1. The importance of this discussion should not be underestimated. 2. The importance of this discussion can not be underestimated. --rwg On Wed, May 11, 2011 at 2:13 AM, Adam P. Goucher <apgoucher@gmx.com <http://gosper.org/webmail/src/compose.php?send_to=apgoucher%40gmx.com>> wrote:> "If 3 is a prime, then the contrapositive of this sentence is false.">> The contrapositive is:>> "If the contrapositive of this sentence is true, then 3 is not prime.">> which is false. (The contrapositive of the contrapositive is the> original statement, which is true.) You claim that the first sentence is true and the second is false. Why is this any more correct than the claim that the first statement is false and the second statement is true? It's similar to statements like 1. Statement 2 is false 2. Statement 1 is false You can assign the truth values (T, F) or (F, T) without contradiction. But I'm not sure it's really correct to say that these are meaningful statements that are true or false at all. Is the statement "This statement is true" true or false? I don't find this any more paradoxical than the trio 1. The statement directly below this one is false. 2. The statement directly below this one is false. 3. 2 + 3 + 5 Statements 1 and 2 are the same statement, yet they have different truth values. A more troublesome paradox: What about the statements: 1. 2 + 2 = 4 2. You will mail me a check for a thousand dollars tomorrow. 3. An odd number of these three statements are true. Which of these 3 statements are true, and which are false? Andy