There are two kinds of mathematics. At the outset of his Elements of Algebra, Euler describes the one normally considered the only kind, quantity mathematics, as the study of “what is capable of increase or diminution.” This book is about the other mathematics, attribute mathematics, in which nothing ever gets bigger or smaller. More specifically, it is about some of what attribute mathematics can do toward the full digitalization of thought and language. The matter is relevant not only directly to linguistics and philosophy but also indirectly to electrical engineering and neuroscience. The twenty-first century will be that of the brain. Human existence will gradually be turned inside out as tools such as genetics and Boolean algebra allow us to see ourselves function on the smallest scale while it is happening. For now, establishing what goes on in the mind in terms of thought and language mainly relies on what comes out of the mouths of speakers or issues from the pens of writers. But since the spoken or written word successfully transmits purport, what is essential to the structure of thought and language inside the mind ought to be externalized in sound waves or written symbols transferring purport. As regards this structure, it will be assumed that most everything in the brain is digital, that is, On (1) or Off (0). The brain can do many things, but only so much. What are the limits? The search is for final definitions, beyond which thinking is impossible. Final definitions should make electrical engineers happy.

A native of Flanders, Leo Depuydt studied ancient Greek, Latin, and Near Eastern languages and civilizations at the Catholic University of Leuven, the Hebrew Union College in Cincinnati, the Hebrew University of Jerusalem, and the Eberhard Karls University in Tübingen, and briefly worked and lived at a Benedictine abbey in Bruges before completing his doctoral work at Yale (1985–1990), where he also taught as Senior Lector in Coptic and Syriac (1989–1991). He has authored, or co authored as editor, eleven books and written about 110 articles and 40 reviews on topics relating to ancient and medieval manuscripts, languages, and history, with primary focus on ancient Egypt. He has been at Brown University since 1991, teaching in its Department of Egyptology, which was reconstituted in 2005 as the Department of Egyptology and Ancient West Asian Studies to reflect a wider focus on the origins of science and the humanities in the ancient Near East.