Calling things by their true names

Descriptive markup and the search for a perfect language

C. M. Sperberg-McQueen

Founder and principal

Black Mesa Technologies LLC

Technische Universität Darmstadt

Copyright © 2015 by the author. Used with permission.

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Calling things by their true names

Descriptive markup and the search for a perfect language

Balisage: The Markup Conference 2015
August 11 - 14, 2015

Some of you will have heard of, and some of you may have read, Umberto Eco’s book The Search for the Perfect Language [Eco 1993]. I read the book some time ago (I think in 1998), because it sounded like a book about SGML and XML. And, of course, it is. Because everything is about SGML and XML because SGML and XML are about everything and if SGML and XML are not attempts at creating perfect languages I’d like to know what they are. I’d like to talk, today, about some aspects of descriptive markup and their relation to the idea of a perfect language.[1]

There’s a certain satisfaction in thinking that the work we do is following in the footsteps of people like Leibniz and other who have worked on the perfection of language. Leibniz as it happens is the last person (in the western tradition at least) whom philosophers still take seriously as a philosopher, who took seriously the notion of developing a perfect language. So we’re also, as Eco’s account makes clear, following in the footsteps of a lot of crazy idealists like L.L. Zamenhof, the inventor of Esperanto, and Giuseppe Peano, who in addition to being a great mathematician and the creator of the Peano Axioms, which are at the foundation of modern mathematics and which play a crucial role in Gödel’s Incompleteness Proof among other things. Peano published the Peano Axioms in a book written in Latin, because he was trying to encourage the use of Latin as an international scientific language. That was a few years before he decided that no one wants to use Latin because no one outside Italy actually studies Latin hard enough in school and concluded that the right thing to do was to make Latin easier to write. So he proposed Latino sine Flexione, that is to say, Latin without any inflections, declensions, or conjugations — Latin that makes any classicist who sees it weep.[2]

But let’s focus on Leibniz. I would rather think of myself as following in the footsteps of Leibniz than as following in the footsteps of the amusing but eccentric collection of characters who follow Leibniz in Eco’s account of perfect languages. Leibniz’ perfect language is always really perfect, in part because it’s always a project, and never a product. When he writes about it he is almost always seeking support to work out the details — he never actually got the funding to do it — so his vision remains unrealized and perfect in the way that our plans are always perfect, even when our implementations aren’t. His basic idea is that we need two things.

First, we want what Leibniz calls a character realis or characteristica realis. It’s hard to know exactly what he meant by either of these phrases because the translators — both the translators into English and the translators into any other modern language — render these phrases unhelpfully as real character or real characteristic (or the etymological equivalents in other modern languages). That is, they shift the word forms from Latin to English (or French, or German), but otherwise leave his Latin alone. If we ask What does that mean? — it clearly doesn’t mean characteristic in the modern English sense — the translator essentially looks at us and says, You get to figure that out because I couldn’t; that’s why I left it alone.

The phrase real character sometimes appears to denote a system of categories, an analysis of thought of composite ideas into simpler ideas. And sometimes it seems to mean a writing system, a symbol system, an ideography for writing down references to such ideas. So as a whole the real character seems to be some kind of combination of what we would call an ontology and an ideographic script. Leibniz mentions explicitly the notion, widespread in the 17th and early 18th centuries, that Chinese is a model for the kind of thing he is talking about.

As it happens, Chinese is not a model after all, because Chinese is not an ideographic script; like every other known human writing system, it is a logographic script. And it’s clear that Leibniz did not want a logographic script. With logographic scripts, of course, as you can guess from the name perhaps, the basic idea is that you have something in writing and say What does that bit of writing mean? pointing at it, the answer is That represents the following word or sequence of words: ... Writing systems represent linguistic objects, and then the linguistic object may denote real things, may talk about reality. But the mapping from the written word to things goes by way of an intermediate stop in whatever natural language you are writing in.[3]

In Leibniz’ day, Chinese was often thought to be purely ideographic because the same script is used all through China, by people whose natural languages are not in fact mutually intelligible. Chinese characters are also used to write Japanese and Korean within limits (very strict limits that essentially defeat the idea that there is anything relating to ideography here). But the Chinese script is not in fact ideographic, but logographic.

But there are examples of ideographic scripts. Mathematical notation is an ideographic script. This is sometimes doubted, because mathematical expressions can be verbalized. And it is true that we all learn how to read mathematical notations aloud. But x with a superscript 2 following it means x squared or x to the power 2, however we care to verbalize it. It represents an idea, not a particular form of English words. Germans learn how to verbalize it, Anglophones learn how to verbalize it, French speakers learn how to verbalize it, everybody who learns mathematics learns how to verbalize it, but here the relationship of script to language and idea are quite different: the written symbol directly denotes the thing (or, as Leibniz would say, the res). So mathematical notation is an example of a real character, or an ideography. Chemical notation can similarly be seen as ideographic.

