## 1. Introduction



Scientific realism requires belief in the unobservable entities
posited by our most successful scientific theories. It is widely held
that the most powerful argument in favour of scientific realism is the
no-miracles argument, according to which the success of science would
be miraculous if scientific theories were not at least approximately
true descriptions of the world. While the underdetermination argument
is often cited as giving grounds for scepticism about theories of
unobservable entities, arguably the most powerful arguments against
scientific realism are based on the history of radical theory change
in science. The best-known of these arguments, although perhaps not
the most compelling of them, is the pessimistic meta-induction,
according to which reflection on the abandonment of theories in the
history of science supports the expectation that our best current
scientific theories will themselves be abandoned, and hence that we
ought not to assent to them. (See
 SS2
 below and the entry on
 scientific realism
 for more on these arguments.)



Structural realism was introduced into current philosophy of science
by John Worrall in 1989 as a way to break the impasse that results
from taking both arguments seriously, and have "the best of both
worlds" in the debate about scientific realism. With respect to
the case of the transition in nineteenth-century optics from
Fresnel's elastic solid ether theory to Maxwell's theory
of the electromagnetic field, Worrall argues that:



> 
> 
> There was an important element of continuity in the shift from Fresnel
> to Maxwell--and this was much more than a simple question of
> carrying over the successful empirical content into the new theory. At
> the same time it was rather less than a carrying over of the full
> theoretical content or full theoretical mechanisms (even in
> "approximate" form) ... There was continuity or
> accumulation in the shift, but the continuity is one of form or
> structure, not of content. (1989: 117)
> 
> 
> 



According to Worrall, we should not accept standard scientific
realism, which asserts that the nature of the unobservable objects
that cause the phenomena we observe is correctly described by our best
theories. However, neither should we be antirealists about science.
Rather, we should adopt structural realism and epistemically commit
ourselves to the mathematical or structural content of our theories.
Since there is (says Worrall) retention of structure across theory
change, structural realism both (a) avoids the force of the
pessimistic meta-induction (by not committing us to belief in the
theory's description of the furniture of the world) and (b) does
not make the success of science (especially the novel predictions of
mature physical theories) seem miraculous (by committing us to the
claim that the theory's structure, over and above its empirical
content, describes the world).



Worrall's paper has been widely cited in an extensive literature
in which various varieties of structural realism are advocated or
criticised, and different notions of structure are discussed. These
contemporary debates recapitulate the work of some of the greatest
philosophers of science of the late nineteenth and early twentieth
centuries. The increasing mathematisation of physics through the
nineteenth century, with electromagnetism and thermodynamics lacking
mechanical and material models, and then the advent of quantum and
relativity physics, prompted a variety of structuralist responses.
Worrall says he found his structural realism in Henri Poincare
(1902 [1905]; 1905 [1907]) whose structuralism was combined with
neo-Kantian views about the nature of arithmetic and group theory, and
with conventionalism about the geometry of space and time. (The
prevalence of Kantian themes in the literature on structural realism
is discussed further below; for more on Poincare and structural
realism see Giedymin 1982; Gower 2000; and Zahar 1996, 2001, and
below.) Ernan McMullin (1990) argues that Pierre Duhem was a realist
about the relations found in laws but not about explanations in terms
of an ontology. According to Worrall (1989), Barry Gower (2000) and
Elie Zahar (2001), Duhem too was a kind of structural realist, though
there are passages in Duhem that more readily lend themselves to an
instrumentalist interpretation (see the entry on
 Pierre Duhem).
 Milena Ivanova (2015a) compares the thought of Duhem and
Poincare in respect of conventionalism and structural realism,
identifying significant differences between their views as well as
similarities. Gower's (2000) historical survey of structural
realism discusses how it figures in the thought of Ernst Cassirer,
Moritz Schlick, Rudolf Carnap and Bertrand Russell. Stathis Psillos
(1999) explores the connections between structuralism and the
Ramsey-sentence approach to scientific theory in the development of
Carnap's philosophy from logical positivism to ontologically
relativist empiricism (Ramsey sentences are discussed in
 SS3.2
 below). Other important pioneers of structuralism about science
include Arthur Eddington (see French 2003), Grover Maxwell (see
Ladyman 1998 and
 SS3.1
 below) and Hermann Weyl (see Ryckman 2005).



Ladyman (1998) distinguished epistemic and ontic forms of structural
realism in arguing for the latter. Many of those who have taken up
structural realism have been philosophers of physics who have
developed various forms of ontic structural realism, most notably
Steven French. Others, including Worrall, have made it clear that
their structural realism is a purely epistemological refinement of
scientific realism. On the other hand, Bas van Fraassen (1997, 2006,
2007, 2008) defends an empiricist and non-realist form of
structuralism about science, based on his view of scientific
representation and motivated by an illuminating reconstruction of the
origins of structuralism in the debate about the epistemology of
physical geometry in the nineteenth century (see also Bueno 1999, 2000
on structural empiricism). Other kinds of structuralism abound in
current analytic philosophy. These include causal structuralism
concerning the individuation of properties, mathematical structuralism
concerning the nature of mathematical objects, and structuralism about
laws and dispositions. Following the debates about structural realism
in the philosophy of science in the early twentieth century, the
notion of structure in general, and the idea of modal structure in
particular, have also become prominent in analytic metaphysics.
Clearly, there many different notions of structure, and many different
kinds of structural realism. This article reviews the main issues and
provides a guide for further reading.


## 2. The Best of Both Worlds?



Scientific realism became dominant in philosophy of science after the
demise of the forms of antirealism about science associated with the
logical positivists, namely semantic instrumentalism, according to
which theoretical terms are not to be interpreted as referring to
anything, and theoretical reductionism, according to which theoretical
terms are disguised ways of referring to observable phenomena. These
forms of antirealism rely upon discredited positivist ideas about
scientific language, such as that it can be divided into theoretical
and observational parts, that much of it should not be taken
literally, or that its empirically surplus content is redundant. Bas
van Fraassen (1980) revitalised the debate about scientific realism by
proposing his constructive empiricism as an alternative. His
antirealism is sceptical rather than dogmatic, and does not depend on
the distinction between theoretical and observational terms. He allows
that terms such as "sub-atomic particle" and
"particle too small to see" are perfectly meaningful and
should be taken literally (the former term is theoretical and the
latter term is not but both purportedly refer to unobservable
entities). On the other hand, he holds that it is perfectly rational
to remain agnostic about whether there are any such particles, because
he argues that to accept the best scientific theories we have only
requires believing that they are empirically adequate, in the sense of
correctly describing the observable world, rather than believing that
they are true simpliciter. (For more on constructive empiricism see
Monton 2007.)



How then are we to decide whether to believe in the full theoretical
truth of scientific theories, including what they say about
unobservable entities such as electrons and black holes, or whether to
believe instead only that our best scientific theories are empirically
adequate? Van Fraassen argues that since the latter belief is
logically weaker and yet as empirically contentful as the former
belief it is natural for an empiricist to go only as far as belief in
empirical adequacy. On the other hand, many philosophers are moved by
the fact that belief in only the empirical adequacy of our best
scientific theories leaves us unable to explain the phenomena that
they describe. Inference to the best explanation is widely believed to
be an important form of reasoning in science, and the production of
explanations of the world is often supposed to be one of the main
successes of science. When the target of explanation becomes science
itself and its history of empirical success as a whole, we arrive at
the no-miracles argument famously presented by Hilary Putnam as
follows:



> 
> 
> The positive argument for realism is that it is the only philosophy
> that doesn't make the success of science a miracle. (1975:
> 73)
> 
> 
> 



The no-miracles argument is elaborated in terms of specific features
of scientific methodology and practice. Richard Boyd (1985, for
example) argues that in explaining the success of science, we need to
explain the overall instrumental success of scientific methods across
the history of science. Alan Musgrave (1988) says that the only
version of the no-miracles argument that might work is one appealing
to the novel predictive success of theories. Some realists, such as
Psillos (1999), have gone so far as to argue that only theories which
have enjoyed novel predictive success ought to be considered as
falling within the scope of arguments for scientific realism.



Colin Howson (2000), P.D. Magnus and Craig Callender (2004), and Peter
Lipton (2004) argue that the no-miracles argument is flawed because in
order to evaluate the claim that it is probable that theories enjoying
empirical success are approximately true we have to know what the
relevant base rate is, and there is no way we can know this. Magnus
and Callender argue that "wholesale" arguments that are
intended to support realism (or antirealism) about science as a whole
(rather than "retail" arguments that are applied to a
specific theory) are only taken seriously because of our propensity to
engage in the "base rate fallacy" of evaluating
probabilities without knowing all the relevant information. They think
we ought to abandon the attempt to defend scientific realism in
general rather than on a case-by-case basis.



This assumes that the wholesale arguments against scientific realism
do not work. Of these the underdetermination argument, according to
which the existence of empirical equivalents to our best scientific
theories implies that we should withhold epistemic commitment to them,
is is often dismissed by realists as generating doubt about
unobservables that is no more worrying than doubting other minds or
the external world. They argue that since scientists find ways of
choosing between empirically equivalent rivals, philosophers ought not
to make too much of merely in-principle possibilities that are
irrelevant to scientific practice (see Laudan & Leplin 1991;
Leplin & Laudan 1993; and Kukla 1998). (Kyle Stanford (2006)
defends an underdetermination argument called "the problem of
unconceived alternatives" with reference to the history of
science, so perhaps not all underdetermination arguments are *a
priori* and theoretical.)



The power of the arguments against scientific realism from theory
change is that, rather than being *a priori* and theoretical,
they are empirically based and their premises are based on data
obtained by examining the practice and history of science. Ontological
discontinuity in theory change seems to give us grounds not for mere
agnosticism but for the positive belief that many central theoretical
terms of our best contemporary science will be regarded as
non-referring by future science. So-called "pessimistic
meta-inductions" about theoretical knowledge take many forms and
are probably almost as ancient as scepticism itself. They have the
basic form:



> 
> 
> Proposition *p* is widely believed by most contemporary
> experts, but *p* is like many other hypotheses that were widely
> believed by experts in the past and are disbelieved by most
> contemporary experts. We have as much reason to expect *p* to
> befall their fate as not, therefore we should at least suspend
> judgement about *p* if not actively disbelieve it.
> 
> 
> 



More precisely, Larry Laudan (1981) gave a very influential argument
with the following structure:


1. There have been many empirically successful theories
in the history of science which have subsequently been rejected and
whose theoretical terms do not refer according to our best current
theories.
2. Our best current theories are no different in kind
from those discarded theories and so we have no reason to think they
will not ultimately be replaced as well.



So, by induction we have positive reason to expect that our best
current theories will be replaced by new theories according to which
some of the central theoretical terms of our best current theories do
not refer, and hence we should not believe in the approximate truth or
the successful reference of the theoretical terms of our best current
theories.



