A statement which is neither true nor false?

Answer 1

Im Pretty sure it should be

"This Statement is False"

It is largely a matter of definition. It also could be: "Green ideas sleep furiously."

Wolfgang Pauli had little patience with poorly phrased or poorly structured propositions. He said on occasion: "This is not right; it isn't even wrong!"

It is best to regard such a statement as neither right nor wrong, but meaningless. One good test (not universal, but useful) is to see whether the negation of the statement is true. A logically valid statement in most systems is either right or wrong; if it is right its negation is wrong and if it is wrong its negation is right.

Let us try the test on the above examples:

"This statement is not false." That is neither more obviously true than "This statement is false", nor more obviously false.

"Green ideas do not sleep furiously" That too is not particularly true or false; what does it mean for an idea to be green or to sleep? Or for sleeping to be furious or not?

Those two statements accordingly are not meaningful by our test.

Consider two other statements:

2+2=4

and

2+3=7

(Note, I did not say 2+2 eggs or drops of water, just abstract 2+2, right?)

Are those statements meaningful? One seems to be wrong, but it still does seem meaningful. Lets try negating the statements, by replacing the = with <> meaning "either greater or less, and therefore not equal"

Our true statement: 2+2=4 becomes 2+2<>4, which is false. That suggests that either way around it is meaningful, whether true or false.

Our false statement 2+3=7 becomes 2+3<>7 which is true. That suggests that either way around this statement also is meaningful, whether true or false.