There are some propositions that rational substances know are true but do not know why they are true. This concept is illustrated when one reflects on problems associated with self-referentiality (Godel's theorem). Physicists also work with a priori ideas that they take as givens, notions without which thought would be impossible. One should not be amazed therefore if Non now argues that there are ideas that are necessarily true (they obtain in every counterfactual situation) which cannot be proved true. Conversely there are also ideas that do not contradict any formal logical schema; however, they may be false in all possible worlds.
One example: "nothing is red and green all over" (at the same time or in the same way). Paul Davies insists that one can deny this proposition without contradicting any formal logical scheme. But any such denial is probably false in all possible worlds. Rational substances therefore affirm the proposition's validity and soundness. It is a necessary a priori proposition. Logical necessity requires that the proposition "nothing is red and green all over" obtain in all counterfactual situations.
What about the proposition, "God does not exist"? Davies maintains that the denial of God's existence does not contradict any formal logical scheme either. Yet the proposition could be false in all possible worlds. Could it be the case that the proposition "God exists" is an a priori necessary proposition that obtains in all possible worlds and that while we have good reason for believing the proposition is true, we cannot prove that it is factual?
Maybe the words "God exists" are similar to "Doug cannot prove this statement is true." Can you prove the last proposition is true?
Go right on ahead.