The most common realist response to this argument is to restrict
realism to theories with some further properties (usually, maturity,
and novel predictive success) so as to cut down the inductive base
employed in
 (i)
 (see Psillos 1996). Moreover Peter Lewis (2001), Marc Lange (2002)
and Magnus and Callender (2004) regard the pessimistic meta-induction
as a fallacy of probabilistic reasoning. However, there are arguments
from theory change that are not probabilistic. Note first that there
are several cases of mature theories which enjoyed novel predictive
success, notably the ether theory of light and the caloric theory of
heat. If their central theoretical terms do not refer, the
realist's claim that approximate truth explains empirical
success will no longer be enough to establish realism, because we will
need some other explanation for the success of the caloric and ether
theories. If this will do for these theories then it ought to do for
others where we happened to have retained the central theoretical
terms, and then we do not need the realist's preferred
explanation that such theories are true and successfully refer to
unobservable entities.



Laudan's paper was also intended to show that the successful
reference of its theoretical terms is not a necessary condition for
the novel predictive success of a theory (1981: 45), and there are
counter-examples to the no-miracles argument.


1. Successful reference of its central theoretical terms is a
necessary condition for the approximate truth of a theory.
2. There are examples of theories that were mature and had novel
predictive success but whose central theoretical terms do not
refer.
3. So there are examples of theories that were mature and had novel
predictive success but which are not approximately true.
4. Approximate truth and successful reference of central theoretical
terms is not a necessary condition for the novel-predictive success of
scientific theories



> 
> 
> So, the no-miracles argument is undermined since, if approximate truth
> and successful reference are not available to be part of the
> explanation of some theories' novel predictive success, there is
> no reason to think that the novel predictive success of other theories
> has to be explained by realism.
> 
> 
> 



There are two common (not necessarily exclusive) responses to
this:


1. Develop an account of reference according to which the abandoned
theoretical terms are regarded as successfully referring after
all.



Realists developed causal theories of reference to account for
continuity of reference for terms like "atom" or
"electron", even though the theories about atoms and
electrons have undergone significant changes. The difference with the
terms "ether" and "caloric" is that they are
no longer used in modern science. However, as C.L. Hardin and
Alexander Rosenberg (1982) argue, the causal theory of reference may
be used to defend the claim that terms like "ether"
referred to whatever causes the phenomena responsible for the
terms' introduction. This is criticized by Laudan (1984) as
making the reference of theoretical terms a trivial matter, since as
long as some phenomena prompt the introduction of a term it will
automatically successfully refer to whatever is the relevant cause (or
causes). Furthermore, this theory radically disconnects what a
theorist is talking about from what she thinks she is talking about.
For example, Aristotle or Newton could be said to be referring to
geodesic motion in a curved spacetime when, respectively, they talked
about the natural motion of material objects, and the fall of a body
under the effect of the gravitational force.
2. Restrict realism to those parts of theories that play an essential
role in the derivation of subsequently observed (novel) predictions,
and then argue that the terms of past theories which are now regarded
as non-referring were non-essential and hence that there is no reason
to deny that the essential terms in current theories will be retained.
Philip Kitcher says that: "[n]o sensible realist should ever
want to assert that the idle parts of an individual practice, past or
present, are justified by the success of the whole" (1993:
142).



The most detailed and influential response to the argument from theory
change is due to Psillos (1999), who combines strategies
 (I)
 and
 (II).
 Hasok Chang (2003), Kyle Stanford (2003a,b), Mohammed Elsamahi
(2005), and Timothy Lyons (2006) criticize Psillos's account.
Other responses include Kitcher's (1993) model of reference
according to which some tokens of theoretical terms refer and others
do not. Christina McLeish (2005) criticizes Kitcher's theory by
arguing that there are no satisfactory grounds for making the
distinction between referring and non-referring tokens. McLeish (2006)
argues that abandoned theoretical terms like "ether"
partially refer and partially fail to refer. Juha Saatsi (2005) denies
premise (a) and claims that there can be approximate truth of the
causal roles postulated by a scientific theory without its central
terms necessarily successfully referring (see also Chakravartty 1998).
There is no consensus among those defending standard realism in the
face of theory change by adopting the selective approach of (II) with
an account of reference.



Consider again the much-discussed case of the ether. Psillos argues
that Fresnel's use of the term "ether" was essential
to his successful theorising, but that it referred to the
electromagnetic field. Worrall (1989) argues that the project of
defending realism by securing reference for abandoned theoretical
terms is missing the point of the problem as well as the key to its
solution. It is plausible to take "field" to be a new way
of referring to what the ancients and early moderns termed
"aether" or "ether". Fields like the ether
permeate all of space and are posited to explain optical, magnetic and
other phenomena. Anaxagoras is said to have introduced the idea of the
ether to propel the planets, and subsequently there were many ethers
to account for various things. Fresnel's optical ether was
supposed to be a solid and Maxwell's field behaves very
differently and is said to be immaterial. However, from our current
perspective the ether has much more in common with the field, than
atoms do with the indivisible particles of antiquity (Stein 1989), and
so continuity of reference is not the issue. The reference of the term
"energy" at least overlaps in classical and quantum
theories because quantities in each coincide in the limit as the
number of particles increases. This does not solve the problem that
the radical ontological and metaphysical differences between the
theories pose for the realist. Different theories often use the same
terms, to say very different things about what the world is like. The
question of which terms refer, does not settle the whether it is
plausible to say that the metaphysics and ontology of the theory is
even approximately true, because in many case the same theoretical
term is still used despite radical changes.



The argument from theory change threatens scientific realism because
if what science now says is correct, then the ontologies of past
scientific theories are far from accurate accounts of the furniture of
the world. If that is so even though they were predictively
successful, then the success of our best current theories does not
mean they have got the nature of the world right either. The task of
providing an adequate theory of approximate truth that fits the
history of science and directly addresses the problem of ontological
continuity has hitherto defeated realists, but a much more tractable
problem is to display the structural commonalities between different
theories. Hence, a form of realism about the structure of theories
might not be undermined by theory change. Gerhard Schurz (2009) proves
a structural correspondence theorem showing that successive theories
that share empirical content also share theoretical content.



The structuralist solution to this problem is to take the metaphysical
import of successful scientific theories to consist in their giving
correct descriptions of the structure of the world, where this
structure can be captured with different ontologies. Theories can be
so different as to be contrary to each other, while both represent the
same structure in the phenomena. Consider the theory according to
which combustion is the emission of phlogiston that was dominant in
chemistry prior to the end of the eighteenth century. Despite their
radical disagreement about the nature of combustion both phlogiston
theory, and the oxygen theory of Lavoisier that succeeded it, regard
combustion, respiration and the calcination of metals as the same kind
of process, and reciprocal to another kind of process exemplified by
the smelting of ore. Furthermore there are tables of affinity that
were formulated by the phlogistonists that can be reinterpreted in
terms of Lavoisian chemistry (see Schurz 2009 and Ladyman 2011).
Hence, even in this case there is continuity of structure despite the
central entity of the old theory not existing at all according to the
new theory



There are numerous examples of continuity in the mathematical
structure of successive scientific theories. Indeed the principle that
old ones should be recovered from new ones in some limit was
explicitly formulated by Niels Bohr as the methodological principle
known as the "correspondence principle", according to
which quantum-mechanical models ought to mathematically reduce to
classical models in the limit of large numbers of particles, or in the
limit of Planck's constant becoming arbitrarily small relative
to the action of the system. There are many cases in quantum mechanics
where the Hamiltonian functions that represent the total energy of
mechanical systems imitate those of classical mechanics, but with
variables like those that stand for position and momentum replaced by
Hermitian operators. There is a now a large literature in philosophy
of physics that considers different characterisations of the structure
of theories, and how it relates to to the relations between them, and
their empirical content. Simon Saunders (1993a) discusses the
structural continuities between classical and quantum mechanics and
also shows how much structure Ptolemaic and Copernican astronomy have
in common. Harvey Brown (1993) explains the correspondence between
Special Relativity and classical mechanics. Jonathan Bain and John
Norton (2001) discuss the structural continuity in descriptions of the
electron, as does Angelo Cei (2005). Votsis (2011) considers examples
of continuity and discontinuity in physics. Robert Batterman (2002)
discusses many examples of limiting relationships between theories,
notably the renormalization group approach to critical phenomena, and
the relationship between wave and ray optics. Holger Lyre (2004)
extends Worrall's original example of the continuity between
wave optics and electromagnetism by considering the relationship
between Maxwellian electrodynamics and Quantum Electrodynamics. Alisa
Bokulich (2008) considers the quantum-classical transition in detail
arguing for what she calls "interstructuralism" as an
approach to intertheory relations that emphasises structural
continuities and correspondences. Zenker and Gardenfors (2015)
adopt a conceptual spaces approach to the continuity of theory
structure. Joshua Rosaler (2015) analyses intertheory relations in
physics arguing that local relations between models in different
domains must be considered as well as global relations between
theories. Manero (2022) argues for the stability of Lie algebras over
theory change in physics.



The most minimal form of structuralism focuses on empirical structure,
and as such is best thought of as a defence of the cumulative nature
of science in the face of Kuhnian worries about revolutions (following
Post 1971). See Katherine Brading's and Elaine Landry's
(2006) "minimal structuralism", and Otavio Bueno's
(1999, 2000) and van Fraassen's (2006, 2007, 2008) structural
empiricism (Ryckman 2005 calls the latter "instrumental
structuralism"). For a range of recent work on the problem of
theory change see Lyons & Vickers (eds.) 2021.


## 3. Epistemic Structural Realism (ESR)



Structural realism is often characterised as the view that scientific
theories tell us only about the form or structure of the unobservable
world and not about its nature. This leaves open the question of
whether the natures of things are posited to be unknowable for some
reason or eliminated altogether. Hence, Ladyman (1998) considers
whether Worrall's structural realism should be understood as a
metaphysical or epistemological modification of standard scientific
realism. Worrall's paper is ambiguous in this respect. That he
has in mind only an epistemic constraint on realism--commitment
to the structure of our best scientific theories but agnosticism about
the rest of the content--is suggested by his citation of
Poincare who talks of the redundant theories of the past
capturing the "true relations" between the "real
objects which Nature will hide forever from our eyes" (1905
[1907: 162]). So one way of thinking about structural realism is as an
epistemological modification of scientific realism to the effect that
we only believe what scientific theories tell us about the relations
entered into by unobservable objects, and suspend judgement as to the
nature of the latter. (ESR is called "restrictive structural
realism" by Psillos 2001.) There are various forms this might
take. (See French & Ladyman 2011.)


1. We cannot know the individuals that instantiate the
structure of the world but we can know their properties and
relations.
2. We cannot know the individuals or their
intrinsic/non-relational properties but we can know their first-order
relational properties.
3. We cannot know the individuals, their first-order
properties or relations, but we can know the second-order structure of
their relational properties. Russell (1927) and Carnap (1928) took
this extreme view and argued that science only tells us about purely
logical features of the world.



