How would I ask a more specific question ... ?
Refer to Gödels incompleteness theorem.
The first incompleteness theorem states that no consistent system of
axioms whose theorems can be listed by an effective procedure (i.e.,
an algorithm) is capable of proving all truths about the arithmetic of
the natural numbers. For any such formal system, there will always be
statements about the natural numbers that are true, but that are
unprovable within the system. The second incompleteness theorem, an
extension of the first, shows that the system cannot demonstrate its
What is Gödels theorem?
What Godel's theorem says is that there are properly posed questions
involving only the arithmetic of integers that Oracle cannot answer.
In other words, there are statements that--although inputted
properly--Oracle cannot evaluate to decide if they are true or false.
Such assertions are called undecidable, and are very complicated. And
if you were to bring one to Dr. Godel, he would explain to you that
such assertions will always exist.
Even if you were given an "improved" model of Oracle, call it OracleT,
in which a particular undecidable statement, UD, is decreed true,
another undecidable statement would be generated to take its place.
More puzzling yet, you might also be given another "improved" model of
Oracle, call it OracleF, in which UD would be decreed false.
Regardless, this model too would generate other undecidable
statements, and might yield results that differed from OracleT's, but
were equally valid.