The dilemma we face in philosophy today is that there are all sorts of contradictions arising from juxta-positions of individually well established concepts. The need to focus strongly (convergently) onto specifics —which are necessary to sustain the necessary digital mode of information— has left us with a multitude of mis-matches between different foci of knowledge. A typical response of idealistic-would-be philosophers is that we need a revolutionary change in our worldview to harmonise these conflicts.  However the typical response of academic philosophers is to specialise: to try to find limited re-interpretations of specific, fairly innoculous, concepts which, if adopted, might relate more plainly to their juxtaposed neighbours.

This is a way of maintaining some semblance of “philosophic thinking”. But it is not moving an inch towards conceptualising the overall synthesis we so urgently need.

The urgency of this need is that formerly sacrosanct Western culture is fragmenting across the board, and civilisation will collapse eventually, unless we can bring it all together again.

The good news is that the discovery of anti-maths allows a radical, amazingly resonant, change in our overall worldview. The not-so-good-news is that very few thinkers seem to be open to this kind of reflection.  The new synthesis is clearly a development based on Kant’s brilliant insight that the laws of science are essentially artefacts created by the (unknown) way that our consciousness works. Or, in other words, that these laws are necessary, in the sense that if they were not there, we would not be here… as sentient beings. They are pre-conditions for our vivid consciousness.

Anti-maths provides the space needed to conceptualise this necessity. It offers a new unbounded abstract playground like maths, but one not paralysed by rigidity, regimentation and timelessness.

The era when it was thought that timelessness was the essence of reality has passed.

A great future for civilisation looms, but getting there will involve rethinking the introverted specialisation mindset which is causing the problem.

It is hardly surprising that we are going through a passage of history when cognitive confidence is on the floor, and the alarm arising from the sheer number of palpable contradictions is taking its toll.  There are unforced contradictions everywhere, and the notion that we could try to harmonise them all, looks exceptionally daunting… too daunting to contemplate. So most initially idealistic would-be philosophers give up in despair, while academic, “professional” philosophers stick to their limited treadmill… of finding credible scholastic re-interpretations of standard concepts.

The overall result is that today philosophy has gone flat. We are stuck in a passage of history where the human race’s capacity to understand its living context, and especially its most fruitful, secure way ahead, is risibly feeble.  And there seems to be no visible way in which the fly might be shown the way out of the flybottle.  Genuine progress was made by the leading philosophers in the 20^thcentury, chiefly via their rejection of platonism as the basics of mathematics and meaning generally.  Wittgenstein was the genius who pioneered this insight. But he ran into an abyss of self-doubt when it became clear that he had been the Jewish rich-boy who had inadvertently tipped the adolescent Hitler into a raving anti-semitic.

But there was a surge, which started with the Vienna Circle and led to Popper, Ayer, Ryle, Austin, Berlin and Lakatos. This surge forward came to an abrupt end, though, when Imre Lakatos died young in the 1970s.  There was no one left to take the positivity of this promising anti-platonic thinking, forward.

Mathematics urgently needed a new raison d’etre, as it was suddenly automated by the digital computer, and its potential capacity to organise future projects became public knowledge.  This vision of plentiful future utility was a second Economic Revolution which sat oddly with the (verging on silly) in-house concepts of higher maths. This insight effectively demoralised and de-oriented the High Priests of maths.

Unfortunately higher mathematics itself had let itself slide into a cult… which focused on discoveries “most likely to awe the educated public”.  (This awe had the self-serving effect of raising the status of the superstars of maths onto cloud nine.) A dichotomy had opened-up. Was mathematics essentially committed to being a Service Discipline which would help the human race, or was it an Alladin’s Cave of stranger and stranger conceptual surprises which would Startle, Wow and Bemuse the adoring lay leaders of civic society?

Most of the High Priests of Maths were individuals who hated the nitty-gritty, sloppiness and mess of ordinary living. They much preferred the elegance and rule-governed routines of maths. For them the arrival of computers was a shock to the nth degree. The tradition they followed —of looking for the most astonishing new, unexpected maths concepts— had started around 1830. (It was arguably the repost of the intellectual circes of Germany and France to Newton’s amazing discoveries.)

It started with “imaginary numbers” and aimed itself at the most unexpected ideas…  until it was plainly veering towards fantasyland.  Its leaders evidently  became intoxicated by their own discoveries: items like the notion that sets were the fundamental mathematic objects, that totalities existed which were larger than infinity, that dimensions could be 1.5.  (A ‘dimension’ is a degree of freedom. It is hardly possible to have fractions of this.)  The High Priests were probably unaware that they had been living dangerously for many years. But in the 20^thcentury they raised their drive for new “awesome truths” to new levels which were, by now, visibly over the top.

The name of the game was to shock and non-plus their brightest contemporary lay acquaintances… via peddling further and further way-out follies.  An unwise triumphalism grew up around this cult of going-for “quasi-impossible” awesome truths. It appeared at first that they could “get away with it”…quite easily —because their authority was beyond dispute.  No lay person was ever likely to say “Boo!” to them.

But with the arrival of the computer the mathematic establishment became alarmed, and it blew its own credibility when it tried to impose “New Maths” based on lionising sets —onto every school on Earth. This crashed disastrously, and muddled a generation, and left much of the formerly accumulated educational wisdom of the ages in tatters.  But the High Priests hushed it up, stuck to their self-serving role as awesome-truth-peddlers, bided their time, kept a low profile, and tried to carry-on as usual.

They reckoned that, if they kept quiet for long enough, the leaders of lay opinion would show their short memories and forget that the fiasco of “New Maths for Schools” had been a blunder to the nth degree.

They were right. The leaders of lay opinion did forget this crucial fact.

So the question “However did philosophy manage to find itself in this rut of despair?” has a simple answer: it has failed to reject awesome-truth-peddling as the raison d’etre of maths.

Maths had been the backbone of Western Culture for two thousand years. But its own High Priests had comprehensively failed to understand why it continued to enjoy the special favour of the civic establishment. They thought their work was highly favoured because it dug-out bizarre truths… ones which seemed to contradict commonsense.  It never occurred to them that for centuries many of the admiring leaders of the lay population were thugs, and that they wanted the best maths to plan their campaigns and civic projects.

We have to go back to Rene Descartes to find a philosopher who roundly  recognised that the uncomfortable doubts which lead to philosophy are mostly rooted in inherent conceptual shortfalls in mathematics.

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CHRISTOPHER ORMELL around 1^st December 2025.  chrisormell@aol.com