Psillos (2001) refers to the "upward path" to structural
realism as beginning with empiricist epistemological principles and
arriving at structural knowledge of the external world. The
"downward" path is to arrive at structural realism by
weakening standard scientific realism as suggested by Worrall. Both
paths are criticized by Psillos. Russell (1927) was led along the
upward path by three epistemological principles: firstly, the claim
that we only have direct access to our percepts (Ayer's
"egocentric predicament"); secondly, the principle that
different effects have different causes (which is called the
Helmholtz-Weyl Principle by Psillos); and thirdly, that the relations
between percepts have the same logico-mathematical structure as the
relations between their causes. This led him to the claim that science
can only describe the world up to isomorphism, and hence to
 (3)
 above since according to him we know only the (second-order)
isomorphism class of the structure of the world and not the
(first-order) structure itself. Russell's upward path is
defended by Votsis (2005). Beni (2017a) considers the upward path in
the light of the science of perception. Katherine Brading and Elise
Crull (2017) explore the link between Poincare's
philosophy of science and ESR, as does Ivanova (2015b) focusing on the
connection with conventionalism and neo-Kantianism. Beni (2018) takes
the downward path to ESR using information-theory.



Most defenders of ESR assume that there must be individual objects and
properties that are ontologically prior to relational structure.
Matteo Morganti (2004) differs from other epistemic structural
realists by arguing for agnosticism about whether there is a domain of
individuals over and above relational structure. Mauro Dorato argues
for ESR on the grounds that structural realism needs entity realism to
be plausible (2000) (but perhaps ontic structural realism can also be
reconciled with entity realism to some extent (see below)).


### 3.1 Kantian ESR



As mentioned above, Poincare's structuralism had a
Kantian flavour. In particular, he thought that the unobservable
entities postulated by scientific theories were Kant's noumena
or things in themselves. He revised Kant's view by arguing that
the latter can be known indirectly rather than not at all because it
is possible to know the relations into which they enter.
Poincare followed the upward path to structural realism,
beginning with the neo-Kantian goal of recovering the objective or
intersubjective world from the subjective world of private sense
impressions:



> 
> 
> what we call objective reality is... what is common to many
> thinking beings and could be common to all; ... the harmony of
> mathematical laws. (1905 [1907: 14])
> 
> 
> 



However, he also followed the downward path to structural realism
arguing that the history of science can be seen as cumulative at the
level of relations rather than objects. For example, between
Carnot's and Clausius' thermodynamics the ontology changes
but the Second Law of Thermodynamics is preserved. While Worrall never
directly endorses the Kantian aspect of Poincare's
thought, Zahar's structural realism is explicitly a form of
Kantian transcendental idealism according to which science can never
tell us more than the structure of the noumenal world; the nature of
the entities and properties of which it consists are epistemically
inaccessible to us (as in
 (2)
 above). Ivanova 2013 considers how Perrin's experiments
converted Poincare to atomism despite his previous opposition
to it, but did not lead him to abandon his neo-Kantianism. Michela
Massimi (2011) develops a different neo-Kantian perspective on
structural realism.



Frank Jackson (1998), Rae Langton (1998), and David Lewis (2009) also
advocate views similar to ESR. Jackson refers to "Kantian
physicalism" (1998: 23-24), Langton to "Kantian
Humility", and Lewis to "Ramseyan Humility". Peter
Unger (1979) also argues that our knowledge of the world is purely
structural and that qualia are the non-structural components of
reality. Jackson argues that science only reveals the
causal/relational properties of physical objects, and that



> 
> 
> we know next to nothing about the intrinsic nature of the world. We
> know only its causal cum relational nature. (1998: 24)
> 
> 
> 



Langton argues that science only reveals the extrinsic properties of
physical objects, and both then argue that their intrinsic natures,
and hence the intrinsic nature of the world, are epistemically
inaccessible. Jackson points out that this inference can be blocked if
the natures of objects and their intrinsic properties are identified
with their relational or extrinsic properties, but argues that this
makes a mystery of what it is that stands in the causal relations.
Lewis' structuralism is based on the centrality he gives to the
Ramsey sentence reconstruction of scientific theories that is the
subject of the next section.


### 3.2 ESR and Ramsey Sentences



A position called structural realism, that amounts to an
epistemological gloss on traditional scientific realism, was advocated
by Grover Maxwell (1962, 1968 [1972], 1970a, 1970b). Maxwell wanted to
make scientific realism compatible with "concept
empiricism" about the meaning of theoretical terms, and he also
wanted to explain how we can have epistemic access to unobservable
entities. The problem as Maxwell saw it was that theories talk about
all sorts of entities and processes with which we are not
"acquainted". How, he wondered, can we then know about and
refer to them and their properties? The answer that he gave, following
Russell, was that we can know about them by description, that is we
can know them via their structural properties. In fact, he argues,
this is the limit of our knowledge of them, and the meanings of
theoretical terms are to be understood purely structurally. The way
that Maxwell explicates the idea that the structure of the theory
exhausts the cognitive content of its theoretical terms, is to
consider the Ramsey sentence of the theory (Ramsey [1929] 1931).
Ramsey's method allows the elimination of theoretical terms from
a theory by replacing them with existentially quantified predicate
variables (or names in the case of the influential D. Lewis 1970). If
one replaces the conjunction of assertions of a first-order theory
with its Ramsey sentence, the observational consequences of the theory
are carried over, but direct reference to unobservables is
eliminated.



If we formalise a theory in a first-order language:

 
\[\Pi(O\_1,\ldots,O\_n; T\_1,\ldots,T\_m),\]


where the *O*s are the observational terms and the *T*s
are the theoretical terms, then the corresponding Ramsey sentence
is

 
\[\exists t\_1,\ldots,t\_m \Pi(O\_1,\ldots,O\_n;t\_1,\ldots,t\_m).\]


Thus the Ramsey sentence only asserts that there are some objects,
properties and relations that have certain logical features,
satisfying certain implicit definitions. It is a higher-order
description, but ultimately connects the theoretical content of the
theory with observable behaviour. However, it is a mistake to think
that the Ramsey sentence allows us to eliminate theoretical entities,
for it still states that these exist. It is just that they are
referred to not directly, by means of theoretical terms, but by
description, that is via variables, connectives, quantifiers and
predicate terms whose direct referents are (allegedly) known by
acquaintance. Thus Maxwell (and Russell) claimed that knowledge of the
unobservable realm is limited to knowledge of its structural rather
than intrinsic properties, or, as is sometimes said, limited to
knowledge of its higher-order properties. It is arguable that this is
the purest structuralism possible, for the notion of structure
employed refers to the higher-order properties of a theory, those that
are only expressible in purely formal terms.



This is an epistemological structural realism meant to vindicate and
not to revise the ontological commitments of scientific realism. On
this view the objective world is composed of unobservable objects
between which certain properties and relations obtain; but we can only
know the properties and relations of these properties and relations,
that is, the structure of the objective world. However, there are
serious difficulties with this view which were originally raised by M.
H. A. Newman in 1928 and which have been recently discussed by
Demopoulos and Friedman (1985 [1989]). The basic problem is that
structure is not sufficient to uniquely pick out any relations in the
world. Suppose that the world consists of a set of objects whose
structure is *W* with respect to some relation *R*,
about which nothing else is known. Any collection of things can be
regarded as having structure *W* provided there is the right
number of them. This is because according to the extensional
characterisation of relations defined on a domain of individuals,
every relation is identified with some set of subsets of the domain.
The power set axiom entails the existence of every such subset and
hence every such relation.



As Demopoulos and Friedman point out, if [?] is consistent, and if
all its purely observational consequences are true, then the truth of
the corresponding Ramsey sentence follows as a theorem of second-order
logic or set theory (provided the initial domain has the right
cardinality--and if it does not then consistency implies that
there exists one that does). The formal structure of a relation can
easily be obtained with any collection of objects provided there are
enough of them, so having the formal structure cannot single out a
unique referent for this relation; in order to do so we must stipulate
that we are talking about the intended relation, which is to go beyond
the structural description. "Thus on this view, only cardinality
questions are open to discovery!" (1985: 627 [1989: 188]);
everything else will be known *a priori*.



This leads Demopoulos and Friedman to conclude that reducing a theory
to its Ramsey sentence is equivalent to reducing it to its empirical
consequences, and thus that:



> 
> 
> Russell's realism collapses into a version of phenomenalism or
> strict empiricism after all: all theories with the same observational
> consequences will be equally true. (1985: 635 [1989: 195])
> 
> 
> 



Similarly, Jane English (1973) argued, though on the basis of
different considerations, that any two Ramsey sentences that are
incompatible with one another cannot have all their observational
consequences in common. Hence it seems that if we treat a theory just
as its Ramsey sentence then the notion of theoretical equivalence
collapses onto that of empirical equivalence. (Demopoulos 2003 argues
that similar considerations show that structural empiricism also
collapses truth to empirical adequacy; he also discusses the
relationship between Newman's problem and Putnam's
Paradox. Votsis (2003) argues that the conclusion of the Newman
argument doesn't undermine ESR after all. Gordon Solomon (1989)
defends Richard Braithwaite's claim that Eddington's
structuralism (see
 SS4.1
 below) is vulnerable to Newman's argument.)



Jeffery Ketland (2004) argues in detail that the Newman objection
trivialises the Ramsey sentence formulation of ESR. Worrall and Zahar
(2001) argue that the cognitive content of a theory is exhausted by
its Ramsey sentences but that, while the Ramsey sentence only
expresses the empirical content of the theory, the notion of empirical
content in play here is sufficient for a form of realism. In his 2007
paper, Worrall sets out an account and defense of epistemic structural
realism and responds to objections that have been raised to it,
including the Newman problem. Cruse (2005) and Melia and Saatsi (2006)
defend the Ramsey sentence approach against model-theoretic arguments
by questioning the assumption that all predicates which apply to
unobservables must be eliminated in favour of bound variables. Mixed
predicates such as "extended" are those that apply to both
observable and unobservable objects. The Newman objection does not go
through if mixed predicates are not Ramsified, because a model of the
Ramsey sentence will not necessarily be one in which what is claimed
regarding the mixed properties and relations holds. In response,
Demopoulos (2011) points out that the Ramsey sentence of a theory with
mixed predicates where the latter are not Ramsified will be true
provided the original theory is satisfied--hence the claim that
the content of the Ramsey sentence is merely the observational content
of the original theory plus a cardinality claim is still true when
mixed predicates are considered. Melia and Saatsi (2006) also argue
that intensional notions, such as naturalness and causal significance,
may be applied to properties to save the Ramsey sentence formulation
of ESR from triviality. (This recalls the defence of Russell's
structuralism against Newman discussed in Hochberg 1994.) Demopoulos
also raises two problems with this strategy: firstly, even non-natural
relations can have significant claims made about them in a theory, and
secondly, the cognitive significance of unramsified theories is
independent of a commitment to "real" or
"natural" relations. Hence, Demopoulos insists that the
Ramsey sentence of a theory and the theory itself are importantly
different (see also Psillos 2006b). Peter Ainsworth (2009) gives an
accessible account of the Newman problem and the responses that have
been given to it. Ladyman (1998) and Ladyman and Ross (2007) argue
that the Newman problem does not arise for ontic structural realism
because it eschews an extensional understanding of relations.



In his 2011 paper, Demopoulos argues that there are three very
different views in the work of Russell, Ramsey, and Carnap
respectively, which have in common versions of a core structuralist
thesis that he identifies. All the accounts he considers make use of
Ramsey sentences; Demopoulos investigates the logical properties of
the Ramsey sentence and arrives at an argument against the
structuralist thesis. Friedman (2011) argues that Carnap's
account of theoretical terms involving the Ramsey sentence approach is
not vulnerable to the Newman problem. The relationship between
Friedman's views on the relativized *a priori* and
structural realism is interrogated in Ivanova (2011).



