An Esoteric Guide to Spencer Brown’s Laws of Form #6
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.