Kriterion - Journal of Philosophy 35 (2):135-150 (2021)

Richard Lawrence
Eberhard Karls Universität Tübingen
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.
Keywords elementary algebra  variables and values  mathematical practice  scope  range  canonical form
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DOI 10.1515/krt-2021-0007
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