The word mysticism is “problematic but indispensable.” Definitions are typically steeped in religious terminology, and elaborations jumble together various behaviors, beliefs, and experiences.
I’d like to introduce a definition which rests on first principles rather than religious concepts, and explore how this definition applies in both religious and non-religious contexts.
Mysticism is a belief in the existence of a specific form of knowledge. This knowledge must satisfy three criteria to be considered mystical:
It must be ineffable
It must be attainable
It must matter
Let’s examine each of these properties.
The most defining feature of mystical knowledge is ineffability, or an inability to be articulated. This is the essence of the myst root, from the Greek for "to close" or "to conceal." If someone happens to acquire mystical knowledge, they can’t share it with others, or even prove there’s something worth knowing.
Ineffability leaves mysticism on shaky, intrinsically unscientific ground. But as we’ll see, this does not preclude its existence—there are some simple examples of ineffable truths.
One of the most famous examples is a thought experiment known as Mary’s Room:
Mary is a brilliant scientist who is, for whatever reason, forced to investigate the world from a black and white room via a black and white television monitor. She specializes in the neurophysiology of vision and acquires, let us suppose, all the physical information there is to obtain about what goes on when we see ripe tomatoes, or the sky, and use terms like "red", "blue", and so on. She discovers, for example, just which wavelength combinations from the sky stimulate the retina, and exactly how this produces via the central nervous system the contraction of the vocal cords and expulsion of air from the lungs that results in the uttering of the sentence "The sky is blue". ...
What will happen when Mary is released from her black and white room or is given a color television monitor? Will she learn anything or not?
Common sense says yes: Mary learns what the color blue looks like. This is a perfect example of ineffable knowledge. There is no way to explain to somewhat what blue looks like though words, numbers, diagrams, etc. It has to be experienced directly.
(Some philosophers disagree. See  for details, a counterargument, and a shameless ad hominem.)
Here’s a very different example: imagine you know yourself to be a particularly humble person. Others have expressed this to you, and careful examination of your own thoughts and behavior has led you to the same conclusion. But it’s impossible for you to articulate this! Say “I’m a very humble person” and your audience will believe the opposite. The only way to convey your humility is to demonstrate it over time, and hope people notice.
Knowledge is useless if it remains out-of-reach. Since most knowledge is attainable, let’s talk about some counterexamples: knowledge that remains out of our grasp.
The canonical example is Solipsism. No matter how hard we try, we can never be certain that other minds exist. My own mind is the only one I can experience directly, and everyone else might simply be a character in my dream.
There’s an interesting corollary here: the existence and identity of God is unattainable knowledge. Even if a giant head were to form in the clouds, telling us it’s God, controlling the weather and the stock market—we’d still have to wonder: is it just a hallucination? Am I dreaming right now? Even if it’s real, might there be another, bigger God above the clouds?
So when someone claims concrete mystical knowledge about the nature of God or Eternity or whatever else, we should take this with a degree of skepticism. As I’ll argue below, there are truths that can be inferred from direct experience, but it’s common for self-described mystics to externalize and overstate them. They project subjective experiences onto objective reality in ways that do not hold.
(This is why I dislike definitions of Mysticism that call it “union with God”—that may very well be what’s happening behind the curtain, but there’s simply no way to know. Even God must sometimes wonder if He’s dreaming.)
The third criteria for mystical knowledge is that it has to matter.
Knowledge matters when it can improve our quality of life, often through a change in behavior. Knowing exercise is good for me gets me active; knowing my partner loves me stabilizes and improves my mood; knowing the earth is warming will help us mitigate, if not avoid, disaster.
That some ineffable knowledge might matter is not immediately apparent—colorblind folks get by alright.
Now that we’ve listed out the three criteria, and provided examples of knowledge that meet (or fail to meet) each one individually, let’s see if we can find examples that meet all three.
The most trivial example of mystical knowledge is the Psychedelic Experience:
It is trivially attainable: all you need is 1-3 grams of dried mushrooms.
It is ineffable: this aspect can only be truly appreciated by the experienced, but no amount of study can adequately convey the feeling of a trip.
Does the Psychedelic Experience constitute knowledge? At the very least, the experiencer learns what it’s like to trip, much as Mary learns what the color blue looks like.
In my own experience, the knowledge that these subjective states are available to us, that they’re a part of the world, is precisely what engenders the positive effects. The research bears this out: the subjective effects are a critical component of the therapeutic effects, not a side effect of the chemical.
