“It was not just in the Andante of the Second Quartet that I remembered having translated (almost involuntarily) the distant memory of bells which in the evening at Montgauzy — and this is some time ago — came to us from a village called Cadillac when the wind blew from the west. From this dull sound a vague dreaminess arose, which, like all vague dreams, is literally untranslatable. Only, does it not happen often that some exterior fact numbs us so that our thoughts become so imprecise that in reality they are not thoughts, and yet are nevertheless something in which we can take pleasure? The desire for things which do not exist perhaps, and this is indeed where music holds sway.” – Gabriel Fauré, as quoted in At the Piano with Gabriel Fauré
“Through the fire and through the flames, you won’t even say your name. Only ‘I am that I am.’ But who could ever live that way?” – Vampire Weekend, Ya Hey
“The road up and the road down are one and the same.” – Heraclitus
“I am the relation between myself and observing myself.” – Henri von Foerster, Understanding Understanding: Essays on Cybernetics and Cognition
Many of us have personally experienced the remarkably profound effect that music has on our recollection of the past. When I think back to the summer I spent in Japan five years ago, I can bring to mind a hazy visual image of the places I visited, or maybe some snippets of conversation that I had with the locals. But listening to just the first few seconds of Vampire Weekend’s song “Hannah Hunt,” which I listened to obsessively that summer, evokes with stunning precision not just the musky fragrance in the Japanese air and other similarly vivid senses. It elicits, in a way that pure recall simply cannot, the deeply personal experience of what it was like to be me during that period in my life.
These words may be utterly meaningless to you because they are not descriptive. That is precisely the point.
It is not merely my “state of mind” as a 14-year-old that the music elicits forth; such a phrase connotes nothing more than a mere collection of partially-formed thoughts and angsty adolescent insecurities, which, while formative, do not capture the totality of my lived experience of being in that moment in time. Nor is it a “mood,” which also doesn’t fully express the feeling of peering out of my interior consciousness into the exterior world. There is an integral component of my subjective experience – my awareness, my sense of being in time – that is utterly untranslatable, in the words of Fauré. Words fail at this level of description.
When audiences seek to communicate the transporting effect of a sublime musical work they often discover that they are pushing the boundaries of language. The author and music critic E.T.A. Hoffman wrote of Beethoven’s music that it “opens the realm of the colossal and immeasurable” and “leads the listener away into the wonderful spiritual realm of the infinite.” Several works in Beethoven’s opus, including the aptly named Tempest sonata and the “Storm” movement of the Pastoral Symphony, seek to invoke immense forces of nature that utterly outstrip our deeply-rooted yearning to tame and control the environment around us. Embedded within this and other works is the notion that humans are subject to phenomena that surpass our rational capacity to comprehend them. Beethoven’s musical form illustrates these limitations insofar as he often composed works that were nearly impossible to form, as the music theorist Dmitri Tymoczko insightfully points out. The melody in the Tempest sonata, for instance, requires a high B-flat that was simply out of reach of the five-octave pianos that existed in Beethoven’s time. The music, in shifting to a lower key, thereby reflects its own restraints and shortcomings. Beethoven seeks the note in spite of – or perhaps even because of – the knowledge that his instrument cannot play it. Our reach exceeds our grasp in the same way that, as Tymoczko puts it, our apprehension exceeds our comprehension.
Among his vast opus, Beethoven’s 9th most powerfully expresses this notion of aspiring for an ideal that cannot be sufficiently embodied in any material form. Schiller’s “Ode to Joy,” the poem to which the final movement of the 9th is set, calls for humans to know God even though he resides in a celestial canopy beyond the mortal realm. It is no coincidence that the formal structure of Beethoven’s composition falls apart here, since his form mirrors his attempt to, in the words of music journalist Tom Service, “put listeners in touch with our microscopic futility as individuals and even as collective humanity faced with the depths of creation.” As such, the 9th resides at and exposes the limits of human understanding. Its thunderous euphony is meant to arouse the transcendent sensation of encountering the incommunicable divine. When you’re in the right frame of mind to unconditionally open yourself up to the glory of the music, you catch a glimpse of a feeling that is beyond enjoyment, beyond delight, and even beyond emotion. (1) You cannot adequately describe it. The 9th, like all sublime works of art and monuments in nature, reveals our ability to grasp sensations that lie beyond our rational capacity to comprehend them. Awareness of our ignorance is more rewarding than knowledge or certainty in this instance. It is precisely our inability to make sense of the sacred that renders it so extraordinary. Reason alone cannot yield this feeling of wonder; after all, it is what we cannot know that fills us with the greatest sense of awe.
