Mark – thank you for this! My response:
I also see boundaries, as illusory as they are, in the context of meditation, but especially meditations which unfold over long periods of time (e.g., centuries). As with any boundary, its degree of clarity can be purposive (beyond the practicality of watchmaking) and in serving as such, has its benefits and its detriments. Clear demarcations can be exceedingly helpful, especially in generating energy based on the tension which can result. As much suffering as the (artificial) split between psyche and matter beginning in the late 17th century caused, it led to immense development in certain areas and, perhaps more importantly, it led to a certain liberation (e.g., the liberation or emancipation from the perceptible, the tangible, the visibly limitable). And in preparation for writing a series of notes on my review of and response to James Hillman’s paper The Measure of Events: Proclus’ Proposition 117 in the View of an Archetypal Psychology, I worked with two and a half millennia of the history of mathematics and science and found evidence that the unconscious itself appeared to be supportive of and energizing the split in favor of abstraction and the striving for the infinite. Crucially, there was a very real readiness for Descartes’ position (as opposed, for example, to Leibniz’ position). However, as I hinted at in my previous response, we are reaching its limits, the exhaustion of its possibilities, resulting in The Spiritual Problem of Modern Man.
In my note The Abyss and The Alchemical Vessel, I explore our coming to the abyss in terms of five specific examples of limits:
- A. Decidability in mathematics
- B. Computability in computer science
- C. Complementarity in quantum physics
- D. Non-locality in quantum physics
- E. Quantum entanglement
Let me focus on decidability, which is the application of a given mathematical system to determine if a statement made in the language of that system is true or false in a finite number of steps, one critical mathematical system we’re all familiar with being the axiomatic-deductive system. Kurt Gödel proved, in 1931, that there are statements which can be formed in such a system of a certain power (e.g., the power of Peano’s axioms), assuming the system is consistent (the axioms lead to no contradictions), which can neither be proven true nor proven false in a finite number of steps (i.e., those statements are undecidable). In working with this result as a meditation, what becomes clearer is the fact that mathematical systems are, in fact, provisional (e.g., one can make a stronger mathematical system by adding as an axiom the undecidable statement of the previous mathematical system, or one can change from an axiomatic-deductive mathematical system to something different). In other words, such can weaken the view that mathematics has “God status.”
On the other hand, as a person who has worked with Number theory, both in mathematics proper and in depth psychology, it is very difficult to see the rules followed by the Natural numbers as not being pre-existent. I am appreciative of, for example, cognitive science’s approach (e.g., the book Where Mathematics Comes From: How The Embodied Mind Brings Mathematics Into Being by George Lakoff and Rafael Nuñez) to showing how mathematics was created, but I am simply left unconvinced, especially given the rather startling results in Number theory which don’t seem to be addressed in such works. But, while it is amazing that different cultures across vast distances of time and geography arrived at the same mathematical laws for certain areas, I am also very open to the crucial differences in how each culture sees and employs mathematics, one new discipline for this being ethnomathematics. Furthermore, I am open to those who view infinite mathematical objects as being problematic and sticking to only that part of mathematics which can be constructed. Such heightens the consciousness of the benefits and detriments of seeing mathematics as eternal in the Platonic sense. But, from a depth psychology perspective, it is understandable how Jung, his closest collaborator Dr. Marie-Louise von Franz, and physics Nobel laureate Dr. Wolfgang Pauli, came to see the Natural numbers as (psychoid) archetypes of order, the simplest of the archetypes. One advantage to seeing them this way is that it offers a neutral language which could facilitate a deeper collaboration between depth psychology and the hard sciences.
You wrote “Now, since the originals are themselves probabilistic, any deductions that follow from them also end up as contingent — but they aren’t always treated that way.” I agree with this. However, I want to espouse some of the benefits of certainty. I have found that, while contingency is good, it can be exceedingly difficult to navigate in this way (this is shared with the difference in living between objective truths and truths realized individually). My concern is that too much emphasis on contingency can sometimes depotentiate moving forward; de-energize the entire process, especially during stressful periods of doubt and frustration. Certainty, though illusory and though it can be problematic, in its best moments, can energize the movement beyond seemingly impenetrable hurdles.
Finally, let us consider another benefit of fixed and clear distinctions – safety. You brought up Jung’s statement of organized religion being a defense against religious experience. Crucially, sometimes this is absolutely necessary! Real religious experience can be absolutely horrifying and can completely overcome and shatter the individual. This possibility is why Jung was quite careful as to whom he recommended the path of individuation. For those who were not psychologically mature, he would recommend they stay with their organized religion (he would also recommend this for those whose religion served as a proper container of their psychological needs). Only those who were psychologically mature and could endure such powerful religious experiences would he recommend individuation. Just think of the Swiss Saint Niklaus von Flüe popularly known as Brother Klaus. He was a family man until, as Jung wrote, he “saw the head of a human figure with a terrifying face, full of wrath and threats.” As a result of that single experience, Brother Klaus spent many years of the most strenuous spiritual effort in a monastery working through this experience. Jung himself, after his break with Freud in 1913, went through an exceedingly dangerous spiritual emergency which required him to spend the rest of his life working through (“to give birth to the old in a new time”). Precious few can do this kind of work, and sometimes when such experiences are thrust upon a person, a (temporary) defense can be certainty, at least about certain things, which allows the safer channeling of the immense energies involved in those experiences.