[R939.Ebook] Free PDF Laws of form (Bantam book), by G Spencer-Brown
Free PDF Laws of form (Bantam book), by G Spencer-Brown
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Laws of form (Bantam book), by G Spencer-Brown
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- Sales Rank: #3574714 in Books
- Published on: 1973
- Binding: Mass Market Paperback
- 135 pages
Most helpful customer reviews
48 of 51 people found the following review helpful.
An outstanding intro to logic without Quantifiers
By A Customer
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.
45 of 50 people found the following review helpful.
Laws of Form ( huh? )
By Thomas Howard Hoover
In a way, George Spencer-Brown's "Laws of Form" is an elaborate math puzzle. The author has given you the bare minimum of information to figure out what the heck he is talking about; your assignment ( should you choose to accept it ) is to investigate the fields of logic, symbolic logic, Boolean logic, and set theory, to attempt to reconstruct the mathematics behind the so-called Calculus of Indications presented in the book. In my own case, it took almost seven years of occasional attention to come up with the essential idea behind the math, namely the symmetry between AND-spaces and OR-spaces. It may not take you that long.
Contrary to what some other reviewers have written, Bertrand Russell did not praise this book--he seems to have been just as baffled by it as anyone else. He did praise the ideas presented in the book, but only after Spencer-Brown met with him and explained it to him.
It seems likely that the sections of the book were developed as lecture notes to be handed out in class. Presumably the professor would tell you what he was talking about, and the handouts would be supplemental reading. Unfortunately, all that we get in the book is the supplemental reading.
When you are looking for a tool, you don't want, or need, a math puzzle. This is why the notation and concepts presented in the book have never caught on with philosophers, mathematicians and engineers in spite of their clear superiority over the techniques of syllogism logic, symbolic logic, Boolean logic and set theory.
I have had a lot of fun with this book, but you shouldn't think you're going to get a lot out of it in your first reading.
...
37 of 42 people found the following review helpful.
We Take the Form of Distinction for the Form
By Louis H. Kauffman
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 < inside > 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 propels us into temporality. Chapter 11 shows how digital
circuitry has the structure of that apparently metaphysical
discussion.
And the theory of types? Well take a look at your Godel-Bernays set theory and realize that the usual resolution is to imagine sets and classes, with classes a bit more imaginary than sets.
(A set is a member of a class. A class is never a member of anything.) The usual technical solution is to introduce imaginaries in the "right" place and to tell the users what they can say and what they cannot say. Spencer-Brown is rude enough and honest enough to admit this situation right in the beginning. There is no need for the theory of types because it is a matter of creativity just how you make your distinctions, and how you want to avoid inconsistency.
How will you behave when the next new clever inconsistency in
formal mathematics is discovered? A good reader of Laws of Form will be happy and ready to explore the anomaly.
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