Chapter 26 - Engineering

Portent

To iterate. To change. To violate idempotency. If something is true, should it not stay true?

One way to make sense of self-reference is to treat it as an iterator. Under this interpretation, the Liar’s paradox is simply a short cycle iterator: T, F, T, F, T… Iterators can be studied; mathematically, logically, symbolically, graphically. The scaling law for Boolean iterators is easy to derive.

Each new way of looking at iteration deepens our understanding of it, and thus in part, deepens our understanding of self-reference.

Five tools shall be investigated, each isomorphic with the others.

Primary Docs

Paradigm Discourse:
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Technical Chapter:
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Significance

Given iteration, self-reference becomes a non-problem. The number of self-referential forms (sequential circuits) exceeds the number of non-self-referential forms (combinatorial circuits) by a super-exponential amount. Conventional logic has thus cut itself off from the vast majority of possible logical forms.

These forms are going to challenge conventional notions of equality and transitivity, but they do suggest that the question of completeness can now be answered in the affirmative.

They are also going to demand that we revist the concept of proof, how we demonstrate with confidence the evaluation of a self-referential form, but they take the sting out of the Gödelian discoveries.