So ideography is not really an impossible idea. Leibniz thought it would be extremely useful to have one. He thought it would be useful in part because of the second thing we need, for a perfect language: a perfect language would enable systematic reasoning to be more reliable. It would, Leibniz suggested, provide a calculus ratiocinator, a thinking calculus, or a mechanical technique for thinking. He argued if we did things right, we could put controversy behind us because once you have translated an argument into this universal character, checking the reasoning of the argument becomes a purely mechanical task, like checking a complicated arithmetic calculation. So that to resolve any controversy, all the one disputant has to do is invite the other to a calculating table and say, Let us calculate. Nowadays, we might say (and sometimes do say) Let’s do the math which comes down to something very similar for a particular class of questions.

Why Leibniz thought that a real character as he envisaged it would support reasoning can best be understood if we take a brief digression through the history of logic. At Leibniz’s time, the state of the art for formal logic was Aristotle’s syllogistic. The art of the syllogism had been cultivated and further developed through the Middle Ages, and scholastic philosophy had refined Aristotle somewhat, but the approach remained essentially Aristotelian. By Leibniz’s time, syllogistic was really rather old-fashioned. So Leibniz was swimming against fashion in regarding it as important. He regarded it in fact (rightly) as one of the greatest monuments of human thought, and as the basis for systematic reasoning.

Let us consider a simple example syllogism; many of you will have heard this one. We can reason thus:

  • All Greeks are mortal.

  • Socrates is a Greek.

  • (Therefore) Socrates is mortal.

We have three sentences here: a major premiss, a minor premiss, a conclusion. Each sentence takes the form of a subject and a predicate. In XML, we might write it this way:
  • <subject>All Greeks</subject> <predicate>are mortal</predicate>.

  • <subject>Socrates</subject> <predicate>is a Greek</predicate>.

  • (Therefore) <subject>Socrates</subject> <predicate>is mortal</predicate>.

Syllogisms can take other forms and operate in other modes. Some forms and modes lead to valid conclusions, and others don’t. And the theory of syllogistic is an elaborate account which assigns to modes names like Barbara and Baralipton and Celarent, where the vowels e, a, i, and o denote various properties of the premises (affirmative or negative, universal or particular). In its late medieval and early modern flowering, syllogistic is extremely elaborate and hard to understand.

Leibniz, being among other things a good mathematician and creator of abstractions, reduced the theory of syllogism to a few basic principles and, from those basic principles, developed the entire body of syllogistic theory as it was known in his day. And his perpetual summary is that the predicate is present in the subject. This is a little difficult to understand because our way of thinking about it tends to want to go the other way. We tend to regard logical statements as extensional statements. And when we say All Greeks are mortal, what we are saying is: The set of Greeks is a subset of the set of mortal things. So we would be inclined to say the (set denoted by the) subject is included in the (set denoted by the) predicate, and extensionally that’s true. And in about half of Leibniz’s sketches of logical calculi he uses an extensional approach, and certain problems get solved.[4]

But he keeps coming back in the other half of his sketches on logical calculi to an intensional (with an s) account of logic in which, when we say Greeks we mean all of those things which have the following set of properties: .... And when we’re talking about mortal beings we’re talking about a set of things that have another set of properties. And if all Greeks are mortal, what that means is the set of properties that distinguish being mortal is a subset of the set of the properties that define being Greek. So (on an intensional view) the predicate is always (implicitly) present in the subject.[5] And even though he kept flirting with extensional interpretations of logic, Leibniz stuck by that fundamentally intensional formulation.

Leibniz’s proposal for a perfect writing system for a real character starts from the following observation. We have some ideas that we regard as composite (as made up of other ideas), so if we analyze those ideas, we have simpler ideas. And if we continue this process of analyzing composite ideas into simpler components, we either find an infinite regress (which would seem to suggest that it’s impossible to talk to each another), or we hit bottom with a set of atomic ideas. Leibniz observed we do talk to each another; we have the perception that we are succeeding in communicating. And therefore, without actually proving it, he assumed that we don’t actually have an infinite regress, but we will reach bottom, so that we can analyze human thought into a set of atomic ideas. He didn’t think this would be easy; that was why he was asking for money. And he thought it might take a generation of work by Europe’s academies of science to develop an analysis of human thought into atomic ideas that would suffice for scholarly work. And he addressed in advance the concern that is already forming itself in many of your heads: Well, wait. What if we assume these atoms, and then later we re-analyze things, and we don’t accept those concepts as atomic anymore? He worked out to his own satisfaction that we don’t have to wait for a perfect analysis to make some progress; we can go on, as it were, provisionally. Leibniz’s notion of reasoning also included a lot more on probabilistic reasoning than is common in modern symbolic logic, but that’s another story.

