Taking stock

"Deconstruction insists not that truth is illusory
but that it is institutional." ~ Terry Eagleton


On its face, "parasimplicity" looks a lot like an excuse to make things that are really simple a lot more complex. But, as I hope you've picked up by now, what parasimplicity - or anything else - looks like isn't close to being what it really is. For instance - and this is just a 'for instance' - it also serves as a handy tool for making things that are really complex a lot more simple. The Law of Fives is extremely simple, and as good a shorthand for the very complex things it actually references (which this collection of blogs to date has similarly referenced but at more length, including the obligatory self-similar discussions of the Law of Fives itself). The reduction of all paradoxes to the twin paradigms of All-in-One and One-in-All is another parasimplistic operation (actually the final operation in a chain that begins with the appreciation of all statements as interactions of paradoxes, but we'll get to that).

So, how do we apply parasimplicity? How do mountains become not-mountains, and then not-rivers become rivers? If you've been paying attention, you may already know. What you know may even be what I was trying to say; equally, what you know may be more than what I know. We can't know what we don't know, but we'll get to that, too.

Let's tie in the koan to our five-layer reality cake.

Mountains are mountains and rivers are rivers - this we can consider to be referring to the objective mountains and rivers. Bear in mind that these are not mountains and rivers we can ever directly know: we form subjective impressions of the relations of properties we intuit as belonging to the objective realm, and that is as close as we can get to knowing them.

Mountains are not-mountains and rivers are not-rivers - these not-mountains and not-rivers are not, as you might be forgiven for thinking, equivalent in our model to the subjective mountain- and river-impressions. The not-mountain is the intersubjective mountain: the mountain that emerges from discourse, from interrogation of our subjective mountain-impressions. IF the objective mountain is real, and IF our impressions of it are accurate, and IF we share our impressions truthfully, and IF we don't later edit or filter our consensus to fit some concept of 'truth' - and those are all very big 'ifs' indeed, which we'll review when we turn to Baconian Idols in the near future - then the not-mountain may be apparently identical with the mountain (this is one of the cruder approaches to paradox resolution, in fact - the rejection of the paradox as presented on the grounds that the presentation is corrupted by one or more of these factors). But not-mountains are, well, not mountains..

Mountains are again mountains and rivers are again rivers - these 'again' mountains and rivers are the transcendental mountains and rivers, which we have said are immanent upon the subjective (we might, with a sly wink at Dali, say they are immanent upon the objective as well; in fact Dali's paranoiac-critical method is another rewarding subject for study). We have already said that we can't directly know the objectively real mountain - so how can we possibly hope to know the transcendental mountain beyond? We cannot cross the same river twice (so claims Heraclitus), so how can we know the transcendental river that is beyond all those once-crossed iterations?

The answer is that we need to work against our brilliant knowledge-building engines, our glorious rational Big Brains. We are hardwired to recognize patterns, and we are hardwired to filter and sort the data our brains receive to make it a coherent conscious experience (a trivial example with which you're probably familiar: optics being what it is, the visual data we receive on our retinae is inverted; our brains flip the image over during processing to restore it to its putative objective orientation). However, if we seek the transcendental, that which is equally remote from all things, that in which mountains are again mountains is equivalent to mountains are not mountains or even mountains are rivers - we won't find it after our brains are through processing the data.

Recall that objective entities are entirely separate from subjective ones. Yet our brains, in processing the data from the objective, produce impressions that are subjective and are qualitatively the same as Humean ideas that have no relation to empirical data whatsoever. What this tells us is that the process of rational cognition is capable of bridging the divide that separates objective and subjective - and what that is really telling us is that, somewhere in there, we are working in the transcendental. Each and every one of us, it turns out, is also a Gateless Gate.

The transcendental Universe is self-similar, not only with the objective, but with the myriad subjective Universe-impressions. We could, perhaps, approach some rational understanding of the transcendental if we could somehow simultaneously apperceive all of those possible subjective information-states; but the self-similarity of the Universe, embodied in the Gateless Gate of each self-aware consciousness, makes this unnecessary.

How do you pass through a Gateless Gate? Begin with a gate, and take the gate away so it becomes gateless. Then pass through. 'Get OUT,' as Crowley had it.

The asymptote of reason

“Science may set limits to knowledge, but should not
set limits to imagination” ~ Bertrand Russell

 

Another important mathematician, who produced another important and paradoxical result, was the Austrian Kurt Godel. Where Mandelbrot considered the objective realm, and applied mathematical models to understanding it, Godel’s focus was on the subjective – he was a logician, and he was investigating how we form an understanding of the world rather than what that world might objectively be like.