Beethoven’s 9th has a sublime effect on us even though there is nothing sublime about the musical notes themselves, when they are viewed independently of our aesthetic intuition. Similarly, the words in “Ode to Joy” point towards a sacred, exalted feeling that words themselves cannot capture. Stories that are expressed to us can elicit inexpressible reactions; material paintings call forth immaterial sensations. The form of art, as it does in Beethoven’s 9th and the Tempest sonata, breaks down when it evokes the feeling of sublimity. In other words, form is most successful when it defeats itself; the greatest art exists for the purpose of transcending itself.
As the 9th explicitly suggests, self-transcendent systems like these, which emerge through our appreciation of the irrational, are inextricably linked to spirituality. The Daodejing, the foundational text of Daoism, is essentially a self-transcendent text, as evident in its opening lines: “The Way that can be described is not the absolute Way.” (2) The Daodejing acknowledge that the sacred, once spoken of through language, is no longer sacred; yet nonetheless, the text employs language to reveal the nature of the sacred. As such, the Daodejing appears to contradict itself from the outset. But in this instance, logical contradiction doesn’t invalidate the meaning of the text but rather affirms and elevates it. The mode of communication in the Daodejing, as it is in Beethoven’s opuses, is merely a vehicle for conveying something that surpasses the limitations of the mode itself. Normal understanding, which is essentially logical reasoning, is stuck at the level of language; it receives inputs in words and then outputs, still in words, the broader pattern or significance that it discovers. Language, therefore, can only rise above itself when interpreted on a level of awareness where logical reasoning fails. The Daodejing must be read on this higher plane of intuition because it conveys insight into the sacred, which it depicts as something beyond the grasp of the empirical human mind. Words in language represent God as a concept that we can mentally label and classify, but true experience of the divine requires a mystical, ethereal awareness above and beyond our rational cognition. The Daodejing, once again: “the name that can be given is not the absolute name.” (see 2) It is deeply consistent with the Daodejing that, when Moses asks for God’s name in the Book of Exodus, He responds, “I am that I am.” Any other answer would have undermined a sacred truth, since ordinary language is insufficient to characterize the extraordinary.
Contradiction not only is inevitable in the Daodejing, which suggests that we can know, in some form or another, that which cannot be known, but also serves as a means for expressing a sacred meaning. The yin and the yang in Daoism are two opposites that cannot seem to be reconciled with each other, yet nonetheless they are juxtaposed together in the widely-known taichi symbol. As the German economist-turned-epistemologist E.F. Schumacher once wrote, “A pair of opposites – like freedom and order – are opposites at the level of ordinary life, but they cease to be opposites at the higher level, the really human level, where self-awareness plays its proper role.” I have posted before about opposing forces that complement each other to form whole systems that are distinct from the sum of their constituent elements. This view is accurately encapsulated in the philosophy of dialectical monism, which posits that reality is a unified whole that inherently manifests itself through the conflict or contrast between separate (though not necessarily opposite) entities. The rational mind, as I alluded to above, is deeply uncomfortable with paradox. Hence, our phenomenological experience of the world captures only a limited fraction of reality when confronted with opposing stimuli. For instance, the duck-rabbit illusion depicts both a duck and a rabbit in a single image, yet it seems that we are only ever capable of seeing one or the other at a particular moment in time. Perceiving paradox without resolving the logical tension within it gives a much fuller representation of the world, but it can only happen within a transcendental realm of understanding, where systematic unity is found through the application of reasoning beyond the sphere of objects of experience (3). Indeed, any system that balances two polarities is self-transcendent, because it rises above incompatibility to create harmony. Standing before paradox without viewing it as a problem to overcome is essentially the act of surrendering yourself to the realization that there are some things that your “petty reasoning mind,” in the words of Carl Jung, will never be able to know. “Paradox,” Jung concluded, “is one of our most spiritually valued possessions” because it serves as a means of expressing “the polarity of all life,” the tendency of all things to change into their opposites over time.
