Summary (paper in preparation)

It has often been said that you only need to see one white crow to be able to refute the statement that all crows are black. Many of those who study the paranormal, do so in search of the one 'white crow' case that would refute the assumption that science will be able to explain all aspects of human experience in terms of a materialist, reductionist world-view.

If a parapsychological white crow exists, it would need to be an event or object for which we cannot give an account of how it might have happened or arisen given the laws of our paradigm. Once having arisen, its existence would probably not break any assumed laws of nature, only the process of its arising would be unexplainable. An example might be say linked wooden rings: it could exist without causing any unusual effects, but ordinary physics could not explain how it might arise.

There is an interesting analogy to this thought in the world of metamathematics, and we can use it to draw some interesting conclusions about what the existence of white crows would imply. In this field, mathematicians and philosophers tried to clarify logical reasoning by developing a formal mathematical language to capture logical processes. They would start with certain axioms, then define fixed rules by which axioms could combine or change, and then investigate what new mathematical statements could be derived from the axioms and rules. A collection of axioms and production rules is termed a 'formal system' and it is possible to prove things within such a system that have consequental implications for the deductive systems of normal arithmetic. By a different analogy, one can also argue that the axioms and logical rules of deductive systems mirror, in a simple way, the fundamental concepts and natural laws of physics that tell us what we expect to encounter in the real world. Plainly put, there is a simple analogy between the deductive systems of mathematics and the causal systems of physics.

In 1931, Kurt Gödel stunned the mathematical community by publishing his now famous Incompleteness Theorem. This showed that any formal system whatsoever would contain true statements that cannot be derived from the axioms of that formal system. To show that they are nevertheless true require the use of a more powerful deductive system, of which the given formal system is a subset. Gödel's proof was arguably the most profound discovery in the history of logic, and its implications have prompted intense philosophical and scientific debate over the past 70 years. Gödel's theorem is often loosely paraphrased as meaning that 'there will always be some true things that can't be proven', and 'it's not possible to build intelligent machines'.

To return to our analogy, an inexplicable outcome that exists in a given causal system is like an underivable truth that exists for a given formal system. And just as in mathematics additional axioms and/or inference rules from a greater system are required to show that these statements are true, so in the real world additional fundamental objects and/or natural laws not part of the ordinary world would be required to generate these novel outcomes. If such outcomes actually occur in the ordinary world, the ordinary world must be a constrained subset of a more general real world. We would have to concede the existence of a greater reality of which our normal experience is just a subset. It would imply that this 'General Reality' contains additional objects and rules which are not normally accessible or active within our 'Special Reality', but can nevertheless interact with it under particular circumstances.

So do white crows exist? This may well be debated for many years to come, but to our mind there are cases that are sufficiently pale to justify our thinking about what they would imply, when looked at within this context. In particular, the attributes of candidate white crows could be revealing about the possible nature of 'General Reality', suggesting new directions for experimental work. In our paper we will briefly review some of these indications, including suggestions that mental processes may be part of the causal interactions within 'General Reality', and that 'General Reality' may be hyper-dimensional. We see in this an opportunity for a new approach to the mind/body problem; one that contains elements of monism and dualism but is distinct from either.