There are certain assumptions that are implicit in rational thought. Logical consistency and predictability are two such assumptions. In my past analyses, I have been neglecting another assumption: the assumed truth of observation and experience.
Dreams, imaginations, memories, and illusions may be misleading, but the fact that I have them is always assumed true. The pink flying elephant may not exist outside my imagination, but my daydream of it was real.
If I try to multiply two numbers together, I cannot trust that I will get the right answer unless I also trust that I'm accurately remembering (or experiencing) the two factors. This is analogous to trust in predictability because it is predictability that assures me that the rules of arithmetic haven't changed since the last time I multiplied two numbers together.
In several of my recent posts, I have been commenting on the link between subjective value and truth. I outlined a description of truth wherein we build axiomatic systems from which follow contingent, objective truths, but the axioms that form the foundations of those systems are selected for subjective reasons. This certainly feels true in mathematics, where we are studying the theorems contingent on sets of axioms. The theorems of both Euclidean and non-Euclidean geometry are true contingently upon acceptance of their respective axioms, yet we often have no preference for truths in either system.
What I have been seeking is a reason why the axioms of science should be preferred over alternatives, and, with this last assumption in place, I have found it. The assumptions of science are that the world is logical, that it is predictable, and that observations are axiomatic - precisely the axioms of rational thought. A scientific theory is an axiomatic model that incorporates the axioms of past experience. The predictions of the theory are those experiential axioms that can be added to the system without contradiction.
This highlights the problem with supernaturalism. If, in the course of an inquiry, we give up on any of the three axioms (most supernaturalists prefer to sacrifice predictability), then we exclude the possibility of a rational understanding. The word "supernatural" is synonymous with "inexplicable."