A Self-Eating Expression is meant to be unwound sequentially in the ‘Backward Step’. It is not to be stared at as a static logical complexity which is the way it has been treated in the professional literature. That just sinks you deeper into the swamp. [The ‘Liar’s Paradox’ is a paradox only because we don’t know if Epimenides is a liar or not. He is neither.]
So what was the flower of Peano’s seed?
Following his discovery a professor of mathematics summarizing Godel’s work solemnly intoned: ‘[Godel’s Theorem] ‘requires that the ultimate foundations of Mathematics and all its derivative truths remain a mystery’. [In other words: ‘We don’t really know what we are doing, but we are doing it anyway’.]
Less kindly, it suggests that all Mathematical Modeling cannot be differentiated in any provable way from a manufactured reality in indeterminate Self-Loop.
Mathematician’s hurry to defend their work by drawing lines around terms like ‘Axiomatic’ and ‘Formal’. They are red-herrings. Godel’s Theorem is the tip of the iceberg. The issues with self-reference go deep. Any real foundation must begin by unwinding it all the way and laying it out for view in sunlight.
Are Logico-Mathematical truths intrinsic, hard-wired into Nature? Or are they a man-made convenience, a modeled-understanding of Self and World? Get to True Nothing and find out for yourself.
The repeatedly exploding absurdities, contradictions and paradoxes in Logic and Mathematics, which among all subjects are the most carefully thought out, the most precisely expressed, will not end until the central issue of self-reference in all its forms is confronted head-on.