BY MATTHEW HERBERT
Well, that’s a cheeky way to start.
Wittgenstein: Towering figure in logic and mathematics, member of old Viennese family of eccentric aristocratics gone mad with genius, possibly the greatest philosopher of the 20th century.
Me: Hillbilly turned bureaucrat, blogger, broken down trail runner.
Where’s the connection?
Actually, the thing that makes my link with Wittgenstein improbable is not my humble background or middling life accomplishments. It’s my devotion to the ideas of other philosophers that differ so much from Wittgenstein’s. From Plato I inherited a love for objective, eternal truths. I may not be very good at math or geometry, the main disciplines that discover such truths, but I believe, as Plato did, that the facts of mathematics are special. They are on a radically different footing from “ordinary” facts we observe with our senses.
The ordinary fact that grass is green, for example, is subject to a multitude of caveats indicating that its being true depends on one’s perspective. The chlorofil in grass, for example, is only “green” at the structural level of mid-sized objects; at the moleular level, it is not. Shrink yourself down to microscopic level, and you would not, in fact, see grass as green. Furthermore, green things (like grass) are only green in the types of atmospheres that can broadcast the visible spectrum of light as we know it here on earth. In different environments, different parts of the spectrum could be visible, and green might not be.
And so it goes. Grass is green, but only in the particular embodied, earthbound circumstances we find ourselves.
Mathematical facts are not like this. They do not depend on one’s perspective or physical configuration. They are eternally and objectively true. You can imagine the universe exploding–everything and everyone disappearing–and a new universe being reborn billions of years hence: two plus two will still equal four. Grass may or may not exist in this new reality, and it may or may not be green, but math will endure as is.
Wittgenstein was not convinced of this proposition. For most of his career he was a “nominalist,” someone who thinks the truths of mathematics are mere products of the rules regulating its symbols. The system does not necessarily correspond to any facts outside itself. In other words, you could devise your own system of symbols, and as long as its internal rules of meaning and syntax were consistent, you could produce statements that were “true” under all circumstances. Big deal.
The fact that lots of people subscribe to mathematics as a useful, coherent system does not mean its facts have any more weight than those produced by other made-up systems, say the nominalists. Mathematical truths are merely the outcome of the way we use the language of mathematics; they are hardly the eternal, crystalline truths revered by Plato.
Later in his career, Wittgenstein would modify his nominalism slightly, but he would never go all the way where my intutions led me, into the camp of realists. Realists believe the facts of mathematics correspond with an external reality and that they are always and everywhere true, not mere constructions of symbolic coherence or the consensus of those who use them.
I won’t bore you with details, but there are several other instances where I find myself disagreeing with what Wittgenstein thought. The brochures of university philosophy departments, though, will tell you that philsophy’s value is in teaching you how to think, not what to think. Despite this sentence’s awful triteness, it is true. Philosophy teaches us how to think. And it is in that endeavor that Wittgenstein won me over.
For me, Wittgenstein’s biggest contribution to philosophy is his development of the idea of levels of analysis, a very powerful insight about how we think. Any informed body of discourse–on, say, politics, art, physics, or whatever–proceeds on the assumption of concepts and terminology that are determined by a particular level of analysis.
This is not quite an original thought. Two thousand three hundred years before Wittgenstein, Aristotle taught that any and all analysis should be conducted at the right level of granularity:
It is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits; it is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician scientific proofs.
But this breezy observation is more or less where Aristotle left his idea. It’s a good idea, but hard to act on. Finding the right level of precision is almost always the hardest part of tackling a problem analytically. It’s like telling a baseball player to hit the ball smack-dab in the middle. Great advice, but those who can follow it are probably already good batters.
I contend, though, that Wittgenstein birthed an idea that can actually help us calibrate our sense of precision to the problem at hand–the idea of the language game.
First, a word about what the language game is not. Because many people first encounter this idea as undergraduates in one of the “critical” disciplines that try to subvert what the other disiciplines are saying–the humanities or softer sciences–they tend to think Wittgenstein is using the term subverively himself. He must be trying to warn us that elites are using fancy words to perpetrate a wily intellectual fraud on us. Please banish this thought. If you want to pursue it, read Michel Foucault’s gloss on the Marxist idea of the mystification of terminology. It has nothing to do with Wittgenstein.
