by Christopher Ormell (June 2026)
In recent years there has been a significant loss of public interest in anglophone philosophy, and—as an academic subject studied in universities—its influence has visibly waned. There are still a few philosophers who can attract full houses, but they are much depleted compared with their predecessors. We used to celebrate towering figures such as Sartre, Russell, Whitehead, Wittgenstein, Ryle, Austin, Berlin, Popper, Ayer, Quine, Lakatos, Searle and Habermas … leaders of philosophic thinking who illuminated the mid-20th century. But where are their successors today?
An air of weary despondency seems to have settled onto the once bold, generalised, corner of rigorous meta-thinking in the Anglophone countries. Contributions to the central problems of epistemology in particular have nosedived, and are now virtually nil. The phenomenal rise of IT—recently extended by over-hyped AI—seems to have contributed mightily to a general presumption that diffusing digital information is the only game in town … which “actually works” and “actually matters.” This populist opinion has had the unexpected side-effect that it has thrown doubt onto traditional philosophy. Isn’t traditional philosophy simply an obsolete, old-fashioned, way to do this informative dissemination?
No: because philosophy seeks to make sense of this dissemination, and indeed it seeks to make sense of the perilous human condition—located, as it is—on a minor planet in a nearly incomprehensible, seemingly alien, universe. We are also much less confident about our relationships and behavioural felicity than our ancestors, who took their behavioural felicity on the nod, mostly directly from religion. This was before it (religion) was undermined by a massive tsunami of disciplined, bitty, diverse, technical, specialist, not-yet-falsified, techno-science.
Which is not to say that ancient religious prescriptions of “behavioural felicity” could stand on their own feet—even if the mountain of today’s techno-science were somehow swept away.
The norms of 2,000 years ago can’t stand comfortably on their own feet today (as it used to be assumed that they could), because these norms are seen by today’s blazé youth as dependent on ancient hearsay, dodgy history, ill-defined, obsolete concepts, and antique, essentially feudal, practices.
From this point of view, the survival of Christianity is a miracle. But of course it is the massive truth that only when we view ourselves as a huge family springing from a common source—can hope-of-good-times re-emerge, a hope which is capable of sustaining us. A life without this kind of hope soon becomes a barren wasteland.
However the sombre feeling that a “seemingly alien world dominates everything,” remains. It is a deeply chilling factor. It is quite ironical that the result of Michelson-Morley experiment tells us that the greater universe “out there” has some mysterious connection with human consciousness.
Blaise Pascal (1623-1662) famously commented that the vastness of the celestial spaces, the planets and the stars worried him. Modern technology applied to cosmology, has amplified this kind of “worry” a hundredfold.
The essence of the “worry” lies in the fact that we have little understanding of what happens in deep space: it can look deeply alien.
So what is the “final source of this feeling of confronting a chillingly alien background”? It is rarely recognised by popular commentators that the theorists of physics have had to accept perpetual rebuttal and disappointment, for more than a hundred years. Their best expectations have been continually wrong-footed by new technical discoveries, systematically, again and again, time after time … indeed ever since the awful shock of the Michelson-Morley experiment in 1887. (Which showed that somehow the behaviour of light was relative to the human observer, not to the vast physical status quo of galaxies “out there.” A recent example of failed expectations is the baffling phenomena seen on the ex-planet Pluto.) The theorists of physics have had to put-up with this sickeningly repeated rejection for well over 100 years. Today they are having to admit that the chief movers and shakers in deep space are “dark matter” and “dark energy” —items about which we know almost nothing. The subject “Physics” would, indeed, be in a state of severe mental breakdown, if it were not for the fact that its practitioners tend to receive lavish annual funding from governments and military establishments.
Looking back to the 20th century, we can recognise a general positivity in philosophy associated with the century’s major genius, Ludwig Wittgenstein. He had the talent, the insight and the courage, to criticise and reject the Platonic assumptions which were still being lazily unquestioned by the mainstream math establishment. After Wittgenstein’s linguistic revolution in the 1930s, only Russell, Whitehead and Quine of the thirteen philosophers listed above, clung—pathetically—to the Platonic notion that math was “an objective reality.” Wittgenstein had taken the trouble to look carefully at the modus operandi of ordinary language, and he was thereby able to understand it on the level which counted—which was, in effect, as second nature. This is probably the most significant breakthrough in philosophy since Descartes. The philosopher G. E. Moore commented when Wittgenstein applied for British citizenship in 1939 that he (Wittgenstein) was the “philosophical equivalent to Albert Einstein.” (The compliment was sincere, but Moore had evidently not recognised that Einstein’s treatment of time as a “dimension”implicitly snuffed-out everything which makes living and personal freedom worthwhile. So Einstein had clay feet, which, it seems, nobody then—or now—wants to admit.)
