An Esoteric Guide to Spencer Brown’s Laws of Form #6
(New readers will want to start with the first installment.)
We ended the last installment by discussing the esoteric nature of the injunction. We continue this exploration, and bring this series to a close.
LoF p. 81
- In the command “let the crossing be to the state indicated by the token” we at once make the token doubly meaningful, first as an instruction to cross, secondly as an indicator (and thus a name) of where the crossing has taken us. It was an open question, before obeying this command, whether the token would carry an indication at all. But the command determines without ambiguity the state to which the crossing is made and thus, without ambiguity, the indication which the token will henceforth carry.
This re-affirms that the mark has both a first and second-order character: it names the state of its content (its indication), and it is an instruction (its injunction) to mark that name, to make that distinction which yields that state. Thus every mark is both an indication and an injunction. It is an indication of a content and an injunction on how to get there.
LoF p. 82
- We may consider how far, in ordinary life, we must observe the spirit rather than the letter of an injunction, and must develop the habitual capacity to interpret any injunction we receive by screening it against other indications of what we ought to do. In mathematics we have to unlearn this habit in favour of accepting an injunction literally and at once. This is why an author of mathematics must take such great pains to make his injunctions mutually permissive. Otherwise these pains, which rightly rest with the author, will fall with sickening import upon the reader, who, by virtue of his relationship with respect to the author, may be in no position to accept them.)
All this actually relates to the task of the esoteric teacher, who recognizes that the way in which injunctions are presented (their context) has a quite prominent role to play in affecting the ability of the pupil to take them up. Thus a key aspect of esoteric teaching necessarily involves extensive caveats, personalizations, modifiers, generalizers, and specifiers. It is relational through and through.
In discussing the nature of the primal injunction, “draw a distinction”, GSB notes that
LoF p. 84
- We have here reached a place so primitive that active and passive, as well as a number of other more peripheral opposites, have long since condensed together, and almost any form of words will suggest more categories than there really are.
All this indicates the primal nature of the WILL, its irreducible ontology. All that “is” flows from WILL. But we have seen also that this will is not alone: it is accompanied, in a complex unity, with both a thinking and a feeling, taken in their most primordial sense.
LoF p. 84-85
- We may ask why we do not justify such a convention at once when it is given. The answer, in most cases, is that the justification (although valid) would be meaningless until we had first become acquainted with the use of the principle which requires justifying. In other words, before we can reasonably justify a deep lying principle, we first need to be familiar with how it works.
Again, we have a parallel in esoteric communication. It is not necessary to know why an injunction is made; the point is to follow it. Once followed, it becomes possible to see why it was made, but that explanation is literally occult before the injunction is followed. This is precisely what makes so many esoteric texts seemingly obtuse or even outright non-sensicle. It is also a built-in safeguard: if you don’t think the injunction makes sense, you won’t follow it through, and you won’t gain entry into what is made available by following the injunction. This is to say, you won’t build the transformative capacity required to recognize the need for the injunction in the first place. This is a fascinating element of the spiritual world: it is constantly making itself available to us, but we have to do the work to come to know it. In other words, those people who work esoterically are always self-selected: they elect to pass the initial boundary of unknowing, knowing that the seeking itself will yield everything that is needed: one does not have to start with the answers.
Now, GSB finally makes an explicit revelation:
LoF p. 85
- In all mathematics it becomes apparent, at some stage, that we have for some time been following a rule without being consciously aware of the fact. This might be described as the use of a covert convention. A recognizable aspect of the advancement of mathematics consists in the advancement of the consciousness of what we are doing, whereby the covert becomes overt. Mathematics is in this respect psychedelic.
This is, obviously, an explicit reference to the essence of spiritual/esoteric development, the expansion/extension/transformation of consciousness. It is an elaboration of the principle we came across earlier, by which we can start anywhere and proceed “upwards” or “backwards” to higher or more previous levels. But what makes it “psychedelic” in GSB’s phrasing, is that this very progression is one through which consciousness becomes more capable, more resilient, more able to, as it were, traverse up and down the rungs of Jacob’s Ladder.
LoF p. 86
- In general there is an order of precedence amongst theorems, so that theorems which can be proved more easily with the help of other theorems are placed so as to be proved after such other theorems. This order is not rigid. For example, having proved theorem 3, we use what we found in the proof to prove theorem 4. But theorems 3 and 4 are symmetrical, their order depending only on whether we wish to proceed from simplicity to complexity or from complexity to simplicity.