Just as we can combine atomic ideas into composite ideas, and then combine those composite ideas into further composite ideas of still more complexity, so Leibniz’s conception for the real character was that the symbols for atomic ideas should be combined to form symbols for composite ideas, just as the atomic ideas themselves are combined. So the symbol for any composite idea would be constructed from (and thus automatically contain) all the symbols for its component ideas. One could thus see at a glance, looking at the symbol for any concept, what its fundamental constituents were. That means that checking whether the premiss All Greeks are mortal is true would be a simple question of checking to see whether the symbols that make up the defining features of mortal are present in the the symbol denoting Greeks. We’ll come back to this a little later.

This notion that the way we write things down should exhibit their structure may feel very familiar to you. It feels to me like precisely what we try to do when we develop SGML and XML vocabularies. Now the developers of SGML did not, as far as I know, think that they were imposing on their users the task of creating an ontology or of analyzing human thought into atomic bits. But they were trying to make it possible to develop vocabularies that allowed the reuse of data.

Now, why is it that data for a particular application cannot be reused by another application? In the cases we are familiar with — in the cases that are suitable for treatment with XML — markup does three things. Among the things markup does, it identifies the constituent parts of the document. And by naming things with generic identifiers, it allows us to say that for our purposes, these two things are the same, because they have the same name — they’re both <p>, for example — and these two things are different, because they do not have the same name — one is <p> and one is <ul> or <list> or <section> or what-have-you.

Some names are the same as other names, and some names are different from other names. Those are the two absolutely fundamental services that generic identifiers offer us.

And the reason that data intended for one application cannot always be reused for another application is that many applications ignore some of the distinctions important for other applications. If the data are tagged for typographic processing, for example, and if we say (as we often do) for the purposes of display or print rendering some things which are different will be treated the same way — perhaps we will italicize not only technical terms but also foreign words and emphatic words and subtitles — then those distinctions are not needed for typography. And the reason we can’t reuse typesetting tapes to do all of the things we might want to do with documents is that we don’t always want to treat those things as the same. And if you ask yourself, how do we know what things we will always want to treat the same way and never want to treat differently, the answer is we will always want to treat things that we think of as the same in the same way. We may choose to take things that are different and treat them in the same way, but unless we are engaged in a kind of experimental typography in which technical terms are italic on odd-numbered pages and bold on even-numbered pages unless they are powers of two, then we will always want technical terms, if that’s one of our basic, primitive categories, to be treated the same way.

This is such an obvious point that it can take a while to work out its implications (though in the 1980s and 1990s it didn’t take very long for people to start acting as if it were obvious). What that boils down to eventually is that if you want really good descriptive markup, you need to say what things are. What do you think this is?

This led many SGML and XML practitioners to a beautiful sense of freedom and power: it’s like being Adam and getting to name all of the animals. That’s incidentally another reason that XML and SGML have always felt to me as though it were a search for a perfect language, because the Adamic language was for many centuries regarded as quite obviously the most perfect of all languages, if we could only recover it. Eco is very good on that part of the history. And even now when, for reasons I’ll come to shortly (I hope), we don’t always aim quite as high as Leibniz was aiming, we are interested in using markup to exhibit the structure of things, to visualize things, to make diagrams of thing, to make it easier to look at particular aspects of things. Liam Quin’s paper on diagramming XML and Priscilla Walmsley’s paper on detecting and visualizing differences between complex schema, both give good examples of that continuing interest [Quin 2015, Walmsley 2015]. The elevator pitches Tommie Usdin recommended to us in her opening talk seem also to require that we identify the essentials of our story, as a way of making things clear to the people we are talking to [Usdin 2015].

Leibniz was not the first person to worry about these things. And Leibniz was able to be confident that from a set of atomic ideas we can generate all of the huge variety of concepts that we use in natural language in part because he had read Ramón Llull. Ramón Llull was a 13th century Majorcan minor nobleman who led — as so many 13th century saints seem to have done — a life of dissolution and sin until he had a conversion experience, joined a friary, and became a theologian. And in a vision on the side of a mountain God revealed to him the method in which he could find the truth and convert the heathens. Llull’s method, which he refined in book after book after book over a period of decades, with variations over time, basically involves identifying what, for purposes of my exposition, I will call fundamental concepts and assigning symbols to them and combining the symbols to make other concepts. So, in the final exposition of his great art, the work called the Brief Art (or ars brevis, although it’s not actually all that brief), Llull uses the alphabet consisting of the letters B C D E F G H I K. (The letter A is left out because being the first letter of the alphabet it should denote the divinity and the unity of all of those things. B through K are aspects of A, as it were.) And he assigns to each letter a principle: goodness, magnitude, eternity or duration, power, wisdom, will, strength, truth, glory. And then to each symbol he assigns a relation: difference, agreement, contrariety,[6] beginnings, betweenness, end, being greater, being equal, being less than. Then, to each symbol he further assigns a question, and a subject, and a virtue, and a vice. Once this infrastructure of symbols and meanings is set up, from a simple combination of letters like BCD, Llull can create essentially all of the sentences that we can create by combining the words goodness, difference, whether?, God, justice, or avarice, with magnitude, agreement, which?, angel, wisdom, or gluttony, and eternity (or duration), contrariety, of what?, heaven, fortitude, or lust. It’s easy to see that the number of sentences we can form is very large, no matter how exactly we imagine the rules for sentence construction to be set up (Llull is rather vague on this topic, by modern standards); the ability to produce a large number of combinations from a small number of basic constituents is precisely what is meant by the phrase combinatorial explosion.[7]

