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:

"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.

LoF emerged from work in electronic engineering its author did around 1960, and from subsequent lectures on mathematical logic he gave under the auspices of the University of London's extension program. LoF has appeared in several editions, the most recent being a 1997 German translation, and has never gone out of print.

The mathematics fills only about 55pp and is rather elementary. But LoF's mystical and declamatory prose, and its love of paradox, make it a challenging read for all. Spencer-Brown was influenced by Wittgenstein and R. D. Laing. LoF also echoes a number of themes from the writings of Charles Sanders Peirce, Bertrand Russell, and Alfred North Whitehead.

The entire book is written in an operational way, giving instructions to the reader instead of telling him what "is". In accordance with G. Spencer-Brown's interest in paradoxes, the only sentence that makes a statement that something is, is the statement, which says no such statements are used in this book. Except for this one sentence the book can be seen as an example of E-Prime.

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 primary algebra reveals striking connections among logic, Boolean algebra, and arithmetic, and the philosophy of language and mind.

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