Laws of Form

By George Spencer-Brown and G. Spence Brown

Book Overview

Studies the mathematical and logical implications of a new calculus developed from a definition of Boolean algebra This description may be from another edition of this product.

• Format: Paperback
• Language: English
• ISBN: 0525475443
• ISBN13: 9780525475446
• Release Date: March 1979
• Publisher: E. P. Dutton
• Length: 141 Pages
• Weight: 0.66 lbs.
• Dimensions: 5.0" x 1.0" x 7.0"

Customer Reviews

We Take the Form of Distinction for the Form

I take the key sentences in Spencer-Brown's Laws of Form to be the first two sentences at the beginning of Chapter 1: "We take as given the idea of distinction and the idea of indication, and that one cannot make an indication without drawing a distinction. We take therefore the form of distinction for the form." This book is a carefully crafted and beautifully written account of how the act of imagining a distinction gives rise to worlds of multiplicity from a unity where no distinction is actually possible. The first mathematics that so arises is remarkably close to the boolean mathematics with which all logicians, engineers and philosphers are familiar. Once discovered it is easy to exhibit. Let stand for a typographical distinction between outside outside. Note that in imagining distinctions using linear typography, one must make extra cuts between right and left. Drawing circles in the plane is easier (and C. S. Peirce did this long before Spencer-Brown). Spencer-Brown uses a planar notation that is simple to write and less easy to type. In any case, we make a mathematics from the distinction . Think of as an "elementary particle" that can interact with itself in two ways. 1. It can interact with itself and produce itself, or it can produce two copies of itself from itself. ----- Read the dotted line in either direction. 2. It can interact with itself to cancel to nothing, or a pair of two copies of the particle can emerge from nothing. > ----- Yes that's nothing on the right hand side, but maybe you would like a symbol for nothing. Ok. Let # stand for nothing. This means that you can erase # or put it in whenever you want to, and that means anywhere. Then we have < < > > ----- # With these modes of particle interaction we have an arithmetic of distinctions. For example < < > < > > -----< < > > ----- # The patterns of this arithmetic have their own algebra, and when one makes the critical distinction between < > as an operator, and < > as a value, this algebra gives rise to the patterns of boolean algebra. There is much more, but the key point is the simplicity of this approach. This simplicity can be applied to many complex systems to locate the key patterns that make them tick. The mark < > is itself an imaginary boolean value. At the outset the mark could be any imagined distinction at all, and the reader will have to ask how those distinctions managed to appear so solid and real. Two marks in a line do not create an inside and an outside. You the reader accomplished that trick. Then again, the mark was not boolean until the context became boolean, and operators separated from operands. This separation is a departure from the beginning. Later considerations in Chapter 11 of Laws of Form about imaginary values are related to this original imaginary state. The temporal interpretation of values i such that < i > = i calls the state of distinction into question, and either returns us to the imaginary source or pr

An outstanding intro to logic without Quantifiers

This book is indeed not much more than a very elegant re-exposition of Boolean algebra and the propositional calculus.Furthermore, the essence of Brown's mathematical innovations were discovered by C S Peirce as early as 1885 (but published only after LoF was published). Nevertheless, LoF is no mean feat.It radically simplifies sentential logic, switching circuit calculations, syllogisms. I use this book to solve logic problems arising in the computer programs I write.Outside of electrical engineering, only a few mathematicians and logicians work with logic and Boolean algebra, which should be as commonly known as calculus and linear algebra.I purchased this book in 1974, and have read many times since. EMail me at econ159@it.canterbury.ac.nz if you want a copy of my academic paper explaining the value of Spencer Brown's achievement.

A cheaper edition, please, please!!

This book is indeed mainly a new (but better) notation for Boolean algebra, a review of how Boolean algebra can be used to represent formal logic, all with New Age trappings derived from Wittgenstein, R D Laing, and from dubious etymology. To top it all off, Spencer Brown's claim that his formalism would be needed to prove the Four Color Theorem and Fermat's Last Theorem has been emphatically falsified.Nevertheless, this is an astounding book. Boolean algebra is the formalism upon which all of information technology rests. Formal logic deserves a far greater place in educational practice than has been the case in recent decades. A number of Brown's more basic ideas should be incorporated into the junior high curriculum. Finally, some of Brown's advanced ideas such as the imaginary truth value, that memory precedes time, and so forth, deserve more academic attention than they have gotten to date. I emphatically believe that there is a lot here from which the professional mathematician and logician could benefit.

E=MC^2

Spencer-Brown's articulation of the Laws of Form is of the same order of magnitude as Einstein's Theory of Relativity.I have been reading and re-reading this book for more than 20 years. In full, at least 8 times. Countless "hits" to review specific ideas.Reviewers here who have panned LOF might be right in thinking that my appreciation for this work is based on what I have read into it, not what it contains intrinsically.On my first reading, I was perplexed and somewhat disappointed ("That's it?") But I felt that it deserved a second, more deliberate reading. I'm not a mathematician, but my fourth reading was assisted by conversations with a professional scholar of logic systems. And by my fourth reading I was better prepared to appreciate the subtlety and power of LOF.The concepts regarding time as a function of memory (instead of the reverse) still awe me.If I could only take three books with me (to Mars, to the future, to the past), LOF would be the *first* that I grabbed."The universe is constructed in such a manner that it can see itself." - GSB / LOF

Important

Philosophers, mathematicians, teachers, or anyone interested in logic or semiotics should acqaint themselves with this thin rigorous volume which advances a propositional form. The implications are the real reward as this singular exercise encourages investigation and invention in the representation of knowledge, a point of departure with real practical value. If you've read Bateson, Brand, and the second order cybernetics gang, this is a natural. If not, you will be intrigued into a rewarding realm of fundamental inquiry.