This reveals an important esoteric point: there is no single path of development. Paths of development share injunctions — but the order in which they are carried out CAN be somewhat arbitrary. Generally there are definite limits to the level of arbitrariness in order, beyond which the higher-order rule of timing changes the outcome drastically. In Laws of Form, note that GSB indicates a switch of theorems 3 and 4, but not, say of 3 and 16. This is WHY there are such things as “canons”, or definite repeated types of groups of injunctions, because within those groups elements are somewhat interchangeable, but are not interchangeable between groups without potentially serious consequence (one could even have justification in calling some of these potential consequences “evil”).
LoF p. 90-91
- One of the most beautiful facts emerging from mathematical studies is this very potent relationship between the mathematical process and ordinary language. There seems to be no mathematical idea of any importance or profundity that is not mirrored, with an almost uncanny accuracy, in the common use of words, and this appears especially true when we consider words in their original, and sometimes long forgotten, senses.
This relation, of course, is no surprise to an esotericist. The profound, even magical link between speech and reality is well known in every esoteric tradition that I am aware of, even going back to the most primal spirituality of all that is still active today, the shamans of the Bushmen. Many, many books have been written on this connection. The most recent advance in this realm has been taken by Rudolf Steiner and the artistic and therapeutic speech work based on his indications.
LoF p. 92
- Much that is unnecessary and obstructive in mathematics today appears to be vestigial of this limitation of the spoken word. For example, in ordinary speech, to avoid direct reference to a plurality of dimensions, we have to fix the scope of constants such as ‘and’ and ‘or’, and this we can most conveniently do at the level of the first plural number. But to carry the fixation over into the written form is to fail to realize the freedom offered by an added dimension. This in turn can lead us to suppose that the binary scope of operators assumed for the convenience of representing them in one dimension is something of relevance to the actual form of their operation, which, in the case of simple operators even at the verbal level, it is not.
I mention this quote because it points to the need to get beyond the induction/deduction polarity in the construction of knowledge. We need to include abduction, which is implicitly multidimensional, as a valid third form of reasoning. This form of reasoning, mentioned earlier, is precisely what Steiner elucidated in a much more in-depth and direct fashion in his distinction of the Imaginative, Inspirative, and Intuitive faculties. These all build upon the esoteric seed that C.S. Peirce was waking up to in his recognition of abduction.
LoF p. 93
- The validity of a proof thus rests not in our common motivation by a set of instructions, but in our common experience of a state of affairs. This experience usually includes the ability to reason which has been formalized in logic, but is not confined to it.
This is where the question of the logic of logic is raised, and to which the idea of an aesthetic epistemology (my PhD dissertation work) is addressed. The “common experience of a state of affairs” can be taken to refer to what Steiner called the “given” and what Eugene Gendlin calls a “preconceptual multiplicity” or “precognitive unity” of experience itself. GSB continues:
LoF p. 93
- It seems open to qu estion why we regard the proof of a theorem as amounting to the same degree of certainty as the demonstration of a consequence. It is not a question which, at first sight, admits of an easy answer. If an answer is possible, it would seem to lie in the concept of experience.
GSB is leading himself here to the edge of what Steiner began with in his epistemological work The Philosophy of Freedom. It also points to the modern work of Gendlin on the nature of experience. The point is that what GSB is driving at leads to one of these moments where we have to go “up” or “back” to a higher order: we have to cross. This crossing comes about by paying attention to the difference between the content of our thoughts and the way that those thoughts arise. This means that GSB is right, we need to pay more attention to experience, because it is here that we will find the place from which logic itself arises, and which becomes the recursive beginning of epistemology (and proof). We have already noted important features of this very process. GSB notes, using language that is not meant to be esoteric, but, which, if we have read Steiner, is quite apt from an esoteric standpoint:
LoF p. 94
- But since the procedures of the proof are not, themselves, yet codified in a calculus (although they may eventually become s o), our certainty at this stage must be deemed to be intuitive.
Quite so, but intuitive in a way not likely meant by GSB. In the Esalen conference, GSB is very specific about the nature of proof and how it differs from demonstration, as we saw back near the beginning. Now we can recognize something more about why there is such a difference: it has to do with the human being’s ability to transform consciousness, to move up and down the cosmic ladder to higher and lower orders. Computers only work laterally.
LoF p. 95
- In discovering a proof, we must do something more subtle than search. We must come to see the relevance, in respect of whatever statement it is we wish to justify, of some fact in full view, and of which, therefore, we are already constantly aware. Whereas we may know how to undertake a search for something we can not see, the subtlety of the technique of trying to ‘find’ something which we already can see may more easily escape our efforts.
