Structuralism has become an umbrella for various ideas in various philosophical discourses, to wit:
1. Philosophy of Science. Structural Realism, whether Epistemic or Ontic, is a variety
of Scientific Realism in the realism debate in philosophy of science, having roots in
the work of Bertrand Russell, Henri Poincaré, Arthur Eddington and Ernst Cassirer,
and has been resuscitated by J.S. Worrall and elaborated and defended by S.
French, and his student James Ladyman. Worrall’s student Ioannis Votsis is
another propounder. See the Stanford Encylopedia Lemma Structural Realism for
details.
2. Philosophy of Science. Structuralist conceptions of theories and models in science
began in the work of E.W. Beth, and were elaborated and defended since the
1970ies by B.C. van Fraassen; P.C. Suppes, expounding a sibling view since the
end of the 1950ies, is another founding father, with his slogan ‘to axiomatise a
scientific theory is to define a set-theoretical predicate’; Suppes’ student J.D. Sneed
took it further and in Germany a Structuralist School arose, with W. Stegmüller,
C.U. Mouliness, W. Balzer, and others, which has remained active until this day.3. Philosophy of Mathematics. N. Bourbaki first characterised mathematics as the
study of abstract structures. But only since P. Benacerraf’s classic paper ‘What numbers could not be’ (1965) arose a philosophical view on mathematics that somehow was different from Formalism and Intuitionism, and that seems tailor-made for Category-Theorists. The recent Homotopic Type Theory (HoTT), propounded as a new foundation for mathematics, also proclaims itself as
essentially structuralist.
4. Metaphysics. Quite recently structuralism also has to encompas views in
metaphysics. A prominent metaphysicisan like T.D. Sider calls his own view
structuralist.

In the background is a vici project of F.A. Muller, funded by NWO, called The Structure of
Reality and the Reality of Structure (with one post-doc and two PhDs), which aims to erect
a new formal theory of structure, to inquire into the possibly structure-preserving Relativity and Quantum Revolutions in physics in the first half of the 20th Century, and into
interpretations of Quantum Field Theory. The project will run for five years (2013–2018).