The Paradox of Postmodernism
Human beings have always struggled to account for themselves in their explanations of how the world works. Subjectivity and knowing are perhaps the hardest things to deal with in any such system. This is precisely because we are part of what we are measuring. We are embodied, and we experience the world from within it, as part of it. In this manner the senses provide at once both an interface and a barrier to the external, what we know of the world can only be known through them, leaving room for doubt. It is up to the faculty of human reason to take raw sense data and construct a model of reality, to sort out what can be said to exist (ontology), what we know and how we know it (epistemology), and how to construct meaning from these conclusions (ethics). This interplay between sense and reason is the impetus of mathematics, science, philosophy, and art
In everyday practice of these fields, we find ourselves more concerned with what is apparently true, rather than actually true. One can build a perfectly functioning representation of the world using appearances and approximations, in fact we do this all the time. In every applied science and art, the numbers are rounded, some ideas are left unexplored, and some dots unconnected, all within a given tolerance. We avert our gaze from the depth of infinity, lest we be rendered paralyzed and hapless to live
Certainty, on the other hand, is a whole other ball game. In order to know anything, you first must know everything. Often, the first question to ask is, “How does my model of reality account for itself?” This is precisely where we run head first into a fundamental barrier, antimony, or mutual incompatibility. Like Epimenides, the wily Creten philosopher who famously proclaimed “all Cretans are liars” Antimony relies on self-reference to create paradox, keeping certainty forever out it's own grasp
However that certainly hasn’t kept us from trying. This is particularly true of the 20th century, where the very success and precision of our models brought us to the point where self-referential paradox was unavoidable. This is the story of trying to push through paradox, either to explain what we thought we already knew, or as a means of arriving at total knowledge of the world. In many respects, self-referential paradox was the fundamental problem of the 20th century; it occupied and haunted the minds of Einstein, Wittgenstein, Gödel, Duchamp, and many others
This goal of this essay is to sketch in broad terms the modern trajectories of these four fields; mathematics, science, philosophy, and art, and show how each addresses and deals with self-referential paradox as it presents itself. From there, I’ll examine how this leads to the phenomenon of postmodernism in the arts and sciences, and offer further comment on it effects in field of art, where I am most familiar. I’ll conclude by humbly offering some suggestions on a way out of this mess, or at least some strategies for circumnavigating it.
Plato's Allegory of the Cave, the quintessential formulation of sensual doubt in the history of Western philosophy, brought to you in the rich, buttery voice of Orson Welles.
We begin at a time which our four subjects were barely separate from each other, the world of the ancient Greeks. From that incubator of Western thought emerged was a vision of the world as static and unchanging, governed by heavenly, Platonic bodies. Whether it was Plato, Aristotle, or the Pythagoreans, (Heraclitus is an intriguing counterexample) one of the main thrusts of Greek thought was that the world presented to our senses, with its apparent change, flux, and chaos is a distortion of our human condition, and hence is untrustworthy. Thus it is through reason alone that the “real” can be separated from the unreal, and the eternal nature of things can be understood
The scientific undertaking of the western world would follow along these lines. The idea of reason as the means for understanding (rather than theology) in fact was one of the main ideological underpinnings of the scientific revolution. What Isaac Newton encapsulated in brief, elegant sets of laws was not just a tool for understanding and manipulating the world, but also belief in the fundamentally mechanical nature of the universe. Central to this conception is that his world, like the Greek’s, is perfectly knowable. If one were to calculate the position, direction, and velocity of every particle in the universe, one would attain a God’s eye view of things, the entirety of the past, present and future would be calculable and visible all at once. This would be an inconceivably ambitious undertaking, but the point was that it was fundamentally possible. One is also struck by how aesthetically pleasing and arguably spiritual this idea is. Similarly, Samuel Morse, the inventor of the telegraph (and accomplished painter), fantasized that by accurately recording all the minute perturbations in the Earth’s atmosphere, every sound that ever occurred on the planet could be reconstructed, from the conversation at breakfast to the decrees of Caesar. Though it seems contradictory to us, to him mechanism meant that there were ghosts in the air.
The Doppler effect describes the change in pitch as a source of sound moves past at an observer, but it also describes the way light and spacetime bends in accordance to the relative velocity of two observers.