Structural realism is supposed to help with the problem of theory
change. As Maxwell himself pointed out, his structural realism is a
purely semantic and epistemological theory. The Ramsey sentence picks
out exactly the same entities as the original theory. It does not
dispense with reference, but it makes that reference a function of the
(place of the theoretical terms in the) overall structure of the
theory, as manifested in the Ramsey sentence. Hence, Ladyman (1998)
argues that in general epistemological forms of structural realism do
not significantly improve the prospects of standard scientific realism
and that structural realism should be thought of as metaphysically
rather than merely epistemically revisionary. The problem of
ontological discontinuity is arguably left untouched by simply
adopting Ramsification. In fact, it seems even worse if contextualism
about the meaning of theoretical terms is adopted. Cei and French
(2006) and Cruse (2005) also argue, on different grounds, that
Ramsification is of no help to the structural realist.



Versions of ESR that employ the Ramsey sentence of a theory and the
distinction between observational and theoretical terms are embedded
in the so-called "syntactic" view of theories that adopts
first-order quantificational logic as the appropriate form for the
representation of physical theories. According to Zahar (1996: 14) the
continuity in science is in the intension rather than the extension of
its concepts. He argues that if we believe that the mathematical
structure of theories is fundamentally important for ontology, then we
need a semantics for theories that addresses the representative role
of mathematics directly. Such an account of scientific representation
is allegedly found in the so-called "semantic" or
"model-theoretic" approach associated primarily with
Patrick Suppes, Fred Suppe, Ron Giere and Bas van Fraassen, and more
recently da Costa and French (2003). The relationship between
structuralism and the semantic view is discussed by van Fraassen
(1997, 2008), and Thomson-Jones (2011). Chris Pincock (2011)
criticises structural realism on the basis of an analysis of the role
of mathematics in scientific representation. See also Beni (2019) for
the development of a form of structural realism together with an
account of representation in general. Wallace (2022) argues that the
mathematics-first view of scientific representation of the semantic
view leads naturally to ontic structural realism.


## 4. Ontic Structural Realism (OSR)



Worrall's statement of structural realism in his 1989 paper is
not explicitly epistemic, and some of his remarks prompt a different
interpretation:



> 
> 
> On the structural realist view what Newton really discovered are the
> relationships between phenomena expressed in the mathematical
> equations of his theory. (1989: 122)
> 
> 
> 



Some philosophers of physics had already more explicitly signalled a
significant departure from traditional realist metaphysics. For
example, Howard Stein says:



> 
> 
> [O]ur science comes closest to comprehending "the real",
> not in its account of "substances" and their kinds, but in
> its account of the "Forms" which phenomena
> "imitate" (for "Forms" read "theoretical
> structures", for "imitate", "are represented
> by"). (1989: 57)
> 
> 
> 



Michael Redhead (1999: 34) says: "the best candidate for what is
'true' about a physical theory is the abstract structural
aspect". Accordingly, Ladyman (1998) argues that structural
realism ought to be developed as a metaphysical position according to
which, since the continuity in scientific change is of "form or
structure", the success of science should be accounted for in
terms of the representation of modal relations among phenomena, not in
terms of continuity of reference to objects and properties. Giere
(1985) first suggested that a form of structural realism results from
conjoining modal realism with constructive empiricism to form a modal
empiricism. The idea of modal structure is central to OSR in the work
of French, Ladyman, Ross and others, and is an abstraction of causal
structure and nomological structure, that is intended to also include
symmetry principles and perhaps more (the structure of dispositions
described by Mumford (2004) and Psillos's (2002) idea of
nomological structure are more restrictive ideas of modal structure).
The reason why it is claimed that some modal structure is retained on
theory change, as well as the approximate truth of empirical
regularities, is that counterfactuals, explanations and predictions
are retained in a limited domain or regime when an old theory is
superseded. For example, the reason the same side of the Moon always
faces the Earth was explained by Newton in the third book of the
Principia in terms of a gravitational tidal lock, and this explanation
and related counterfactuals and predictions are retained in current
physics even though Newtonian gravitation has been superseded by
General Relativity. Nora Berenstain and Ladyman (2012) argue that a
commitment to natural necessity is implicit in arguments for
scientific realism, and that all scientific realists should be
realists about modal structure as a form of natural necessity, and so
should reject Humean supervenience. However, Esfeld (2009) develops a
Humean take on structural realism, as does Lyre (2010). Ruyant (2019)
considers how to understand continuity of modal structure in the
history of science in terms of a modalised Ramsey sentence which he
argues supports modal empiricism as distinct from structural
realism.



OSR has attracted most sympathy among some philosophers of physics and
physicists. This is natural since, while Worrall's motivation
for introducing structural realism was solely the need for a realist
response to the pessimistic meta-induction, the proposal of OSR in
Ladyman (1998) and its development in French and Ladyman (2003a,b) and
their subsequent work was also motivated by two other problems:


1. identity and individuality of quantum particles and
spacetime points, and entanglement;
2. scientific representation, in particular the role of
models and idealisations in physics.



Their concern with
 (a)
 followed that of many of the pioneers of structuralism in
twentieth-century philosophy of science including Cassirer, Eddington
and Weyl. (Russell's and Carnap's versions of
structuralism were more directly motivated by epistemological and
semantic problems than by ontological issues arising from physics.)
French did seminal work on the identity and individuality of quantum
particles with Michael Redhead (French & Redhead 1988). In
relation to
 (b),
 Redhead also wrote a classic paper on theories and models (1980), and
French and Ladyman (1999) defended and developed the model-theoretic
approach to scientific theories; Ladyman and Ross (2007), Gordon
McCabe (2007), French (2014) and Wallace (2022) all defend OSR
as a view that takes account of the ineliminability of mathematics in
how physics represents.



OSR may be advocated as a response to current physics as a whole (for
example, see Tegmark 2008), or in part (see below). Karim
Thebault (2016) considers quantisation in order to formulate
OSR. Dorato and Morganti (2022) consider structural realism as an
ontology for Rovelli's Relational Quantum Mechanics. Saunders
and David Wallace have deployed structuralism to solve the problem of
how macroscopic objects with more or less determinate properties can
be recovered from the Everett interpretation of quantum states (the
so-called preferred basis problem) (Saunders 1993b, 1995, and Wallace
2003). Saeed Masoumi (2021b) defends OSR by considering how to break
the underdetermination of different forms of Newtonian physics.
(Different versions of OSR are also elaborated and defended against
various criticisms in Ladyman and Ross (2007), French and Ladyman
(2011), Ladyman (2011), French (2014) and further sources cited
below.)



Ontic structural realists argue that current physics teaches us that
the nature of space, time and matter are not compatible with standard
metaphysical views about the ontological relationship between
individuals, intrinsic properties and relations. On the broadest
construal OSR is any form of structural realism incorporating an
ontological or metaphysical thesis that inflates the ontological
priority of structure and relations. The attempt to make this precise
splinters OSR into different forms (three of these are discussed in
Ainsworth (2010) and he argues against two of them), and all of the
following claims have been advocated by some defenders of OSR at some
time (and some of them overlap, or differ largely or solely only in
emphasis).



(1)
Eliminativism: there are no individuals (but there is relational
structure).


A crude statement of ESR is the claim that all we know is the
structure of the relations between things and not the things
themselves, and a corresponding crude statement of OSR is the claim
that there are no "things" and that structure is all there
is, and in particular there are no individual things. This is called
and "eliminative structural realism" by Psillos (2001) who
objects to the elimination of objects from ontology, and
"radical structuralism" by van Fraassen (2006), who argues
it collapses the distinction between abstract and concrete structure
and between pure mathematics and physics. For a recent defence of an
explicitly eliminativist version of OSR see French (2010, 2016,
2019a). For a form of eliminativism about individuals in metaphysics
developed without reference to structural realism see Dasgupta
(2009).



Eliminativism is criticised on the grounds that there cannot be
relations without relata. This objection has been made by various
philosophers including Cao (2003b), Dorato (2000), Psillos (2001,
2006a), Busch (2003), Morganti (2004) and Chakravartty (1998, 2003)
who says:



> 
> 
> one cannot intelligibly subscribe to the reality of relations unless
> one is also committed to the fact that some things are related. (1998:
> 399)
> 
> 
> 



The idea is that structure requires individuals, since structure is
relations, and relations require relata which are individuals. Even
many of those sympathetic to OSR object that it amounts to crediting
relations without relata (Esfeld & Lam 2008; Lyre 2004; Stachel
2006; and Yaghmaie 2021).



However, there are at least two ways to make sense of the idea of
relations without relata:


1. The idea of a universal. For example, when we refer to the relation
referred to by "larger than", it is because we have an
interest in its formal properties that are independent of the
contingencies of its instantiation. To say that all that there is are
relations and no relata, is perhaps to follow Plato and say that the
world of appearances is not properly thought of as part of the content
of knowledge. (See Esfeld & Lam 2008: 5, and the opening epigram
in Psillos 2006a) This Platonic version of OSR is perhaps what Howard
Stein has in mind:



> 
> 
> ... if one examines carefully how phenomena are
> "represented" by the quantum theory... then...
> interpretation in terms of "entities" and
> "attributes" can be seen to be highly dubious... I
> think the live problems concern the relation of the Forms ... to
> phenomena, rather than the relation of (putative) attributes to
> (putative) entities .... (Stein 1989: 59)
> 
> 
>
2. The relata of a given relation always turn out to be relational
structures themselves on further analysis. As Stachel puts it,
"it's relations all the way down" (although he
denies the claim, 2006). See Saunders (2003d: 129) and Ladyman and
Ross (2007) for the idea that there may be no fundamental relata, and
hence that it is relational structure all the way down. The idea that
there may be no fundamental level to reality is discussed in Schaffer
(2003). Much discussion of OSR in ever form relates to issues of
fundamentality and the relative ontological priority of objects,
properties and relations. Horgan and Potrc (2000) take the fundamental
level to be the whole universe so that there are not really any
relations because there is only one thing. Schaffer 2010 argues that
there are no external relations, in the sense that all relations are
internal to the one thing that is everything. Other metaphysicians who
doubt, deny or downgrade relations include John Heil, E.J.Lowe and
Peter Simons (see Marmodoro & Yates 2016).



Another response to the relations without relata objection is to argue
that OSR does not require that there be no relata, just that the
relata not be individuals. However, there is no unanimity about the
difference between individuals, objects, and entities among
philosophers. One way of putting the issue is to ask whether all
objects are individuals, or whether individuals are objects satisfying
some additional criteria (for example, having identity over time or
transworld identity, see Ladyman 2016). Clearly, debates about OSR are
not productive unless the terminology is univocal, and the
philosophical logic of individuals, objects and relations is explicit,
and, given the extent of disagreement among philosophers about these
matters, the sources cited here and in general should be read with the
possible differences in terminology in mind.



(2)
There are relations (or relational facts) that do not supervene on
the intrinsic and spatio-temporal properties of their relata.


