When Elites Start Lying

by Christopher Ormell (May 2026)

It is becoming quite evident that today’s modern, “Western” civilisation is in decline. The non-negotiable standards of behaviour, which we used to take for granted, have visibly lost much of their punch. For a long time savvy commentators have pointed out that older members of society understandably tend to get the false impression that society is “going to the dogs.” The reasoning behind this is that common practises have changed, and these oldsters have failed to appreciate how the new alternatives work.

But now the slick assumption that this syndrome explains today’s decline in standards, is, itself, “Going to the Dogs!” The shortfalls we experience are too frequent, too brazen, and too serious, to be waived-away by this cliché. We are driven reluctantly to the conclusion that some invisible, unknown social/political factor is sapping the elusive, priceless, enduring nerve which successfully energised “Western” progress and rational culture for centuries.

All kinds of explanations of this sapping have been aired, mostly based on theories which put the blame on “too much influence from” various kinds of dubious social practice. It might be poverty, unemployment, substance abuse, dysfunctional “education”, neglected child-rearing, lax policing, red tape, social media, pornography, ennui, multiculturalism, advertising lies, PR, pressure groups, weak religion, pollution, excessive sugar, alcohol, fast food, street violence, misogyny, family breakdown, welfare payments—you name it.

All these dubious phenomena have been treated as symptoms of “Western civilisation in decline,” but they were present as obstacles in one form or another in the past, and they weren’t regarded—then—as sufficiently powerful to nullify a robust legacy of civilised progress and hope.

The thesis of this essay is that lapses by the two most admired, sincerely trusted, elites have let themselves, and Western civilisation itself, dangerously down. It is one thing for a group, known to be opportunistic, to sneakily fudge its proclamations. But when that group is a much admired, sincerely trusted elite, the damage to common human morale increases a hundredfold.

The most honoured elite used to be pure math. It was an activity variously described as the “Queen of the Sciences” and the “Language which God must have used when He created the universe.” But around 1900 the High Priests of Math decided that they were being seriously oppressed, by being treated as backroom fixers whose principal raison d’etre was to solve tedious technical problems for the physicists. So the higher mathematicians staged a virtual UDI (Unilateral Declaration of Independence) of Math—away from its former science connections—and onto its amazing, aesthetic triumphs. It’s authors asserted that math had shown by its fantastic, exotic, abstract discoveries, that it had “come of age”, and therefore that it deserved the public status of being a free-standing Intellectual Artform.

It was not a development which was totally unexpected. Throughout the 19^th century so-called “pure modern mathematicians” had been more and more openly “doing their own thing” compared with their 17^th-18^th century predecessors. This “doing the scholar’s own thing” began with imaginary numbers, non-numerical algebras and non-Euclidean geometry: three fields introducing an astonishing new kind of doubly-pure math. It was a major culture shock which had suddenly arrived out of the blue (around 1830). This sudden major extension of math into a more hyper-abstract mode, originated in Europe. It seems to have materialised as an expression of Continental discontent. It’s leaders  seemed to have been seriously miffed (embarrassed) by Isaac Newton’s brilliant breakthroughs in calculus, dynamics and gravitational theory. Newton’s methods stemmed from feet-on-the-ground thinking combined with sharp focusing onto actual phenomena, carefully observed and measured. These Newtonian methods open-mindedly registered the empirical facts as they were: they didn’t attempt to impose fancy preconceptions. They were the X-factor which provoked the Industrial Revolution, because now a kind of “Bible” existed (Dynamics) which told engineers exactly how any new, imagined machine would behave. Maths had suddenly acquired serious physical applications, and the Continental brotherhood (plus a few sisters) were not happy. They preferred to treat the awe-dazzling elegance of math as its main attraction.

So the drive which ushered-in the new doubly-pure math was a kind of reaction,  springing from an intense elegance-mindedness. The general Continental mindset was, we know, more socially disciplined, more militaristic, and more forcibly imposed, than that of the UK. (Militaristic discipline inevitably prevailed on the far side of the English Channel, because there were frequent tensions building-up between neighbouring states. The UK’s culture was much less stressed: because the country was protected by a surrounding ocean, as well as a dominant navy.)