Now, to be honest, it’s not entirely clear exactly what Llull thought he was doing. He gives his treatises titles like Method of Finding the Truth so that it sounds like he thinks his method is a way of deciding questions and learning things, proving true facts about the world. By analogy with modern systems like context-free grammars, from which a mechanical process can generate all possible grammatical sentences, and no non-grammatical sentences, we may be tempted (that is, we are certainly tempted) to believe the Llull is creating a system which will generate true sentences and only true sentences. But it’s not quite so simple. Every now and then Llull remarks that applying the prescribed procedure to a particular configuration of symbols will result in a sentence which is false, or suggest an inference which is invalid. The user of Llull’s technique, that is, must understand which sentences to accept as true and which to reject as false. This leads Eco and others to say that Llull and the user of Llull’s technique are only getting out of the system precisely what they already know. Eco writes that Llull’s methods

do not generate fresh questions, nor do they furnish new proofs. They generate instead standard answers to an already established set of questions. In principle the art only furnishes 1,680 different ways of answering a single question whose answer is already known. It cannot, in consequence, really be considered a logical instrument at all.

Eco considers Llull’s treatment of the question Whether the world is eternal and concludes:

At this point, everything depends on definitions, rules, and a certain rhetorical legerdemain in interpreting the letters. Working from the chamber BCDT (and assuming as a premise that goodness is so great as to be eternal), Lull deduces that if the world were eternal, it would also be eternally good, and, consequently, there would be no evil. But, he remarks evil does exist in the world as we know by experience. Consequently we must conclude that the world is not eternal. This negative conclusion, however, is not derived from the logical form of the quadruple (which has, in effect, no real logical form at all), but is merely based on an observation drawn from experience. [8]

I’m not entirely certain that Lull’s method is quite as vacuous as Eco suggests. I think it may be possible to view it as a kind of heuristic. You want to solve a certain problem, you can think about it in these ways, and the combinatorics will show you new ways to think about it. Maybe there is an algorithm for providing all possible combinations of ideas so that when you think about it, you will say, Oh, wait, that one will help.

Modern books on heuristics are not much different. If you read Polya’s book How to Solve It [Polya 1945], he will not tell you exactly how to solve your problem. He gives you hints about ways to think about it that may help. But you are responsible for recognizing that this one will help, or at least trying it and seeing if it helps. Polya does not generate fresh questions, nor furnish new proofs. He helps the reader find ways to think about your problem which may enable the reader to formulate relevant questions which put the problem in a new light, and which may, if all goes well, lead to fresh proofs. If we do not find Llull’s method as helpful as Polya’s, it may merely be that we are not as interested in theology as Llull was (or that we are more interested in geometry and the other branches of mathematics Polya talks about).

Leibniz had other predecessors. The first Secretary of the Royal Society of Great Britian, John Wilkins, wrote an enormous book called An Essay towards a Real Character and a Philosophical Language [Wilkins 1668]. There’s that phrase, real character again. Now, most people, if they have heard the name John Wilkins at all, know the name from a short piece by Borges in which Borges says Wilkins reminds him of a certain Chinese encyclopedia [Borges 1981]. (Some people have thought that this Chinese encyclopedia is a real Chinese encyclopedia. It’s not; Borges made it up.) In this encyclopedia, the Celestial Emporium of Benevolent Knowledge,

it is written that animals are divided into: (a) those that belong to the Emperor, (b) embalmed ones, (c) those that are trained, (d) suckling pigs, (e) mermaids, (f) fabulous ones, (g) stray dogs, (h) those that are included in this classification, (i) those that tremble as if they were mad, (j) innumerable ones, (k) those drawn with a very fine camel’s-hair brush, (l) others, (m) those that have just broken a flower vase, (n) those that resemble flies from a distance.

This piece became famous in part because Michel Foucault read it and laughed so hard that he decided to call the entire history of western philosophy into question. Perhaps what we think looks as ridiculous from outside as this classification looks to us.

Borges tells us that he has never actually seen Wilkins’ book, because even the national library of Argentina lacked a copy. We, on the other hand, can read Wilkins because the book has been scanned as part of the Early English Books Online project. There are scans available on the web, and it has been transcribed by the Text Creation Partnership, so that there is even a TEI-encoded version publicly available.