20th century science, on the other hand, is marked by a stark contrast to the mechanistic worldview. For starters, Newtonian space and time are absolute, one second and one foot hold the same value throughout the universe. On the other hand, Einstein’s theory of relativity (now 100 years old btw), describes a fabric of spacetime which can dilate, stretch, or compress according to the relative velocities of two observers, meaning they’ll have differing measures of one second and one foot. Similarly quantum mechanics demonstrates that one can either measure the position or velocity of a particle, but not both simultaneously. Furthermore, it is the act of observation that prevents us from doing so. In other words there is no privileged, objective position from which to measure universe. Like the Greenwich observatory is to the time zones, spacetime as it occurs to us on Earth is only an arbitrary standard.
Lorenz found that no matter where he started his weather simulation from, given enough time it will resolve to this shape when plotted graphically. This is remarkable considering that the simulation is highly unpredictable. This shape was dubbed the Lorenz Attractor, it and other "strange attractors" give us a glimpse at the tantalizing structure underneath chaotic systems .
Along with relativistic phenomena, the mechanistic worldview was broken by the introduction of complexity into science. Complexity describes the behavior of deterministic, yet dynamic systems that show an extreme sensitivity to initial conditions. Complexity manifests itself everywhere in the natural world, from biology to meteorology, cosmology, chemistry, geology, and in countless other places. Edward Lorenz, a mathematician and meteorologist, discovered this phenomenon in the context of modelling weather systems on a computer. He noted that no matter how accurately he input the starting conditions of his weather simulation, he could not do so completely, and the small differences would snowball into drastically different results over time. Despite the fact that the rules of his simulation were straightforward, the outcome could never be predicted very far into future. Determinism does not equal predictability.
James Clerk Maxwell devised a thought experiment that beautifully demonstrates this. In it, there is a tank of gas containing two chambers, separated by a small aperture, which is controlled by a malign “demon”. The demon, unscrupulous as he is, only allows high energy particles through to one side, and low energy particles to the other, thus separating them and decreasing the entropy of the tank. Where Newton’s second law of thermodynamics would only guarantee statistically, not certainly, that the particles would mix and reach a state of equilibrium, Maxwell’s demon shows us that the average state of the particles is fundamentally different from their individual states. In an amusingly poetic metaphor, the demon breaks the gears of Newton’s heavenly mechanical universe, using only the wrench of minutia. The devil, so to speak, is in the details.
This douchebag has nothing better to do than drink Coors Light, listen to Florida Georgia Line, and fuck up my thermodynamic equilibriums.
So where does this leave science after losing the mechanistic worldview? One of the major shifts has been a change in the emphasis and methods of science from objective truth seeking to system building and interpretation. One of the key points is that science no longer focuses on the observational, but also the theoretical. The deeper one goes into microscopic and macroscopic phenomena, the more one encounters non-testable, non-falsifiable entities and systems in the current body of work. This was the critique of Richard Feynman, one of the pioneers of quantum mechanics, against string theory, that it has no connection to observational reality, allowing scientists to make it up as they go along. Regardless, it is an example of the increasingly blurring boundary between science and pseudoscience. One of major scientific problems facing the 21st century may very well be “What is science?
The story of modern mathematics is almost entirely a story of self-referential paradox. After a long period of outward expansion beginning with Newtown and Leibnitz, mathematicians in the 19th century turned their focus inward to the foundations of the subject, looking for rigorous definition of the most basic concepts of number, provability, and truth. Their response was to treat mathematics as logic, boiling all proof down to axioms (fundamental theorems that do not need to be proven) and rules of inference, which can be applied to the axioms to produce new theorems, and theorems from those theorems, and so on. Many of the brilliant modern mathematicians, Cantor, Dedekind, Hilbert, Peano, (and many others left out by my ignorance) were involved in this project in one way or another. Notable to our narrative is Gottlob Frege, a German mathematician and philosopher who at the turn of the century had developed a system of formal logic that he believed provided a rigorous foundation for mathematics. However, a young Bertrand Russell found a fatal flaw in Frege’s system, specifically that of self-reference. Frege’s logic dealt with objects, and collections of objects called sets. Sets can also be empty (null set) or contain other sets. Russell noticed that a problem arises when one considers a set of all sets that do not contain themselves. As a metaphor consider a town in which every man either shaves himself, or is shaven by the town barber. Russell’s Paradox is analogous to asking “Then who shaves the barber?”
