Renormalization and the Formulation of Scientific
Realism

James D. Fraser∗

Forthcoming in Philosophy of Science

Abstract

Providing a precise statement of their position has long been a central
challenge facing the scientific realist. This paper draws some morals about
how realism ought to be formulated from the renormalization group frame-
work in high energy physics.

1 Introduction

Many philosophers of science subscribe to scientific realism. Unfortunately, there
is much less agreement about what this doctrine amounts to. My suggestion in this
paper is that the renormalization group framework in high energy physics provides
a useful case study when it comes to the question of how realism ought to be
formulated. The claim that the renormalization group has important implications
for a realist view of quantum field theory (QFT) has been mooted in the past
by David Wallace (2006, 2011), and more recently by Porter Williams (2017). I
develop this line of thought in a broader context here and argue that there are
lessons to be learned for the broader realism debate. On the one hand, the role the
renormalization group plays in identifying aspects of QFT models we should take
representationally seriously supports a local approach to articulating the realist
thesis; rather than attempting to explicate how theories latch onto the world in
general terms it shows that resources found in particular scientific contexts can
be a crucial part of this story. On the other hand, it points to a strategy for
responding to Kyle Stanford’s “trust argument”. Stanford challenges the realist
to tell us what of our current theories will survive future scientific progress. While
this can seem to be an impossible task in the abstract I will suggest that it may
become more tractable at the local, theory-by-theory, level.

The plan for the paper is as follows: section 2 provides an opinionated overview of
some key issues surrounding the formulation of realism, section 3 introduces the

∗Email: jamesf09@hotmail.co.uk.

1



renormalization group and explains how it helps substantiate a realist analysis of
QFT models, and section 4 draws out some broader morals for the formulation
problem.

2 The Formulation Problem

What is scientific realism? A naive answer is that it is the claim that our best
confirmed scientific theories are true. It quickly becomes obvious that constru-
ing realism in this way renders it a wildly implausible doctrine however. One
much-discussed reason is the pattern of theory change found in the historical
record. Examples of theories which made accurate predictions in their day but
later turned out to be false are legion in the history of science, and while philoso-
phers with realist sympathies have pushed against the idea that this undermines
the connection between empirical success and truth entirely, they typically ad-
mit that it gives us grounds to doubt that current theories get everything exactly
right. There are also ample indications within contemporary science itself that
our theories are not entirely veridical. To take a particularly stark example, our
most fundamental physical theories, QFT and general relativity, furnish mutually
inconsistent accounts of what the world is like, and powerful theoretical arguments
suggest that a completely new framework is needed to fully describe gravitational
phenomena.

What should the would-be realist replace this naive formulation with? What seems
to be needed is a more modest epistemic attitude towards predictively successful
theories: something stronger than merely taking them to be empirically adequate,
as the constructive empiricist advises, but weaker than believing everything they
say about the world. A common move when outlining the realist position in its
broad brush strokes is to replace the word ‘true’ in the naive formulation with ‘ap-
proximately true’. Ultimately though, this only postpones the problem, as what
it means for a theory to be approximately true stands in dire need of clarification.
While there is a great deal of disagreement over how a more precise formulation of
realism should be developed in detail, some consensus has emerged about the gen-
eral form it should take. It is widely agreed, amongst both contemporary realists
and anti-realist critics, that any formulation worthy of serious consideration must
be ‘selective’, recommending we commit ourselves to some parts of a successful
theory’s content, while rejecting, or remaining agnostic about, others. The chal-
lenge to spell out the sense in which successful theories are approximately true
can then be answered, at least in part, by pointing to a subset of their claims
about the unobservable which hit their mark.1 This selective approach owes its
popularity to the dominant realist approach to the challenge of historical theory

1To be sure, many questions remain about approximate truth and its role in the formulation of
realism. Some selective realists ascribe the property of approximate truth to individual theory
constituents, for instance, so there is a residual puzzle about how to make sense of this notion
at this level of particular theoretical claims.

