Interpreting Measures of Meaning: Introducing Salience Differentiated Stability

In digital studies of the use of words in intellectual history, meaning is measured based on the idea of Firth that a word can be characterized by the company it keeps. The words that are literally close to it in the texts in which it is written should tell us something about what the word means. In practice, we will look at meaning being measured by a method called Pointwise Mutual Information or PMI for short. However, even granting that we use PMI, this description is still quite vague and allows for multiple different ways to interpret 'the company a word keeps' in the practice of coding an actual algorithm to discern this company. In this paper we will look specifically at the choice to 1. use all words close to another or 2. use merely the ones that are most disproportionately present. Using work from contemporary philosophers of language Mark Wilson and Sally Haslanger, we argue that both capture an aspect of meaning, 2 capturing the most salient way to understand a word, and 1 capturing the subtle, not so salient, but nonetheless important ways in which words are used overall. Then we will look to measure the overall stability in word meaning, the degree to which it is used similarly in different texts within a corpus. Having characterized PMI, salience and stability we will introduce Salience Differentiated Stability or SDS, a value indicating both the salient and less salient stability of a word, which will help identify words that are simpler or more shifty than they at first appear. Lastly we will test the use of this new value by doing a case study of the salience differentiated stability of common terms in early modern physics text books.