But Wittgenstein himself hardly radiated the success he had achieved by negating Platonism. In spite of this major triumph, he never quite managed to clarify the meaning of math, and without expelling Platonism from the mathematic culture, his triumph was only partial and compromised. He was, incidentally, harassed systematically by the pugnacious attack dogs of the math establishment: which didn’t help. His famous mantra was “Don’t look for the meaning, look for the use!” But whatever was the “use” of math? The idea that math “gathered its meaning from its applications to science and technology” was—at the time—an obvious non-starter, because solving problems in mathematical-physics only seemed to be a tiny corner of the subject; there were vastly more published “pure” math books, monographs and papers than “applied.” (This was before the arrival of solid-state computers around 1960. After the arrival of reliable computers, a huge expansion of uses of math began. In this way the tables gradually began to turn. Today it is a truism that math is involved in virtually every aspect of human activity. But there has still been no widespread (Peircean) recognition that math is essentially the “science of hypotheses”—or, if you prefer, that it is essentially the ideal “path-finder” for theories, projects, schemes, etc. when they are at the beginning of their cycles. )
The arrival of reliable computers was also, simultaneously, a massive cultural shock for the diehard gurus of math. It posed a deadly existential threat to their raison d’etre—a culture shock of more than ten on the Richter scale. The mainstream apologists for pure, higher math were thrown into confusion. They tried to survive by doubling-down on their notion that higher math was a “Superior Intellectual Artform.” But this sounded too much like “a self-serving ego trip” to win public support. The naïve metaphysical era, when all kinds of strange endeavours were treated as being “valuable suis generis”, had passed. Some commentators argued that pure, higher math did very occasionally throw up new concepts needed in physics. But such events were visibly becoming rarer and rarer.
Once the youthful influencers of higher math had abandoned their historic commitment to science around 1900, the underlying motifs and programmes of their (now more “creative, elegance” remit) were nowhere near the specialist kind of hard realistic thinking needed in physics: they were much too artificial, aesthetic and far-fetched. Higher math had, in effect, become a—pathetically beached—whale. The newly fashionable computer establishment treated it (higher math) as a harmless—though “useless”—mind game, which naturally appealed to the 0.1% of the population who had special personal mathematic talents. But the subject had lost much of its original credibility by wandering into a metaphysical fantasyland, with its commitment to unverifiable transfinite sets.
One of the main uses of the new computers was to bring them to bear-onto complex problems in technology, science, and civic development. There were thousands of these problems—so the main “use of math” began, finally, to show. These were the masses of “uses of math” which had been conspicuously absent during Wittgenstein’s lifetime. But the rump of surviving Wittgensteinian protagonists seemed to overlook this crucial breakthrough. In effect they were blindsided by the computerists, who had meanwhile adopted the convention that this problem-solving activity was “down to the brilliant electronics” (sic) of their computers, not to the personal cognitive labour of thinking-through how to align symbolic computerised math skills with messy real-life problem situations. (This was like saying that the Bible was “extremely special,” “because it was a massive printing challenge!” or boasting that the Tour de France was “won by the bicycle of the rider who came-in first!”) So hardly anyone noticed that Wittgenstein’s interpretation of ordinary meaning had been unexpectedly vindicated. It was a development which should have rescued Wittgenstein’s reputation, and revived his linguistic revolution from the earlier obstacle that “use cannot be the source of meaning in math, because most of higher math is not useful.” Now computers had shown that math had thousands of new uses, and that the profusion of these many “uses” justified the theory that its utility was the ultimate source of it’s meaning.
(The question “How do math applications really help the human race?” was still treated as a mystery, because Charles Peirce’s insight that it was essentially a hypothesis-illuminating activity had been rejected by the math hierarchy since the 19th century. )
Most professional mathematicians intuitively reject what they see as “the uses of math,” probably because the so-called “applications” they met at school and college were obviously pseudo applications—awkward, unrealistic, bogus questions cobbled together by textbook writers, who were trying to ensure that their readers would practice the necessary manipulations.