2



change. In response to pessimistic inductionists, realist commentators have urged
that the empirical success of superseded theories did not depend on their claims
which conflict with present science. Rather, the theoretical constituents of these
theories that were really responsible for their accurate predictions are retained in
their successors, and therefore have a shot at describing the world as it is. The
lesson that has been drawn from the debate over theory change then is that the
realist’s epistemic optimism ought to be directed at the parts of a theory which
underwrite, and explain, its predictive successes, rather than its representational
content as a whole.

This idea is sufficiently vague that it can be fleshed out and interpreted in very
different ways, leading to a proliferation of selective formulations of realism in
the recent literature. There are many points of divergence between these variants
but I will focus here on two key questions which the renormalization group sheds
interesting light on: whether the selectivist should spell out their commitments
in global or local terms,2 and whether it is possible to implement the selective
strategy prospectively, in advance of future scientific developments.

Once a broadly selective approach to the formulation problem has been adopted,
the obvious question is which parts of our theories should we be committed to.
There are different particular answers to this question, but there are also different
types of answer. A more global answer (in my terminology) aims to provide
a general characterization of the belief–worthy content of any successful theory.
Saatsi (2015) calls this sort of approach ‘recipe realism’: the ideal being a formula
which takes in theories and spits out beliefs about the world in a completely
regular way. One brand of realism which has sometimes been understood in these
terms is epistemic structural realism.3 Following Worrall (1989), contemporary
incarnations of this doctrine have been inspired by episodes of theory change in
physics in which posited entities, such as the luminiferous ether and gravitational
field, are dropped, but continuities exist at the level of mathematical structure.
The conclusion drawn is that it is the structural claims of our theories which the
realist ought to put their faith in. One attempt at making this precise has been to

2The global/local axis I am invoking here should not be confused with the question of whether
arguments for realism ought to be construed globally or locally. The no-miracles argument
has traditionally been understood as a meta-scientific inference starting from the success of
science as a whole, but this approach has recently come under attack, with some advocating
a shift towards more local arguments found within science itself as the core motivation for
realism (Magnus and Callender, 2004; Saatsi 2009). What I am interested in here, however,
is how the realist thesis should be stated—in principle at least, this is a separate issue from
how it is defended. One might favour global arguments for realism while cashing out the
specific commitments engendered by your epistemology of science on a theory-by-theory basis,
for instance.

3I should note here that while structural realism is often read as a global selective formulation
of realism it is not clear that its advocates understand it this way. French and Ladyman (2010,
32), for instance, state that “[t]he job of predicting what will be preserved and what abandoned
by future science belongs to science itself not to philosophy”, apparently disavowing the idea
that the notion of structure delineates which parts of successful theories we should trust in
Stanford’s (2006) sense. Still, this caricature of structural realism will be a useful foil for the
localised approach to the formulation problem I will introduce shortly.

3



identify the structural content of a theory with its Ramsey sentence, apparently
furnishing a procedure for picking out the claims the structuralist ought to commit
themselves to which can be applied across the board. Many contemporary brands
of realism at least aspire to this sort of blanket statement about which aspects of
our theories get things right.

No formulation of this kind has achieved anything close to widespread acceptance
however. One problem is that the diversity of science makes generalization a risky
business. Recipes for identifying veridical content that are compelling in one area
of science may be much less so in others—Stanford (2003) attacks structural re-
alism, for instance, by pointing to examples from biology in which mathematical
structure does not seem to be preserved through theory change. Another worry is
that the drive towards generality leads global formulations to abstract away from
peculiarities of particular theories which are relevant to appraising their represen-
tational success. While both Newtonian gravity theory and thermodynamics can
arguably be described as sharing structure with more fundamental physical theo-
ries, the specific structural claims that are retained at the fundamental level are
quite different in each case, as is the sort of explanation this affords of the theory’s
empirical successes. Even in contexts where the structuralist intuition has some
purchase then, the distinction between structural and non-structural claims seems
to be too coarse-grained to pinpoint the parts of a theory which drive its success.
Ultimately, global formulations tend to find themselves in the uncomfortable po-
sition of being simultaneously too general and not general enough to convincingly
carry out the selective project.

