Laws of Triple Form
© Nathaniel Hellerstein, 2018
Laws of Triple Form
Synopsis 3
Introduction
5
Chapter 1: Brownian Forms 6
Chapter 2: The Third Form 14
Chapter 3: Kleenean Logic 18
Chapter 4: Inner Order 21
Chapter 5: Completeness Theorems 25
Chapter 6: Three Marks 29
Chapter 7: Pivot 33
Chapter 8: Orderings 35
Chapter 9: Trinary Logics 37
Chapter 10: Self-Reference 42
Chapter 11: Voter’s Paradox 45
Synopsis
This book is a reply to George
Spencer-Brown’s “Laws of Form”. It extends his form calculus to 3 values; and
it covers the triple-form calculus’s laws, tables, axioms, theorems, normal
forms, deductive completeness and self-reference. Then it introduces two more
forms of distinction; these generate three logics on the three logics, with new
laws, and with paradoxes that summarize deduction.
Chapter 1: Brownian Forms
Form arithmetic
Form algebra
Isomorphic twice to Boolean logic
Normal forms
Complete deduction
Incomplete re-entrance
Chapter 2: The Third Form
The Liar
Ternary forms and algebra
Chapter 3: Kleenean Logic
Isomorphic to Kleenean logic
Differentials
Bochvarian operators
Chapter 4: Inner Order
Majority
Min
Inner order
Chapter 5: Completeness Theorems
Anchored normal forms
Deductive completeness
Self-reference
Chapter 6: Three Marks
Three marks
Trinary algebra
Chapter 7: Pivot
Pivot definition and laws
Chapter 8: Orderings
6 orders on the three forms
Chapter 9: Trinary Logics
Majorities
Octohedral distribution
The Hexagram
Chapter 10: Self-Reference
Kleenean and Bochvarian logics in the
Hexagram
Complete Self-Reference in the
Hexagram
Incomplete Self-Reference in the
Hexagram
Chapter 11: Voter’s Paradox
Voter’s Paradox
Trilemma deduction
Syllogisms by Trilemma
Introduction
This book is a reply to George
Spencer-Brown’s “Laws of Form”. His book describes a system with two values and
two permutations. It is a bracket-based version of two-valued Boolean logic.
This book describes a bracket-based system with three values and six
permutations; a version of three-valued Kleenean logic.
This book has many “exercises for the student”, so as not to deny
the ambitious student the pleasure of re-discovery of these calculations. It’s
also because this book is a work in progress. I might include answers to some
of these exercises in later editions of this book.
Like
“Laws of Form”, this book ends with a break in its order. “Laws of Form” ends
by evoking the Liar Paradox, which subverts the Boolean deductive scheme
previously described. But it also presents the Brownian modulator, whose
workings are explained by paradox logic.
This
book ends by evoking the Voter’s Paradox, which destabilizes the fixedpoints
previously constructed. But it also presents the Some-All-None Trilemma, which
generates all of syllogistic logic.
No comments:
Post a Comment