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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