These sorts of concerns have led some philosophers to move towards a more local
response to the formulation problem (Barrett, 2008; Saatsi 2015, 2016). Instead
of trying to specify how successful theories relate to the world in one fell swoop,
this approach implements the selective strategy on theory-by-theory basis. The
question of what sort of doxastic attitude we ought to take towards the theoreti-
cal claims of Newtonian gravity, for instance, is answered via a close study of the
theory itself, rather than invoking some general criterion for realist commitment.
Barrett (2008) points, in particular, to foundational research on geometrized for-
mulations of Newtonian gravity (surveyed in Malament, 2012), which allows us
to precisely describe how some of its extra-empirical content is embedded within
general relativity, as doing the real work in spelling out the sense in which the
theory is approximately true. This is a thoroughly theory-specific story and the
thought is that carrying out the selective strategy in practice will typically turn
on local scientific arguments and resources. The local realist still adopts a general
epistemic stance towards science: they take the empirical success of our theories
to be explained, at least for the most part, by the fact that they are getting some-
thing right about the world. But the task of spelling out the specific claims about
the world engendered by this stance is delegated to philosophers of the specific
sciences.

While this move avoids some of the difficulties plaguing global formulations how-
ever, it seems to have a serious cost when it comes to the issue of prospective

4



applicability. The local selectivist might be able to point to intertheoretic re-
lations with general relativity to clarify the representational status of Newtonian
gravity, but what about general relativity itself? A global selective realist will have
an answer here; they will wheel out their formula for identifying belief-worthy con-
tent. But what can the localist, who eschews this kind of response, say? The cases
which Barrett and Saatsi point to as exemplars for the way that the approximate
truth of theories can be cashed out locally invariably turn on their embedding
within more fundamental theories. Consequently, realism about our current best
theories might seem to end up amounting to little more than a promissory note:
the local selective realist claims that general relativity latches onto reality in a way
which explains its success, but exactly how we cannot yet say.4 Just as Newton
had no idea which parts of his theory of gravity would be preserved in contem-
porary gravitational physics, we seem to be in a similar epistemic situation with
respect to current fundamental physics.

This sort of worry is the basis of Stanford’s (2006) “trust argument”. According to
Stanford any form of realism worthy of the name must tell us which features of our
theories we can trust now, not merely in retrospect. I suspect that the perceived
need to respond to this challenge is a key reason why defenders of realism have
sought to defend a global formulation of their doctrine that can be projected into
the future. An alternative reaction to this line of attack however is to simply refuse
the bait and deny that the realist needs to state their epistemic commitments
prospectively. After all, the claim about general relativity sketched above clearly
goes beyond the constructive empiricist’s stance towards the theory—they would,
of course, remain completely agnostic about general relativity’s claims about the
unobservable and deny the need for an explanation of its empirical success in terms
of its extra-empirical representational success. Saatsi (2016) simply bites the bullet
here and calls his local version of realism ‘minimal realism’ in recognition of the
fact that some intuitions about what a realist attitude towards current scientific
theories amounts to are not necessarily borne out on this formulation.

It is at this juncture in the dialectic that the renormalization group becomes inter-
esting. The application of renormalization group methods in high energy physics
provides another example of how local theoretical resources can play an important
role in substantiating a selective realist reading of a theory. Crucially though, this
story is prospective in character, operating in advance of developments beyond
the standard model of particle physics. What this suggests is that abandoning a
global formulation of realism does not necessarily mean ceding the possibility of
prospective commitments entirely, and a localised realism need not be as minimal
as Saatsi suggests.