Jung valued paradox so highly because he thought that it could be a “better witness to truth than a one-sided, so-called ‘positive’ statement.” Logical systems are founded upon such one-sided statements, which can only ever be true or false. Mathematical theories are dismissed as self-contradictory if they are found to contain axioms that are both true and false. For instance, the preeminent mathematician and philosopher Bertrand Russell’s dream of grounding mathematics in naive set theory fell apart when he found that it contained one such gaping inconsistency, also known as Russell’s paradox, which deals with the set of all sets that are not members of themselves. If it were true that such a set is a member of itself, then it would not be a member of itself. Alternatively, if it were the case that such a set is not a member of itself, then it must be a member of itself. In other words, it is both true and false that the set is a member of itself. An intuitive example of Russell’s paradox is a barber in a village who shaves all the residents that don’t shave themselves. The barber both can and cannot shave himself.
Self-referential statements like Russell’s paradox often produce logical inconsistencies. Epimenides’ paradox – which essentially states “this sentence is false” – can’t merely be either true or false, since it negates itself if true and affirms itself if false. As such, in their 1913 magnum opus Principia Mathematica, Russell and fellow philosopher Alfred North Whitehead developed a new form of set theory involving strict hierarchies that prohibited self-reference. In Russell and Whitehead’s formalism, which expressed logic purely in terms of mathematical symbols, new theorems could effectively be generated through operations on other ones, but with one crucial caveat: a theorem could never refer back to itself.
For a while, Russell and Whitehead’s system was thought to be totally self-consistent, until the great mathematician Kurt Gödel discovered a lurking paradox in 1931. Because of the formal language in which Principia was written, each theorem could be represented as a number. Subsequently-derived theorems could be “created” through the multiplication of these Gödel numbers, as they were called. In a flash of supreme insight (which involves a great deal of mathematics beyond the scope of this essay), Gödel was able to generate two theorems that share the same Gödel number, such that inserting a Gödel number into a function could yield itself as the output. Consequently, the statement “the theorem U does not have a proof” could be manipulated into “this theorem does not have a proof,” which is analogous to Epimenides’ paradox. If proven, it does not have a proof, and if not proven, then it is proven. Gödel extrapolated his discovery of this simultaneously true and false theorem to a broader conclusion: namely, any consistent axiomatic system of mathematics will contain theorems which cannot be proven.
Self-reference eventually results in the demise of logic, so many people are deeply, sometimes irrationally, uncomfortable with it, even if they are not familiar with Gödel’s incompleteness theorem. (4) Self-reference is problematic for mathematical formalisms and computational systems (although self-recursion can often act as an incredibly powerful tool in computing languages), but for human beings, it is deeply elevating. It is not merely the act of addressing or pointing back to oneself; it is the process of producing a dialectic within a unitary whole. A system that functions on itself creates a subject-object duality between the entity that is acting upon itself and the entity that is acted upon. The subject and the object are opposed to each other, yet they are nonetheless integrated into a single ensemble, much like the duck and the rabbit are two different animals in the same body. Any axiomatic system of mathematics is essentially true and false because it contains statements of both of these varieties. The aim of most mathematicians, like Russell and Whitehead, is to segregate the system into hierarchies, such that one theorem, which is either true or false, can only ever be determined in relation to other, equally one-sided theorems. Truth and falsehood are separate. But self-reference is implicitly present in all logically consistent systems, including those where it is expressly forbidden. Self-reference gives rise to the dissolution of polarities in logical systems, such that they rise above the binary, true-false dichotomies of logic to form statements that are both true and false. In other words, statements of reason refer to themselves in order to attain that which cannot be reasoned: paradox! They are no different from musical works and spiritual texts that exceed their own limitations by acknowledging their own limitations. It is deeply paradoxical that self-referential systems don’t remain trapped within themselves, but instead transcend themselves. How does that make sense?
It does not, but that’s precisely why it’s true.
(1) Experiences like this are often described as “ecstatic” or “mystical.” If you’ve never had such an experience and you think that what I’m saying is hippy woo woo, then you should meditate more or read this relevant essay for some context.
(2) Here, I am quoting Beck Sanderson’s translation.
(3) It seems like Kant discusses a somewhat similar idea in his Critique of Pure Reason. As someone who hasn’t read or studied Kant, I can’t speak to the ideas in his work. These webpages are useful references that will do much greater justice to Kant’s metaphysics.
(4) In his book I Am a Strange Loop, the cognitive and computer scientist Douglas Hofstadter recounts an incident from his childhood in which a store manager refused to let him point a camera to the TV screen where its images were being televised live.