# “This statement is false” - Propositional Logic

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.

• Honestly, this is a bad example that's not really worth considering. It won't hinder your understanding of the subject to ignore this. – Kaynex Mar 16 '16 at 3:31
• @Kaynex It bothers me tremendously to skip it though. – user185744 Mar 16 '16 at 3:32
• @AsafKaragila, should we close one of them? – goblin Mar 16 '16 at 6:00
• Ha! Not the proper attention? You received three answers that had to guess your knowledge and mathematical aptitude. You want better suited answers? Write better questions. – Asaf Karagila Mar 16 '16 at 6:15

• I don't know if the statement conforms to an $n$-ary logic for some suitable $n \geq 3$ (I am sceptical if there exists such an $n$, though.) I would reply to your instructor that we cannot create a truth table since we cannot decide the truth value for that statement. – eltonjohn Mar 16 '16 at 10:27