OK… So Spencer-Brown isn’t wrong, he’s just cataphatic.

The (cataphatic) Laws of Form

George Spencer-Brown did an incredible job of breaking it down to the barest of bare-bones. But he could have gone further – he just didn’t see it.

He thought the ‘Distinction’ was “perfect continence” (yes, he notes that ‘continence’ refers to the archaic meaning – to contain – contain yourselves!), because he was, and quite possibly still is, stuck in ‘CT mode‘. And it’s only in ‘CT mode’ that boundaries logically ‘contain’ Things – because you’re only looking at the Things themselves! AT mode, the apophatic perspective, one looks at the boundaries themselves – and that’s how I can’t ‘see’ it as Things ‘containing’ Things – when it comes to the boundaries, all one can say is that Things are adjacent.

A lot emerges from this divergence of perspective: Kurt Gödel’s Incompleteness Theorems hinge upon it and reveal it clearly:

  • Either your system of formal logic (capable of describing basic arithmetic) is going to be consistent (i.e. not self-contradictory) but necessarily incomplete (i.e. unprovable statements, preferably relegated to the starting axioms).
  • Or your system of ‘formal logic’ will be complete (all statements are provable) but necessarily inconsistent (will have self-contradictions).

Here, the CT mode thinker would choose the ‘consistent but incomplete’ door while the AT mode thinker would choose the ‘inconsistent but complete’ door.

And each is ‘not’ the other – they are mutually exclusive and (quite possibly) inverses of each other (easy to see when you look at the ‘in-‘ prefix used for each).

The ‘normal physics’ of Mechanics and the General Laws of Relativity used in Astrophysics fall on the ‘cataphatic’ side of things. But the ‘quantum physics’ of quantum mechanics, at the smallest scales now searching for the ‘boundaries’ themselves, fall upon the ‘apophatic’ side of things.

So which is it then? A bit of both – depending on how you look at it. I hate to say that, but both perspectives are just as real, just as true. I suspect that the cataphatic laws of form can be reached using apophatic laws of form – but only on the fact that “is” is “not not” – i.e. that cataphasis is really only ‘apophatic apophasis’ so to speak.

So Wherefore the twain shall meet? I don’t know. I know of one place they meet though: the human mind. We humans are capable of ‘mode-switching’ whenever we need to.

Another area where it seems that apophasis and cataphasis seem inextricably intertwined is Economics and the study of property. Ownership is apophatic – what’s mine is not yours, and what’s yours is not mine – but in ‘transactions’, it is invariably cataphatic in that I have to ‘take it out of something’ – i.e. the more I have the less you have (which is also apophatic come to think of it – the inverse-relationship between having more or having less) and the necessary inequality that arises from fixed resources. The zero-sum-game. “TANSTAAFL” and all that.

It dawns on my that my adjacency theory is a humble and amateurish attempt at the Apophatic Laws of Form. I’m afraid it won’t be as impressive as Spencer-Brown’s work nor as poetic as the Hindu Vedas or the Buddhist sutra the Avatamsaka Sutra

A 3D rendering of Indra's net.
All things are reflections of all others.

Though I didn’t know it at the time, the structures that I have seen emerge from adjacency theory exactly fit the Hindu and Buddhist concept of ‘pratitya samutpada’ and ‘sunyata’ and if you’ve read any Buddhist texts there is mention of a ‘jewel net’, “Indra’s Net” to be exact – where each ‘node’ is a reflection of all others – well, now you know what they really mean. Each adjacent Thing is ‘not’ all others, simultaneously. So in all honesty I can’t claim anything whatsoever about my work here – it’s all been done before by someone else. If you want an Apophatic Laws of Form before I finish writing my book (if that’ll ever happen) then I suggest you read the sutras and the Vedic texts.

That being said, I haven’t given up on my work. Why? Because I’m curious! I wanna see where the rabbit hole goes!

Well, that’s it for today; thanks for reading,

Taomath

Leave a Reply

Your email address will not be published. Required fields are marked *