When you read Wilkins, instead of just the parody of Wilkins in Borges, I expect that many of you will have the same reaction I did, which is Well, no, he’s not crazy at all. Wilkins’s work reads like a very complicated spec that involves a lot of serious work and a number of unavoidable compromises. (Perhaps Wilkins should be regarded as the world’s first Working Group editor. Except that he had, essentially, a Working Group of one.) The experience of reading Wilkins is not unlike the experience of reading, say, any proposal for a top-level ontology written by people in artificial intelligence or in the semantic web. Actually, it is slightly different: I feel more sympathetic towards Wilkins; I’m not quite sure why.

Ontologies in the sense of AI and the semantic web are also a continuation of Leibniz’s concerns, a continuation that for all of his hundreds of pages and hundreds of bibliography entries Umberto Eco doesn’t talk about. But they show us that the notion of perfect languages is alive and not dead after all. The idea of perfect languages has, however, been split in two. People developing ontologies don’t normally expect to make them into languages or make them components of languages. They are there to enable reasoning, but not necessarily to capture arbitrary utterances.

The other branch of modern work that descends from Leibniz’s concerns is, of course, further work on the systemization and automatization of reasoning: logic. One of the creators of modern logic, Gottlob Frege, explicitly identified his goal as the creation of a language in the spirit of Leibniz [Frege 1879]. Now, to my great astonishment, he did not regard himself as creating what Leibniz called a calculus ratiocinator, or thinking calculus. He thought he was creating a universal character, and his belief is a source of continuing puzzlement to me, both because Frege makes such a sharp (and value-laden) distinction between the two, and because, if one does want to make the distinction, Frege’s work looks very much more like a thinking calculus (it is, after all, a system for logical inference) than like a language or set of atomic ideas (since for all non-logical concepts Frege has recourse to conventional mathemetical notation). Perhaps Leibniz was not, after all, the last person philosophers take seriously as a philosopher to try to build or want us to build a perfect language; maybe that was Frege.

Now, when they hear talk about identifying the atomic units of human thought and defining things explicitly so that we can reason about them, a lot of people get nervous, because surely that amounts to an attempt to banish ambiguity and vagueness, and make everything purely regular. And it might. But in fact, one of the great (and occasionally surprising) things about modern logic is that it has far more capacity (or at least tolerance) for vagueness and underspecification than we sometimes give it credit for. At the heart of this mystery is the fact the modern logic is developed without any fixed vocabulary: it is, if you will, Leibniz’s calculus ratiocinator without his characteristica realis. The only thing modern logicians say about vocabulary is that, yes, there are identifiers; they mean whatever they mean — which is to say, they mean what the person using them says they mean. The actual interpretation, that is formally speaking the mapping from identifiers to objects in the domain of discourse, is completely outside of scope for formal logic. Half of the books on formal logic I have on my shelf don’t actually talk about the structure of an interpretation; they just say That’s out of scope.

Modern logic says, in effect, You have these ideas. You can reason about them this way. What that means is you can make them as vague or as underspecified as you need. So the kind of ambiguity and vagueness that Yves Marcoux was talking about as being essential parts of the formalization of his application domain [Marcoux 2015] — that’s consistent with modern logic. It’s not actually a contradiction of Leibniz’s goal. It is possible to have logic that follows, if you will accept the metaphor, the cowpath of human thought rather than imposing a sort of rectangular system of paved sidewalks.

Another aspect may be worth mentioning. Many of the attempts at perfect languages that Eco talks about really will work only if they are universally successful. They depend crucially on the network effect to have a reason for being. If everybody learns Esperanto, then anybody can talk to anybody else in Esperanto, and we will never, any of us, need to learn a third language. We’ll have our native language, we’ll have Esperanto, and that will suffice. And in the long run, anyone who has ever compared an N-to-N translation problem with a translation into a interlingua and then back out (which gives you a two times N translation problem) will know it would be better — the overall cost to society would be much lower — if everybody would learn an intermediate language. But such a choice would require the same willingness to ignore the short term in favor of the long term that Sam Hunting was talking about the other day [Durusau and Hunting 2015]. The long-term payback only accrues if the entities involved have survived through the short term. And so a lot of entities really want short-term return, and if you’re given the choice between learning a language that would be useful if and only if everybody else in the world learns it and learning a language which is useful now because a lot of people in the world already know it, then you will learn Chinese or English or whatever the lingua franca is in your geographic region. Maybe you will learn Esperanto for other reasons. But if you’re learning it because you hope to use it as a universal language, you will probably be disappointed for a few more centuries.

Jean Paoli, who was one of the co-editors of the XML spec and who performed the signal service of persuading the product groups within Microsoft to support XML, had a very straightforward way of saying this, which I call the Paoli Principle: If someone invests five cents of effort in learning your technology, they want a nickel’s return, and they want it in the first 15 minutes. If they do see an advantage within 15 minutes, then okay. Maybe they will persevere with your new technology. If they don’t see a return within 15 minutes, you’ve probably lost them.