The historical event which probably laid the foundation of math’s reputation for extraordinary usefulness, was the building of the pyramids at Giza. These vast edifices were successfully constructed by a society which—by historic standards—was very, very poor. However did this come about? The answer is that the illuminative power of a body of fully established simple math created a secure confidence in the team which planned the scheme. Plato was born 2,000 years after these ancient math-inspired builders had completed their triumph. He knew the Great Pyramid was “there” in Egypt, and he knew that it was the main wonder of the ancient world. But he was so mesmerised by the aesthetic elegance and cool rationality of pure geometry, that he forgot to ask himself how these—long since dead—Egyptians had managed such unbelievable, unlikely, breathtaking feats.
Incidentally it was Wittgenstein (1887-1951) who pioneered the idea of truth tables in his youthful book, Tractatus Logico Philosophicus, published in 1921. Truth tables were the cue needed later to get solid-state transistors to process electronic pulses which mimicked basic commands like ‘also,’ ‘not,’ ‘as well as,’ ‘if not’… These operations were vital elements in the programs needed to get computers rolling.
However by 1960, Wittgenstein’s posthumous reputation had faded somewhat, because he had become more introverted, pessimistic, and guilt-ridden towards the end of his life. (“Guilt-ridden” because Adolf Hitler had been at the same school as him, and he (Hitler) had malevolently painted “a rich Jewish boy” as a pariah in Mein Kamph.) After Ludwig died, his followers tended to identify-with his uniquely bitter-sweet cultural pessimism. They also tried to justify their approach by writing prolix, wordy, papers, sometimes about the meaning of bland terms like ‘the,’ ‘perhaps,’ ‘and,’ and ‘or.’ This had the effect of trivialising philosophy, because the big questions (“whither the human condition?” and “the physical essence of the universe?”) were neglected and forgotten. This so-called “Linguistic Philosophy” was supposed vitally to clarify the meaning of philosophically crucial words. But it ended-up as de facto verbal fog—in effect it obfuscated the meaning of many words which had previously been treated as self-evident.
As a result, Linguistic Philosophy went out of fashion. We still need it, though, in a lean, targeted form. What we urgently need is an analysis of “extraordinary,” not “ordinary” language. It is the extraordinary zones of math-language and religion-language which most urgently require commonsense analysis. Instead, both these extraordinary kinds of language have seen their ancient mystique manically defended by their apologists.
After 1960, Imre Lakatos (1922-1974) was, for a short time, in the forefront of thinking about the meaning of math, but he died young, and since then there has been virtually no significant official epistemologic progress in math, still less any prospect of new modes of physical understanding. The huge direct emotional appeal of religion has, among its surviving fans, effectively closed-off any serious, sceptical analysis. (Theologians, in other words, have tended to turn towards feelings—not rationality—to persuade their readers.) Philosophy has ended-up like a wounded bird, which can no longer fly, but can still waddle about on the ground. This “waddling” is moral philosophy. The tragic and often needless muddles which are inevitably generated by a post-modern pandemonium—the state we have now been struggling-in for fifty years—haven’t helped. The notion that “‘truth’ is a meaningless word,” had long since been in circulation, but it started to shake intellectual opinion in the 1970s: part of its effect has been to paralyse philosophic curiosity. (It was probably a roundabout way of saying that the awful discoveries of 1887 and 1901 were still hopelessly unresolved, and no-one was even trying to make sense of them.)
Let’s say at once that the word ‘truth’ is central to philosophy, and that it has an unquestioned crucial, essential, vital, inescapable meaning. It is an incontestable truth that the Earth is an approximate sphere spinning in space. So even the most extremely pessimistic thinkers (“nihilists”) can hardly deny this conclusion, especially since the media coverage of the recent Artemis lunar trip staged by NASA. The key question is whether there are bottomless pits of incomprehension, or not. Even the most diehard nihilists are apt to believe that their dentists tell them the truth, when they say that “the truth is that this tooth needs to be extracted”.
Let’s say at once that the USA , Canada, Australia, New Zealand and the UK are free societies, and anyone who has unfortunately sunk into deep depression, can utter the remark that there are baffling things about the world which no one can any longer hope will ever be explained satisfactorily. This kind of despair is quite common. But it is not a good meme to spread, still less celebrate. Before 1887 there was an unspoken buoyancy about faith in science, which has since evaporated. Much of the evaporation is a dismal result of the physicists fudging—when they decided to treat time as a dimension, they were simply locking the door to any sort of enlightenment or mental clarity.
