Chapter 2 - Paradox

Portent

Self-reference has been at the heart of the major limit theorems of the last century, from Russell’s paradox in set theory, to Gödel’s incompleteness theorems in math, to the halting problem in software engineering. In any sufficiently complex system, self-reference intrudes, unwanted, unwelcome, and unexpected, violating assumptions we were absolutely certain of. It is the ultimate revealer of paradigm barriers.

A first attack was achieved last century by G. Spencer-Browns in his seminal work, The Laws of Form where he solved the logical paradox problem by introducing imaginary truthvalues. Their applicability to quantum systems is one of the theses of this work.

Primary Docs

Paradigm Discourse:
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Technical Chapter:
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Significance

Boolean and Imaginary truthvalues form cojugate bases for logic. Can that property be exploited to understand conjugate bases in quantum physics? Logic and quantum theory may share structural constraints, not just metaphors. Thus, the title of this book, The Paradigm of Paradox.