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Philosophical temperament

June 30, 2014

In this post I’d like to follow up once more on a theme I’ve been exploring recently, this time to extend John Henry Newman’s calculus metaphor from a single line of inquiry to the polyphony of language. But much of this post, while in the spirit of Newman, will go beyond what I imagine Newman himself would have agreed to.


Now, Newman goes quite far, I think, along the road to the major insights of 20th century philosophy of language–to the recognition, made by thinkers as diverse as Ludwig Wittgenstein and Mikhail Bakhtin, that we also have only indirect and limited access to what our words mean; that our words mean less precisely than we imagine, and depend for their meaning on the future as well as the past and present. Newman knows that the things we say about reality only approximate closer and closer to that reality, and that only time can tell how close any particular statement was. But he pays insufficient attention to how our words mean, not absolutely, but relative to the language in which they are spoken. There are moments in the Grammar where his reflections on language are quite insightful–I’m thinking, particularly, of his account of polysemy, and his excursus on the interrelated doctrines of the Trinity–but they’re not put together into any coherent theory.

More often, Newman looks, not at the difficulty of meaning precisely, but at the difficulty of converging on a given truth accurately. His account of language tends to rest at the simple division of thought into “real” and “notional”: either we have something concrete in mind, or we don’t, and it’s just a useful but potentially misleading abstraction. This approach gives us little help understanding how our abstractions work: how they fit together, either provisionally, or in such as way that (as Newman seems to think) we can pass back from abstraction to reality. If the modernist philosophy of language is right, this division is arbitrary, and so is the problem it raises. We need, not to see how we move back and forth between concrete precision and abstract vagueness, but how it is that we use language–how we give voice to many different thoughts–when we are incapable of being perfectly precise.

Put differently: we must understand, not just how we can reach a secure position on a single issue, but how we can hold together our positions on many issues when no issue can be definitely resolved and all of the issues interrelate with one another. We must look, not just at the (mathematical) limits of certain lines of inquiry, but at the ratios of lines of inquiry with one another. The relevant metaphor is no longer calculus, but harmonics. Our goal is no longer to step back from time to see where the lines converge; there are no longer lines to follow. Rather, our goal is to find how to move in time between the issues that concern us without stumbling into dissonance.


Naive philosophy of language, we might say, resembles naive Pythagorean harmonics, also called just temperament: each note, that is, each meaning, stands in a simple, definite, proportion to each other. The tonic to the octave is 1:2; the tonic to the dominant, 2:3; the tonic to the fourth, 3:4. We know exactly what each word statement means relative to each other statement, and can easily specify it.

Such harmonics offer a good account of what we do when we sing, but it’s a bad idea to just-temper a piano. Pick a note as the basis. Go up twelve perfect fifths, and you’ll be on the same note as if you ascended twelve octaves. But the latter, naively, should have a pitch ratio to the basis of (1:2)^7, that is, 1:128; the former, (2:3)^12, that is, 4096:531441, or about 1:129.746. A small difference, but one big enough to cause real problems. If you decide to tune each note according to the most simple pitch ratio available, the piano will sound fine–if you play with the 1:1 note as the tonic. Play in any other key, and it’ll be out of tune.

The usual solution, called equal temperament, is to tune the piano such that all semitones have the same ratio: since an octave has a ratio of 1:2, and there are twelve semitones in an octave, we give each semitone a ratio of 1:2^(1/12), that is, about 1:1.0595. But note this “about.” Equal-tempering is, in fact, impossible; it is in a mathematical sense irrational, and so can only be determined through an evaluation of a limit. We can approximate the desired ratio to an arbitrary degree of precision, but cannot actually reach it.

To return from metaphor-land: when we begin using the instrument of writing, it becomes necessary to keep our language in tune. Under just-tempering, only some of our concepts make sense together. There are some philosophical chords that must not be thought. Under equal-tempering, on the other hand, we can describe, but can never precisely specify, how our various concepts relate to one another. As time goes on we are ever progressing closer to perfect sense, without ever arriving.


Most modern philosophers, I think, imagine themselves to be questing after something like equal temperament. It’s an admirable goal, though an impossible one. But I’m not convinced that it should be ours. To take back up the metaphor, many options remain for how to tune an instrument; I’d like to explore two, each of which has its own particular application.

In the first, called well temperament (as in the “well-tempered clavier”), all ratios are rational, none are simple, and some approximate simplicity better than others. Well-tempering can be thought of as a compromise between just and equal: it is achievable, and sounds more right than equal-tempering in most keys, but sounds worse in others, and always worse than a perfect just-tempering. Well-tempering, however, preceded equal, and does not even imagine its possibility. It seems, not perfect equality, but to open up options. It allows us to play multiple keys on a single instrument while giving each key its own “color.”

The second I would discuss is not a kind of temperament, but the recognition we need only temper instruments that we tune in advance. With stringed instruments, like the violin, we need only tune the four strings according to 2:3 ratios. The rest the placement of the musician’s fingers determines. When he would play a perfect octave (1:2) above a string, he puts his finger 1/4th of the way down the string above it, for a ratio of (2:3)x(3:4)=1:2. When a perfect fourth (3:4) below a string, he puts his finger 1/9th of the way down the string below it, for a ratio of (3:2)x(8:9)=4:3. When he wants a minor third above that, he puts his finger 7/27ths of the way down the string, because (8:9)x(5:6)=20:27. That 1/4 and 7/27 are different numbers does not matter to him.

The work of well-tempering resembles the work of a dictionary. It gives each word its meaning, and the words that it ensures work well together, do. But inevitably, there will be words that can be used together in a way that the dictionary cannot account for. The dictionary tries to capture the color of most different branches of discourse, especially the most important ones, but always leaves some out.

Violin tuning, on the other hand, resembles nothing so much as a recognition that meanings change over time; or, more accurately, that it is not words, nor sentences, but statements that have meaning. To mean one’s words like a violin, rather than a piano, is to write while giving up on the idea of fixing one’s language once and for all. It is to cease worrying that a word in one place might have a different tone than in another, so long as the progression of one’s meanings can be followed. It is to be open to philosophical vibrato.


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