The theme of the author’s six essays in The New English Review (NER) on-line journal has been the De-mystification of Mathematics, a project which Ludwig Wittengstein tried to accomplish, but on which he was unable to make much progress. Now two posts have appeared in The New English Review respectively rubbishing Wittgenstein’s philosophy generally (Prof. Samuel Hux) and his rejection of metaphysics in particular (Robert Lewis). In this blog two comments which the author posted in the on-line journal are re-posted.
Samuel Hux’s essay in the July issue of the NER offers a superficial, scathing account of Wittgenstein’s philosophy. He accuses Wittgenstein of not being a genuine philosopher. This is the present author’s reply:
<<Yes, Wittgenstein is infuriating, probably the most baffling of the great philosophers. I was a postgraduate philosophy student in Oxford in 1953 when a Memorial Meeting was held after his demise at Somerville College. All the big beasts of Oxford philosophy were there… behaving as if they were in church mourning the loss of a saint… showing sides of their usually irreverent, sceptical selves one would never have guessed they had. They were right to think that a great philosophical giant had passed away, but probably hardly one person in that large gathering had a clear, lucid understanding of why his main message was so important.
Incidentally scoring points against his Tractatus is a waste of time because he himself disowned it afterwards. It was a youthful folly. It mirrored Russell’s philosophy of logical atomism, a blind alley which foolishly treated human knowledge as a great heap of precise atoms-of-information. By 1929 both Wittgenstein and Ramsey had also become aware that Russell’s so-called ‘Paradox’ was much more than a little local difficulty. It was, rather, a devastating reductio ad absurdum of neoplatonic mathematics (maths based on sets): a Contradiction which was logically necessary. It meant that Plato’s account of meaning would no longer do. Plato had “solved” the perennial problem about the meaning of mathematical terms via-a-vis ordinary words, by generalising the notion of meaning in mathematics, which, he thought, consisted of ideals. The orthocentre of a triangle scratched in the sand was a point, but the orthocentre studied in geometry was not this imperfect point, it was an ideal point —something this imperfect point might become if it were refined to the nth degree. Similarly, Plato claimed, a particular scruffy cat was not what the word ‘cat’ referred-to: rather it was an ideal cat —what a cat entirely free of defects would look like. This had been, in its day, a brilliant synthesis, because on the face of it mathematical meaning was hard to place..
To give up the platonic notion of meaning, which is Wittgenstein’s great message, is about as difficult as giving up bread or breathing. It has been the subliminal assumption built-into more than 2,000 years of profound reflection, philosophical texts and humanistic genius. Most philosophers today, having lost patience with the byzantine style of Wittgenstein’s later writing —as vividly described by Samuel Hux— have relapsed and gone back to the now broken-backed, but still comfortable, Platonic assumption.
So why did Wittgenstein fall down so badly in his later writing in presenting his insight —a failing he himself recognised? Well he was the victim of the attack dogs of the mathematic establishment, for rubbishing their fudged ‘Party Line’ which brazenly claimed that the Russell Contradiction could be “solved” by banning a set from meeting its own membership criterion. (If so, the Contradiction did not exist, and had never existed!) It was a coincidence of history that Ludwig and Adolf Hitler had been pupils at the same school in Linz. But this became a dreadful implicit burden when it became plain that Ludwig was evidently the young Jewish rich boy demonised in Hitler’s Mein Kamph. >>
Robert Lewis’s essay ‘The God Particle’ in the July issue of the NER is an interesting attempt to revive metaphysics as a mode of philosophical reasoning. Lewis bases his approach on the principle that every powerful idea has a polar opposite. Here is the present author’s comment:
<<One unexpected consequence of Robert Lewis’s good idea —which we might call the ‘Existence of Polar Opposites principle’ is that there must be a polar opposite to mathematics. The bad news is that a secular priesthood has been in place, and has had such a tight stranglehold on interpreting and teaching maths for more than 2,000 years, that it never occurred to them to try to understand their subject better: an essential preliminary to conceptualising its opposite. The good news is that I have set out the basics of just such an ‘anti-mathematics’ discipline in my six essays in the New English Review starting with ‘The day Western Logic caved’ in the September 2021 issue. (The others are in the Nov, Jan, March, May, June issues.)
. To understand mathematics better requires a great deal of patience, trying to get to the heart of the reasoning. But I’m afraid this sets a standard which, as Wittgenstein was first to see clearly, is not going to allow us —when reasoning in philosophy— to take metaphysics at face value. Metaphysics is like loose money —it looks potent and positive, but in the last analysis no one quite knows where its meaning is coming from. It also lacks sustainability or, in other words, the capacity to lead to progressive problem-shifts as introduced by Imre Lakatos in the 1970s. It is really the experience of negotiating progressive problem shifts which gives one the feeling of gaining grip.
. When the idea of a Deity (monotheism) was being mooted in the ancient world it was a big step forward in explaining the existence of the universe. It was also a whopping abstraction, one which sprang no doubt from the potency and dominance of mathematics at that time. The Deity hypothesis had immense credibility. The only agencies any one had ever heard of —which were capable of great feats of creativity like new cities, temples, monuments— were leaders like Mausolus, Alexander, Hannibal, Augustus Caesar. So the hypothesis that a supermind (=God) must have created the universe was a no brainer.
. But the concept of ‘mind’ is not a simple, basic ‘given’. Lewis Carroll guyed it in Alice’s Mad Hatter’s Tea Party where the works of the watch have been removed and replaced by butter and jam! We now know, thanks to the cybernetic insights of the last sixty years, that we can mimic some of the simplest attributes of mind with digital electronic circuitry. The brain, of which we know very little (for example where it stores its prodigious memories) is evidently a highly structured biological marvel, which, in some way we do not understand, manages to give us the experience of consciousness. There are only two options here. Either it is a wholly deterministic machine which can be described using mathematics, or it is a purposive, affective, creatively self-conscious agency which, hopefully, will be described in the future using anti-mathematics. There have been over-enthusiastic mathematicians —people like Laplace, Russell, Keynes— who should have known better who have plumped for determinism. Most lively, sensible people can see, however, that we undoubtedly have freewill and that determinism is a potentially dreadful weapon in the armoury of dictators and tyrants.
. So the most likely conclusion is that anti-mathematics will eventually be able to find a credible way to describe —but only in lucid qualitative terms— how the human brain works.
. At this point we reach a ‘Eureka singularity’ in human experience, because this brain will be capable in principle of creating the anti-mathematical structure which it, itself, consists of. It will of course embody a huge tranche of ‘common wisdom’ which we unconsciously acquire while growing up. This Eureka singularity is therefore a solution to the problem of how a supermind could come into being, and it fixes its location —inside the heads of every member of the human race. It also reveals the source of most of the metaphysic headaches which have been circulating since Emmanuel Kant first glimpsed the possibility of this creative singularity. (NB Eureka singularity is the anti-thesis of the much-bandied nightmare singularity postulated by some “experts” who have fallen for their own over-hyped AI illusions.) >>
CHRISTOPHER ORMELL 1st August 2022