What does it mean to ‘give’ the value of a variable in an algebraic context, and how does giving the value of a variable differ from merely describing it? I argue that to answer this question, we need to examine the role that giving the value of a variable plays in problem-solving practice. I argue that four different features are required for a statement to count as giving the value of a variable in the context of solving an elementary algebra (...) problem: the variable must be in the scope opened by the problem statement; the values given must be in the range of the variable, which is determined by the problem; the statement giving the values must represent a complete solution; and it must be in a canonical form. This account helps us better understand elementary algebra itself, as well as the use of algebraic tools to analyze phenomena in natural language. (shrink)

This paper takes a closer look at ordinary thought and talk about motivating reasons, in an effort to better understand how it works. This is an important first step in understanding whether—and if so, how—such thought and talk should inform or constrain our substantive theorizing. One of the upshots is that ordinary judgments about motivating reasons are at best a partial and defeasible guide to what really matters, and that so-called factualists, propositionalists, and statists are all partly right, as well (...) as partly wrong, when it comes to the question of what motivating reasons “are”. (shrink)