Now, many of us have struggled with managers with 15-minute attention spans, and many of us probably think the world would be a better place if they had longer attention spans (say, at least 30 minutes). But people are the way they are, and if we want to persuade them, we need to pick them up where they are rather than demanding that they change.

Another way in which what we do is sometimes different from what Leibniz was talking about is that we have learned that vocabularies are often a lot simpler when they do not attempt absolutely universal coverage, so we get simplification efforts like the one Joe Wicentowski was talking about the other day [Wicentowski and Meier 2015]. I think it is probably a common experience within the room that really complicated schemas that attempt to blanket an entire application domain tend to be really, really big and really, really hard to learn, and to spawn simplification efforts left and right. So, we often straddle this divide; we create those big schemas, but then we also create partial schemas because partial schemas are easier to understand, easier to use, and easier to teach. And as long as they suffice for a particular sub-application area, they’re extremely useful. We don’t place the burden of supporting all of scholarship on every vocabulary that we write, only on a few of them.

Another difference, at least as of this conference. Some of us will say, Wait, not everything needs to be explicit. David Birnbaum taught us that sometimes things don’t have to be explicit [Birnbaum and Thorsen 2015]. Even when they’re clearly relevant, we may get by without tagging them, without making them explicit. I still have to think about that, because I’ve always thought the purpose of markup is to make things explicit, and it does make things explicit. David has now pointed out that it does not follow that we must use markup to make explicit representations of everything we wish to think about. We may be able to get by without such explicit representations, and if we are worrying about return on investment, the resulting reduction of effort may make all the difference.

And we don’t normally actually reduce all of the concepts in our vocabularies to atomic thoughts. Some of us think it would be really interesting as an intellectual exercise, and possibly as a tool in documentation, to say what atomic ideas go together to make up the notion of chapter, say, but in practice the public vocabularies we use don’t actually define those atomic ideas. And they don’t need to. All we say is we’re going to need chapters; we’re going to need paragraphs. They have some things in common; they are different in other ways.

Mostly we are happy that we have been successful over the last decades describing concepts like those purely in natural language, without trying to identify their atomic constituents. Partly that’s laziness — sorry, intelligent use of resources. Partly, however, it’s that for whatever reason — possibly because we actually are sitting in working groups, some of us — we no longer share Leibniz’s faith that every time we analyze a composite idea into its constituent atoms, we will get the same result. Leibniz used the analogy of prime and composite numbers, and some of you will remember that a proposition called the Prime Number Theorem tells us that every number has a unique decomposition into primes. Every time we factor the number 728, we will get the same decomposition into primes, and there is only one such decomposition. Can any of us believe that everybody who decomposes the concept of chapter or section into its constituent parts will get the same answer every time they do it? I don’t believe it, and our practice tells me that none of us believe it. So, leaving some of those things inexplicit is one of the ways we achieve agreement and inter-communicability.

The biggest difference, though, between what we do and what Leibniz wanted to do is that the entire field of markup since before ISO 8879 was a work item is founded on saying no to the idea that we will have a single language. The Gencode Committee, formed by the Graphics Communication Association in the late 1960s, was chartered, as I understand it (I wasn’t there), to design a set of generic codes that everyone could use. And I don’t know how many meetings they had before they said, No. And, like many a Working Group after them, they rebelled against their charter and said, We’re not going to do that. We’re going to do something better; we’re going to do something different. The Gencode Committee escaped to the meta level. They said, We will define a meta language that allows you to define the tags you want. (Then we do not have to endure the hours of disagreement that are necessary to reach agreement on whether to call it chapter or section or div.)

So, maybe we’re not actually following in the footsteps of Leibniz. We don’t seem to aim for languages that exhaustively categorize the atomic units of our thought, or that absolutely anyone can use without change for their own purposes. Sometimes we don’t even aim for vocabularies that make explicit all of the features of our texts, even the ones we think are relevant.

And yet sometimes when we struggle long enough with a particular problem in document analysis and modeling, we achieve solutions that just feel right. And that is an exhilarating experience. That exhilaration is a lot like the feeling offered by some poetry, which is perhaps appropriate. When I took a course in the writing of poetry as an undergraduate, the instructor told told us that, in her view, poetry is calling things by their true names.

When we design our systems — our languages and their supporting software — some of what’s needed is technique, and some of what’s needed is inspiration. From other people’s work, we can improve our own technique, and from other people’s examples, we can often draw inspiration. With luck, Balisage this year has provided you both, with tips on technique and inspiration for your own work. Thank you for coming.


