produce an argument for the reliability of argument.

So: a ground is not necessary, and no ground of the right kind can be given. We have to start from the playability of the game.