the death options for the philosopher were as follows: if the sentence is true, then he would be hanged. if the sentence is false, then he would be beheaded. if the sentence cannot be assigned a truth value, then he would be fed to lions. if the sentence is inherently self-contradictory, then he would be shot with an arrow. if the sentence is an unproven mathematical statement, then he would be left to die from starvation. if the sentence is not stated within ten minutes, then he would be poisoned. if the sentence cannot be understood easily, then he would thrown from a tall mountain.