Editing Laws of Form (section)

==Reception==
Ostensibly a work of formal mathematics and philosophy, ''LoF'' became something of a [[cult classic]]: it was praised by [[Heinz von Foerster]] when he reviewed it for the ''[[Whole Earth Catalog]]''.<ref name="Computing a Realit">{{cite journal |last1=Müller |first1=Albert |title=Computing a Reality Heinz von Foerster's Lecture at the A.U.M Conference in 1973 |journal=Constructivist Foundations |date=2008 |volume=4 |issue=1 |pages=62–69 |url=https://constructivist.info/articles/4/1/062.foerster.pdf}}</ref> 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 primary algebra reveals striking connections among [[logic]], [[Boolean algebra (logic)|Boolean algebra]], and arithmetic, and the [[philosophy of language]] and [[Philosophy of mind|mind]].

[[Stafford Beer]] wrote in a review for ''[[Nature (journal)|Nature]]'', "When one thinks of all that Russell went through sixty years ago, to write the ''[[Principia Mathematica|Principia]]'', and all we his readers underwent in wrestling with those three vast volumes, it is almost sad".<ref>{{Cite journal |last=Beer |first=Stafford |date=1969 |title=Maths Created |journal=Nature |volume=223 |issue=5213 |pages=1392–1393 |doi=10.1038/2231392b0|bibcode=1969Natur.223.1392B |s2cid=5223774 }}</ref>

Banaschewski (1977)<ref>{{cite journal | url=https://projecteuclid.org/download/pdf_1/euclid.ndjfl/1093888028 | author=B. Banaschewski | title=On G. Spencer Brown's Laws of Form | journal=Notre Dame Journal of Formal Logic | volume=18 | number=3 | pages=507–509 | date=Jul 1977 | doi=10.1305/ndjfl/1093888028 | doi-access=free }}</ref> argues that the primary algebra is nothing but new notation for Boolean algebra. Indeed, the [[two-element Boolean algebra]] '''2''' can be seen as the intended interpretation of the primary algebra. Yet the notation of the primary algebra:
* Fully exploits the [[Duality (mathematics)|duality]] characterizing not just [[Boolean algebra (structure)|Boolean algebra]]s but all [[Lattice (order)|lattice]]s;
*Highlights how syntactically distinct statements in logic and '''2''' can have identical [[Semantics of logic|semantics]];
* Dramatically simplifies Boolean algebra calculations, and proofs in [[sentential logic|sentential]] and [[syllogism|syllogistic]] [[logic]].
Moreover, the syntax of the primary algebra can be extended to formal systems other than '''2''' and sentential logic, resulting in boundary mathematics (see {{section link||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 primary algebra. Spencer-Brown eventually circulated a purported proof of the four color theorem, but it was met with skepticism.<ref>For a sympathetic evaluation, see {{harvp|Kauffman|2001}}.</ref>