The interpretation of entangled states in quantum mechanics in terms
of strongly non-supervenient relations is due to Carol Cleland (1984).
However, the idea that there could be relations which do not supervene
on the non-relational properties of their relata runs counter to a
deeply entrenched way of thinking among some philosophers, whose
conception of structure is usually based on predicate logic and set
theory. Hence, it is often assumed that a structure is fundamentally
composed of individuals and their intrinsic properties, on which all
relational structure supervenes. The view that this conceptual
structure reflects the structure of the world is called
"particularism" by Paul Teller (1989) and "exclusive
monadism" by Dipert (1997). It has been endorsed by many
philosophers, including Aristotle and Leibniz.



Spatio-temporal relations might be exempted from this prescription
since the idea that the position of an object is intrinsic to it is
associated with a very strong form of substantivalism. Hence, a
standard view is that the relations between individuals other than
their spatio-temporal relations supervene on the intrinsic properties
of the relata and their spatio-temporal relations. This is David
Lewis's Humean supervenience:



> 
> 
> [A]ll there is to the world is a vast mosaic of local matters of
> particular fact, just one little thing and then another ... We
> have geometry: a system of external relations of spatio temporal
> distance between points (of spacetime, point matter, aether or fields
> or both). And at these points we have local qualities: perfectly
> natural intrinsic properties which need nothing bigger than a point at
> which to be instantiated ... All else supervenes on that. (1986:
> x)
> 
> 
> 



Tim Maudlin argues against this on the basis of quantum entanglement
and argues that this means the end of ontological reductionism, and
abandoning the combinatorial conception of reality that comes from
thinking of the world as made of building blocks, each of which exists
independently of the others (1998: 59) and: "The world is not
just a set of separately existing localized objects, externally
related only by space and time" (1998: 60). Similarly, advocates
of OSR such as French and Ladyman emphasise that the non-supervenient
relations implied by quantum entanglement undermine the ontological
priority conferred on individuals in most traditional metaphysics.
Some relations are at least ontologically on a par with individuals,
so either relations are ontologically primary, or neither is
ontologically primary or secondary. (Oliver Pooley 2006 and Esfeld
& Lam 2008 hold the latter view, but Esfeld 2003, 2004 goes
further and claims that if there are intrinsic properties they are
ontologically secondary and derivative of relational properties [see
below].) Primitive nonsupervenient relations of entanglement are a
form of primitive modal structure. As discussed above and below, many
advocates of OSR take the objective modal structure of the world to be
ontologically fundamental, in the sense of not supervening on the
intrinsic and spatio-temporal properties of their relata. The
operational theory research programme in physics considers quantum
mechanics in a more general space of theories that is analogous to the
space of possible worlds of modal logic. Emily Adlam (2022) interprets
the different constraints placed on correlations in different
operational theories as different specifications of modal structure.
See also Constructor Theory (Deutsch 2013), which is a formalism for
physical theories based on possible and impossible transformations of
states.



(3)
Individual objects have no intrinsic natures.


On this view, individual objects of a particular kind are
qualitatively identical. They are not individuated by an haecceity or
primitive thisness. Classical particles can be and often are so
regarded, because if a principle of impenetrability is adhered to, no
two such particles ever have all the same spatio-temporal properties.
If there are spatio-temporal properties that distinguish each thing
from every other thing, the identity and individuality of physical
objects can be reduced to other facts about them. The bundle theory of
individuation was developed by empiricists to account for the
individuation of physical objects in terms of properties that are
within the reach of natural science (such properties are called
"qualitative" by Saunders).



This is a standard metaphysical position that implies nothing so
radical as any version of OSR. It is relevant because it is often
taken to require the Principle of the Identity of Indiscernibles
(PII), which states in contrapositive form that there are no distinct
objects having all the same properties (the discernibility of the
distinct). PII is trivially true if its scope is taken to include
properties that involve particular objects such as haecceities since
clearly no two objects have the same haecceity, so it must be
restricted so that such properties are not in its scope. The problem
with PII is that prima facie in Quantum Mechanics entangled quantum
states of many particles attribute exactly the same intrinsic and
relational properties to each of them. For example, the famous singlet
state of two fermions, such as electrons, attributes to the pair the
relation that their spins in any given direction are opposite to each
other, but does not attribute a definite spin in any direction to
either particle alone. Given that they may also be attributed exactly
the same spatial wavefunction, as when they are both in the first
orbit of an atom, for example, then such particles would seem to
violate PII. This leads to a dilemma that was articulated by Steven
French and Michael Redhead (1988); either quantum particles are not
individuals, or they are individuals but the principle of
individuation that applies to them must make reference to some kind of
empirically transcendent haecceity, bare particularity or the
like.



French and Krause (2006) argue that quantum particles and spacetime
points are not individuals, but that they are objects in a minimal
sense, and they develop a non-classical logic according to which such
non-individual objects can be the values of first-order variables, but
ones for which the law of identity, "for all *x*,
*x* is identical to *x*", does not hold (but
neither does "*x* is not identical to *x*").
Katherine Brading and Alexander Skiles (2012) consider the
plausibility of arguing for structural realism on the basis of this
underdetermination. The relationship between OSR and PII is assessed
in Ainsworth (2011). The appeal to this problem of metaphysical
underdetermination is criticised by Chakravartty (2003), who argues
that it cannot be significant since it also obtains in the case of
everyday objects. Morganti (2004) argues in favour of transcendental
individuation, and also points out that if quantum mechanics is not
complete and there are hidden variables as in Bohm theory, the quantum
particles may be individuated by their intrinsic and spatio-temporal
properties after all. Saunders argues that there is no
underdetermination for reasons explained in
 (5)
 below.



(4)
There are individual objects or things, but they do not have any
irreducibly intrinsic properties.


Michael Esfeld (2004) rejects
 (1)
 and argues that:



> 
> 
> (a) relations require relata
> 
> 
> 



but denies that:



> 
> 
> (b) these relata must have intrinsic properties over and above the
> relations in which they stand.
> 
> 
> 



As mentioned above Esfeld holds that there are things and relations
but neither is ontologically primary or secondary. On this view, all
the properties of individual objects are relations to other objects.
This view is called "moderate structural realism" by
Esfeld (and Esfeld & Lam 2008, 2011 and see also Lam & Esfeld
2012). It avoids the problems with
 (1)
 above, and is compatible with
 (2)
 and
 (3).
 Any version of
 (4)
 that is combined with (3) arguably makes individuals ontologically
dependent on relational structure (see
 (6)
 below).



Benacerraf (1965) argues that there cannot be objects possessing only
structural properties. The idea of such objects is denounced as
"mysticism" by Dummett (1991), and criticised in the
context of structural realism by Busch (2003). These objections go
back to Russell:



> 
> 
> ...it is impossible that the ordinals should be, as Dedekind
> suggests, nothing but the terms of such relations as constitute a
> progression. If they are to be anything at all, they must be
> intrinsically something; they must differ from other entities as
> points from instants, or colours from sounds. What Dedekind intended
> to indicate was probably a definition by means of the principle of
> abstraction...But a definition so made always indicates some
> class of entities having... a genuine nature of their own (1903:
> 249 [ch. XXX, SS 242]).
> 
> 
> 



On the other hand, D.W. Mertz (1996) defends "network instance
realism" and rejects the "tyranny of the monadic"
arguing that individuated relation instances are ontologically
fundamental. McKenzie (2016) argues on the basis of considering
fundamentality in particle physics that particles are not defined by
intrinsic properties.



(5)
Facts about the identity and diversity of objects are
ontologically dependent on the relational structures of which they are
part.


Saunders (2003a, 2003b and 2006) argues that there is a notion of
discernibility (discussed by Quine 1976) that is satisfied even by
electrons in the singlet state described above. Two objects are
"weakly discernible" iff they satisfy some relation that
is irreflexive in the pair of them. By the uncontentious converse of
PII, sometimes known as "Leibniz' law", namely the
Principle of the Indiscernibility of Identicals (or contrapositively
put, the Distinctness of the Discernible), if the relation
\(a\mathbin{R}b\) holds but the relation \(b\mathbin{R}a\) does not,
then there must be distinct relata \(a\) and \(b\). Electrons in the
singlet state stand in the relation of having opposite spin, and, an
electron cannot have an opposite spin to itself, so, argues Saunders,
they are weakly discernible. In this way the facts about the identity
and diversity of objects are ontologically dependent on the
qualitative relations they bear to each other.



This runs counter to the usual way of thinking according to which
there are individuals in spacetime whose existence is independent of
each other, and facts about the identity and diversity of these
individuals are determined independently of their relations to each
other (Stachel 2006 calls this "intrinsic individuality").
It is widely held that relations between individuals cannot
individuate (account for the identity and diversity) of those same
individuals or, as it is often put, "relations presuppose
numerical diversity and so cannot account for it". The argument
is that without distinct individuals that are metaphysically prior to
a relation, there is nothing to stand in the relation irreflexively
that is supposed to confer individuality on the relata. The issue was
famously discussed by Russell (1911), and see also MacBride (2006).
Ladyman and Ross (2007), Saunders (2006) and Stachel (2006) argue that
facts about the identity and diversity of fermions are not intrinsic,
and obtain only in virtue of the relations into which they enter. On
this view the individuality of quantum particles is ontologically on a
par with, or secondary to the relational structure of which they are
parts. Stachel (2006) calls this "contextual
individuality" and he extends this to spacetime points (see
 SS4.3
 below).



Hannes Leitgeb and Ladyman (2007) note that in the case of
mathematical structures there is nothing to rule out the possibility
that the identity and diversity of objects in a structure is a
primitive feature of the structure as a whole that is not accounted
for by any other facts about it (Ladyman (2007) also discusses such
primitive contextual individuality). One important question so far not
much discussed is whether on the contextualist view the identity and
diversity of the objects depends on the whole structure or just part
of it. Another important issue is which if either of identity and
diversity is primitive. Ladyman, Linnebo, and Pettigrew (2012) present
some results about the relative strengths of different forms of
discernibility in languages with and without names and identity (see
also Ladyman 2015, 2016). In particular it turns out that weak
discernibility in a language without names is equivalent to absolute
discernibility in a language with names. In the light of this it is
perhaps not surprising that in the recent literature the position that
quantum particles can be absolutely discerned after all is defended in
different ways by various authors (see Bigaj 2022 for a recent and
comprehensive discussion of questions about the identity and
individuality of quantum particles). Bigaj (2014) interprets the
ontological dependence of objects on relational structures in terms of
counterfactual identification, not identity and diversity, to propose
an essentialist version of non-eliminativist OSR. For criticism of
non-eliminative OSR in particular see Chakravartty (2012).



(6)
There are no self-subsistent objects, and relational structure is
ontologically subsistent.


This claim is associated with quantum holism and holism more generally
(see Horgan & Potrc 2000 and 2002). As mentioned above this is
arguably implied by the conjunction of
 (3)
 and
 (4),
 and also by
 (5).
 The basic idea of ontological self-subsistence is that of being able
to exist without anything else existing. The notions of ontological
dependence and ontological subsistence are often employed in
discussions of structuralism, but are in need of clarification (see
Linnebo 2007). Kerry McKenzie (2014) uses Fine's recent analyses
of ontological dependence to argue against eliminativist OSR and in
favour of moderate structural realism based on a case study from
particle physics, and McKenzie (2020) formulates OSR in terms of
determination. Vassallo, Naranjo, and Koslowski (2022) defend a
metaphysics of self-subsisting structures for classical mechanics.