A lot of reflective people, though, seem to want to avoid contradicting these pessimists, because they can’t see any glimmer of a resolution, either in the immediate, or in the foreseeable, future. There is not the slightest glimpse of a happy resolution… it is now taken for granted that darkness prevails: a huge swathe of over-analysed physics and hyper-abstract math has been built on this desolate platform. So the people who still remain open-minded, don’t, for the most part, want to push for an unwarranted public hopefulness. They don’t want to dangle false expectations of hopefulness. An unsubstantiated optimism of this kind would soon be dashed, and would only lead their friends and contacts astray. This has become the overall feeling. (The notion that science can only claim—via Popper—that today’s scientific results are “not-yet-falsified,” is quite close to this attitude. Actually there is a total of (millions of) results and facts which are manifestly true, such as that Washington is the capital of the USA, and that the Moon is not made of green cheese! No one seems to want to recognise that this is a considerable body of unquestioned truths.)
Nihilism is a self-justifying stance, because anyone who thinks there are bottomless pits of incomprehension—and has given-up searching—is extremely unlikely to find enlightenment at the bottom of any of these pits. So this attitude is quite stoic. Those who embrace it are consciously choosing to live a life devoid of hope about this kind of progress. (They may, of course, display hopefulness about whether their football team will win its games, or about their chance of success on the tables of Las Vegas!)
Mathematical science requires axioms, and these come along with the side-effect that one treats these axioms as “given,” not as targets for further elucidation. This strongly suggests that mathematics is NOT the ideal language for bringing-out the secrets of physical reality: it can only go so far. It will, inevitably, come up against the need to accept (and use) taken-for-granted axioms.
Let’s say it as it is. The world we experience is predominantly a scene of transient events, including a few mass-transformative landslides. There is, of course, a background of relatively permanent features such as ancient oaks, roads and buildings. But they, too, are essentially transient of a longer span. Bishop Butler (1692-1752) recognised this in the 18th century, when he remarked that probability was a “guide to life.” No one really believes that an electron or proton exists for ever: they, too, must eventually come to naught. Plato’s notion that “Only the timeless is real” is absurd. It has been paralysing humankind’s natural curiosity—shamelessly, brazenly, counter-intuitively—for more than two millennia. It is not just wrong … it is infinitely wrong.
It has been a classic, frequently used, sentence in introductory logic textbooks that “All men are mortal.” So the gurus of higher math know that they are not going to live for ever, but they act as if they are. Aristotle and Shakespeare, two of the greatest synoptic thinkers in human history, saw clearly that everything around us is transient, including ourselves. So how did the highest cadre of mathematicians come to adopt the contrary mantra that only “timelessness” and “eternity” were real? (“Eternity” was treated as a “place,” whereas it was really just a way of talking about open-endedness.)
How did it happen that they stuck with this nonsense?
Well, there were various inter-connected facts:
- it had the immediate consequence that it put their “take” on what math does (= supposedly “search for abstract elegance”) at the top of the tree, (and the concept which fascinated most higher mathematicians most was “infinity”… like “eternity” not a place, but a way of talking),
- it gave school math the most authoritative status—thus ensuring, that 99% of the children who were exposed to it, would reject it, and turn away-from its (to them) barren aims. Thereby they ended-up with mathphobia, which effectively discredited any later adverse feelings they might have incubated,
- this meant that the math establishment would become a super-elite, with no possible checks or balances—no opposition whatever, a law unto themselves—and this would ensure that the status quo in schools remained. They High Priests of Math had contrived to secure a position which no-one outside their charmed circle could challenge—a blue-chip infallibility!
- it meant that the majority of the intelligent population could only look-on in awe at the abstruse mental gymnastics of this allegedly “superior,” “out of this world,” math fraternity,
- the math status quo also reflected a common attitude among the elite mathematicians that the real world is “distasteful, messy, awkward, sloppy and painful.” They much prefer the disciplined rule-following culture of higher math, its wacky creativity, its ingenious, abstruse, reasoning, and—most of all—the amazing elegance of its configurations.