Illustration of Russell's Paradox, brought to you by the guys that draw IKEA manuals.
Undaunted, Russell along with Alfred North Whitehead composed the Principia Mathematica, a monolithic and jarringly technical logical treatise devoted entirely to removing self reference from logic. Once complete, Principia promised an exhaustively purified foundation for mathematics, achieving what Frege had set out to do. But it was not to be. Like the Frege system before them, it was proven to be flawed. This time it was by Austrian mathematician Kurt Gödel, in a paper entitled, On Formally Undecidable Propositions in Principia Mathematica and Related systems. From this paper came Gödel’s First and Second Incompleteness Theorems, which prove that any formal axiomatic system of sufficient strength will contain propositions that are true, but unprovable. He did this with a clever trick called Gödel numbering, in which he coded statements made in the system of Principia into corresponding “Gödel Numbers,” which had equivalent, or isomorphic meaning. In this manner, statements can then be fed back into Principia notation, allowing the self reference that Russell and Whitehead worked so tortuously to prevent. It’s a very technical proof, but essentially Gödel is saying that for any formal system T, there is a statement G, such that G is unprovable in T. This is roughly equivalent to the Epimenides, or liar paradox, “This sentence is a lie.”
For every formal axiomatic system T, one can construct a Gödel statement G that lies outside the bounds of provability in T.
The significance of Gödel’s Incompleteness Theorems is that it not only proves the system Principia Mathematica to be incomplete, but any possible formal system that can be constructed. You could revise your system T to include T2, which allows G to be proven, but then T2 would itself be susceptible to its own G2, and so on to infinity. In a sense, this seems entirely reasonable, just as in physics there can be no perpetual motion machines, in logic there can be no complete, self-contained formal axiomatic system, there must a “push” from the outside. In a fell swoop, Gödel had demolished the great project of the 19th century. Mathematics, it seems, cannot account for mathematics
Philosophy, by extension, is concerned with many of these same problems (as many mathematicians were involved in both fields). Where epistemology had been the central focus of Western philosophy since Descartes, logic and meaning became the axis of philosophy in the 20th century. Along with this program came an intense self-awareness and scrutiny of language and other systems of meaning. Essentially, the question of philosophy shifted from “What do we mean?” to “How do we mean?”. Quintessential to this line of philosophy is Ludwig Wittgenstein, a pupil of Bertrand Russell, who also came from a background in mathematics and engineering. Wittgenstein’s project was the analysis of language and meaning, about which he developed two different, conflicting theories throughout his life. First, he developed a “picture” theory of meaning, in which words are seen as depicting objects in the world, with language as a whole creating a picture of reality. He later abandoned this idea for a theory of meaning as use, by which he meant that words themselves are arbitrary, and in order to understand what a word means, one must look at how it is used, and how it fits into the total background of culture. “A language is a way of life”, by which he meant that two speakers of a language are able to communicate because the speaker and the listener both share a similar mapping of words to concepts dictated to them by the culture at large. Every word has meaning by virtue of the meaning of every other word, hence language as a whole is not a picture that stands for reality, but a system of agreed upon symbols that stands in for reality. Hence his famous aphorism “The meaning is the use”
Meanwhile, the world of art was dealing with these problems in its own way. In many respects, the project of modernism in art is analogous to the project of mathematics, in that both are methods of modelling reality that were struggling with the question of how to model themselves. Clement Greenberg, one of the standard chroniclers of modernism, devised a narrative of the progression of modern painting as the incremental flattening of the canvas, of art becoming more aware of itself, shifting its goals from creating an illusion of space as the Renaissance masters did, to exploring painting as an object in its own right, without the need to depict anything. Central to this narrative of modernism is the dialectic. Owing its origins to Plato, and its formalization to Hegel, the dialectic is a method for arriving at knowledge of the world via a series of dialogues, in which one party posits a point, then another posits a counterpoint, addressing the weaknesses of the former, and from the interaction of these two comes a synthesis, which in turn becomes a new point, and the cycle continues. It is by this method that we successively hone in on truth, dispelling our misconceptions and illusions about the world with each pass. This was the modus operandi of modernism in art, each successive school was responding to the statements of the previous, incrementally extricating itself from renaissance illusionism, further abstracting and purifying itself, and becoming the ground for the schools to follow.
