Maths for Renewing Reason – 69

Maths for Renewing Reason – 68
02/01/2026

We are living in an era in which respect for truth has, alas, been widely rubbished.  If we need anything to save us from chaos, dereliction and confusion, it is a renewal of respect for truth.  In the past it was regarded as self-evident that truth was the most important of the moral values… because accounts of beauty, elegance, sympathy, responsibility, bravery… etc. needed to be true, otherwise discussing them was a waste of time.

Truth, in a word, was the essential precondition for any form of virtue or moral worth.

So how did truth come to be so widely rubbished? It was because it had dawned on some perceptive observers that there were important questions about the nature of human beings and the nature of the universe which seemed to deny any possible, conceivable resolution. Many of the cleverest people in the world had come to this utterly hopeless, defeatist conclusion:  that there was a bottomless pit of incomprehension which would (and must) defeat the brainiest problem-solvers… for ever.

When did this shameful switch to defeatism —instead of optimism— happen?

It became “Official” in 1919.

1919 was the year when newspapers around the world carried an amazing scoop.  It was the discovery that light could bend.  Large headlines screamed <<Newton disproved!>>. This brought to an end the long (200 year) era in which the UK had been regarded as the leader of science.  

The new account of gravitational physics (Einstein’s Theory of Relativity) was immediately favoured and adopted as the Official Story. However it turned out to be full of contradictions… contradictions which betrayed a lack of feet-on-the-ground discipline, or if you prefer, the strong sense of realism which Newton had propounded .  If time was another kind of spatial dimension, the future was “already there”. In which case freedom, choice, creativity, progress and reform were all illusions. The future would be what was already ordained, not some product of human yearning + determination.

Many were demoralised and started lamely muttering <<There is no such thing as the truth!>>. (They actually knew perfectly well that a million commonplace truisms were true.)

They were quite wrong. The heartland of truth is mathematics, because the truths of maths can be checked twice, four times, eight times. 16 times, etc. thus reducing the element of doubt to as small a size as you like.  This is, in effect, absolute truth, because the size of doubt involved can be reduced to be less than any tiny size you care to set.

Unfortunately, the High Priests of Maths had decided around 1900 that they would welcome exotic mathematical results like the existence of transfinite sets which couldn’t be checked. They thought that their concept of transfinite sets was so splendid, so thrilling and so mysterious, that it would easily keep maths afloat without any need for checking. 

They were wrong (intoxicated)… by the immense sophistication their set-based methods had flaunted.
They had completely failed to see why the educated population admired maths: this admiration sprang from the illumination that maths could throw onto vast projects like building the pyramids and going to the Moon.

We now know that ordinary sets are not mathematic objects, because they introduce words into maths which are not mathematically defined. The most fundamental ideas of set-based maths were an illusion.  

 

NOTE You can send your comments on the reasoning promoted on this website by sending your thoughts to: per4group@gmail.com
CHRISTOPHER ORMELL around February 1st 2026. 
chrisormell@aol.com