(7)
Individual objects are constructs


French (1999) and French and Ladyman (2003a) maintain that individuals
have only a heuristic role. Poincare similarly argued that
"the gross matter which is furnished us by our sensations was
but a crutch for our infirmity" (1898: 41). Ladyman and Ross
(2007) argue that objects are pragmatic devices used by agents to
orient themselves in regions of spacetime, and to construct
approximate representations of the world. Anyone who defends
eliminativism as in
 (1)
 above must similarly offer a non-*ad hoc* account of the point
and value of reference to and generalization over objects in science.
For example, cognitive science may show that we are not able to think
about certain domains without hypostatising individuals as the bearers
of structure. This is a subject for further study.



The articles in Landry and Rickles (2012) explore some of the above
issues. See McKenzie's (2013) review of the collection. See also
the collection Bokulich and Bokulich (2011). Jo Wolff (2012) considers
the relationship between objects and structures, arguing that the
former are not reducible to the latter, and suggesting that a form of
ontic structural realism may be defended in terms of the claim that
objects are ontologically dependent on structures.


### 4.1 OSR and Group Theory



A symmetry is a transformation of some structure or object which
leaves it unchanged in some respect. A group of symmetry
transformations is a mathematical entity comprising the set of
transformations, including the identity transformation and an inverse
of each transformation, and the operation of composing them, where the
result of two composed transformations is also itself in the original
set. Mathematical objects can be characterised in terms of which
symmetry transformations leave them unchanged or invariant, and
symmetries of various kinds are associated with physical laws (see the
entry on
 symmetry and symmetry breaking).
 Poincare first understood the Galilean and Lorentz
transformations as groups. These groups express fundamental features
of reality, namely the dynamical symmetries of Newtonian and
Einsteinian physics respectively. Poincare understands group
structure in Kantian terms as a pure form of the understanding in
accordance with his epistemic form of structuralism.



Other pioneers of structuralism shared his appreciation of the
importance of group theory in the metaphysics of physics. Cassirer
held that the possibility of talking of "objects" in a
context is the possibility of individuating invariants (1938 [1944]).
Similarly, Max Born says:



> 
> 
> Invariants are the concepts of which science speaks in the same way as
> ordinary language speaks of 'things', and which it
> provides with names as if they were ordinary things, (1953: 149)
> 
> 
> 



and:



> 
> 
> The feature which suggests reality is always some kind of invariance
> of a structure independent of the aspect, the projection. (1953:
> 149)
> 
> 
> 



He goes so far as to say:



> 
> 
> I think the idea of invariant is the clue to a relational concept of
> reality, not only in physics but in every aspect of the world. (1953:
> 144)
> 
> 
> 



Eddington says:



> 
> 
> What sort of thing is it that I know? The answer is
> *structure*. To be quite precise it is structure of the kind
> defined and investigated in the mathematical theory of groups. (1939:
> 147)
> 
> 
> 



The idea then is that we have various representations of some physical
structure which may be transformed or translated into one another, and
then we have an invariant state under such transformations which
represents the objective state of affairs. The group structure is
primary and the group representations constructed from this structure
have a derivative status. Representations are extraneous to physical
states but they allow our empirical knowledge of them. Objects are
picked out by the identification of invariants with respect to the
transformations relevant to the context. Thus, on this view,
elementary particles are hypostatisations of sets of quantities that
are invariant under the symmetry groups of particle physics.



For example, one of the most fundamental distinctions between kinds of
particles is that between fermions and bosons. This was described
group theoretically by Weyl and Wigner in terms of the group of
permutations, and the former's approach to relativity theory was
similarly group-theoretic. In the case of quantum mechanics Weyl
asserts that:



> 
> 
> All quantum numbers, with the exception of the so-called principal
> quantum number, are indices characterising representations of groups.
> (1928/1931 [1931: xxi])
> 
> 
> 



The central point of philosophical relevance here is that the
mathematical idea of invariance is taken by Weyl to characterise the
notion of objectivity. It is this that liberates physics from the
parochial confines of a particular coordinate system. For Weyl
appearances are open only to intuition (in the Kantian sense of
subjective perception) and therefore agreement is obtained by giving
objective status only to those relations that are invariant under
particular transformations.



Weyl's views were revived by Sunny Auyang (1995) in an
explicitly neo-Kantian project which attempts to solve the problem of
objectivity in quantum mechanics and quantum field theory (QFT).
Auyang seeks to extract the "primitive conceptual
structure" in physical theories and she too finds it in what she
calls the "representation-transformation-invariant
structure". This is essentially group-theoretic structure.
Auyang, like Born and Weyl, thinks that such invariant structure under
transformations is what separates an objective state of affairs from
its various representations, or manifestations to observers under
different perceptual conditions. According to her events are
individuated structurally.



Ryckman (2005) describes the history of relativity theory and
Weyl's role in it. Ryckman argues that the work of Eddington and
Weyl was profoundly influenced by the phenomenology of Husserl. The
latter also seems to have understood objectivity in terms of
invariance. (Ryckman calls Kantian structural realism
"transcendental structuralism". OSR is what he calls
"transcendent structuralism".) Group theory in the
development of structuralism deserves further historical analysis. It
played a crucial role in epistemological reflections on geometry in
relation to Klein's Erlanger programme (Birkhoff & Bennett
1988). French (1998, 1999, 2000) and Castellani (1998a) have explored
the ontological representation of the fundamental objects of physics
in terms of sets of group-theoretic invariants by Cassirer, Eddington,
Schrodinger, Weyl, Wigner, Piron, Jauch and others. See Bueno
(2019), and Marquis (2020) for a recent discussion of structuralism in
the history of mathematics in which group theory played a prominent
role as it does in quantum field theory. On the other hand, Roberts
(2011) criticizes the idea that structure can be understood as group
structure in the context of quantum physics. Others have used other
parts of mathematics to understand structuralism. Hannes Leitgeb
(2021) develops a non-eliminative structuralism about graphs. See
 SS4.2
 below for OSR and category theory, and
 SS4.4
 and
 SS6
 for OSR and information theory.


### 4.2 OSR and Quantum Field Theory



There are states of quantum fields that can be identified with there
being definite numbers of particular particles, but general states
cannot. Particles are standardly thought of as particular excitations
of the field sometimes called "field quanta". Hence, the
problem of metaphysical underdetermination raised by French and
Redhead (1988) in the context of non-relativistic many particle
quantum mechanics is obviated in the context of quantum field theory,
because a particles-as-individuals view is not an option since, loose
identifications of particles and field quanta not withstanding, field
quanta are not individual things (see Bigaj 2018). Redhead (1999)
reviews the interpretative issues with QFT and argues for OSR in the
light of them. Much earlier, Cassirer rejected the Aristotelian idea
of individual substances on the basis of physics, and argued that the
metaphysical view of the "material point" as an individual
object cannot be sustained in the context of field theory. He offers a
structuralist conception of the field:



> 
> 
> The field is not a "thing", it is a system of effects
> (*Wirkungen*), and from this system no individual element can
> be isolated and retained as permanent, as being "identical with
> itself" through the course of time. The individual electron no
> longer has any substantiality in the sense that it *per se est et
> per se concipitur*; it "exists" only in its relation
> to the field, as a "singular location" in it. (1936 [1956:
> 178])
> 
> 
> 



Cao in his book on quantum field theory sometimes sounds like an ontic
structural realist, because he denies that the structures postulated
by field theories must be "ontologically supported by
unobservable entities" (Cao 1997: 5). However, in his (2003a) he
explicitly criticises OSR and argues for a version of ESR in the
context of a discussion of quantum field theory. Saunders (2003c and
d) also criticises Cao for underestimating the difficulties with a
non-structuralist form of realism in the light of the history of
quantum field theory. Berghofer (2018) argues that quantum fields have
intrinsic properties and that this undermines OSR.



In gauge quantum field theories, which are our best current physical
theories of all the forces other than gravity, each field is
associated with a particular symmetry group, and the unification of
theories was achieved by looking for theoretical structures with the
relevant combined symmetry (U(1) for quantum electrodynamics, U(2) for
the electroweak theory and SU(3)/Z(3) for the strong interaction.)
Lyre argues for OSR in the interpretation of gauge symmetry. He argues
that



> 
> 
> the traditional picture of spatiotemporally fixed object-like entities
> is undermined by the ontology of gauge theories in various ways and
> that main problems with traditional scientific realism...can be
> softened by a commitment to the structural content of gauge theories,
> in particular to gauge symmetry groups. (2004: 666)
> 
> 
> 



He goes on to note that his favoured interpretation of gauge theories
(in terms of non-separable holonomies) is one according to which the
fundamental objects are ontologically secondary to structure because
the objects of a theory are members of equivalence classes under
symmetry transformations and no further individuation of objects is
possible. Similarly, Kantorovich (2003) argues that the symmetries of
the strong force are ontologically prior to the particles that feel
that force, namely the hadrons, and likewise for the symmetries of the
so-called "grand unification" of particle physics in the
Standard Model of particle physics (but see McKenzie (2014) for a
different view as cited above). However, There are "unitarily
inequivalent" representations of the algebra of quantum field
theories, and Howard (2011) and Ruetsche (2011) argue that this poses
a problem for algebraic conceptions of structure. French (2012)
responds, while David Glick (2016) argues for pluralism about
structure in OSR on the basis of unitary inequivalence. McCabe (2007)
presents the structure and interpretation of the Standard Model in
ontic structural realist terms saying:



> 
> 
> In terms of structural realism...fibre bundle cross-sections can be
> treated as the structures which lie beyond the empirical phenomena.
> (2007: 6)
> 
> 
> 



French (2019b) addresses the Standard Model in terms of his account of
OSR. Federico Benitez (2023) distinguishes between framework theories
and interaction theories in assssing structural realism in the context
of the Standard Model.



The ontology of fields and especially the status of vacuua, virtual
particles and gauge fields is much contested. Malament (1996) and
Halvorson and Clifton (2002), among others, argue that there is a
fundamental conflict between relativistic quantum field theory and the
existence of localisable particles. Similarly, when it comes to
quantum field theory in a curved spacetime, "a useful particle
interpretation of states does not, in general, exist" (Wald
1994: 47, quoted in Stachel 2006: 58). Fraser (2008) argues that there
are no particles in quantum field theory on the basis of a theorem in
algebraic quantum field theory (Haag's theorem). Wallace (2006,
2011) adopts a different approach, considering the practice of
Lagrangian or "effective" quantum field theory, which
makes explicit that the theory does not describe interactions at
certain energy and length scales, and arguing for a view of particles
as scale-dependent emergent entities. Ladyman (2015) similarly argues
that the current scientific understanding of particles exemplifies the
claims of Ladyman and Ross (2007) that composition is dynamical, and
that ontology is scale-relative.



If fields are construed as properties of space-time points or regions
and then the issue becomes whether the spacetime points are
individuals and this question is bound up with the debate about
substantivalism in the foundations of General Relativity as discussed
in the next section.


