A statement is a sentence that has a truth value, either true or false. Several types of sentences are not statements – questions and commands, for instance – because they do not have truth values. Another type of sentence that is not a statement can be called nonsense.
Nonsense sentences are not statements for the same reason as questions and commands; they cannot be said to be true or false. There are two types of nonsense sentences that we usually encounter in studies of logic.
1.) First are sentences in which the words have no meaning, and thus cannot be said to communicate truth. A classical example is the Lewis Carroll poem “The Jabberwocky” which starts,
T’was brillig and the slithy toves did gire and gimble in the wabe.
This seems to be a sentence; it has a subject and predicate, and the words can be identified as to their parts of speech. But it cannot be said to be true or false, and thus we call it nonsense.
2.) Then there are sentences in which the truth value is impossible to nail down. The standard example for this type is
This sentence is false.
This sure looks like a statement. But what is its truth value? Is it true? If so, then it is false, as it claims. But is it false? Then it is false that it is false, and therefore true. You see that a truth value cannot be applied to this sentence in any settled way.
Similar issues occur with the liar paradox: Were someone to claim, “Everything I say is a lie,” is that sentence also a lie? The apostle Paul touches on this when he quotes a Cretan saying that Cretans are always liars (Titus 1:12).
There is also the story of the missionary captured by cannibals who sentence him to death but give him a choice of methods, saying, “If you tell us something true, we will boil you in oil. If you tell us something false, we will burn you at the stake.” The missionary, who had thankfully studied his logic, replied, “You will burn me at the stake.”
Think about it.