4This obviously threatens our ability to use general relativity to identify belief–worthy parts of
Newtonian gravity, so this problem is apt to flow upwards, affecting non-fundamental theories as
well. Barrett and Saatsi are, of course, keenly aware of this point and offer different responses.
Barrett (2008) emphasizes that the transition from Newtonian gravity to general relativity can
still be understood as eliminating descriptive error, while Saatsi (2016) styles it as an exemplar
that can gives us a handle on how a theory’s representational success could possibly explain its
empirical success.

5



3 The Renormalization Group and Selective Realism

The renormalization group is a widely-applicable framework for investigating the
behaviour of systems at different length and energy scales. The basic strategy is
to study the action of a coarse-graining transformation—an operation which takes
us from an initial model to a new one that lacks some of the degrees of freedom
associated with variations at small length scales/high energies but shares its large
scale/low energy properties. How this procedure is implemented depends a great
deal on the sort of systems one is interested in, and consequently renormalization
group methods take on diverse forms in different areas of physics (and beyond).
I will focus here on the application of renormalization group methods to QFT,
and specifically on the momentum space approach pioneered by Kenneth Wilson
(Wilson and Kogut, 1974).

This story starts with the path integral expression for the partition function, Z.
This crucial quantity encapsulates basically everything there is to know about a
QFT model. In particular, all of a theory’s correlation functions (vacuum expec-
tation values of field operators at disparate space-time points) can all be derived
from it. For a single field φ, the partition function is associated with a functional
integral:

Z =

∫
DφeiS[φ], (1)

where S[φ] is the action of the model, and the measure Dφ indicates that a sum
is being taken over all possible configurations of the field. As is well known, there
are grave difficulties with precisely defining this integral for a field that varies
over a continuous space-time. One way around this problem is to introduce an
ultraviolet cutoff Λ—an upper limit on the possible momenta of field states. A
straightforward way of doing this is to place the theory on a lattice so there is a
minimal distance over which the field can vary. Once this is done it is possible
to give a precise meaning to the path integral. The Wilsonian renormalization
group is then based on setting up a coarse-graining transformation on cutoff QFT
models of this kind.

Wilson’s insight was that, instead of evaluating the whole path integral at once,
we can start with the contribution due to high momentum field configurations,
whose fourier transforms have support above some value µ. This part of the path
integral can be computed separately and absorbed into a shift in the action. In
symbols: ∫

|p|≤µ
Dφ
∫
µ≤|p|≤Λ

DφeiS =
∫
|p|≤µ
Dφei(S+δS). (2)

This defines a transformation that takes us from an initial cutoff QFT model to a
new one, which has a lower cutoff, and a modified dynamics, but behaves like the
original (specifically, sharing its long range correlation functions). This is often
informally described as ‘integrating out’ the field modes associated with variations
on small length scales.

6



Figure 1: The renormalization group flow of scalar field theories to a surface
spanned by renormalizable parameters.

We can view this transformation as inducing a ‘flow’ on a space of models, with
dimensions corresponding to all possible interactions between fields. Studying
this flow has proved to be a powerful source of information about the scaling
properties of QFT models. The most important discovery for our purposes is the
phenomenon of universality in the low energy regime. It turns out that QFT
models with wildly different dynamics display very similar low energy behaviour.
Consider, for the sake of concreteness, the class of scalar field theories with actions
of the form:

S =

∫
d4x
[1
2

(∂µφ)
2 −

1

2
m2φ2 −

∞∑
n=2

λ2n
2n!

φ2n
]
. (3)

where m is a mass parameter and {λ4,λ6, ...} are couplings for possible inter-
action terms. Under repeated applications of the coarse-graining transformation
the renormalization group flow of this class of theories can be shown to be at-
tracted towards a two dimensional surface spanned by m and λ4 (as shown in
figure 1).5 This behaviour is believed to hold generally: while infinitely many
interaction terms between a set of fields are possible the renormalization group
transformation induces a flow towards a finite dimensional surface spanned by so-
called renormalizable parameters—those with non-negative mass dimension. This
means, in essence, that large classes of QFT models look the same at suitably
large length scales.

