This is not just a hard lesson for mathematicians or scientists to grapple with
It applies to any system based on axioms, or definitions, axiom-like propositions
Such as the law
Any system of entitlement or regulation
Any system of taxonomy or classification
Strictly, Gödel’s proof shows that you cannot prove that any system is not, at some point, self contradictory, but I choose to believe that it means there will always be self-contradiction in the system
This is why we need, at the highest level, judges who are wise & clever – to work out a way to resolve a contradiction (for now)
One corollary of Gödel’s theorem is that even if you add new rules you will only create a larger system with its own unprovable statements
This may come as a particular blow to the current generation of Labour politicians, policy wonks & journalist/inquisitors
You do not make the system watertight by adding even more rules or definitions or targets
Take the business of schools admissions
The government just paid lawyers to check through the written policies produced by several thousand schools, with the aim of removing all ‘technical’ flaws or serious breaches of the regulations designed to make things ‘fair’
And next day, Alice Miles wrote an article in The Times which points to a glaring gap in the system
But even if there are no holes, there will always be a Catch-22
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