The esoteric path relies upon that which is there for us already; what it does is to make what we already see transform through the revelation of a higher context IN it. We then see more than we see, and this is the esoteric analogy for mathematical “proof”. GSB continues:
LoF p. 95
- This might be a helpful moment to introduce a distinction between following a course of argument and understanding it. I take understanding to be the experience of what is understood in a wider context. In t his sense, we do not fully understand a theorem until we are able to contain it in a more general theorem. We can nevertheless follow its proof, in the sense of coming to see its evidence, without understanding it in the wider sense in which it may rest.
In other words, the esoteric path of development OCCURS from the ‘bottom up’ (or the inside out) but is LED from the top down (or the outside in). Wider and wider contexts are revealed for what was previously already known, changing what is known in the transformation of the knower to the state in which that higher context becomes revealed.
LoF p. 96
- Following may thus be associated particularly with doctrine, and doctrine demands an adherence to a particular way of saying or doing something. Understanding has to do with the fact that what ever is said or done can always be said or done a different way, and yet all ways remain the same.
This is a very important esoteric point, and is the key to the dissolution of fundamentalism of any type. Steiner uses the metaphor that while there is but one mountain, there are many paths to the top. Or more explicitly helpfully, he says:
“One must postulate the following: no single matter is to be comprehended only by means of what is said about the matter itself, but by means of much else that is disclosed concerning totally different matters. This will develop the conception that what is vital is to be found not in any single truth but in the harmony of all truths. This must seriously be considered by anyone intending to carry out the exercises.” (Rudolf Steiner, How to Know Higher Worlds, preface to the third edition, my italics).
The exercises are simply those designed to awaken the esoteric capacities latent in all of us. This, coupled with the very clear recognition that “There is, in truth, no difference between esoteric knowledge and all the rest of man’s knowledge and proficiency. This esoteric knowledge is no more of a secret for the average human being than writing is a secret for those who have never learned it.” (How to Know Higher Worlds, chapter 1).
Of course, this is exactly the point that I am trying to make in exploring GSB’s Laws of Form. I am simply taking LoF as the starting point, which could have been anywhere, for esoteric continuation. This whole essay is an attempt to bring a vertical movement of knowing to the text LoF as a “thing” at level N; an attempt to move towards N+1. My hope is that by doing this here (now it is all just back at N for you, the reader) in a very explicit way, you can take up this same type of transformation.
LoF p. 110
- To any person prepared to enter with respect into the realm of his great and universal ignorance, the secrets of being will eventually unfold, and they will do so in a measure according to his freedom from natural and indoctrinated shame in his respect of their revelation.
This whole statement doesn’t need to be connected to any esoteric principle because it is one overtly. He continues, still in an esoteric vein:
LoF p. 110
- To arrive at the simplest truth, as Newton knew and practised, requires years of contemplation. Not activity. Not reasoning. Not calculating. Not busy behaviour of any kind. Not reading. Not talking. Not making an effort. Not thinking. Simply bearing in mind what it is one needs to know. And yet those with the courage to tread this path to real discovery are not only offered practically no guidance on how to do so, they are actively discouraged and have to set about it in secret, pretending meanwhile to be diligently engaged in the frantic diversions and to conform with the deadening personal opinions which are being continually thrust upon them.
If this isn’t a description of what the esoteric pupil encounters, I don’t know what is.
LoF p. 110
- In these circumstances, the discoveries that any person is able to undertake represent the places where, in the face of induced psychosis, he has, by his own faltering and unaided efforts, returned to sanity. Painfully, and even dangerously, maybe. But nonetheless returned, however furtively.
This may seem like something of a pessimistic view, and is likely informed by GSB’s personal biography, but I had to include it because of his inversion of the concept of sanity is very apropos. He concludes:
LoF p. 134
- The very act of dwelling for a while with even a simple form can evidently tax the whole of one’s powers, so that to leave the simple forms before one is properly familiar with them can result in many unrewarding, or largely unrewarding, mathematical excursions.
GSB leaves us with a very profound point. Esoterically, progress is not made by advancing quickly, or by taking any kind of “shortcut”, but is rather constantly built up on the basis of continually refined, basic characterological traits, such as those described by Steiner in the six basic exercises. The point is not to “have” any particular knowledge, capacity, or power, but simply to do the work. Steiner points out that, no matter what we do, the extent to which we progress is never solely determined by our work in the moment, but is contingent upon a whole range of factors that span many aspects of the spiritual world, such as karmic considerations, but that even moreso, there is always an element of grace involved. Thus, the work itself, stated another way, is merely all in preparation for the appearance of grace.