Judged by scholastic standards, the new doubly-pure math was more difficult, more advanced and more mysterious—and hence more admired by scholastics— than the plain math of Newton (at least if one only counted academic brownie-points). It didn’t claim to be useful, but it claimed to be an inquiry into the depths of amazingly “deep” logical reality.

This new paradigm, which had started around 1830, began to grow slowly during the 19^th century. At first “imaginary numbers” provoked some derision, but when de Moivre’s theorem showed how to use them unexpectedly to derive striking trigonometric formulae, the derision disappeared. The first major step forward was Georg Boole’s invention of set theory in the 1850s. This was followed by Cantor’s exotic notion of the transfinite in the 1880s. Both Boole and Cantor were idiosyncratic, creative individuals whose discoveries came with profound, but potentially tricky, implications.

Cantor’s unimaginably massive transfinite sets had an effect similar to that of religion: they seemed to be opening-up hitherto unguessed vistas of logical reality.  It was as if Cantor had discovered that God had an older brother, and indeed various other relations, with all sorts of mazy mathematic implications. David Hilbert, the most talented mathematician of his day, called the Cantor’s transfinite notion a ‘Paradise.’ He even swore in 1900 that nothing would induce him to give it up. This was a catchy, spectacular, ploy, but one which negated the basic principle of math—that strict logic, not rosy emotion, is the discipline which must call the shots.

So the aim of this tacit Continental Math UDI around 1900 was to try to turn math into an Intellectual Artform; a condition which presupposed that math was an “end in itself,” a glorious cognitive activity in its own right, with no need to earn brownie-points from the technical work its members occasionally did, to help their physicist colleagues.

The question, which should have been addressed at the time, though, was whether math actually had the degree of public support and depth of admiration needed to flourish autonomously (inevitably in “splendid isolation” style) in a fiercely competitive, pragmatic environment. The leading math gurus of 1900 evidently thought that it did. They were—it is now obvious—wrong. They had been intoxicated by Cantor’s notion of exotic transfinite sets, and the apparent “dawn of a new era,” in which math would become gloriously unified into a grand logical synthesis based on pure sets!

Unfortunately Cantor’s much glorified transfinite sets harboured a hidden flaw—their total bodies of elements had to include hosts of indefinable mathematic objects. It was a cardinal tenet of math that its objects must be well defined. But the total number of potential definitions was only an ordinary infinity. This meant that there were nowhere nearly enough potential definitions to define all the elements of a single transfinite hoard.

There were math giants at the time (Kronecker, Poincare, Borel) who realised that this negated the whole notion of the transfinite. But their views were brushed aside. A majority of “modern mathematicians” seemed to “believe what they wanted to believe” (a la Hilbert). They treated the new status of math as an “Intellectual Artform” —as a justification for this stubborn stance. Rigour had ceased to be the final authority in math.

Which brings us back to sets.

The leading gurus of math had been, in effect, blinded by the unexpected discovery of set theory by George Boole in The Laws of Thought, 1854. Set theory presented a new form of non-numerical algebra, not one created out of the blue, but a suite of rules robustly founded on commonsense. The leading continental gurus of math couldn’t believe their luck. This abstract breakthrough surely vindicated their earlier decision to pursue the three somewhat “way-out new math branches” which had surfaced around 1830.

But the blinding effect of this Boolean euphoria, had a downside. These gurus simply forgot to notice that nearly all the sets highlighted by George Boole were not bona fide mathematical objects!

Failures to notice things can be, we know, disastrous. This one has recently (but more than 100 years overdue) turned out to be dynamite.