The mystical knowledge conferred by meditative states takes much the same form as psychedelic states: it is a subjective experience, and the knowledge mainly consists of what it feels like and that it’s accessible. Additionally, the experienced meditator gains knowledge about how to access these states, remain in them, and explore the surrounding territory.
Again, meditative states satisfy all three conditions:
They are attainable: this is a bit harder to verify than with psychedelics—it may require months or years of practice.
They matter: practitioners tend to change in tangible and even extreme ways. Many become vegetarian, spend large amounts of time in seclusion, or report changes in mood ranging from reduction in anxiety to bliss.
They are notoriously ineffable: even the most down-to-earth meditation manuals can feel opaque, so teachers often resort to indirect means.
Common examples of meditative states include ego death, pīti or rapture, satori, and unknowing. Within traditions, there are typically stated relationships or hierarchies between states (e.g. the jhānas), which can help orient practitioners. Across traditions, it’s anyones guess how different meditative states line up.
Another class of mystical truths do not appeal to subjectivity. These can be truths about language, the mind, or truth itself; they reference the same medium that contains them. They are often articulated as paradoxes, like “all unqualified statements are false.”
Zen kōans often deal in truths like these. Some examples:
Shuzan held out his short staff and said, "If you call this a short staff, you oppose its reality. If you do not call it a short staff, you ignore the fact. Now what do you wish to call this?"
A monk asked Tozan, "How can we escape the cold and heat?" Tozan replied, "Why not go where there is no cold and heat?" "Is there such a place?" the monk asked. Tozan commented, "When cold, be thoroughly cold; when hot, be hot through and through.
A dog walked by. The monk asked Joshu, "Has that dog a Buddha-nature or not?" The monk had barely completed his question when Joshu shouted: "MU!"
These kōans are meant to convey the limitations of language and dualistic thought. The lessons may not be readily apparent to the casual reader, and I’m no zen master, so I’ll refrain from commenting. But I’ll speak to another example which is often misattributed to Zen:
It’s easy to jump to a “yes” or “no” answer, and find a way to defend it. But it’s better to dwell in the ambiguity, to meditate on the interrelations between reality (the tree), perception (the sound), and language (the question).
The situation is best illustrated by what I like to call the Penrose Trinity:
The diagram illustrates:
The mental world arising out of the physical world (i.e. the growth of brains)
The platonic world arising out of the mental world (i.e. language, concepts, ideas, forms, and especially mathematics)
The physical world arising out of the platonic world (i.e. the mathematically patterned nature of reality)
To be clear: none of this is to make a particular point about reality or the nature of the tree question. If you find yourself disagreeing, good! Confused? Even better! The point is, the more you stew on the paradox here, rather than retreating to a single reductive answer, the more you’ll grok a metacognitive truth that you won’t quite be able to articulate.
We’ve enumerated two types of mystical truths:
Subjective truths, like the psychedelic experience
Metacognitive truths, like the interrelationship of perception, matter, and language
My belief is that the first type is fundamentally ineffable—no amount of work or progress will allow us to understand the quality of an experience without experiencing it directly. New classes of drugs, meditative techniques, and biofeedback might speed up the process, but each individual will need to experience in order to know.
The second type, however, might simply need an adequately powerful logical framework. In particular, Gödel was able to rigorously prove some metalogical, self-referential truths. The right ontology and axioms might allow us to do something similar for some of the ideas conveyed in Zen koans. Until then, we’ll have to settle for paradox.
Rationalism is a philosophy which holds that reason is the primary source and test of knowledge. It is a massively successful philosophy, responsible for the wealth of scientific and mathematical knowledge we’ve built over the last two millennia.
But I hope I’ve shown that reason cannot be the sole arbiter of truth. There are ineffable truths which cannot be approached with or defended by reason. And some of these are both accessible and important, placing them in the domain of mystical knowledge.
We might start to think of Rationalism and Mysticism as two sides of one coin, two complementary approaches for acquiring and validating knowledge. But first, Mysticism will need to come of age, and develop a level of rigor that has been present in Rationalism for centuries. Then maybe we can cultivate a legion of experts who are well versed in both, and begin to develop bridges between them.
 The wikipedia article lists some good responses to Mary’s Room. They mainly focus on whether “knowledge” is a good word for what Mary gains, which generates interesting discussion about what, precisely, she gains by leaving the room. But ultimately it’s a semantical distinction that doesn’t have much bearing on the ideas presented here. The only material objection is Daniel Dennet’s, but this seems to come from a circular belief that “all scientific knowledge about color” must necessarily include “what it looks like.” I contend that Daniel Dennet is a p-zombie.