Appendix III

G. Spencer-Brown



"The most important Western philosophical book since Wittgenstein’s Tractatus. No one else has gone down to the very roots of thinking like this."  Alan Watts

"The ancient and primary mystery which still puzzled Ludwig Wittgenstein, namely that the world we know is constructed in such as way as to be able to see itself, G. Spencer Brown resolved by a most surprising turn of perception.... His book should be in the hands of all young people."      Heinz von Foerster, Whole Earth Catalog

G. Spencer Brown's calculus of indication, "a new calculus of great power and simplicity" (Bertrand Russell).

And: "a work of genius" (L.L. Whyte).

G. Spencer-Brown, in his notes on Chapter 12 (“Re-entry into the form") points out no less than universal purport, separate realities, the great cosmic joke, our great discovery and our reasons for covering it up again.

We cannot escape the inference that what is considered real…is tokens of expression. Since tokens of expression are considered to be of some substratum, the universe itself, as we know it, may be considered to be an expression of a reality other than itself.

Let us then consider, for a moment, the world as described by the physicist. It consists of a number of fundamental particles which, if shot through their own space, appear as waves, and are thus of the same laminated structure as pearls or onions, and other wave forms called electromagnetic which it is convenient, by Occum’s razor, to consider as traveling through space with a standard velocity. All these appear bound by certain natural laws which indicate the form of their relationship.

Now the physicist himself, who describes all this, is, in his own account, himself constructed of it. He is, in short, made of a conglomeration of the very particulars he describes, no more, no less, bound together by and obeying such general laws as he himself has managed to find and to record.

 Thus we cannot escape the fact that the world we know is constructed on order (and thus in such a way as to be able) to see itself.

 This is indeed amazing.

Not so much in view of what it sees, although this may appear fantastic enough, but in respect of the fact that it can see at all.

But in order to do so, evidently it must first cut itself up into at least one state which sees, and at least one other state which is seen. In this severed and mutilated condition, whatever it sees is only partially itself. We may take it that the world undoubtedly is itself (i.e., is indistinct from itself), but, in any attempt to see itself as an object, it must, equally undoubtedly act so as to make itself distinct from, and therefore false to, itself.

 It seems hard to find an acceptable answer to the question of how or why the world conceives a desire, and discovers an ability, to see itself, and appears to suffer the process. That it does so is sometimes called the original mystery. Perhaps, in view of the form in which we presently take ourselves to exist, the mystery arises from our insistence on framing a question where there is, in reality, nothing to question. However it may appear, if such desire, ability, and sufferance be granted, the state or condition that arises as an outcome is, according to the laws here formulated, absolutely unavoidable. In this respect, at least, there is no mystery. We, as universal representatives, can record universal law far enough to say

and so on, and so on, you will eventually construct the universe, in every detail and potentiality, as you know it now; but then, again, what you will construct will not be all, for by the time you will have reached what now is, the universe will have expanded into a new order to contain what will then be.

In this sense, in respect of its own information, the universe must expand to escape the telescopes through which we, who are it, are trying to capture it, which is us. The snake eats itself, the dog chases its tail.

Thus the world, whenever it appears as a physical universe, must always seem to us, its representatives, to be playing a kind of hide-and-seek with itself. What is revealed will be concealed, but what is concealed will again be revealed. And since we ourselves represent it, this occultation will be apparent in our life in general, and in our mathematics in particular. What I try to show in the final chapter, is the fact that we really knew all along that the two axioms by which we set our course were mutually permissive and agreeable [see below]. At a certain stage in the argument, we somehow cleverly obscured this knowledge from ourselves, in order that we might then navigate ourselves through a journey of rediscovery, consisting in a series of justifications and proofs with the purpose of again rendering, to ourselves, irrefutable evidence of what we already know.

Coming across it thus again, in the light of what we do to render it acceptable, we see that our journey was, in its preconception, unnecessary, although its formal course, once we had set out upon it, was inevitable.  Finis

The “two axioms”

--- In, "mudaju" <mudaju@y...> wrote:
> Could someone please explain or elaborate with his own words the
> basic to concepts from LOF: To call and to cross?
> Thanks.

Well, I doubt if "my own words" will satisfy your inquisitiveness,
but here is my attempt at it:

[1.] "Calling", i.e. naming something, creates a boundary between what
is named and what is not named (to say the _least_).

[2.] "Crossing", i.e. canceling a boundary, means to reverse the
process of calling, arriving "where we started".

Boundaries can be crossed, or cancelled, depending on our point
of view, or interpretation of this process.
And boundaries are formed (all the time) at will.

E.g. My definitions (above) are such a boundary.
By "understanding", you cross this (artificial) boundary.

If I hold on to the boundary, created by the above definitions,
I might seem or sound "defensive".
If you rush to cross every boundary presented before you,
you might seem or sound "aggressive".

People who dwell in names, are defensive about them.
People who dismantle the names (or concepts) of others
are (regarded as) "aggressive".
In reality, nothing is named, and nothing is ever crossed.
The rest is toothpaste, for logicians' teeth. ;-) Regards, George Stathis

In its chapter 11, the calculus is extended into infinity and thus into the paradoxical. Very elegantly the paradox is shown to be self-referentiality, to deal with it into the calculus is introduced the concept of time. This results in oscillating expressions. (?)

Intention: “…to separate what are known as algebras of logic from the subject of logic, and to realign them with mathematics.”

The Form: “What we imagine to be the structure of content” which in turn is what we imagine to be contained in the form.

The Calculus: the mathematics of form. Laws of Form unites form with content. “It transcends the form of many distinctions by taking distinction itself as the form.”

Distinction = a form of closure.