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Concept
Laws of Form
Summary
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 Meguire's (2011) term for the union of the primary algebra and the primary arithmetic. Laws of Form sometimes loosely refers to the "primary algebra" as well as to LoF.
The preface states that the work was first explored in 1959, and Spencer Brown cites Bertrand Russell as being supportive of his endeavour. He also thanks J. C. P. Miller of University College London for helping with the proof reading and offering other guidance. In 1963 Spencer Brown was invited by Harry Frost, staff lecturer in the physical sciences at the department of Extra-Mural Studies of the University of London to deliver a course on the mathematics of logic.
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 second series of editions appeared in 1972 with the "Preface to the First American Edition" which emphasised the use of self-referential paradoxes. the most recent being a 1997 German translation, and has never gone out of print.
LoFs 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.
Official source
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