Grammar, Numerals, and Number Words:<br> A Wittgensteinian Reflection on the Grammar of Numbers

Abstract

What account of meaning is sufficient for understanding expressions? Using numbers and number-words as familiar forms of expression, I shall try to make an apology of Wittgenstein’s treatment of meaning. My apology is of two parts. The first part attempts to address two questions: Firstly, how do we account for our knowledge of mathematical objects such as those of numbers, numerals, and number-words? Secondly, how do we account for the meaningfulness of their application outside the domain of mathematics?

As a reply to the f irst, I shall say no more than affirm, following Wittgenstein, the simple fact that our knowledge of mathematical objects such as those of numbers, numerals, and number-words is accounted for by how we learn a given language. As a reply to the second, I shall argue that said meaningfulness may be explained solely by an appeal to Wittgenstein’s account of languagegames and consequently of grammar. The second part puts forward, albeit in a general way, the idea that the correctness of a move in language is made possible not only by rules of grammar, as Wittgenstein puts it, but also by rules of grammatical salience which are also embedded in language itself.

Keywords: Grammar, grammatical salience, meaning, meaning as use, numbers, numerals, number-words, Wittgenstein