So what did he really mean? Wittgenstein’s language game is any specialized discourse designed to deal with a particular task or themtic area. What characterizes the language game is that (1) it defines the acceptable useage of terms and grammar for anyone who needs to address its task, and (2) it works. In Philosophical Investigations, the second of Wittgenstein’s landmark books, he outlines what a very basic language game could look like:
Let us imagine a language for which the description given by Augustine is right. The language is meant to serve for communication between a builder A and an assistant B. A is building with building-stones: there are blocks, pillars, slabs and beams. B has to pass the stones, and that in the order in which A needs them. For this purpose they use a language consisting of the words “block”, “pillar”, “slab”, “beam”. A calls them out;—B brings the stone which he has learnt to bring at such-and-such a call.——Conceive this as a complete primitive language.
For the builders, the best level of analysis is the one that individuates blocks, pillars, slabs and beams, and nothing else. They have no need for terms expressing broader composites (say, wall, buttress, etc.) or smaller parts, like molecules. Their language gets the job done.
Why does Wittgenstein start with such obvious observations about language? At the time he was writing the Philosophical Investigations, philosophy was gripped by an idea that language could and should be made ever more precise. Science led the way: however finely science divided up the world, all our language shoud follow suit. (If you are interested in this idea, see A.J. Ayer’s Language, Truth and Logic, one of the finest introductions to what came to be known as analytic philosophy.)
By the mid-20th century, many philosphers believed their prime directive was to translate ordinary-language sentences into a special form of symbolic logic (at which Wittgenstein was highly adept). This exercise, they believed, would reveal a sentence’s correspondence with the pristine structure of reality and help dsitinguish between terms that signified something real and those that were erroneous or merely metaphorical.
It was a good idea, but it went too far. Science was constantly revealing new, more precise levels of the world’s structure, and it was a fool’s game to try to adapt ordinary language to mirror its progress. Wittgenstein himself had helped bring this folly about in his first landmark book, the imposingly named Tractatus Logico-Philosophicus. There, Wittgenstein argued that language created a picture of reality. Its job was to depict the structure and dynamics of reality as accurately as possible. If science or logical analysis could reveal it, humans could talk about it in ever greater detail and accuracy.
By the time he wrote the Philosophical Invetigations, Wittgenstein had come to view his picture theory of meaning as too doctrinaire. Real people used language for a “motley” of reasons, and the utility of their useage did not necessarily depend on ever-sharpening precision. He even came to mock this analytic mindset he helped inspire. Precision is a fine thing, Wittgenstein came to believe, but like most fine things, it is not always better in greater quantities. He wrote:
When I say: “My broom is in the corner”,—is this really a statement about the broomstick and the brush? Well, it could at any rate be replaced by a statement giving the position of the stick and the position of the brush. And this statement is surely a further analysed form of the first one.—But why do I call it “further analysed”?—Well, if the broom is there, that surely means that the stick and brush must be there, and in a particular relation to one another; and this was as it were hidden in the sense of the first sentence, and is expressed in the analysed sentence. Then does someone who says that the broom is in the corner really mean: the broomstick is there, and so is the brush, and the broomstick is fixed in the brush?—If we were to ask anyone if he meant this he would probably say that he had not thought specially of the broomstick or specially of the brush at all. And that would be the right answer, for he meant to speak neither of the stick nor of the brush in particular. Suppose that, instead of saying “Bring me the broom”, you said “Bring me the broomstick and the brush which is fitted on to it.”!—Isn’t the answer: “Do you want the broom? Why do you put it so oddly?”
I quote this passage at length because it is one of the most revelatory and useful ones I have ever read. I have probably read tens of thousands of pages of philosophy; this one stands out for speaking vividly to philosophy’s main task–clarifying the methods of analysis so that we can think more clearly about real problems. Only 2,300 years after Aristotle (!), Wittgentein’s idea of a language game actually affords some purchase on this maxim.
But then again, isn’t Wittgenstein just recommending we optimize precision according to the purpose of our chosen language game? If your language game is “particle physics,” you’d better be prepared to prepared to re-analyze sentences about atoms into sentences about protons, neutrons and electrons, and so forth. But if your game is “housecleaning,” you’ll just sound silly if you refine terms to account for finer structures and more recondite dynamics than those relevant to the task at hand.
Believe it or not, though, one of the 20th century’s most respected philosophers of science believed science worked more or less like a Wittgensteinian language game. Although scientists like to think of themselves as discovering the hidden structures of reality, in ever finer detail, Thomas Kuhn believed what they did in practice was to carry out a constant negotiation about the acceptability of professional terminology.
In the long stretches when sicentists were agreed on a general outlook of the world–say Newtonian physics, which nicely explains the behavior of mid-sized objects–Kuhn says they wrote their literature using a common lexicon of accepted terms. He called it “normal” or “puzzle-solving” science. But when a major discovery, like quantum physics, upended the general outlook, scientists had to begin a radical renegotiation of terms. Those who stuck with the old paradigm were gradually “read out” of the literature, as Kuhn phrased it in his standout 1962 book The Structure of Scientific Revolution.
