Laws of Form - Reception

Reception

Ostensibly a work of formal mathematics and philosophy, LoF became something of a cult classic, praised in the Whole Earth Catalog. Those who agree point to LoF as embodying an enigmatic "mathematics of consciousness," its algebraic symbolism capturing an (perhaps even the) implicit root of cognition: the ability to distinguish. LoF argues that the pa (primary algebra) reveals striking connections among logic, Boolean algebra, and arithmetic, and the philosophy of language and mind.

Banaschewski (1977) argues that the pa is nothing but new notation for Boolean algebra. Indeed, the two-element Boolean algebra 2 can be seen as the intended interpretation of the pa. Yet the notation of the pa:

• Fully exploits the duality characterizing not just Boolean algebras but all lattices;
• Highlights how syntactically distinct statements in logic and 2 can have identical semantics;
• Dramatically simplifies Boolean algebra calculations, and proofs in sentential and syllogistic logic.

Moreover, the syntax of the pa can be extended to formal systems other than 2 and sentential logic, resulting in boundary mathematics (see Related Work below).

LoF has influenced, among others, Heinz von Foerster, Louis Kauffman, Niklas Luhmann, Humberto Maturana, Francisco Varela and William Bricken. Some of these authors have modified the primary algebra in a variety of interesting ways.

LoF claimed that certain well-known mathematical conjectures of very long standing, such as the Four Color Theorem, Fermat's Last Theorem, and the Goldbach conjecture, are provable using extensions of the pa. Spencer-Brown eventually circulated a purported proof of the Four Color Theorem, but it met with skepticism. (The Four Color Theorem and Fermat's Last Theorem were proved in 1976 and 1995, respectively, using methods owing nothing to LoF.)