These “modern mathematical gurus” had long since de-bunked and over-looked applications of math. It was not something they even bothered to talk about. They regarded it as a grossly inferior, lesser activity, not worthy of their superior talents. But sets of gloves, plates, saucers, books, horses, clothes, apples, vegetables, etc. —the very sets highlighted by Boole—could not possibly count as mathematic objects, because bona fide mathematic objects require strict logical definitions, and these Boolean examples were miles away from having such definitions. They flouted the sloppiness of everyday words, and, as such. They could not count as “pure math” by any standard. Common sets certainly existed, but they were “applied math” examples.

This was a singularity, an extraordinary—indeed whopping—error in the official historic narrative of “modern mathematics.” A complete de facto professional circle had been blinded by their own ingrained habits, namely a gut disregard for math applications. If they had paused, and brought cool, realistic logic to bear on the situation, they would have realised immediately that only sets of elements (collections of items) which were themselves bona fide mathematical objects could possibly count as bona fide math objects (math sets).

Put more simply: a genuine “mathematical set” had to be a collection of properly defined, mathematical objects, like {pi, e, i} or {1,10,100, 1000}.

The set-items listed above, though—gloves, plates, saucers, books, horses, clothes, apples, vegetables, etc. —could not possibly qualify as properly defined mathematical objects.

Somehow, the leading math gurus blindly overlooked this.

If they had realised their blunder, the gurus would have probably gone-on to realise that bona fide math sets could not possibly be the fundamental building blocks of math, because one needed to know what counted as a “mathematic object” —before one could even identify a single genuine mathematical set!

But no one—out of this circle of exceptionally talented individuals—spotted the absurdity of their position. “Modern math” had inadvertently come off the rails. Two leading figures, Gottlob Frege and Bertrand Russell, had actually pinned their personal futures onto what they regarded as a “must win” widely supported movement—to “unify” math by casting all its branches in the language of sets.

So the shock which came with Russell’s unexpected discovery of “his” Contradiction (1901) added an extra dimension to an already unacceptable scene. Frege, on learning that Russell’s Contradiction had demolished the credibility of his set-unifying scheme, felt that his life’s work had been wasted. Russell, to his credit, doubled-down, and set himself the task of pulling off this elusive synthesis. It was to be a monumental work of mathematical logic: He and his friend Whitehead’s magnum opus, Principia Mathematica. They used every trick in the book to blind the ordinary reader with science. But, when this Principia (Part I, 1910) was published, it received a disappointingly cool reaction. It soon became clear that it was a wasp’s-nest of contradictions. The remaining Parts were published after WW1, but they were full of even more dubious assertions. Eventually Russell reluctantly announced that he had given up his unsatisfactory struggle with mathematical logic.

No official explanation of Russell’s Contradiction was ever found. Russell’s own preferred “explanation” was his “Theory of Types.” It laid down a suite of heavy constraints, which would have to be backed by professional willpower. (All statements had to acquire an Official Level (Order). A statement about a statement of order 3 would be, by definition, a statement of order 4. According to Russell, the Liar should have said “I am making a statement of order 1 which is false!” Russell could then “solve” the Liar’s paradox neatly, by saying that the Liar was making a statement of order 2, so his statement was simply false. But who was going to insist that the Liar must add the phrase “of order 1?” If Russell had paused, and carefully re-considered his “theory,” he would have seen that it was totally dependent on rules like “Every statement has a reference Order,” “No one should ever utter a statement which refers to another statement without saying its Order.” The very notion that every statement must have a definite order, was taking for granted a totalitarian authority which simply does not exist. There were all kinds of vague statements which “referred” to other statements obliquely or to a slight degree. And Russell never explained how a statement which referred to two statements, one of order 1, and one of order 2, could be handled.

There was no supreme authority to impose these preposterous rules. It is not a flattering comment on Russell’s judgment that he committed himself to such obvious nonsense.

But this unexpected, unnoticed blindness, which had led the High Priests of math to be totally unaware that they had gone off the rails, would persist in “modern math” circles well into the 20^th century. The notion that higher math was—they thought—to be regarded henceforward as an “intellectual artform” seemed to be confirmed. It appeared to be fully accepted by the majority of these proud-but-defiant “modern mathematicians.” There were various notable mathematicians in the UK and the USA who distanced themselves from the cult, but they were a minority, not in the higher math mainstream.

