I have read a little bit about the structural realist's position. It is characterised by the belief that there are key ideas that must be retained in scientific theories, namely those mathematical/theoretical 'structures' which made a theory empirically successful since new theories must maintain and build upon the empirical success of older theories.

However, I'm having a hard time interpreting this idea of the retention of a 'mathematical structure'. In Worrall's paper, he uses the example of light as we transitioned from a physical ether theory to Maxwell's theory of electromagnetism. In this transition the 'entities' in the theory changed. In the ether theory, light was taken to be oscillations of some physical medium and was taken my Maxwell to be the oscillations in some field (which seems to be a much more abstract and theoretical concept). In either case, light is taken to be this kind of oscillating thing.

Could someone elaborate on this idea? Are there other examples from theories of physics of this kind of thing?

What about cases where theories have been overtaken by new theories from which the principles of the old theory can be derived?

E.g. You can quite trivially derive Kepler's 3rd law of planetary motion from Newtonian Gravity and motion (which was the 'replacement' for Kepler's laws more or less). Is this an instance of some kind of retention of mathematical structure or am I misunderstanding things?

1 Answer 1


You might find the following helpful :

Originating with Poincare (1905) and before, structural realism (hence forth SR) is a view of scientific theory change asserts that equations, that are retained across instances of theory change, pick out relations that are at least approximately true. This, supporters claim, explains why such equations can be successfully retained across an instance of theory change. While SR commits to knowledge of structure, (i.e. the equations that describe relations) it does not commit to knowledge of the nature of the entities in the retained equations. For its supporters, such as Worrall, SR represents a congenial compromise position that accommodates the main argument from the "no-miracles" argument for scientific realism (Worrall, 1989). "No-Miracles" is the thesis that the success of science stands in need of explanation, the explanation being that successful theories are successful because they are, at least, approximately true. SR's restrictions on the knowledge of "nature" rec ognises that much of the constituents of science do not survive instances of theory change. Entities such as "ether" and "caloric" are cases in point.

However, SR has been subject to considerable criticism recently, most notably by Psillos (1995, 1999, 2001). Psillos argues that the structure/nature distinction provides an implausible version of nature. Structure and nature form a continuum for Psillos. They are not wholly distinct since much of what one might consider "nature" is expressed by laws that entities obey, laws that come in the form of equations, i.e. structure. For example, part of lights "nature" in several classical theo ries of light is that it propagates as a transverse wave, but this "nature" is expressed in equations that survived instances of theory change. (Daniel McArthur, 'Recent Debates over Structural Realism', Journal for General Philosophy of Science / Zeitschrift für allgemeine Wissenschaftstheorie, Vol. 37, No. 2 (Oct., 2006), pp. 209-224 : 209-10.)

You are already familiar with Worrall's work. A useful next step might be to read Psillos, who raises real difficulties for SR.


Poincare, H.: 1905, 'Science and Hypothesis', reprinted in H. Poincare (1913), The Foundations of Science, The Science Press, Lancaster. (Many later reprints.)

Psillos, S.: 1995, Ts Structural realism the Best of Both Worlds?', Dialectica 49,15-46.

Psillos, S.: 1999, Scientific Realism: How Science Tracks Truth, Routledge, London.

Psillos, S.: 2001, Ts Structural Realism Possible?', Philosophy of Science (Proceedings) 68, 13-24.

  • Ah, okay. That makes sense. And yeah, it kind of seems like Psillos missed the point? Perhaps he's right in saying that the nature/structure distinction is a little bit off or poorly defined but it still stands that new theories mathematically retain old theories (as a matter of necessity). So perhaps it is better to say that you can only understand the nature of an entity/of unobserved entities by reference to the equations that describe them. Their qualitative nature is beyond our reach. Jun 17, 2018 at 8:43
  • 1
    Thanks for reply. If Psillos has stimulated a reaction, even if a negative one, perhaps that puts you one step ahead towards clarification. Best - Geoff.
    – Geoffrey Thomas
    Jun 17, 2018 at 8:54

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