What does all this have to do with scientific realism? The thought is that these

5See Polchinski (1984). Duncan (2012) provides a broader discussion of these results and their
significance.

7



renormalization group results give us the means to develop a selective realist read-
ing of current QFTs.

On the one hand, the renormalization group helps us identify features of QFT
models which we should not take representationally seriously.6 Quantum elec-
trodynamics (QED) and the other component theories of the standard model of
particle physics have famously produced some of the most accurate predictions
in the history of science. Much of this success takes the form of estimates of
cross sections for scattering events produced in particle colliders, with the current
threshold on experimentally attainable energies being at the order of 1013eV. The
renormalization group results just discussed reveal that many features of current
QFT models do not really make a difference to these empirical successes however,
in the sense that they can be varied without affecting scattering cross sections at
these energy scales. For one thing, it establishes that these quantities are highly
insensitive to the imposition of an ultraviolet cutoff, as well as the details of how
this is done. We can also vary the dynamics of a model at the cutoff scale with-
out affecting its predictions; adding non-renormalizable interactions to the QED
action, for instance, does not undermine its empirical adequacy. What this tells
us is that many of the claims QFT models make about the world at the funda-
mental level do not contribute to, and are not supported by, the empirical success
of the standard model. Of course, we also have external reasons to doubt that
QFTs describe reality at all scales: the QFT framework itself is expected to break
down as the Planck scale is approached. But the renormalization group gives us
a precise way of pinpointing the parts of current theories that we should disavow,
or at least remain agnostic about.

On the other hand, it seems to provide us with the means to articulate positive
commitments supported by the success of the standard model. The classes of
QFT models which share the same low energy predictions arguably make common
claims about relatively large scale, non-fundamental, aspects of the world. Giving
a precise characterization of this shared content is one of the central challenges
facing the sort of realist view of QFT I am proposing here, but a preliminary
strategy is to point to correlation functions over distances much longer than the
cutoff scale as appropriate targets for realist commitment. These quantities are
preserved by the renormalization group coarse-graining transformation and encode
the long distance structure of a QFT model. They are also directly connected to
its successful predictions—you cannot vary the long distance correlation functions
of a theory without drastically affecting its low energy scattering cross sections.7

6Williams (2017) gives a similar characterization of the role that the renormalization group
can play in identifying representational artifacts, and discusses some more detailed examples of
distortions induced by the imposition of a cutoff, such as Lorentz violations and mirror fermions
which appear when fermionic fields are put on a lattice.

7A potential objection here is that the realist reading of QFT models I have sketched fails to
adequately distinguish itself from empiricism. This is a prima facie worry because correlation
functions are often characterized in operationalist terms via their connection to scattering
cross sections in the physics literature. A key challenge facing this approach to QFT then
is to give a robustly ontological interpretation of the correlation functions, or adopt some
other characterisation of the coarse-grained theoretical claims underlying the success of current

8



Furthermore, in demonstrating that these large scale properties of a QFT model
are insensitive to what is going on at very high energies, the renormalization
group is also telling us that these features are largely independent of the details of
unknown physics at currently inaccessible energy scales. We thus have reason to
be confident that these features of current QFTs will be retained through future
theory change, in one way or another, whatever physics beyond the standard model
has in store for us.8

The picture that emerges from these considerations then is that QFTs enjoy a
kind of coarse-grained representational success, capturing some (relatively) long
distance, low energy, features of the world while distorting its fundamental struc-
ture. A potentially useful comparison here is to continuum models in fluid mechan-
ics, which misrepresent the atomic structure of real fluids but accurately describe
many of their bulk properties. This fits well with the effective field theory ap-
proach to QFT that has come to dominate high energy physics in the wake of
Wilson’s work on the renormalization group; at least part of what is meant when
physicists characterise the standard model as an effective field theory is that it cor-
rectly describes the physics of currently probed scales, but should not be trusted
at higher energies. For the aspiring scientific realist this differentiated attitude
towards the content of QFT models offers a way of making precise the sense in
which these theories are approximately true along selectivist lines.