This is not a healthy state-of-affairs for higher math, or for the rest of humanity. It implies a complete absence of feed-back for the mathematicians. They have only got to make ONE crucial mistake to derail their total exercise, and lose all their credibility. (Their first misstep was treating applied sets as if they were mathematic objects. A set can only be a mathematical object if all its elements are mathematic objects. This immediately ensures that sets cannot be the most fundamental concept in math because you can’t define a single mathematical set unless you already have the concept of a “mathematic object.”)
Philosophy from a common sense point of view is open-minded about whether there are bottomless pits of incomprehension. But we are not compelled to give up. Let’s remember that all the successful pioneers of the modern world refused to give up when they met seemingly impenetrable walls. We can take seriously the supposition that some definite progress might be made. This is the main point of this essay—to argue that “some definite progress might be made.”
We shouldn’t expect too much, though, from philosophy.
Philosophy is not an armchair way of finding hitherto hidden facts about the universe. It can be an exploration of possible new ways to conceptualise “hitherto neglected, potential aspects of the universe”. In this sense, it is another hypothesis-exploring discipline, not unlike the Peircean view of mathematics. Rene Descartes was both an explorer of mathematic hypotheses and of philosophical hypotheses: so he is the best example to follow. He used to be widely called “The Father of Modern Philosophy” and he certainly was the “Father of Newtonian Philosophy,” because Isaac Newton could not have achieved his brilliant results, without the help provided by Descartes’ great prior discovery of coordinate geometry.
Descartes was the first major philosopher since Socrates consciously to use grand thought experiments driven by rigorous imagination. His famous Cogito was a thought experiment which explored the possibility that we might be systematically trapped by a malevolent Demon determined to mislead us. Descartes also floated the clever idea that gravity might be the result of vortices interacting in an aether-like, invisible, astronomic substratum. This turned out to be a red herring, but it was a red herring which needed to be studied and rejected—much as the malevolent Demon was rebuffed. The Demon could not, in the end, prevent us from recognising that we, at least, had the inherent mental power to think and doubt.
Jean-Paul Sartre (1905-1980) was a philosopher, badly demoralised by the collapse of France in WW2, who was probably the last major figure to be quite sure that Descartes had put his finger on the kind of thinking which was needed in philosophy. Most of his contemporaries, however, seized on Descartes’ ill-fated notion that Mind was a kind of “substance” somehow distinct from the substance of “Matter.” (This was arguably Descartes’ big mistake, when he absentmindedly accepted the ossified scholastic mindset which he had previously thoroughly debunked.) Few realistic 20th century philosophers wanted to resort to the long-buried idea of scholastic metaphysics fielding various absolutely autonomous “substances.” Still fewer wanted to recognise a fundamentally “dualistic” universe. But Alfred Whitehead did concede in 1929 that:
“Descartes is obviously right in some sense or other, when he says that we have bodies and that we have minds, and that they can be studied in some disconnection … But if you turn …[this philosophy] into a final cosmology … errors will creep in.”
Also we should remember that the Michelson-Morley experiment shows spectacularly that there is some mysterious connection between physical reality and the human mind. Some of the original Quantum Physicists, e.g. Niels Bohr (1885-1962), tried to build this thought into their concepts, but after WW2 they seem to have been shouted down by a simplistic orthodoxy which shamefully refuses to accept that the physical universe is not as absolutely detached from the world of the human mind as they have been blindly assuming since the 1940s.
The Wittgensteinian account of meaning goes a long way to defusing the relationship between mind and body. Some typical talk about “the mind” can be construed as talk about the advanced dispositions which people have acquired, especially those which field unobvious high-level perceptions about aspects of reality. This is what we are saying when we remark that a promising young person “Has a good mind.” Gilbert Ryle made a bold attempt to treat “the mind” as a (non-existent) “ghost in the machine,” but this brings along a considerable amount of implied anti-intellectualism. And there is little in Ryle’s subsequent writings on mind, to indicate that he was aware that trying to understand human consciousness is probably the greatest enigma we will ever encounter.