### 4.3 OSR and Spacetime Physics



There has been much dispute about how General Relativity relates to
relationism and substantivalism about space and time. The main problem
for the latter is the general covariance of the field equations of
General Relativity: any spacetime model and its image under a
diffeomorphism (a infinitely differentiable, one-one and onto mapping
of the model to itself) are in all observable respects equivalent to
one another; all physical properties are expressed in terms of
generally covariant relationships between geometrical objects. Put
crudely, since the points of spacetime are intrinsically indiscernible
one from another, it makes no difference if we (smoothly) swap their
properties around so long as the overall structure remains the same.
This is made more apparent by the so-called "hole
argument", which constructs diffeomorphic models such that if
they are regarded as physically distinct then there is a breakdown of
determinism. John Earman and John Norton (1987) argue that
substantivalists cannot just bite the bullet and accept this because
the question of determinism ought to be settled on empirical/physical
grounds and not *a priori* ones.



There have been a variety of responses to this problem. Lewis (1986)
and Carol Brighouse (1994) suggest accepting haecceitism about
spacetime points, but argue that it should not worry us that
haecceitistic determinism, that is determinism with respect to which
points end up with which metrical properties, fails. Melia (1999)
criticises the notion of determinism employed by Earman and Norton.
Nonetheless most philosophers of physics seem to have concluded that
if spacetime points do have primitive identity, then the
substantivalist who is committed to them must regard the failure of
haecceitistic determinism as a genuine failure of determinism. Hence,
others have sought to modify substantivalism. Carl Hoefer argues that
the problems for spacetime substantivalism turn on the
"ascription of primitive identity to space-time points"
(1996: 11). Hence, it seems that interpreting spacetime in terms of an
ontology of underlying entities and their properties causes problems
for realism about spacetime.



In response various authors have adopted structural realism about
spacetime. Robert DiSalle (1994) suggests that the correct response to
the hole argument is that the structure of spacetime be accepted as
existent despite its failure to supervene on the reality of spacetime
points. (Masoumi (2021a) also thinks that consideration of the hole
argument supports OSR.) This is akin to the position developed by
Stein (1968) in his famous exchange with Grunbaum, according to
which spacetime is neither a substance, not a set of relations between
substances, but a structure in its own right. Similarly, Oliver Pooley
(2007) argues that eliminativism about individual spacetime points can
be avoided without any tension with General Relativity, if it is
accepted that the facts about their identity and diversity is grounded
in relations they bear to each other. His sophisticated
substantivalism allows that spacetime points be individuated
relationally and not independently of the metric field. This means
embracing contextual individuality grounded in relational structure.
See also Cassirer who says:



> 
> 
> To such a [spacetime] point also no being in itself can be ascribed;
> it is constituted by a definite aggregate of relations and consists in
> this aggregate. (1936 [1956: 195])
> 
> 
> 



The analogy between the debate about substantivalism, and the debate
about whether quantum particles are individuals made by Ladyman
(1998), Stachel (2002 and 2006), and Saunders (2003a,b) is contested
by Pooley (2006). He argues that there is no such analogy, or at least
not a very deep one, on the grounds that there is no metaphysical
underdetermination in GR. According to him the standard formulations
of the theory are ontologically committed to the metric field, and the
latter is most naturally interpreted as representing "spacetime
structure" (90).



Others who have discussed structural realism and spacetime include,
Dorato (2000) who discusses spacetime and structural realism but
rejects OSR, Esfeld and Lam (2008 and 2011) who argue for moderate
ontic structural realism about spacetime (as defined above), and Bain
(2006), who says that:



> 
> 
> Conformal structure, for instance, can be realised on many different
> types of "individuals": manifold points, twisters, or
> multivectors ...What is real, the spacetime structuralist will
> claim, is the structure itself and not the manner in which alternative
> formalisms instantiate it. (2006: 64)
> 
> 
> 



There are interesting connections between spacetime structuralism and
the spacetime functionalism of Eleanor Knox (2019). Bain (2013) argues
that critics of radical ontic structural realism have implicitly
relied on a set-theoretic notion of structure and that a category
theoretic formulation of ontic structural realism is useful in
explicating the structure of physical theories, in particular, general
relativity. Lal and Teh (2017) respond to Bain downplaying the
significance of category theory for structuralism, but their arguments
are contested by Eva (2016). Quantum gravity and structuralism is
discussed by philosophers and physicists in Rickles, French, and
Saatsi (2006).


### 4.4 OSR and the Special Sciences



Much of the work on ontic structural realism focuses on physics, but
various authors have applied it much more widely. Gower (2000) argues
that structural realism seems less plausible about theories from
outside of physics, and Mark Newman (2005) argues that structural
realism only applies to the mathematical sciences in therefore cannot
account for retention of theoretical commitments across theory change
in, for example, biology. However, Sarkar (2020) is more optimistic
about the prospects for structural realism in biology if the focus is
on organisational structure rather than laws, and French (2011 and
2014) also considers the implications of his form of ontic structural
realism for the ontology of biology. French (2016) defends eliminative
OSR across the sciences. On the other hand, Ladyman and Ross (2007)
argue for OSR as part of a form of realism about the sciences as a
whole, invoking the idea of real patterns due to Dennett and developed
as part of Ross's "rainforest realism" (see below).
Harold Kincaid (2008) and Ross (2008) defend structural realist
approaches to the social sciences. Tulodziecki (2016) considers the
prospects of structural realism beyond physics. Ladyman (2008)
considers the causal exclusion problem in the light of OSR, as does
Cordovil et al (2023). Beni (2019) develops a form of structural
realism for the cognitive sciences based on an analysis of
representation and the scientific understanding of the brain in terms
of connectionist networks and activation patterns. Ryan Nefdt (2021,
2023) develops a structural realist account of generative linguistics.
Pierpaolo Donati and Margaret Archer (2015) argue for a relational
ontology of individuals in sociology.



There are two ideas of general application to the special sciences
associated with OSR, namely, effective ontology and real patterns.
Together they provide for a degree of reconciliation of entity realism
and structural realism in recent work, and both involve the idea of
modal structure which is of wider signficance. Arguably in all of
science except perhaps the ultimate physics, ontology is required only
to be "effective" in the sense of applying in some domain
or regime which may be characterised in terms of the kinds of
processes involved, or in terms of scales of energy, length and time.
Most of physics is in fact like the special sciences in the sense of
not being fundamental, and not being applicable in all domains or
regimes. For example, most of condensed matter physics -- the
study of all the properties of solids and liquids--is not
applicable to energy scales at which there is no ordinary matter, as
in the heart of the sun or in the early universe. In physics,
quasi-particles like phonons are taken to exist when their half-life
is effectively infinite relative to the scale of the interactions that
are being studied. As mentioned above, the quantum field theories of
the Standard Model of particle physics, and many other if not all
theories in physics are effective (see Wells 2012). In general,
Ladyman and Ross (2007) argue that ontology is scale-relative, in the
sense that different energy levels and regimes, as well as different
length and time scales, feature different emergent structures of
causation and law, and that we should not assume that there is a
fundamental level to reality.



The question of how the ontologies of the special sciences relate to
more fundamental theories obviously relates to structural realism
because in many cases the strongly empirically successful theories of
the past are also the theories currently used in the relevant domain
(see Robertson and Wilson forthcoming). For example, engineers and
physicists still use Newtonian forces and classical optics despite the
fact the theories about them have more fundamental successors. The
ontology of such theories is effective as part of successful
explanations and predictions. The idea of effective ontology readily
relates to Dennett's idea of real patterns. A real pattern is,
very roughly, something that makes for a simplified description
relative to some background ontology. Real patterns are entities of
whatever ontological category that feature non-redundantly in
projectable regularities. For example, a wave on the beach is a real
pattern to a surfer, or a lifeguard, because it is taken as the basis
for prediction and explanation. Waves are ephemeral and fuzzy real
patterns, and in general real patterns are more or less definite and
durable. David Wallace (2003) argues for the real-patterns account of
effective emergent entities including worlds in the Everett
interpretation as well as quasi-particles. Seifert (forthcoming)
applies the idea of real patterns to chemical bonds which must also be
considered as part of effective ontology. The precise definition of
real patterns is a matter of debate. Ross sought to improve on
Dennett's original definition, Ladyman and Ross further refined
it, and Sune and Martinez (2021) criticise them
and develop their own account. All agree that real patterns must be
projectable in the sense of supporting prediction and explanation and
hence modal. It is natural to characterise this in
information-theoretic term in terms of compressibility, though it may
also be thought about in terms of reduction in the effective number of
degrees of freedom needed to model the dynamics of the system
(Millhouse 2021 argues that compressibility is not apt for capturing
real patterns that are coarse-grained with respect to the underlying
ontology).



Ladyman and Ross (2007) defend Rainforest Realism, which is realism
about the ontologies of the special sciences, by conjoining it with
ontic structural realism in the philosophy of physics. They adopt
scientific realism about effective ontology, and use their account of
real patterns to provide a criterion of existence. According to the
real-patterns account old ontologies are retained in much of
scientific practice because they continue to identify projectible
regularities in their domains of applicability. Relatedly, David Glick
(2021) argues that the basis of the structural realist's reply
to the problem of theory change may be applied synchronically to allow
for a pluralist structural realism. The problems of vagueness of
composition and identity over time, and hence of generation and
corruption all apply to both special science objects and everyday
ones. Composition is often dynamical, especially in science, but the
timescale of the interactions of the parts is very short compared to
the timescale characteristic of the whole. Generation and corruption
are not events at the level of the parts, but real patterns can indeed
be created and destroyed by changes in the behaviour of other real
patterns, and they can also persist over long time scales relative to
the scale of the interactions of their parts. Hence, the real-patterns
account of scale-relative ontology might provide a unified solution
for both problems (Ladyman 2017). Such an account could be interpreted
as being of the pragmatics of an ultimately epistemological kind of
emergence as perhaps for Wallace. However, if there is not, or might
not be, a fundamental level of reality, nor ultimate individuals of
which everything else is made, then all real patterns are on a par. In
this or some other way, the structural realist, like all scientific
realists must give an account of the relationship between the
ontology, causation and law described by theories and models that
apply at different scales and so also in different sciences.


## 5. Objections to Structural Realism



As explained above, there are many different forms of structural
realism and correspondingly, many different objections have been
levelled against it. Obviously, ESR and OSR attract very different
kinds of criticism, and different forms of each also face distinctive
challenges. Varieties of structural realism and objections to it are
also reviewed in Frigg and Votsis (2011). Worrall (2020) defends his
form of structural realism against objections. Some common objections
not already considered above are as follows:



(1)
Structural realism collapses into standard realism.