4 Some Morals

We have only scratched the surface of how renormalization group methods impact
on our understanding of QFT, and many aspects of the preceding discussion are
controversial. Wallace (2006, 2011) and Williams (2017) advance similar (and I
hope complementary) analyses of the epistemic significance of the renormaliza-
tion group but Doreen Fraser (2011) takes a much more deflationary line, which
conflicts with some of the claims endorsed above. There remains a great deal of
work to be done in developing and defending the sort of realist view of QFT just
outlined then.9 I want to conclude however by returning to the broader question
of how scientific realism ought to be formulated.

models.
8The idea that renormalization theory should be understood as isolating features of current
theories which are robust under future theory change is advanced in a prescient paper by
Alexander Rueger (1990). One concern about the way I have developed this claim here, pressed
by Ruetsche (2017), is that it seems to rest on the assumption that future theories can be
situated in the space of possible theories on which the renormalization group transformation
acts. We can be fairly confident that future QFTs can be treated in this way, but when it comes
to quantum gravity theories the question becomes much murkier. The worry then is that these
renormalization group arguments ultimately fall foul of Stanford’s ‘unconceived alternatives’
problem for realism.

9See James Fraser (2017) for a more detailed discussion of this approach to the epistemology of
QFT which describes avenues for future work.

9



What sort of general morals can be extracted from this case study? First and
foremost, it offers further support for a localised response to the formulation prob-
lem. The appeal to the renormalization group framework in the discussion of the
previous section exemplifies the local selective realist’s claim that local scientific
resources often play a crucial role in articulating the relationship a theory bears to
the world. Furthermore, we found no need for an overarching thesis about which
parts of our theories get things right. The resulting analysis of the representational
success of QFT models does, admittedly, chime with the intuitive picture under-
lying epistemic structural realism—the fundamental ontological claims of QFT
models were rejected while non-fundamental, broadly structural, features are sin-
gled out for realist optimism. But the putative distinction between structural
and non-structural features did no real work in identifying appropriate targets
for realist commitment and ultimately adds little to the picture furnished by the
renormalization group. This all suggests that we ought to abandon as misguided
any attempt to provide a fully general characterization of the approximate truth
of empirically successful theories.

What really makes this case significant for the broader formulation debate how-
ever, is that it does not turn on the explicit embedding of a superseded theory
within a more fundamental successor. This has important implications for the
issue of prospective applicability. The worry, remember, was that, without a gen-
eral recipe for identifying the belief–worthy content of a theory, the local realist
will only be able to make a highly tentative and provisional claim about the rep-
resentational success of our current most fundamental theories. Local realists like
Saatsi have basically accepted this conclusion, but reject Stanford’s assertion that
giving up on explicit prospective commitments means giving up on realism en-
tirely. The renormalization group case however, suggests that we do not need a
global formulation of realism to sustain prospective commitments: local theoreti-
cal resources can also play a role in supporting judgements about which parts of
present theories will be preserved through theory change. The information the
renormalization group provides about the dependencies between the high and low
energy properties of QFT models seems to put us in a better epistemic situation
with respect to the standard model than Newton was with respect to his theory
of gravity. This opens up the possibility of a localised response to Stanford’s trust
argument. In some scientific contexts it may be appropriate to eschew prospec-
tive judgements entirely and adopt the sort of minimal realist position advocated
by Saatsi, but where scientific arguments support it, a more full-blooded realist
reading of a theory, which includes commitments about which parts of its content
can be trusted to remain a part of future science, may be possible.

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