The Language of Mathematics: A Linguistic and Philosophical Investigation

by Mohan Ganesalingam

The Language of Mathematics was awarded the E.W. Beth Dissertation Prize for outstanding dissertations in the fields of logic, language, and information. It innovatively combines techniques from linguistics, philosophy of mathematics, and computation to give the first wide-ranging analysis of mathematical language. It focuses particularly on a method for determining the complete meaning of mathematical texts and on resolving technical deficiencies in all standard accounts of the foundations of mathematics. "The thesis does far more than is required for a it is more like a lifetime's work packed into three years, and is a truly exceptional achievement." Timothy Gowers

280 pages, Paperback

First published March 23, 2013

Reviews

[Mateusz · Rating 4 out of 5]

Interestingly, I picked up this book to understand the mathematical notation. As someone who has ease of understanding concepts in physics and math textually, I can not rigorously connect them to the language of math, therefore I lack the apparatus of notation. What this book offered was something different: a syntactic-semantic approach that lays out a general theory of pure mathematics based on a framework more akin to linguistics. It illuminated some important connections that make up my modular theory of magic, especially the chapters on Lakatos' ontochrony and isomorphisms. I will not claim to have understood everything, but I only paid attention to the chapters most useful to me personally and would like to leave the general review of the book's subtleties to trained mathematicians. Perhaps this is anachronistic, but I regard all types as a priori ontological Platonic powers, therefore I treat all mathematics as descriptions of notions and aspects of the Divinities, between the types and manipulation of tokens, according to the Pythagorean metaphysical dictum. Thank you.

[Lucille Nguyen · Rating 5 out of 5]

Ganesalingam won the EW Beth prize for the dissertation that was the direct predecessor to this book, and by God, was it well-deserved. It provides a linguistic analysis of the pure mathematics, taking the best parts of linguistics, computer science, and philosophy to create a system of complete, analyzable, and modular mathematical thought. This results in some interesting results: ways to define number outside of the set-theoretic conception, running into issues with the ante rem conception of mathematical philosophy, and some ways to handle basic identification problems (though not up to the level of Benacerraf's). An exploration of the importance of type systems and its relation to formal type theory is also explored here. A masterclass, quite literally, of mathematical thought.