Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth. Arthur Conan Doyle put these words into the mouth of his creature, Sherlock Holmes. This principle is very hard to use in the real world. Take the example of the caterpillar in the featured photo (black and white version below). Which butterfly does it develop into? I suppose it does not grow into a moth, but maybe it could. It is estimated that there could be about 10,000 species of moths in India, and about 1,500 species of butterflies. So a caterpillar is 6 times more likely to grow into a moth. Butterfly or moth, from this picture, and the internet, it would take half a lifetime to eliminate all the lepidopterans that this caterpillar would not grow into, and so figure out which is the only it could be. The problem of how to eliminate a very large number of hypotheses seems to have inflamed the imagination of several philosophers of science. In the book Zen and the Art of Motorcycle Maintenance, Robert Pirsig gave one answer to this problem: use aesthetic judgement to narrow the field. That way lies danger. I don’t have to explain how difficult it would be to apply this method to the question of the caterpillar.
Conan Doyle’s conceit was to transpose logic from the realm of simple problems into the “real” world. It usually doesn’t work, of course. That’s why great detectives are found in works of fiction, and not in the evening news on TV. Much better to reduce the problem: from colour to black and white. In the realm of formal logic, Leibniz had a simpler formulation: a statement must be either true or false. This led in various ways to the ferment in mathematics at the beginning of the last century. Famous names enter into the debate: David Hilbert, Leopold Kronecker, Hermann Weyl, Ernst Zermelo, Bertrand Russel, Kurt Gödel. In this exploration of black and white I don’t intend to go there. I just wanted to point out the spikes on the back of the butterfly; so much more eye-catching in the B&W version, don’t you think?