‘The Mathematical Discovery Of The Century’

1906-1978

The Godel Iceberg is common knowledge among the mathematically-inclined and there is a large readable literature out there on Godel, Russell’s Paradox and the rest. I’ll limit myself to the outlines.

Bertrand Russell and Alfred Whitehead wanted to produce a founding Bible that built up the rules of Mathematics from the ground-up.

So they began with Peano’s work and titled their opus Principia Mathematica. [1910; Latin titles are always dangerous, vide Wittgenstein and his Tractatus Logico Philosophicus.]

The celebrated 3-volume opus was among other much grander ambitions, an attempt to resolve the conflicts between the observing Subject and his inclusion or exclusion in a Set.

The issue never found a resolution [Russell and Whitehead had to use a variety of sequenced exceptions to hold the logic together]. Until Kurt Godel came along.


In 1952, Harvard University honored the Logician Kurt Godel with an award that read: [For] ‘The discovery of the most significant mathematical truth of the century.’

The award was for Kurt Godel’s seminal paper: ‘On formally undecidable propositions of Principia Mathematica and related systems.’

Godel proved that the consistency of any Formal System cannot be proven using the methods of that System without simultaneously violating the basis of consistency of that System itself [There were other issues such as ‘Completeness’. But this will do for now.]

A Theorem which itself drew upon the work of Jules Richard and others and went forward in seminal revelations that have hugely influenced modern computer, information and cognition theories.

Can you sniff the Self-Loop? 

In a footnote to his paper Godel notes: ‘Any Epistemological Antinomy, such as the ‘Liar’s Paradox’ could be used for a similar proof’. Godel’s resolution relies on the form of a famously curious shout by Epimenides the Cretan who declared: ‘All Cretans are liars!’

‘All Cretans are liars’ is close. It would be closer if, unless you happen to be a Cretan yourself, it read: ‘All men and women are liars’, for then it would include you, the observer, in any interpretation of this claim. Better still: ‘All Words Lie!’ A full-blooded Self-Eating Expression.


The seeming absurdity of the declaration ‘All Words Lie!-itself in words, is intimately related to the assumption of an ‘Independent and Separate Subject’ and from it to the ‘Subject-Object Divide’. The way, the only way to get to its root is to begin at the first presumption of Inquiry, work through the ‘Backward Step’ and wake-up to Śūnyathā.

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