Structuralism (philosophy of mathematics) Structuralism is a
theory in the philosophy of mathematics that holds that
mathematical theories describe structures, and that mathematical
objects are exhaustively defined by their place in such
structures, consequently having no intrinsic properties. For
instance, it would maintain that all that needs to be known
about the number 1 is that it is the first whole number after 0.
Likewise all the other whole numbers are defined by their places
in a structure, the number line. Other examples of mathematical
objects might include lines and planes in geometry, or elements
and operations in abstract algebra. Structuralism is an
epistemologically realistic view in that it holds that
mathematical statements have an objective truth value. However,
its central claim only relates to what kind of entity a
mathematical object is, not to what kind of existence
mathematical objects or structures have (not, in other words, to
their ontology). The kind of existence mathematical objec