Emmanuel Kant (1724-1804) made a huge step forward when he “awoke from his Humean slumbers” and realised that the laws of physics must represent truths which underpin our own existence (i.e. the structures creating our consciousness as sentient beings). This was evidently—in some way—the source of the laws’ “feel” of necessity. Hume had suggested that the laws of physics had a seemingly constant presence, but that this was all we could assume. According to Hume, it was our mental laziness which led us to project a sense of necessity onto them. Hume, though, didn’t propound any alternative explanation for these seemingly constant conjunctions. The telling analogy, on which Kant probably relied, was that if we wore rosy-tinted spectacles, everything we looked-at would look rosy-tinted. The laws of physics included things like the rotation of the Earth and its elliptical orbit round the Sun. These were far beyond the state where they could ever be reversed by human intervention. To treat them as “absolutely necessary” was not irrational: on the contrary, it was strongly supported by feelings invoked by the massive size of the Earth and Sun. When thinking about these phenomena we bring an awareness of the gut inevitability of these cyclical changes, and any involvement of mental laziness as suggested by Hume is spectacularly absent.
(Hume (1711-1776) was, of course, drawing our attention to the known gaps in Newton’s theory of gravity, e.g. its reliance on unexplained “action at a distance.”)
For more than a century-and-a-half there was very little awareness of the kind of mechanisms which could possibly underpin human consciousness. But eventually the electronic computer emerged, and, surprise, surprise, the outlines of (bits of) possible mechanisms began to appear. A group of followers of Dr Pavlov, who called themselves “Behaviourists,” jumped-in where angels refused to tread and swallowed the simplistic idea that the human brain was a kind of bio-computer. Initially they claimed that there was no such thing as “the human mind” —a person, they thought, just “reacted” to what someone else had said, like a ball being rebounded by a tennis racquet.
One of the worst gaffes of modern governance subsequently arose when these simplistic “Behaviourists” were chosen by the mandarins of Mrs Thatcher’s government to apply their “expertise” to managing the UK school system. They were being trusted to energise, grow and empower the minds of millions of children—and hence their life prospects—even though these “Behaviourists” didn’t believe that “human minds” existed!
Later the Behaviourists conceded that “consciousness” was the neural activity in some presently unknown “register” (sic) in the individual’s brain. They were sure this neural activity was deterministic, so they designed their curricula to train these supposedly deterministic bio-computer brains. This “training” consisted mainly of encouraging them to memorise words, facts and processes.
They seemed to be unaware that memorising stuff you don’t really understand is a recipe for bewilderment.
Any mention of the trusted concepts of education in classrooms, i.e., the humanities, culture, history, creativity, morality, legality, civic service, the commongood, etc. was anathema. They made no attempt to tell the public that this was their goal. (If they had admitted that they were rejecting everything educative, there would have been a public outcry about their vandalism.)
So the upshot was—that this was a tacit return to crude Victorian notions of “education.”
Typically, a minority of able students, having gamed the tests and exams—using their reluctantly memorised know-how—rapidly forgot the minimally understood “stuff” they had previously memorised. So this was definitely NOT “education” in the historic meaning of the word. Genuine education energises the mind, enhances curiosity, delivers knowledge of a kind which sticks, and creates a hunger for satisfying explanations. It lasts for a lifetime.
A large section of the less able student cohort, though, tended to switch-off, and make little effort to memorise the official “stuff” which sounded (to them) alien and oppressive.
Today, after this caricature of an “educational” system has been in place in the UK for more than forty years—accompanied by a chorus of bitter criticism from parents, employers and university tutors. This misguided switch from education to grad grind-like sub-standard “training”, is still the status quo. It has resulted in an electorate which has little of the confidence, self-discipline, scepticism, critical thinking or civilised priorities, on which previous generations thrived. This outcome has even thrown doubt over the efficacy of democracy itself, because the masses who have been fobbed-off with sub-standard “education,” are hardly likely to perceive the best, rational, sensible political way ahead; surrounded, as it is, by today’s heavy problematique.
AI has now dramatically surfaced in this dismal world. It has cashed-in on a lack of simple understandings which have become common. It is also making startlingly ambitious claims, hyping what it thinks it is going to be able to do in the future.
The leading AI protagonists appear to imply that their AI-driven software will, eventually, accurately mimic human consciousness. But there is no basis for this conclusion. The Large Language Models (LLMs) which arise from using neural networks are the source of AI. They are essentially deterministic, even though the Barons of Silicon Valley don’t—it appears—quite understand how they work. But we know that the behaviour of these neural networks is deterministic, because the search-patterns which emerge from the neural networks are determined—either by algorithms, or by pseudo-random (complicatedly math-generated) numbers.
