# Do malformed propositions have True/False values?

Many people are familiar with the malformed questions that, no matter which way they are answered, reflect poorly on the person to whom they were asked. For example:

• Have you stopped beating your wife?
• Yes, I have stopped beating my wife.
• No, I have not stopped beating my wife.
• Have you ever gotten away with a murder that you committed?
• Yes, I have gotten away with a murder I committed.
• No, I have not gotten away with a murder I committed.

These informally fallacious questions need not be answered (at least by people that do not abuse their spouses or are murderers) as they are simply malformed and create a dichotomy of an unreal scenario.

However, when we put these into a proposition, I am unsure as to whether or not they actually have truth values or if they are simply malformed propositions as well.

For example:

• I have stopped beating my wife. (True/False)
• I have gotten away with a murder I committed. (True/False)

Must these logically be given a truth value since they are propositions? Or are then invalid propositions altogether? Would the value be False (assuming I have not beat my wife or killed anyone) because ine cannot stop or get away with something that one has not done?

• A related puzzle: given that no total order is defined on the complex numbers, how does one answer the question of whether `1<1+i` — is the inequality true, or false? The correct answer is that it is ill-defined, and that it embeds an assumption about the ordering of numbers which is itself false. Mar 2, 2015 at 16:43