The Mathematical Set

The notion of ‘Unity’ [‘One-ness’] in Mathematics is the struggle to define Sets and Classes and Groupings [Cantor, Von Neumann et al].

The inquiry into Unity taken to its limit, the notions of wholeness and consistency, required immersion into Set Theory [again, Peano pioneered its early application]. And in Set Theory they hit head-on into the Self-Loop.

The Self-Eating Expression comes alive from the shadows anytime something is used on itself, anytime we are wading, knowingly or otherwise, into the swamp of the Self-Loop.

The single tripper-upper? The notion of Self-Reference [recursion, repetition, reflection and numerous variants].


[Georg Cantor famously accused Immanuel Kant of being a ‘Mathematical Ignoramus’. This is beyond funny. It was Kant who in his Critique of Pure Reason warns the reader that he may not use his Principles of Knowing’ in analyzing ‘The Principles of Knowing’; see the Posts.

In the wonder-world of the Self-Loop, the word with the most number of posted definitions the last time I checked seems to be the word ‘Set’, as in Mathematical Set.

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