There is an assumption in these approaches that all you have to do to build a perfect language is find the right set of symbols—whether letters, numbers, or line drawings. The focus on symbols was influenced by other, related popular pursuits of the time such as cryptography, shorthand, and kabbalism (seeking divine messages in patterns of letters in ancient texts). Another influence was the widespread interest in hieroglyphics and Chinese writing, which were believed to represent concepts more directly than alphabetic writing systems. But if your goal is to craft a language capable of mathematically exposing the truths of the universe, the form of the symbols you use is relatively unimportant. What is more important is that systematic relations obtain between the symbols. The number 1 stands for the concept of oneness, and 100 stands for the concept of onehundredness, but, more important, there is a relationship between oneness and onehundredness that is captured by the relationship between the symbols 1 and 100. And it is the same relationship that obtains between 2 and 200. In Beck’s system there is no such relationship between 1 (abandon) and 100 (agarick—a type of mushroom), and if you do find a way to read a relationship into them, it won’t be the same as the one between 2 (abate) and 200 (an anthem). The numbers are just labels for words. They might as well be words. Both Beck and Urquhart had a vague sense that symbols were capable of systematically capturing relationships between concepts, but they never did the hard work of applying this idea to language.
They could have learned a thing or two from the humble Francis Lodwick, a Dutchman living far from home in London whose 1647 book, A Common Writing, was signed simply “a Well-wilier to Learning.” In his preface he apologizes for the “harshnesse of [his] stile” and entreats “a more abler wit and Pen, to a compleate attyring and perfecting of the Subject.” His modesty was partly due to a feeling of inferiority, life-station-wise. He was a merchant with no formal education, which, in the opinion of the author of a later scheme, made him “unequal to the undertaking.” But his modesty was also of the hard-earned type—the modesty that all thoughtful and honest scholars must come to (whatever their life station) when their work reveals a vast, churning ocean of difficulty just beyond the charming rivulet they had glimpsed from afar.
The important insight of Lodwick’s system wasn’t in the symbols he chose (characters that look like capital letters, with various hooks, dots, and squiggles attached) but in the way his symbols expressed relationships between concepts. For example, as shown in figure 4.1, the symbol for “word,” 
, is the symbol for “to speak,” 
, combined with a mark denoting “act of …”: 
. A word is essentially defined as an act of speaking. The symbol for God, 
, is the symbol for “to be,” 
, combined with “act of …,” 
, and “proper name,” 
. God is the proper name of the act of being (something like “The Embodiment of Existence”). The symbol for man, 
, is the symbol for “to understand,” 
, combined with “one who …,” 
, and “proper name,” 
. Man is “The Understander.” Lodwick’s major insight was to derive more complex concepts by adding together more basic ones.
Lodwick had hit upon the third method for creating a mathematics of discourse. It was concerned not with mere letters or numbers or symbols but with the relationships between the concepts they represented. From a limited set of basic concepts, you could derive everything else through combination. Leibniz would later describe this as a “calculus of thought.” The first rule of this calculus was that numbers for concepts “should be produced by multiplying together the symbolic numbers of the terms which compose the concept.” So, “since man is a rational animal, if the number of animal, a, is 2, and of rational, r, is 3, then the number of man, h, will be the same as ar: in this example, 2 × 3, or 6.” The calculations work in reverse as well. If you saw that ape was 10, you could deduce that it was an animal (because it could be divided by 2) but not a rational one (as it can’t be divided by 3).
Figure 4.1: Lodwick’s symbols
Descartes had also considered this idea a decade or two before Lodwick. He mused that if you could “explain correctly what are the simple ideas in the human imagination out of which all human thoughts are compounded … I would dare to hope for a universal language very easy to learn, to speak and to write.” But he never tried his hand at creating such a language, because he thought it would first require a complete understanding of the true nature of everything. While he did think it was “possible to invent such a language and to discover the science on which it depends,” he also thought this was unlikely to occur “outside of a fantasyland.”
Lodwick had hit upon a solution to the problem of how to make a mathematics of language, but the solution introduced a much bigger problem: How do we know what the basic units of meaning are? How do we define everything in terms of those units?
Well, you can start by figuring out the order of the universe. This was not a ridiculous proposition for the seventeenth-century man of science. It was a difficult proposition, and one that anyone could see would most likely never be adequately fulfilled. But that was no reason not to try. This was the age of reason, and so the rational animal got to work.
A Hierarchy of the Universe
The bulk of John Wilkins’s six-hundred-page description of his language is taken up with a hierarchical categorization of everything in the universe. Everything? When I first sat down to confront An Essay Towards a Real Character and a Philosophical Language, I did what any sensible, mature language scholar would do. I tried to look up the word for “shit.”
But where to look? I was holding a dictionary of concepts, not words. They were arranged not alphabetically but by meaning. To get the word for “shit,” I would have to find the concept of shit, which meant I had to figure out which of Wilkins’s forty categories of meaning it fell under.
Wilkins’s categories are organized into an overall structure of the type known as the Aristotelian hierarchy, or Porphyrian tree. This is the genus-species-difference organization we are most familiar with from taxonomies of plant and animal life. The higher positions in the tree are the most general categories, which are split into subcategories on the basis of some distinguishing feature. Daisies, spiders, woodpeckers, tigers, and porcupines all fall under the category of animate substances; they are all living things. But only some of them share the property of being sensate (bye, daisies) or of having blood (bye, spiders) or of being beasts (see ya, woodpeckers) or of being non-rapacious (so long, tigers). As we move down the tree, categories are narrowed and members more precisely defined by their membership.