§22. Frege's idea that every assertion contains an assumption, which is the thing that is asserted, really rests on the possibility found in our language of writing every statement in the form: "It is asserted that such-and-such is the case."—But "that such-and-such is the case" is not a sentence in our language—so far it is not a move in the language-game. And if I write, not "It is asserted that....", but "It is asserted: such-and-such is the case", the words "It is asserted" simply become superfluous.
We might very well also write every statement in the form of question followed by a "Yes"; for instance: "Is it raining? Yes!" Would this show that every statement contained a question?
Of course we have the right to use an assertion sign in contrast with a question-mark, for example, or if we want to distinguish an assertion from a fiction or a supposition. It is only a mistake if one thinks that the assertion consists of two actions, entertaining and asserting (assigning the truth-value, or something of the kind), and that in performing these actions we follow the propositional sign roughly as we sing from the musical score. Reading the written sentence loud or soft is indeed comparable with singing from a musical score, but 'meaning' (thinking) the sentence that is read is not.
Frege's assertion sign marks the beginning of the sentence. Thus its function is like that of the full-stop. It distinguishes the whole period from a clause within the period. If I hear someone say "it's raining" but do not know whether I have heard the beginning and end of the period, so far this sentence does not serve to tell me anything.
Imagine a picture representing a boxer in a
particular stance. Now, this picture can be used to tell someone how he should
stand, should hold himself; or how he should not hold himself; or how a
particular man did stand in such-and-such a place; and so on. One might (using
the language of chemistry) call this picture a proposition-radical. This will be
how Frege thought of the "assumption".