Why do structuralists call numbers positions in a pattern?

In the philosophy of mathematics, structuralists—most notably Michael Resnik and Stewart Shapiro—argue that the primary objects of mathematical study are structures or patterns rather than individual entities.12

Structuralists contend that numbers are not objects in the traditional sense, but are instead positions within these patterns. This perspective is often illustrated by comparing mathematical structures to a baseball defense: the "shortstop" position is a role defined by its relationship to other positions on the field, regardless of which specific player occupies it at any given time.12

Similarly, a number like 4 is viewed simply as the fourth position in the positive integer pattern. Under this view, numbers lack internal properties; their identity is derived entirely from the relations they bear to other numbers within the structure, such as the property of being located between 3 and 5. By defining numbers as positions, structuralists emphasize that mathematics is fundamentally the study of these relational patterns.12