So an in-house triumphalism became the aggressive, taken-for-granted, motif among the dominant math cult. They must have known, at least subliminally, that the great names of math had all been equally interested in “pure” (i.e. executive) and “applied” (useful) maths. But the brash triumphalists imagined that they were riding high, and they didn’t care about these long forgotten geniuses.

The change—which they had foolishly accepted—incidentally took the implicit burden—of higher math being a quest for “absolute truth” —off their backs. No one actually publicly re-conceptualised the subject as now being a study of “abstruse, weird, ornamental configurations which may, or may not, be logically valid.” But the kind of postgraduate problems which young researchers were encouraged to pursue, took on a slightly wider, looser aspect. Lipservice was still being paid to “checking published results,” but as nothing really hung on the implications, the strong, serious, substantiated rigour previously taken for granted, had quietly gone.

The long-term effect could have been foreseen. It was an unwanted explosion of way-out, idiosyncratic, obscure, aesthetic, over-specialised, published math. It eventually led to the nightmare known as “Ulam’s Dilemma,” a term coined by Davis and Hersh in their best-seller The Mathematical Experience. This is the name of a vast archive of millions of obscure-artform math theorems which grew and grew after WW2. Most of these theorems simply cluttered the shelves of university libraries and were rarely read by anyone except their authors.

No single person, however talented, could ever expect to master and understand such a massive corpus of neglected scholarship. Whatever did it all mean? It amounted to a vast mountain of over-bearing, demoralising, obscure activity, which would eventually negate the triumphant mood surrounding the UDI of 1900.

There were other influences which probably contributed to pushing higher math unwittingly into becoming an artform. The most painful was that the Michelson-Morley experiment had posed a logical problem which seemed to defy rationality. However could physical light waves behave as if they were relative to human observers? The mathematicians knew that there was not the slightest chance that they would ever be able to “solve” this improbable problem. Russell’s own unsolved Contradiction had a similar effect.

The end-of-the 19^th century was also a time when popular “aesthetic philosophy” was in the ascendant. At Cambridge the most lively circle of talented thinkers capitulated almost entirely to G. E. Moore’s Principia Ethica. Bloomsbury followed. Art Nouveau flowered. Russell, Keynes, Strachey, Virginia Wolfe, etc were associated with an Aesthetic Movement which thought it was dominating philosophic discourse.

For a short period, aesthetic creativity blossomed, but in August 1914, the nightmare of WW1 broke out. Young soldiers were massacred on an industrial scale. Europe was saved from its self-induced obliteration, by the involvement of the USA in 1917. But after the Armistice, the elites of math and physics had to sew-up the impossible problems—still unsolved—those posed by Michelson-Morley’s and Russell’s Contradictions.

Both elites eventually chose the most disreputable, nasty ploy—fudges.

The math group chose Zermelo-Fraenkel theory, which tried to ban a set from being a member of itself. But the set of all the sets mentioned in this essay is obviously a set mentioned in this essay. This meant that Zermelo-Fraenkel theory could not possibly be right. The math crowd’s response was immediate: it turned Zermelo-Fraenkel theory into a Party Line. Willpower would take-the-strain, where logic had failed. No one seemed to care that it was unmathematical to trust arbitrary willpower instead of logic.

The physics group chose Einstein’s theory. It claimed that time was a 4^th dimension of space. (But a “dimension” is a degree of freedom, and we have no freedom whatever to move about in time.) In this way the physicists tried to “explain” the relative behaviour of light by postulating the most rigid, paralysed, infinitely static, absolute picture of physical reality. It meant that the future was already “there,” and everything which makes living worthwhile was an illusion. By treating active change as a static, timeless presence, it threw out the baby with the bath water. Physical reality needed to be properly explained, not paralysed in a timeless fixture.

These fudges were, in effect, disgusting lies. They were backed to the hilt by two so-called “elites” which were supposed to consist of the most scrupulous, powerful, Godlike, minds.

