George Spencer Brown
A generation has grown up since Laws of Form was first published in English. Human awareness has changed in the meantime, and what could not be said then it can be said now. In particular, I can now refer to the falseness of current scientific doctrine, what I call scientific duplicity: that appearance and reality are somehow different.
Since there is no means, other than appearance, for studying reality, they are definitely the same.
Reversing the false distinctions, we arrive at what I call the triple identity, notably the definitional identity of reality, appearance, and awareness. It is remarkable how all the „building blocks“ of existence appear as triunions. (Compare the so-called „divine trinity“ of Christianity, which is merely a summary of our perception of how to construct the formation of any thing whatever.) It ist he triunion that apparently provides the magic inflatory principle that makes it all seem like it's really there.
The word „there“ supplies the trick. There exists and reality in no „where“ fort he „there“ to be. Nor is there any „when“. All these are constructions of imagination, inventions of apparently stable formations for the apparent appearances. Hence another expression of the triple identity: the identity of imaginability, possibility, and actuality.
A thing is not possible unless it is imaginable, and we could never confirm that it was possible unless it appeared in actuality. Thus what is possible will always be found to exist, and its actual existence (for exemple helium, carbon 60) will be discovered soon after its possibility has been imagined. What exists is formally constructed by postulating the imagination of a hypothetical being that is supposed to perceive it, and different beings will bring about the construction of different existences. (Not only physical existence, but all creation is subject to the same law.) A totally different being will construct a completely different existence: „The world of the happy is altogether different from the world of the unhappy“. Wittgenstein, Tractatus, 1922
Any indication implies duality, we cannot produce a thing without coproducing what it is not, and every duality implies triplicity: what the thing is, what it isn't, and the boundary between them. Thus you cannot indicate anything without defining two states, and you cannot define two states without creating three elements. None of these exists in reality, or separately from the others.
All I teach is the consequences of there being nothing. The perennial mistake of Western philosophers has been to suppose, with no justification whatever, that nothing cannot have any consequences. (The idea that the creation must be a consequence of „something“ is moronic. No thing can have any consequence whatever. If there were originally something, it would poison the whole creative process. Only nothing is unstable enough to give origin to endless concatenations of different appearances.) On the contrary: not only it can: it must. And one of the consequences of there being nothing is the inevitable appearance of „all this“. No problem!
Page XXIX: A Note on the Mathematical Approach
The theme of this book is that the universe comes into being when a space is severed to or taken apart. The skin of a living organism cuts off an outside from an inside. So does the circumference of a circle in a plane. By tracing the way we represent such a severance, we can begin to reconstruct, with an accuracy and coverage that appear almost uncanny, the basic forms underlying linguistic, mathematical, physical, and biological science, and can begin to see how familiar laws of our own experience follow inexorably from the original act of severance. The act is itself already remembered, even unconsciously, as our first attempt to distinguish different things in a world where, in the first place, the boundaries can be drawn any where we please. At this stage the universe cannot be distinguished from how we act upon it and the world may seem like shifting sand beneath our feet.
Although all forms, and thus all universities, are possible, and any particular form is mutable, it becomes evident that the laws relating such forms of the same in any universe. It is this sameness, the idea that we can find a reality which is independent of how the universe actually appears, that lends such fascination to the study of mathematics. That mathematics, in common with other art forms, can lead us beyond ordinary existence, and can show us something of the structure in which all creation hangs together, is no new idea but mathematical texts generally begin the story somewhere in the middle, leaving the reader to pick up the thread as best he can. Here the story is traced from the beginning.