Charles Dodgson

A Talk given in St Mary's, Guildford, on May 17th, 1998

by Mr J.R. Lucas, MA, Fellow of the British Academy

When Charles Dodgson died in 1898, my father succeeded to his rooms, which had been cleared, rather rapidly, by the College. Among the items that had been disposed of were some tiles which had surrounded the fireplace, and which were evidently the inspiration for "The Hunting of the Snark". My father bought them back from a second-hand shop, and they have been in Christ Church ever since. Click here for further details and pictures And if Dodgson had lived a century later, and we were now giving thanks for a life recently ended, we should be commemorating a man much more at home in the weird world in which we live than in the simpler world he actually inhabited. Snarks and Boojums had no place in Victorian metaphysics but are perfectly plausible entities in modern particle physics. Time-reversal was absurd when the White Queen remembered what was going to happen to her, or when the sentence was passed first and the verdict came afterwards, but is now a serious option with some physicists feeling happier, with electrons going backwards in time rather than positrons forwards.

Dodgson was much cleverer than dons mostly are---one of the factors leading to his relative isolation in the Oxford of his day. In part his cleverness was linguistic, and he would have been at home in the linguistic philosophy of the mid Twentieth Century. As it was, he far more quoted in the lectures and articles I encountered in my own youth than Jowett or Mill or any other Victorian academic. Neat little jokes about `Nobody' brought home the difference between quantifiers and proper names, and a fable about ``What the Tortoise said to Achilles'', published in Mind in 1895 (reprinted in Complete Works of Lewis Carroll, New York, n.d., pp.1225-1230), is still a standard reference in undergraduate reading lists to show them the difference between inference and implication. But although a contemporary Dodgson would have shone in the Oxford philosophy of our own age, he would not have been content with it as it was. It was too superficial, too brittle. Dodgson was serious. Deep questions were not to be brushed aside with a jest.

Dodgson was a mathematician, and his view of the world as we know it would have been that of a mathematician rather than a biologist. In the Twentieth Century the mathematicians and physicists have found it much easier to believe in a moderately Christian God than have the biologists. Dodgson would not have ignored neo-Darwinianism, but neither would he have been unduly troubled by it: what Richard Dawkins says is true, but it is not the whole truth. Whereas the Nineteenth-Century materialists were rigid determinists and reductionists, the Twentieth Century has made determinism, and hence also reductionism, a very implausible option. Although Einstein found it difficult to believe in a dice- playing God, the very arguments he used have turned against him, and have given rise to the Bell theorem, the Kochen & Specker theorem and the Two-Colour theorem, which more or less rule out any reasonable ``Hidden-Variable'' amplification of quantum mechanics of the kind that Einstein sought. These are purely mathematical arguments showing the incompatibility of determinism with quantum mechanics as we know it: it might, however, be still made out that quantum mechanics was itself wrong. But a recently dead Dodgson would have known of the experiments of Aspect and his collaborators in Paris in the 1980s which decisively vindicated quantum mechanics and experimentally refuted determinism. Instead of the rigid world of Newtonian mechanics he would see the shimmering fluctuations of wave mechanics, which impose only general constraints, leaving many, many possibilities unforeclosed.

A dice-playing God has often been disparaged as a ``God of the gaps''. But that is to misunderstand the logic of the case. Dodgson was not an Eighteenth-Century Deist, reading the character of the Author of Our Being from His handiwork in nature: he was a child---or perhaps better a grand-child- --of the Oxford Movement, founding his faith on God's revelation of Himself in His son, Jesus Christ. The relevance of modern physics for him would not be that it proved the existence of God, but that it disproved the cogency of current arguments against the existence of God--- in a phrase of Alvin Plantinga's, that it defeated the defeaters. Arguments to show that we were just a collocation of atoms, or just the product of our genes, or just the result of evolution, are shown to be invalid. We are, indeed, made up of atoms, formed by our genes, as a result of evolutionary pressure over millions of years, but we are not just that. The Reductionist Tendency in modern thinking---the claim that, in all sorts of ways, we are nothing but something---loses its purchase if there is no longer some fundamental theory of everything that can in principle give complete answers with absolute precision and 100% certainty. Once further possibilities are no longer ruled out, our natural understanding of ourselves--- that we are more than a collocation of atoms, or what have you---is reinstated. Instead of ``nothing-buttery'' as I might term it, we are free to affirm some form of ``more- thanism'', if that, on other grounds seems true.

A modern Dodgson could have found further grounds for believing more-thanism to be true. The actual Dodgson was one of the pioneers of mathematical logic, and mathematical logic has in this century yielded new, and quite unexpected insights into the nature of reason and hence also of the nature of reality. Gödel's theorem would have been a delight to Dodgson. St Paul told Titus that The Cretans are alway liars (1:12), and many thinkers have considered the ``Liar Paradox'': `This statement is untrue'---if it is true, it is untrue, and if it untrue, it is true. We know from Dodgson's diaries (personal communication from Mr Edward Wakeling) that he was playing with various refinements of the paradox. With the advent of computers we can go further. We can program statments into computers, from which it follows that we cannot program into a computer an adequate concept of truth---or else we would land it in a Liar Paradox. What we can do, instead, is to program some concept of provability: and then, if we consider the statement `This statement is unprovable' (in place of `This statment is untrue'), we see that it must be true but unprovable, where provability is defined, roughly, in terms of the rules a computer could be programmed to follow. He would thus have shown that truth outruns provability, and that, however fully we formalise a system, there will always be further inferences beyond those we have formalised. We can't get things completely sewn up. However far we go, there will still be more things we have yet tied down.

Mathematical logic thus gives a deep argument in favour of more-thanism. Although different from, it is very much congruous with, Dodgson's own argument against reducing inference to implication. And it fits Dodgson's own intellectual personality---his sense of humour, his foibles, his delight in the unexpected. Although a modern Dodgson would be aware of the discoveries of modern science, he would not have been a scientist himself: quark-hunting he would leave to others, and perhaps also the discovery of bosons, which configured by the Identity of Indiscernibles, could never admit of there being both a Tweedledum and a Tweedledee. For himself, he would view this world, as he hoped to enter the next, with the wide-eyed surprise of an innocent child.

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