Jethro’s First Paradox: runs somewhat like this: ‘It is the slow driver who’s in front, the fast driver is always at the tail-end.’ There are other, more famous ones, such as Zeno’s ‘Achilles and the Tortoise’, for instance – Achilles is in a race with the tortoise. Achilles allows the tortoise a head start of 100 yards, for example. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 yards, bringing him to the tortoise’s starting point. During this time, the tortoise has run a much shorter distance, say, 10 yards. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there is an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise; then there’s Aristotle’s paradox of Place: if everything that exists has a place, then Place too must have a place… and so on into an infinite regress, and Russell’s, based on sets, ‘Think of the set, which we call A, which contains exactly ‘all sets which do not contain themselves’. Now, we ask ourselves: does A contain itself? If we try to claim that A does indeed contain itself, then we run into a contradiction, because we just said that every set belonging to A ‘cannot’ contain itself. But if we try to claim that A does not contain itself – which is the same as saying that A does not belong to itself – we’re no better off, because we constructed A such that it contains all sets which do not contain themselves, which would include A.’ Having had something of an interest in Theology, I like Tertullian’s: “The Son of God was crucified: there is no shame, because it is shameful. And the Son of God died: it is wholly credible, because it is unsuitable. And, buried, He rose again: it is certain, because impossible.” [Crucifixus est Dei Filius, non pudet, quia pudendum est; et mortuus est Dei Filius, prorsus credibile est, quia ineptum est; et sepultus resurrexit, certum est, quia impossibile.
— (De Carne Christi V, 4)] Sir Thomas Browne, the XVIImo. C. Medic, ruminating on this declared, ‘Methinks there be not impossibilities enough in Religion for an active faith; the deepest Mysteries ours contains have not only been illustrated, but maintained, by Syllogism and the rule of Reason. I love to lose myself in a mystery, to pursue my Reason to an O altitudo!’ [Religio Medici IX.] .
Another paradox that goes back far is the Liar Paradox, upon which St. Jerome mused: “I said in my alarm, ‘Every man is a liar!’ (Psalm 116). Is David telling the truth or is he lying? If it is true that every man is a liar, and David’s statement, “Every man is a liar” is true, then David also is lying; he, too, is a man. But if he, too, is lying, his statement: “Every man is a liar,” consequently is not true. Whatever way you turn the proposition, the conclusion is a contradiction.
Aristotle had shown the impossibility of motion in this way‘: If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless. – Aristotle, Physics VI:9, 239b5 and Bertrand Russell had considered the Liar Paradox more in mathematical terms, which could be summarised thus: There are things that are true in mathematics (based on basic assumptions). There are things that are false. There are things that are true that can never be proved. There are things that are false that can never be disproved. And that is a problem, because we cannot ever tell if something is true unless we can prove it. Shades of Donald Rumsfeld’s ‘known and unknown unknowns’.
‘Fiddle faddle’, the impatient realist responds; ‘you’re just playing with words. Meanwhile, reality confutes you!’ Diogenes is said to have got up and walked to illustrate the silliness of the Motion Paradox . Yet serious minds have pondered such things as these for millennia, so Kierkegard defended the Paradoxical: Kierkegard had this so say about Paradox: …’one must not think ill of the paradox, for the paradox is the passion of thought, and the thinker without the paradox is like the lover without passion: a mediocre fellow. But the ultimate potentiation of every passion is always to will its own downfall, and so it is also the ultimate passion of the understanding to will the collision, although in one way or another the collision must become its downfall. This, then, is the ultimate paradox of thought: to want to discover something that thought itself cannot think.’
But what has all this playing with words to do with us, today?
Every tiresome day you’re on the road you will have wearily assented to the truth of Jethro’s First Paradox as your zipping along brings you merely to the rear-end of yet another slow procession of vehicles, so here is –
Jethro’s Second Paradox: ‘The more we discover, the less we know; the more we know, the less certain our knowledge.’ In nowhere, I think, is this more evident than in the realm of ‘Science’. Science is about observing regularities and formulating Laws which accurately account for them; Science employs The Inductive Principle, we’re told: observations are made, and reason applied… or so it seemed. The apple fell, Newton observed, the Law of Gravity was discovered. Bertrand Russell was to speak (in hushed tones!) of the lack of proof for the validity of The Inductive Principle; C. D. Broad declared “induction is the glory of science and the scandal of philosophy”: ‘scandal’ because, if science claimed that the only way to know things was by means of … observing regularities, &c., &c.. – there was no Inductive way of demonstrating the validity of this claim. So Pope’s grandiose, not to say blasphemous, statement,
‘Nature and Nature’s Laws lay hid in night:
God said, ‘Let Newton be!’, and All was light.’
was based on an extremely fragile foundation – and that’s even before we learn that, attempting to re-run Newton’s famous Spectrum experiment, a twentieth century scientist concluded that, like many other scientists, Newton had
falsified adjusted his findings. So, perhaps, Karl Popper was being supremely generous when he said, ‘Science may be described as the art of systematic over-simplification.’ In some disciplines, ‘over-simplification’ also bears the name of Fraud, False Accounting….
Long after Rutherford had ‘split the Atom’ in 1917, there were scientists who (perhaps remembering Newton, among others) disputed the claim: after all, Democritus’s (c. 400 B.C.) name for the basic ‘thing’ in the Universe was from the Greek meaning ‘that which cannot be cut’. Hardly was the ink dry on Rutherford’s paper, than his ‘proton’ was to be up-staged: in 1932 a pupil of his discovered the Neutron… and then, in 1959, a further neutrally-charged particle was found the Neutrino, which, like so many of these things, had (in addition to no charge) no mass, and, if I remember correctly, no position… so a ‘thing’ that is invisible, can’t be ‘weighed’, has no energy and no position… and it gets ever stranger, more fanciful, more in the realms of Unicorns, Giants, and Magic Beans: I had to keep checking that the edition of ‘New Scientist’ I was browsing was not the April one, when I read (in 1990?) of ‘Gluons’, particles hypothesised as holding together all this rag-bag of ‘sub-atomic particles’. And then there were ‘Quarks’ Surely, ‘The Charmed Quark’ must have been something from Lewis Carroll’s fervid imagination.
Small wonder, then, that Karl Popper concluded that, ‘Our knowledge can only be finite, while our ignorance must necessarily be infinite.’ [The Growth of Scientific Knowledge – 1963] Is Light wave-form, or particulate – or both? Is there a ‘God-particle’? Is expensively trying to answer this question vital, or of no importance whatsoever? So Karl Popper was, of course, far ahead of Jethro. But here is an insight of his that seems to have chilling relevance to us today: ‘If we extend unlimited tolerance even to those who are intolerant, if we are not prepared to defend a tolerant society against the onslaught of the intolerant, then the tolerant will be destroyed, and tolerance with them.’ Perhaps, then, the Universe is itself a huge Paradox (Americans, who never make do with three syllables when they can use six, might say ‘counter-intuitive’. And finally, a quotation from a little-known Cornish physicist (T.L. Petters): ‘the Physicist is the man who weighs the Imponderable, and unscrews the Inscrutable.’