Laws of Form

Laws of Form (hereinafter LoF) is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. LoF describes three distinct logical systems:

• The primary arithmetic (described in Chapter 4 of LoF), whose models include Boolean arithmetic;
• The primary algebra (Chapter 6 of LoF), whose models include the two-element Boolean algebra (hereinafter abbreviated 2), Boolean logic, and the classical propositional calculus;

Equations of the second degree (Chapter 11), whose interpretations include finite automata and Alonzo Church's Restricted Recursive Arithmetic (RRA).

Boundary algebra is Dr Philip Meguire's (2011) term for the union of the primary algebra (hereinafter abbreviated pa) and the primary arithmetic. "Laws of Form" sometimes loosely refers to the pa as well as to LoF.

Recommended Reading

• Laws of Form, archive of website by Richard Shoup.
• Spencer-Brown's talks at Esalen, 1973. Self-referential forms are introduced in the section entitled "Degree of Equations and the Theory of Types."
• Louis H. Kauffman, "Box Algebra, Boundary Mathematics, Logic, and Laws of Form."
• Kissel, Matthias, "A nonsystematic but easy to understand introduction to Laws of Form."
• The Laws of Form Forum, where the primary algebra and related formalisms have been discussed since 2002.
• A meeting with G.S.B by Moshe Klein