[Borges 1981] Borges, Jorge Luis. The Analytical Language of John Wilkins, tr. Ruth L. C. Simms. In Borges: A Reader, ed. E. R. Monegal and A. Reid. New York: Dutton, 1981, pp. 141-143. (Frequently reprinted.)

[Birnbaum and Thorsen 2015] Birnbaum, David J., and Elise Thorsen. Markup and meter: Using XML tools to teach a computer to think about versification. Presented at Balisage: The Markup Conference 2015, Washington, DC, August 11 - 14, 2015. In Proceedings of Balisage: The Markup Conference 2015. Balisage Series on Markup Technologies, vol. 15 (2015). doi:10.4242/BalisageVol15.Birnbaum01.

[Couturat 1901] Couturat, Louis. La logique de Leibniz, d’après des document inédits. Paris: Felix Alcan, 1901. On the Web in Gallica: Bibliothèque numerique and at

[Durusau and Hunting 2015] Durusau, Patrick, and Sam Hunting. Spreadsheets - 90+ million End User Programmers With No Comment Tracking or Version Control. Presented at Balisage: The Markup Conference 2015, Washington, DC, August 11 - 14, 2015. In Proceedings of Balisage: The Markup Conference 2015. Balisage Series on Markup Technologies, vol. 15 (2015). doi:10.4242/BalisageVol15.Durusau01.

[Eco 1993] Eco, Umberto. La ricerca della lingua perfetta nella cultura europea. Bari: Laterza, 1993. English translation by James Fentress as The search for the perfect language. Oxford: Blackwell, 1995; paperback London: HarperCollins, 1997.

[Frege 1879] Frege, Gottlob. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: Louis Nebert, 1879. Reprinted since by a variety of publishers. On the Web in Gallica: Bibliothèque numerique.

[Leibniz 1982a] Leibniz, Gottfried Wilhelm. Generales inquisitiones de analysi notionum et veritatum. Allgemeine Untersuchungen über die Analyse der Begriffe und Wahrheiten. Hsg., übers. und mit einem Kommentar versehen von Franz Schupp. Lateinish — Deutsch. Hamburg: Felix Meiner, 1982. Philosophische Bibliothek Band 338.

[Leibniz 1982b] Leibniz, G. W. New essays on human understanding. Translated and edited by Peter Remnant and Jonathan Bennett. Abridged Edition. Cambridge: CUP, 1982.

[Leibniz 1996] [Leibniz, Gottfried Wilhelm.] Leibniz. Ausgewählt und vorgestellt von Thomas Leinkauf. München: Diederichs, 1996.

[Leibniz 2000] Leibniz, Gottfried Wilhelm. Die Grundlagen des logischen Kalküls. Hsg., übers. und mit einem Kommentar versehen von Franz Schupp, unter der Mitarbeit von Stephanie Weber. Lateinish — Deutsch. Hamburg: Felix Meiner, 2000. Philosophische Bibliothek Band 525.

[Llull 1993] [Llull, Ramon]. Ars brevis. In Doctor Illuminatus: A Ramon Llull reader. Ed. and tr. by Anthony Bonner. Princeton: Princeton University Press, 1993, pp. 289-364.

[Llull 1999] Lullus, Raimundus. Ars brevis. Übers., mit einer Einführung hsg. von Alexander Fidora. Lateinisch — deutsch. Hamburg: Felix Meiner, 1999. Philosophische Bibliothek Band 518.

[Marcoux 2015] Marcoux, Yves. Applying intertextual semantics to Cyberjustice: Many reality checks for the price of one. Presented at Balisage: The Markup Conference 2015, Washington, DC, August 11 - 14, 2015. In Proceedings of Balisage: The Markup Conference 2015. Balisage Series on Markup Technologies, vol. 15 (2015). doi:10.4242/BalisageVol15.Marcoux01.

[Peano 1889] Peano, Ioseph. Arithmetics principia nova methodo exposita. Romae, Florentiae: Bocca, 1889.

[Polya 1945] Polya, G. How to solve it: A new aspect of mathematical method. Princeton: Princeton University Press, 1945; second edition Garden City, NY: Doubleday Anchor Books, 1957.

[Quin 2015] Quin, Liam R. E. Diagramming XML: Exploring Concepts, Constraints and Affordances. Presented at Balisage: The Markup Conference 2015, Washington, DC, August 11 - 14, 2015. In Proceedings of Balisage: The Markup Conference 2015. Balisage Series on Markup Technologies, vol. 15 (2015). doi:10.4242/BalisageVol15.Quin01.

[Russell 1900] Russell, Bertrand. A critical exposition of the philosophy of Leibniz, with an appendix of leading passages. London: George Allen & Unwin, 1900; new edition 1937, rpt. several times since.

[Sampson 1985] Sampson, Geoffrey. Chapter 2, Theoretical preliminaries in his Writing systems: a linguistic introduction. Stanford, California: Stanford University Press, 1985, pp. 26-45.