Psillos (1995) argues that any form of structural realism must
presuppose a distinction between the form and content of a theory,
and/or a distinction between our ability to know the structure and our
ability to know the nature of the world. Both these distinctions are
illusory according to Psillos because the scientific revolution
banished mysterious forms and substances that might not be fully
describable in structural terms. For Psillos, properties in mature
science are defined by the laws in which they feature, and "the
nature and the structure of a physical entity form a continuum"
(1995: 31). Hence, for Psillos, structural realism is either false or
collapses into traditional realism, echoing the response of Richard
Braithwaite (1953: 463) to Eddington's structuralism. Similarly,
David Papineau argues that "restriction of belief to structural
claims is in fact no restriction at all" (Papineau 1996a: 12),
hence structural realism gains no advantage over traditional realism
with the problem of theory change because it fails to make any
distinction between parts of theories that should and should not enjoy
our ontological commitment. Kyle Stanford (2003b: 570) also argues
that we cannot distinguish the structural claims of theories from
their claims about content or natures. As discussed above, the real
patterns account and the idea of effective ontology can be used to
reconcile structural realism with entity realism to some extent at
least. Clearly, structural realism must be a form of scientific
realism, and how distinct the positions are may be a moot point, but
if scientific realism is not taken to involve a commitment to natural
necessity then it is weaker than OSR characterised in terms of
commitment to modal structure. Positions such as Chakravartty's
semi-realism (2007) and Massimi's Perspectival Realism (2022)
seem to agree with OSR that science describes modal structure.
However, in the former case this is understood in terms of
dispositions or powers which is too restrictive for most ontic
structural realists for whom modal structure must include nomological
structure, symmetry, equilibrium explanation and more (see French
2013). In the case of Perspectival Realism, modal structure is somehow
tied to epistemic perspectives, and while real patterns are defined in
terms of perspectives in Ladyman and Ross (2007), their notion of
perspective is different to that of Massimi.



(2)
Not all structure is retained on theory change.


Many people's first response to structural realism is to point
out that mathematical structure is often lost in theory change too
(see, for example, Chakravartty 2004: 164; Stanford 2003b:
570-572). If structural realism is understood as a form of
selective realism seeking to identify what will be retained in advance
then this makes it hopeless. However, the structural realist is not
claiming that all structure is retained on theory-change, just that
represent the relations among, or structure of, the phenomena in some
domain, and in scientific revolutions the empirical content of the old
theory is recovered as a limiting case of the new theory (so
structural realism is not a form of selective realism, see Ladyman
2021). Post claimed there are no "Kuhn-losses", in the
sense of successor theories losing all or part of the well confirmed
empirical structures of their predecessors (1971: 229). Well-confirmed
relations among phenomena must be retained by future theories. This
goes beyond mere belief in the empirical adequacy of our theories if
we suppose that the relations in question are genuine modal relations
rather than extensional generalizations about actual phenomena.
However, Newman (2010) argues that structuralism cannot deal with the
pessimistic meta-induction. McArthur (2011) argues that structural
realism eliminates both theory change in science and scientific
discovery.



(3)
Structural realism is too metaphysically revisionary.


Considerations from physics and the history of science do not
logically compel us to abandon the idea of a world of distinct
ontologically subsistent individuals with intrinsic properties. The
identity and individuality of quantum particles could be grounded in
each having a primitive thisness, and the same could be true of
spacetime points. Physics does seem to tell us that certain aspects of
such a world would be unknowable. The epistemic structural realist
thinks that all we can know is structure, but it is the structure of
an unknowable realm of individuals. An epistemic structural realist
may insist in a Kantian spirit that there being such objects is a
necessary condition for our empirical knowledge of the world. It may
be argued that it is impossible to conceive of relational structures
without making models of them in terms of domains of individuals.
Certainly, the structuralist faces a challenge in articulating her
views to contemporary philosophers schooled in modern logic and set
theory, which retains the classical framework of individual objects,
and where a structure is just a particular set, namely a set of
objects, and a set of relations, where the latter are thought of
extensionally as just sets of ordered pairs (or more generally
*n*-tuples in the case of *n*-place relations), hence,
some structuralists favouring of category theory as noted above.



Psillos (2001) argues that OSR is not "worked out" as a
metaphysics, and that a strong burden of proof is on those who would
abandon traditional metaphysics (see also Chakravartty 2004 and
Morganti 2011). McKenzie (2017) also complains in a survey of OSR that
the view has not been adequately articulated particularly in respect
of the notions of individual, object and structure. The wealth of work
referred to above makes these charges harder to sustain now, and in
any case it is not clear that OSR's rivals are "worked
out" in any sense that OSR is not. There in no general agreement
among philosophers that any of the metaphysical theories of, say,
universals is adequate, and arguably metaphysical categories inherited
from the ancient Greeks, the scholastics and the early moderns are not
appropriate for contemporary science. Naturalists argue that we should
reject metaphysical doctrines if they are not supported by science.
Michael Esfeld (2004: 614-616) argues against any gap between
epistemology and metaphysics. Similarly Ladyman and Ross (2007) argue
for a kind of verificationism in metaphysics.



A key motivation for OSR is summed up by Ernan McMullin:



> 
> 
> [I]maginability must not be made the test for ontology. The realist
> claim is that the scientist is discovering the structures of the
> world; it is not required in addition that these structures be
> imaginable in the categories of the macroworld. (1984: 14)
> 
> 
> 



However, of course many metaphysicians do not accept these claims.



(4)
Structuralists cannot account for causation.


Busch (2003), Psillos (2006a) and Chakravartty (2003) all argue that
individual objects are central to productive rather than Humean
conceptions of causation, and hence to any genuine explanation of
change. Objects are supposed to provide the "active
principle" of change and causation. French (2006) replies to
this charge invoking the idea of of modal structure discussed above.
Structural realists think in terms of modal structure rather than
causal structure to the extant that physics and other sciences
describe relationships among phenomena of necessity, possibility,
potentiality, and probability the world in ways that are not readily
parsed in causal, dispositional or nomological terms. However, Ladyman
and Ross (2007) argue that causation is very often the pragmatically
indispensable proxy for modal structure in the sciences. For
discussion of these issues see the "final section" of
articles on modality and causality in structural realism in Landry and
Rickles (2012).



(5)
Without positing knowledge of individual objects we cannot explain
why certain properties and relations tend to cohere.


This objection is due to Chakravartty (2003) who points out that
certain properties tend to be found together, for example, negative
charge and a certain rest mass, and then asks "coincidence or
object?". French (2006) replies arguing that for a structuralist
objects just are literally coincidences and nothing more. Once again
the challenge for the critic of structuralism is to show that more
than the minimal logical notion of an object is required, but there
are many contexts in which this seems to be so. In response to this
problem, the theory of real patterns could be developed so that so
that triangulation among different modes of detection is required for
ontological commitment to objects as opposed to minimal real patterns,
but this is a subject for further work. O'Conaill (2014) argues
that OSR cannot account for ordinary concrete objects. Saunders (2016)
accounts for the emergence of macroscopic objects from the quantum in
terms of decoherence.



(6)
Structural Realism collapses the distinction between the
mathematical and the physical.


Many structuralists are motivated by the thought that if mathematics
describes its domain only up to isomorphism, if, in other words, it
only describes the structure of the domain, once the scientific
description of the world becomes largely mathematical, then scientific
knowledge too becomes structural knowledge. However, it may then be
argued that if only the structure of mathematical theories is relevant
to ontology in mathematics, and only structural aspects of the
mathematical formalism of physical theories are relevant to ontology
in physics, then there is nothing to distinguish physical and
mathematical structure. Van Fraassen argues that the heart of the
problem with OSR is this:



> 
> 
> It must imply: *what has looked like the structure* of
> something with unknown qualitative features *is actually all there
> is to nature*. But with this, the contrast between structure and
> what is not structure has disappeared. Thus, from the point of view of
> one who adopts this position, any difference between it and
> "ordinary" scientific realism also disappears. It seems
> then that, *once adopted*, it is not to be called structuralism
> at all! For if there is no non-structure, there is no structure
> either. But for those who do not adopt the view, it remains startling:
> from an external or prior point of view, it seems to tell us that
> nature needs to be entirely re-conceived. (2006: 292-293)
> 
> 
> 



The essence of van Fraassen's objection here is that the
difference between mathematical (uninstantiated/abstract) structure,
and physical (instantiated/concrete) structure cannot itself be
explained in purely structural terms. There is an analogy here with
the theory of universals and the problem of exemplification. A similar
complaint is made by Cao (2003a,b) and discussed in his debate with
ontic structural realists. Esfeld (2013) uses this objection in the
context of the interpretation of quantum mechanics to pose a dilemma
for ontic structural realism. Saunders (2003d) points out that there
is no reason to think that ontic structural realists are committed to
the idea that the structure of the world is mathematical, just that it
is described by it (see also French 2014). Tegmark (2008) explicitly
embraces a Pythagorean form of OSR, but Ladyman and Ross (2007) argue
that no account can be given of what makes the world-structure
physical and not mathematical. If OSR is characterised in terms of
modal structure then the mathematical structure of a scientific theory
is understood as representing the modal structure of its domain, not
as being identical with it.



There are two main versions of mathematical structuralism: a realist
view according to which mathematical structures exist independently of
their concrete instantiations; and an eliminativist position according
to which statements about mathematical structures are disguised
generalisations about their instantiations that exemplify them (see
Shapiro 1997: 149-150.) For an excellent survey see Reck and
Price (2000). The most well known advocates of realist structuralism
in the philosophy of mathematics are Parsons (1990), Resnik (1997) and
Shapiro (1997). Important critiques include Hellman (2005) and
MacBride (2005). The relationship between ontic structural realism and
*ante rem* structuralism has been explored by Psillos (2006a),
Busch (2003), French (2006), Pooley (2006), and Ladyman (2007) among
others. Many questions about objects versus individuals and the
ontological priority of objects, properties and relations arise in
discussions of structural realism and mathematical structuralism. Beni
(2020) argues that the Benacerraf (1965) problem is a problem for
OSR.



(7)
Structural realism lacks a clear notion of structure.


Arenhart and Bueno (2015) argue that the notion of structure is
unclear, and that when made precise the position becomes indefensible
motivating structural empiricism. Kyle Stanford (2010) argues that the
consilience argument of Ladyman and Ross (2007) is based on the
conflation of different kinds of structure. Lyons (2016) argues that
the notion of structure deployed in structural realism becomes
explanatorily vacuous when confronted with the history of celestial
mechanics.


## 6. Other Structuralisms



As discussed above, the information-theoretic real patterns approach
to ontology has been taken up by many ontic structural realists.
Dunlap (2022) explores the connections between information-theoretic
interpretations of quantum mechanics and OSR. A different form of
informational structural realism in the context of the foundations of
computer science is defended by Floridi (2008), and analysed in Bynum
(2014) and Wheeler (2022). See also Beni (2016) and Long (2020) for
the idea of digital ontology. Bueno (2010) argues that informational
structuralism can be developed as a form of empiricist structuralism.
Structuralism first became popular in analytic metaphysics in the form
of causal essentialism. This is the doctrine that the causal relations
that properties bear to other properties exhaust their natures (see
for example, Shoemaker 1980 and Hawthorne 2001). Steven Mumford (2004)
defends a structuralist theory of dispositional properties, and
Alexander Bird's (2007) theory of dispositions is in some ways
structuralist. Anjan Chakravartty's (2007) deploys dispositional
essentialism in the defence of scientific realism. Michael Esfeld
(2009) discusses structuralism about powers. Verity Harte (2002)
discusses an interesting Platonic form of structuralism. Alistair
Isaac (2014) argues for structural realism for secondary qualities.
Ted Sider (2020) develops a form of structuralism in his approach to
metaphysics and philosophical logic.