Non-declarative sentences are e.g. questions or exclamations or exhortions, and are not true or not. The reason for writing "true or not" is that while "true or false" is adequate for many purposes, it is too narrow for some, such as when one considers contingent statements about the future - such as "tomorrow it will rain" - which may be plausibly claimed to be neither true nor false until the future arrives, and one can find out.

The terms "statement" and "proposition" tend to be confused, but don't need to come to the same. Indeed, one often convenient definition of the latter term is that a proposition is the meaning of a statement - so that the same proposition may be stated by different statements, either in the same language, e.g. with synonyms, or in other languages.

Also, it should be noted that not all well-formed declarative sentences in a natural language are statements in the given sense. Chomsky has as an example "Colourless green ideas sleep furiously", which is grammatical, but not precisely meaningful in English, as the meanings of the terms it contains are commonly understood.