One of the implicit assumptions of Modernist dialects is that there is and "end" to art. Kazimir Malevich, White on White, 1918. With this piece, Malevich famously declared that he had finally culminated the history of art and achieved pure abstraction, and that art was over.
Alfred H Barr's 1936 poster for a MOMA exhibition, detailing the progression of Modern Art
What we have here is what in mathematics would be called a recursive algorithm. We take one movement as an input, create a counter-movement, synthesize these two, and feed the result back into the equation. Now there’s no need to take this literally, there’s plenty of room to argue which movement begat which other movements, and it’s perfectly acceptable to say that a particular movement was responding to more than two precursors, or was the impetus for multiple responses, or was a dead end. The important underlying conceptual point about modernism is that there is a general progressive trend in art that flows in one direction, forward. Following this line of thought, we could say that there is a linear, hereditary relationship between all of the schools of modernism. One could trace the progression of 1960’s minimalism backwards to 1870’s impression in a finite succession of steps
The dialectic trend continues more or less until the 1960's, where for multiple reasons it begins to break down. This is the birth of post-modernism, an account of art, culture, and society that rejects the dialectic narrative of modernism. The program of post modernism was one of deconstructing the narratives, beliefs, and assumptions of modernism, rejecting the notion of progress in art, and highlighting the role of galleries, museums, universities, and other art institutions in providing context definition for art. It is here we see artists taking interest in ideas from philosophy, particularly those of Wittgenstein.
Examples of Wittgensteinian Art. Marcel Duchamp, Fountain, 1917. Renee Magritte, The Human Condition 1933. Joseph Kosuth, A Four Color Sentence 1945, and One And Three Chairs 1965. All of these works deal with the tautological nature of art and meaning. Kosuth even wrote a manifesto in in 1969 entitled Art After Philosophy, which details how art is to respond to the questions rraised by Wittgenstein's philosophy.
However, the interesting thing about post-modernism is that it can be viewed as a meta-dialectic response to modernism itself. Just as revising your formal system from T to T2 removes paradox G and replaces it with G2, post-modernism only kicks the problems of modernism one level up. This is because postmodernism is attempting to overthrow dialectal modernism by using dialectics. The name “post-modernism” itself signifies a dialectic response to modernism. We could attempt to resolve the situation by constructing a post-post-modernism, but we would face the same difficulty again, and so on to infinity. This is Russell’s Paradox in dialectic form. In other words Postmodernism is a paradox. Like Gödel’s Incompleteness Theorems were to mathematics, post-modernism dismantled the progressive narrative of modernism and demonstrates that any such program of art, including itself, is equally doomed.
The "Ouroboros" of Post-Modernism
Here we find math, science, philosophy, and art converging on the same dead end. The thematic thread that runs between all of them is the loss of the objective world. All four fields, as a result of an earnest attempt to explain themselves, no longer depict an external, Platonic world, but a reality constructed by observers, with particular attention paid to the language and systems we use to construct meaning. Where we previously turned to theology and myth as a brute stopping point for these difficulties, we now have no such luxury.
Post-modernism has run its course. What started as a project of liberation from our own illusions about the world gives us no ground to construct a new one. What we are left with is nihilism, cynicism, and the great edifice of our times, irony. Irony is the symptom of post-modernism gone wrong. It has become the default attitude towards the world. Irony absolves us from responsibility for our thoughts and beliefs. It is the appearance of protest, and the pretense of a solution. As David Foster Wallace once said, “Irony is the song of a bird that has come to love its cage.
Nowhere is this more evident than in contemporary art. Anyone who is acquainted with it is well familiar with the concept of art about art. The art world today is marked by passive self-critique, relentless self-reference and self-canonization, and endless re-evaluation and re-contextualization of itself. This is apparent in the increasingly specialized education required to view and understand art, the abundant jargon and terms that art now hangs on like crutch rather than uses as a tool. The concept of the “art world” itself connotes art as an isolated sphere of human activity, where art becomes a series of references to itself that are meant to be understood by an inside crowd, presumably with a lot of money.
Kazuhiro Tsuji, Andy Warhol, 2014 Fabienne Leclerc Mind Games 2007. Instead of engaging in dialogue with itself and with philosophy, contemporary art only references it. The more gimmicky, the better.
