As idealized descriptions of mathematical language, there is a sense in which formal systems specify too little, and there is a sense in which they specify too much. They are silent with respect to a number of features of mathematical language that are essential to the communicative and inferential goals of the subject, while many of these features are independent of a specific choice of foundation. This chapter begins to map out the design features of mathematical language without descending to the level of formal implementation, drawing on examples from the mathematical literature and insights from the design of computational proof assistants.

@article{Thedesignofmathematicallanguage,
title = {The design of mathematical language},
abstract = {As idealized descriptions of mathematical language, there is a sense in which formal systems specify too little, and there is a sense in which they specify too much. They are silent with respect to a number of features of mathematical language that are essential to the communicative and inferential goals of the subject, while many of these features are independent of a specific choice of foundation. This chapter begins to map out the design features of mathematical language without descending to the level of formal implementation, drawing on examples from the mathematical literature and insights from the design of computational proof assistants.},
url = {http://philsci-archive.pitt.edu/19508/},
year = 2021,
author = {Jeremy Avigad},
comment = {},
urldate = {2021-11-20},
collections = {easily-explained,notation-and-conventions}
}