Laws of Form: Encyclopedia II - Laws of Form - The book

Laws of Form - The book

There are several editions of LoF, the first in 1969, the most recent (a German translation) in 1997. The mathematics fills only about 55pp and is not difficult. But LoF's mystical and declamatory prose style, and its love of paradox, make it a challenging read for mathematicians and non-mathematicians alike. In this and other respects, Spencer-Brown was much influenced by Wittgenstein and R. D. Laing. At the same time, LoF also echoes a number of themes from the work of Charles Peirce, Bertrand Russell, and Alfred North Whitehead.

Ostensibly a work of formal mathematics and philosophy, LoF became something of a holistic classic, praised in the Whole Earth Catalog. Those who agree point to the Laws of Form 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 reveals striking connections among logic, Boolean algebra and arithmetic, and the philosophy of language and mind.

Some (e.g., Banaschewski in the 1977 Notre Dame Journal of Formal Logic) argue that the pa is 'merely' Boolean algebra, but the implication that Boolean algebra is mathematically trivial is unwarranted. Proponents counter that the beauty of the pa stems from its having the expressive power of 2 despite its minimalist syntax. The pa simplifies truth functional and syllogistic logic as well as 2, and highlights how syntactically distinct statements in logic and 2 can have identical semantics. [1] argues that the real mathematical value of the pa is its dramatic simplification of Boolean algebra. Moreover, the syntax of the pa can be extended, giving rise to boundary mathematics (see Related Work below).

LoF claims 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 published a claimed proof of Four Color; for a sympathetic evaluation, see [2]. Nevertheless, that claimed proof met with skepticism and Spencer-Brown's mathematical reputation, as well as that of LoF, went into decline. N.B. The Four Color Theorem and Fermat's Last Theorem were proved in 1976 and 1995, respectively, using methods owing nothing to LoF.

Adapted from the Wikipedia article "The book", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki