In a text I am reading, the section on Propositional Logic says that a proposition is a statement that is either true or false, but not both true and false. Also, from this lecture online, the instructor says that we must be able to associate a truth value to a proposition.
The text I mentioned contains as an example of an assertion that is not a proposition the following:
(1) "this statement is false."
In the margin, the text says that the form of this statement makes it impossible to designate a truth value to it and the instructor in the lecture says simply that, "if [the statement] is true, then it is false, and if it is false, then it is true."
However, why exactly is it impossible to for (1) to have a truth value? What does it mean to say that if (1) is true, it is false, and conversely?
Response to Asaf Karagila
As has been pointed out, I have already asked this question very recently yesterday but it has not received proper attention. This question is one that I feel can be put to rest if only someone would provide an explanation that is direct and suitable for my level, which is that of a novice.