This is exactly where post-modernism is detrimental to art. The lack of underlying narrative or direction leaves art vulnerable to overcapitalization. If a work of art has no reason to exist other than to make money, then it is best done establishing itself within the canon of art history, hence the self-reference described earlier. This also gives rise to the phenomenon of the curator, the high priest of the art world, interpreting and preaching the gospel of contemporary art to the initiated. What started as a logistical role of storing, transporting, and displaying objects became one of advocating artists, and encouraging meaningful artistic dialogue. In many respects this has deluged into to that of a glorified tastemaker, directing and predicting market trends, and using celebrity to draw attention to exhibitions, museums, and galleries (Pharrell Williams, James Franco, Madonna, Katy Perry and many others are great examples of the celebrity curator). Curating is also ubiquitous in the world of marketing today, from fine art to “curated shopping experiences” that are the current buzzword in retail and online shopping.
Dude needs curate himself a new hat.
So what is to be done about the self-defeating zeitgeist of our times? It is obvious to me that the current response, irony, sarcasm, and nihilistic self-indulgence, are only a holding pattern, not a way out. But how do you play a game in which every move is rigged? The flaw is in the assumption that there is a move to be made, and in the neglect of the fact that is simply a game. Modernism, Postmodernism, mathematics, science, philosophy, and art, these only models of reality, not reality itself, and as such they have no bearing on how the world actually works.
So throw your hands up, and walk away. Let it all burn to the ground, and from the ashes start anew. Do not try to defend certainty, and do not rebel against it, as both lead to paradox (in the case of the latter, consider the paradoxical argument “the only truth is that there is no truth”). As Rajneesh would say, “do not be for, do not be against, simply be.” Rather than engaging in fruitless dialogues about the world, pick them up and put them down as you find useful, and instead focus on what you, personally, find interesting about the world.
On that note, I’d like to bring up what is often overlooked by postmodernism, especially in art, namely aesthetics. Beauty is considered naïve in the postmodern world. It is suspicious of it, and for good reason. Often when we encounter something beautiful it is in the context of an advertisement, or a consumer product. The movie resolves to a contrived ending with no loose ends, the pop song always goes to the minor chord at exactly the right moment, the woman in the magazine has inhumanly perfect skin. These objects are trivially beautiful, their focus is on pleasure rather than understanding. Real beauty is something akin to the sublime of the Romantics, a combination of ecstasy and terror that reminds us simultaneously of how unique and insignificant we are
We can try to dispel aesthetics as a social construction. We can say that our notions of beauty and ugliness are taught to us by culture, but we cannot explain where these feelings come from. It doesn’t matter that a person prefers a cheeseburger to salad, or that a culture prefers lighter skin to darker skin, the question is why anyone prefers anything to anything. Beauty is an impulse, not a property. It is the expression of our embodiment, of a will towards the world, as a result of desires. Most importantly, our experience of beauty is primary, it comes to us before we analyze and try to define it within a given system. We cannot understand anything without first understanding it aesthetically
While aesthetics may not have much to do with empirical truth, it certainly plays a role in our perceptions about what is valuable and worth pursuing. In many cases aesthetic considerations precede and motivate empirical research. Remember in the beginning where I mentioned aesthetics and elegance influencing Newtonian physics? Even today you hear cutting edge scientists talking about an “elegant” unified theory of everything, as if beauty were a necessary property of scientific truth. Why is this so? Can the truth not be ugly, or complicated, or obscure in some fashion? Is this a reflection of the Platonic conflation of “the good,” as everything that is true and beautiful? I don’t have the answers, but I’ll admit that my first impulse is to say that the truth is beautiful, but always in ways that are unexpected. Regardless, I think science and mathematics have a lot to learn from aesthetics, at the very least in regards to the analysis of their own motivations.
Stephen Hawking retired his search for a "Theory of Everything" in consideration of Gödel's Incompleteness Theorem.
Albert Einstein famously remarked, "the most beautiful thing we can experience is the mysterious." The fact of the matter is that there are limitations to what we can know. That doesn’t make what we’ve accomplished any less valuable, it doesn’t mean that we should give up on our endeavors, and it doesn’t give license to intellectual anarchy. It simply means that while there’s an infinitude of things yet undiscovered, things that we don’t even know that we don’t know, we should also learn to live with uncertainty, as it is bound to follow us wherever we go. This world is and will forever remain a mysterious place. And there’s nothing wrong with that.