We also know, personally, that the human mind is sovereign, because we know that we can always freely choose to reject any conceivable supposedly “compelling, deterministic” line of action, however painful. Michel Foucault (1926-1984) bravely threw himself in front of a car in Paris to prove—to himself—that he had freewill.
And because we have this remarkable freewill, we know that human consciousness has the power to affect physical reality. Dr Johnson showed this when he kicked a stone. This is miles away from the capability of an AI-driven bot. The bot may sound “humanlike,” but it is in the end a deterministic gadget, which either slavishly copies a mass of previously unnoticed human angles and sayings (on which the LLM was trained), or quietly follows pre-programmed goals.
It follows that a large proportion of the future is not-yet-determined, i.e, “up for grabs.” AI can’t “perceive” this large part of the future because it isn’t “there.” As a consequence it (AI) is snookered, because, when it comes to the crunch, it lacks the supposed guidelines which it naively assumed were “there.” And—even more fundamentally—it lacks freewill. When it is flummoxed, it resorts to guessing and inventing “facts”! Some current AI-driven software actually comes with the initial warning that the AI “may make mistakes.”
But although this AI craze is fraught with half-truths and illusions, we are now getting quite close to understanding some of the initial outlines of our (imperfect) human consciousness.
Anti-math, too, has begun to surface, and it makes all the difference. It presents us with just the relevant modelling language we need. Human beings, we know, are mortal, and this essential transience tell us compellingly that Anti-math must be the style of abstract modelling needed if we are ever going to understand consciousness. (The notion that ordinary math could do this—a simplistic dream which has been swallowed by Silicon Valley—is risible, because math is essentially a rigid, timeless, paralysed language.)
Once anti-math is fully established, it will, no doubt, become the spearhead of scientific theorising, i.e. “science Mark 2.” Science Mark 2 will be the quest for fully secure, reliable anti-math models of scientific phenomena.
So it is reasonable to expect that an exceedingly complex sophisticated Anti-math (ECSAM) structure will eventually emerge and present us with an accurate model of the human brain. We have hardly begun to understand how the human brain works, but we do know that it won’t be a structure paralysed by its own timelessness.
Crucially, this ECSAM structure will include a capacity to reify itself into existence, probably via (anti-math generated) DNA, supplemented by exposure, after birth, to thousands of hours of intimate parental, guardian and teacher response. (The objects of anti-math, like the objects of ordinary math, are created by human will-power. This willpower makes them real: it is reification by determined mental power.) It means that the human brain—conceptualised in this way—has the magic effect of being able to choose its own behaviour. This brings a five-star Eureka Moment into town—a moment to savour, because this is the basis of our freewill. Of course it cannot do many things which would contradict the anti-axioms on which its very existence relies. It is also constrained by the daunting fact that, the anti-axioms which were needed to reify its own existence, have also reified more than seven billion others! This might make it sound like solipsism, but sheer symmetry and sustained socialisation tends to alleviate this “solipsistic” effect. (Unhappily nowadays, though, solipsistic consciousness does trap some lone immature individuals, who seem to have lost the wherewithal to relate to others.)
On reflection, it appears that the anti-axioms which underpin our existence will also have massive side-effects—ones which will simultaneously bring into existence a vast astronomic universe, and nearer to home, a vast biosphere of living organisms, plants and animals. This is not to imply that they are, in any sense, “illusions.” They are of course perfectly “real” by the standards we use when we consider our own reality.
So the best years of science lie ahead: there are going to be endless fascinating scientific-Mark 2 problems to unravel. The world—conceptualised anew as a vast edifice of stable transient objects and events—is going to take over. It will gradually come to make sense.
The new philosophy is an expression of a “super enlightenment” we can deduce from anti-math, the supposed light of math having effectively deserted us. (Peircean math can retain its light, but it has been snuffed out for more than a century by the combined pressures of aesthetic math and arrogant computing.)
Humankind now has the preliminaries to “come of age”, and to accept that it must take in hand the whole responsibility needed to keep civilisation on the road. The buck—which President Truman famously said stopped on his desk—now stops on all our desks. We don’t yet know most of the detail, but the overall implications are clear, and the implicit completion is breathtaking. It all makes sense. A multitude of ominous shadows which, it seemed, might carry unspeakable horrors, have disappeared. A promising future, which should reveal a progressively cheerful enlightenment, looms.
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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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