those thoughts are real, and interact according to the same rules that the realist says govern the interaction of objects.

Living molecules – genes – are merely molecules, obeying the same laws of physics and chemistry as non-living ones. They contain no special substance, nor do they have any special physical attributes.

But if we take the view that science is about explanations, we see that this rule is really a special case of something that applies naturally to all problem-solving: theories that are capable of giving more detailed explanations are automatically preferred.

Thus, if ethics and aesthetics are at all compatible with the world-view advocated in this book, beauty and rightness must be as objective as scientific or mathematical truth.

Yet that is exactly what we do observe. However sparse the photons are, the shadow pattern remains the same. Even when the experiment is done with one photon at a time, none of them is ever observed to arrive at X when all four slits are open. Yet we need only close two slits for the flickering at X to resume.

Gödel proved first that any set of rules of inference that is capable of correctly validating even the proofs of ordinary arithmetic could never validate a proof of its own consistency.

Much of medicine, in other words, is still in the rule-of-thumb era, and when new rules of thumb are discovered there is indeed more incentive for specialization.

Quantum computation, which is now in its early infancy, is a distinct further step in this progression. It will be the first technology that allows useful tasks to be performed in collaboration between parallel universes.

But all that is only to criticize intuitionism from the outside. It is no disproof; nor can intuitionism ever be disproved. If someone insists that a self-consistent proposition is self-evident to them, just as if they insist that they alone exist, they cannot be proved wrong. However, as with solipsism generally, the truly fatal flaw of