So both the two abstruse “elites” made a disgraceful—viciously anti-social—blunder when they consciously tried to lead the responsible, intelligent public into accepting fudges. How did they think the responsible public would respond, when they saw that they had been monstrously fobbed-off? These fudged “explanations” were brazenly offered in bad faith; a false step which could only utterly demoralise the responsible circles which hold society together. When Wittgenstein and Ramsey met up at Cambridge in 1929 they were flabbergasted that the once much-admired leadership of math had blown its own good reputation.

And if—many ordinary observers must have wondered—they had gone to this trouble because there was no alternative, the truth must be very dark indeed. There was no attempt to stop ordinary responsible people from falling into a bottomless pit of pessimism and despair.

It utterly destroyed the trust which alone could hold society together—a glue which was already in short supply.

We should, of course, note that the world in which these decisions were made, had been reduced to a near-nihilistic, wasteland level by the industrial massacres and dereliction of WW1. This might explain why suicidal fudged solutions were pronounced in the 1920s by both the “elites,” but it doesn’t excuse these dreadful lapses. It is evident, with the advantages of hindsight, that they should have said that the quest must go on relentlessly and that nothing must be left unturned in the struggle to find genuine solutions.

So, when it became public knowledge that the two “elites” had become frauds, a post-modern pandemonium became, unbelievably, “the norm.” This seemed to encourage all kinds of pathetic, idiosyncratic individuals to step-in—where angels feared to tread. It led to charlatans and demagogues presuming that they could save the day, where official experts had failed. Crass, raw, laughable. ignorance was now being treated as more trustworthy than established knowledge. Only fools and idiots imagined that this was the way back to sound, understandable resolutions.

This is a catastrophe of dreadful proportions, and a powerful movement of responsible people needs to be urgently marshalled to stamp it out. If we don’t stamp it out, the outcome is likely to be Armageddon.

In my March essay, “Trying to Understand the Universe: How the Universe is Becoming More Accessible,” I listed seven lines of positive thinking which provide the confidence needed to search for new solutions to the horrendous problems which came to light in 1887 and 1901. The eighth, and most potent development, though, is anti-math, because this long overdue abstract logos, enables us to explore abstract models of ourselves and our built-in imperfections, while explaining the massive by-products of the axioms needed to establish—as Kant foresaw more than 200 years ago—our own sentience, humanity and rationality.  The outlines of a comprehensive humanistic model of the cosmos-and-us are beginning to emerge: a self-generating model which leaves no room for unexplained assumptions. This is good news. Against all the odds, a new, more comfortable, more rational, world is beckoning.

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Christopher Ormell is an older philosopher of mathematics who solved Russell’s Contradiction in 1959. The solution was published in Mind, and was noticed with approval by Karl Popper, but otherwise ignored. Later he found a mirror image of Descartes’ classic Cogito argument which he launched in a six-article series in the journal Cogito (1992-4, also ignored. It was a proof that absolute unpredictability was logically possible but mathematically impossible.) He discovered superparadoxes, which generate vast numbers of contradictions (put online in 2003). He earlier found the first formula for the nth prime number without using trigonometric functions. (Math Gazette 1967). He discovered explicit formulas for calculating [x] and |x|. He later spent 29 years searching for an elementary solution to Fermat’s last theorem. This putative reasoning has now been on-line for more than five years. (A prize was offered for its refutation, but so far, no flaw has been found.)  His main work, though, has been discovering a wholly unsuspected, spectacular, polar-opposite to math … Anti-Math, which quite unexpectedly brings methods, similar to those of math, to bear on the logical implications of transient forms. These forms are imposed—by willpower—securely onto random sequences. The result: Anti-Math enables the brilliant, civilised, moral thinking of Kant to re-occupy centre-stage.  We are beings who manage to secure our own existence by unconsciously applying life-affirming definitions to a wholly independent, unexplainable, neutral-random substratum. Websites: philosophyforrenewingreason.com, and mathsforrenewingreason.com.

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