[Usdin 2015] Usdin, B. Tommie. The art of the elevator pitch. Presented at Balisage: The Markup Conference 2015, Washington, DC, August 11 - 14, 2015. In Proceedings of Balisage: The Markup Conference 2015. Balisage Series on Markup Technologies, vol. 15 (2015). doi:10.4242/BalisageVol15.Usdin01.

[Walmsley 2015] Walmsley, Priscilla. Comparing and diffing XML schemas. Presented at Balisage: The Markup Conference 2015, Washington, DC, August 11 - 14, 2015. In Proceedings of Balisage: The Markup Conference 2015. Balisage Series on Markup Technologies, vol. 15 (2015). doi:10.4242/BalisageVol15.Walmsley01.

[Wicentowski and Meier 2015] Wicentowski, Joseph C., and Wolfgang Meier. Publishing TEI documents with TEI Simple: A case study at the U.S. Department of State’s Office of the Historian. Presented at Balisage: The Markup Conference 2015, Washington, DC, August 11 - 14, 2015. In Proceedings of Balisage: The Markup Conference 2015. Balisage Series on Markup Technologies, vol. 15 (2015). doi:10.4242/BalisageVol15.Wicentowski01.

[Wilkins 1668] Wilkins, John. An essay towards a real character, and a philosophical language. London: Printed for Sa. Gellibrand, and for John Martyn, 1668. Scanned pages are available from multiple sources in the Web, including: Early English Books Online, Bayerische Staatsbibliothek, Google Books, and second copy (Munich) at Google Books. The TEI encoding made by the EEBO Text Creation Partnership mentioned in the text is at the EEBO TCP site.

[1] These remarks were first given as the closing talk at Balisage 2015; I thank Tonya Gaylord for transcribing them. I have taken the opportunity to revise some wordings in the interests of making the text easier to read, and to add some notes.

Thanks are due to the Technical University of Darmstadt for the opportunity to spend the summer semester of 2015 there as a visiting professor teaching (among others) a seminar devoted to the history of perfect languages. I am grateful to the participants in the seminar for their insights and questions.

[2] Tracking Leibniz’s thinking on this matter is slightly complicated: he published almost nothing during his lifetime, many of his manuscripts remain unpublished, and what has been published has a convoluted publication history that will discourage most casual students. The most informative account of Leibniz’s thought about perfect languages is given by Couturat 1901; Russell 1900 agrees with Couturat in general, but is less informative on the topic of particular concern here. For primary texts, perhaps the most convenient source for those able to read German is Leibniz 1996; I don’t know of a similarly useful collection in English. Some passages of Leibniz’s New essays on human understanding [Leibniz 1982b] do touch on the topic, but at best peripherally.

On Zamenhof, see the relevant section of Eco’s chapter 16, The international auxiliary languages.

The Peano Axioms were first published in Peano 1889.

[3] A clear account of the concepts of logographic and ideographic scripts is given by Sampson 1985; he has been criticized by later linguists for countenancing the idea that ideographic scripts are possible in principle.

[4] Couturat 1901 provides a useful survey of the principles of syllogistic and a detailed account of Leibniz’s work in the field; Franz Schupp publishes a number of Leibniz’s manuscripts on logic in Leibniz 1982a and Leibniz 2000.

[5] For simplicity, I am restricting the discussion here to universal affirmative statements like All Greeks are mortal; the adjustments and qualifications needed to handle negative universal, particular affirmative, and particular negative statements would take us too far afield. (And Leibniz himself neglected all of these qualifications in his summary formulation about the predicate being present in the subject.)

[6] The reader may well be puzzled by the difference between contrariety and difference; eventually Llull remarks that difference is a broader term, encompassing both contrariety and consonance (or agreement).

[7] For Llull, see Eco 1993, chapter 4 The Ars magna of Raymond Lull. The most accessible account in Llull’s own words is that given in his Ars brevis; convenient editions and translations include Llull 1993 and Llull 1999.

[8] The quotations are from Eco’s chapter on Llull, in the subsection headed The alphabet and the four figures, pp. 63 and 64 in the paperback edition.

Eco’s account may not be completely fair to Llull’s logic. In the Ars brevis, Llull addresses this question in a way that does seem directly related to the method: Whether the world is eternal. Go to the column BCD and maintain the negative. In the compartment of BCTB you will find that if it were eternal there would be many eternities differing in kind. These are concordant, according to the compartment BCTC, but contradict each other, according to the compartment BCTD, which is impossible. It therefore follows that one must maintain the negative answer to this question, and this is proved by rule B. [Translation mine, based on a comparison of Bonner and Fidora.] Llull’s argument does exhibit a facility that justifies Eco’s reference to legerdemain, but it appears on the surface to be tied tightly to the combinations derived from the triple BCD; Eco’s suggestion that the conclusion has nothing to do with the method seems to need much more by way of substantiation.