We could argue that Godel and Mandelbrot were considering the same substance from opposite sides – that Mandelbrot was actually modeling subjective representations and Godel in truth modeling objective realities; we tend to assume that there is a high degree of concordance between subjective representations we can all intersubjectively communicate and objective entities we can all subjectively observe. This is not necessarily the case, as Descartes found to his dismay, and that is why I draw the distinction here between the logical models of Godel and the applied mathematics of Mandelbrot.

When we talk about a logic, we are talking about a framework in which statements represent either properties or relations of entities – this is why I say a logician deals with the subjective realm, because of course the Cartesian theater is constructed out of these same substrates. A logic consists of axioms, and rules for deriving statements from these axioms, and for assigning these statements some truth value. The most commonly understood forms of logic are bivalent, taking truth values of True or False – and, commonly, what we understand to be true is really just that which we observe to be agreed upon. This is not a particularly logical way of considering truth, as it happens, and we’ll come back to talk some more about the consequences of that later.

For right now, we’re going to follow Godel in the examination of a particular question about logic: how far can a logic go? Is it possible for us to conceive of a logic which allows us to examine every possible statement and assign it a truth value?

Godel was looking at logics that could describe arithmetical properties and relations; Mandelbrot’s work indicates that such properties and relations are sufficient to describe very complex processes in the natural world (indeed, Mandelbrot’s work has applications in many fields including sociology and econometrics). Accordingly, his conclusion that in fact no logical system could completely and consistently describe the natural numbers – and, by extension, the world, although Godel himself didn’t go that far with it – says something very important about the limits of human knowledge.

Godel actually devised a whole new numbering system in pursuing his complex proof of the undecidability of certain formal mathematical propositions, but we don’t need to in order to grasp the central idea. We can use a thought experiment to produce the same result.

Consider the case where we actually can design a thorough logic for assigning a valid truth value to any statement – such a logic is programmable into a computer, and allows us then to build a Universal Truth Machine. Any question we put to the Universal Truth Machine can be parsed by it, analyzed with its powerful logic, and identified as True or False.

Suppose now that we test our Universal Truth Machine, and give it this statement to chew on: “the Universal Truth Machine will find this statement to be false.” The Universal Truth Machine can understand this statement, but it can only find it to be false if the statement is in fact true, and its programming defines True and False as exclusive opposites. By the same token, the Universal Truth Machine cannot find the statement true unless it is in fact false. Therefore, our machine cannot give an answer – cannot prove the statement – and so cannot, in fact, be universal.

Godel’s genius was in formalizing a statement that can be represented in any sufficiently developed logic, and that proves for any logic that it somewhere hits this problem. It must, therefore, be either incomplete – being unable to prove the Godel statement – or inconsistent – being able to prove that it is simultaneously true and false without crashing. This fascinating result leads to the peculiar conclusion that our own brains, which encode sufficiently developed logic to model the world, are themselves subject to Godel’s Incompleteness Theorem. That’s a rabbit-hole for another day, however.

Higher ground

“The infinite vibratory levels, the dimensions of interconnectedness
are without end.” ~ Alex Grey

 

This leaves us with four different conceptions of existence, within any or all of which some entity may be understood to be. We can see how some entity may be understood to exist in several of these simultaneously; the entities, while distinct, can be linked to one another but can also exist independently. The entities in the objective world all inter-relate with one another: they all exist within the same objective world, at least as far as we can tell. In the same way, our subjective world consists of entities which coexist and correlate within that unique subjective world rather than within a range of them. Intersubjective entities relate in a more complex way, insofar as the unique understanding of the intersubjective symbol within each subjective observer's Cartesian theater informs both the unique understanding of other subjective observers and also the intersubjective meaning attached to the symbol itself - but again these intersubjective entities coexist with one another on the same 'level' as it were. Ideals, similarly, exist on their own 'level' - and yet we have already stated, and can easily say in everyday experience, that entities existing severally on discrete levels relate to one another. These metarelations between things that exist in different senses can be seen as existing in some larger dimension, in the same way as a succession of two-dimensional images can be layered over one another in a third dimension to become a richer and truer whole, and it is this dimension of existence, distinct from the first four, that we call the transcendental. The metarelations of transcendental reality are theoretically perceptible in the same way as the simple relations of subjective reality, and the process of metaperception in this fashion is the subject of the koan I quoted back at the beginning.

Now you have been given access to a somewhat fuller expression of the seemingly simple expression 'I can only be,' and a somewhat fuller elaboration within that context of the opening koan, I have reached a point at which this narrative can pause. If you are still confused, rest assured that this is because I still haven't begun to properly express myself yet. Do not make the mistake of reading into that refrain any sort of promise that 'proper expression' will ever be forthcoming; but strive for the faith that sustains me - the faith that any expression will, in the fullness of its flowering, become sufficiently proper that it achieves some measure of intersubjective potential.

Feel free to share your reactions to this. Let's make some Art.