(Sektion 136: Philosophische Untersuchungen von Ludwig Wittgenstein).

136. In the end giving "This is how things are" as the general form of propositions is the same as giving the definition: a proposition is what can be true or false. Then, instead of "This is how things are" I could have also said: "This is true". ("But also: This is false".) But now it is the case that:

'p' is true = p
'p' is false = not-p

And to say that a proposition is what can be

true or

false comes down to this: We name something a proposition, when in our language we apply

the calculus of truth functions to it.

Now it looks as if the definition--a proposition is whatever can be true or false--fixes what a proposition is by saying: what fits to the concept 'true' or what the concept 'true' fits, is a proposition. So it is thus as if we have a concept of true and alse with which we could fix what a proposition is and what is not. What intervenes with the concept of truth (as with a cogwheel) is a proposition.

But this is a bad picture. It is as if one says "The chess king is the piece that one can say is in check." But that can only mean that in chess we only give check to the king. So as the proposition that only a proposition can be true can only say we predicate "true" and "false" only of what we call propositions. And what a proposition is, is in one sense determined by the rules of forming propositions (the German language, for example), in another sense through the use of the signs in the language-game. And the use of the words "true" and "false" can also be a constituent part of this game; and then they belong to propositions, but they do not 'fit' it. As we could also say that giving checks belongs to our concept of the chess king (in the way of being a constituent part of it). To say that giving check did not fit our concept of pawns, would mean that a game in which we would give check to the pawns, in which the losers were the ones who lost their pawns,--such a game would be uninteresting, or stupid, or to complicated, or something of the kind.