Staving Gary Shannon: >So many shakey asumptions! How many members are there >in the International Organization of Solopsists? According to several members I've asked, one. On the subject of unprovable statements, we have Gödel's incompleteness theorem. Consider a rule-based system of logical inference which is sufficiently complex to describe its own axioms and rules of inference. It is then possible to formulate in that system a statement to the effect of "Given the axioms and rules of inference of this system, this statement is unprovable." (Gödel described a method for doing so.) If the statement were to be false, then it would be possible for the system to prove a falsehood. It would therefore be inconsistent, and useless as a method for obtaining truth. In a self-consistent system, therefore, the statement must be true. It is therefore unprovable. Thus the existence of true but unprovable statements is a logical necessity. Pete