How does mathematical structuralism describe the number 4?

In the philosophy of mathematics, mathematical structuralism—developed by Michael Resnik and Stewart Shapiro—posits that the primary objects of mathematical study are structures or patterns rather than individual entities.12

Under this framework, the number 4 is not considered an object in the ordinary sense. Instead, it is defined simply as a position within a structure, specifically the fourth position in the positive integer pattern.12

Structuralists argue that numbers lack internal properties. Any properties attributed to the number 4 are strictly structural, derived solely from the relations it bears to other numbers within the pattern, such as its position between 3 and 5. This is analogous to a position in a baseball defense, such as shortstop; the position itself is a role defined by its relation to the rest of the field, rather than an object possessing inherent physical characteristics like height or weight.12