By the way, “paradigm” is not just a neat term for this way of thinking about science. It is the term Kuhn himself chose to describe what are essentially Wittgensteinian language games “played” by scientists. To say biology is in a post-Darwinian paradigm is simply a nifty way of saying biologists now share a language game that enshrines and proceeds on the assumtion of Darwin’s principles. I don’t mean to sound overbearing, but if you consider yourself in any way an intellectual and you have not read Kuhn’s Structure of Scentific Revolution, go read it now. It is the book that gave us the phrase “paradigm shift.” Discovering what the term signified when it was fresh is a pleasure.
Kuhn’s book caused a stir because it seemed to say scientists changed paradigms, not because they were factually wrong about the world, but because they were overwhelmed by the partisans of a new, winning set of terminology. If we are going to give Kuhn credit where he earned it, for enlightening us on the way science proceeds in practice, we might as well blame him as well for darker things he wrought, and this seems a good place to do it.
Kuhn’s idea of a professional paradigm shift, laid at the altar of the radical intellectual left, fueled “critical” and “literary theorists” to conclude that science was “really” just a discipline for imposing certain dogmas on those too powerless to defend themselves. You know–the ideological narrative of the power elite.
Kuhn would have said we can be agnostic about whether facts really change the minds of scientists without sounding the death knell for truth, but the critical and literary theorists were already off to the races. Science, like the police and colonialism, was just one more tool for oppressing the masses, they said.
It was a dark time. In 1996 the physicist Alan Sokal nicely parodied critical theory when he submitted a junk paper arguing that quantum gravity was just a social and linguistic construct, not a “fact” about “reality.” Sokal got his paper published in Social Text, a leading journal of critical theory, by mimicking the style of its favorite authors–essentially emulating their language game.
So what, if anything, did Sokal prove?–that academic language games really are just frivolous excercises in generating new terminology? Without wading through all the arguments pro and con, my own view of language games is that they offer a provisional perspective on the world that lets one conduct the educated guesswork involved in optimizing precision.
If that sounds garbled, it’s because I am not a brilliant philosopher. Daniel Dennett, however, is, and he is also an heir to Wittgenstein, so I will let him do my work for me. As we try to make sense of the world, Dennett says, we adopt a provisional stance. If the stance is useful, we acknowledge (sometimes explicitly but usually implicitly) that its basic axioms, principles and terminology are conducive to discovering the truth, and the stance becomes less provisional. It starts to harden into something like a paradigm.
Adopting the right paradigm, though, is no mere matter of negotiating terms. The terms have to work, and as they work, they tend to group themselves into different levels of precision.
Joshua Rothman beautifully captures Dennett’s idea of stances, levels and precision in a recent profile in the New Yorker. He writes:
Some objects are mere assemblages of atoms to us, and have only a physical dimension; when we think of them, [Dennett] says, we adopt a “physicalist stance”—the stance we inhabit when, using equations, we predict the direction of a tropical storm. When it comes to more sophisticated objects, which have purposes and functions, we typically adopt a “design stance.” We say that a leaf’s “purpose” is to capture energy from sunlight, and that a nut and bolt are designed to fit together. Finally, there are objects that seem to have beliefs and desires, toward which we take the “intentional stance.”
If you’re playing chess with a chess computer, you don’t scrutinize the conductive properties of its circuits or contemplate the inner workings of its operating system (the physicalist and design stances, respectively); you ask how the program is thinking, what it’s planning, what it “wants” to do. These different stances capture different levels of reality, and our language reveals which one we’ve adopted. We say that proteins fold (the physicalist stance), but that eyes see (the design stance). We say that the chess computer “anticipated” our move, that the driverless car “decided” to swerve when the deer leaped into the road.
Life, like science, is an experiment. My experiment has led me to analyze the world in almost exactly the same style as Dennett, if several notches below him in terms of insight achieved. There are certain stances that seem indispensable for understanding the world. They are not written in stone. We discover them and, yes, in a certain sense, create them as we probe the world around us. That does not mean we make it all up, but it does mean that our language and thought take an active role in dividing the world up into its constituent parts and describing their structure and dynamics.
Wittgenstein was right when he said language creates a picture of the world. But that picture will never be finished, and we can never step outside it to check whether our stance (or paradigm or language game–you pick) is the right one. But, in the word’s of Wodehouse, Wittgenstein’s favorite comedic writer, we do not repine; we stagger on.