Introduction and Overview
1.1 Introduction
The philosophy of scientific explanation originated with the work of the the logical
positivists, formalized by Carl Hempel and Paul Oppenheim in the 1960s (see their
essays in (Colodny, 1962), for example). In excising metaphysics from philosophy
and replacing it with logic and scientific observation, they found that many aspects
of science needed specification and formalization. Their efforts to define quotidian
concepts of science like theory choice, inductive support, and explanation succeeded
in simultaneously laying a groundwork for future questions on these topics (many of
which had not been previously considered by philosophers) and revealing fundamental
inconsistencies in their own program. Virtually all work on scientific explanation of
the last fifty years has been targeted at responding to and resolving the shortcomings
of the two models of explanation expounded by the logical positivists: the deductonomological
(DN) model, and the inducto-statistical (IS) model, collectively known
as covering law models.

Much has been written about both these models, (See (Salmon, 1989b) and
(Kitcher, 1989) for particularly good expositions), so I will not dwell on them here
any more than required for a brief outline of each. The rough idea of the DN model
is that an explanation consists of a deduction (hence deducto) taking as premises (a)
one or more laws of nature (hence nomological) and (b) the specifics of a situation. A statement S (the explanandum) is said to be explained if it can be deduced by formal
logic from (a) and (b). Another, more intuitive way of thinking about this model is
that S is explained if one can show that S should be expected, given known laws and
the circumstances surrounding the content of S. The IS model, on the other hand,
begins with a statistical law from which one induces the explanandum.

These pictures of explanation face a number of insurmountable problems (for
instance- no one has been able to point to a single law of the sort that Hempel
requires for the DN model). Two major responses have arisen in their stead. The first,
a distant relation of the DN and IS models that avoids many of their problems and
which I will call the “unificationist account”, was first posited by Michael Friedman
in his (1974) and has been expanded on famously by Philip Kitcher (there are several
papers, but (Kitcher, 1989) is the most encompassing). The idea is that to explain
S, one should try to fit it into a framework of other statements, all of which one
believes to be true and which are dependent on and consistent with each other. More
precisely, one tries to find a pattern of argument that can be used to relate many
disparate phenomena back to a relatively small number of first principles. Although
different from Hempel’s account, again the intuition is that to explain something is
to show that it is expected, in this case by showing how it relates (presumably in a
more complex way than either the DN or IS account allows, although each could be
construed as a special case of the unificationist account) to other true statements.

The second response, which I will call the “causal account”, has two major instantiations,
respectively supported by Wesley Salmon (see (Salmon, 1985),(Salmon,
1997), and (Salmon, 1998)) and Nancy Cartwright (see especially (Cartwright, 1983)).
There are some important differences between Cartwright and Salmon. In general,
however, I will tend to focus on Cartwright more than Salmon because her position
is stronger, more radical, and, in the end, more interesting. For now, suffice it to
say that the common ground between the two accounts is that explanations should be thought of as causal stories, focusing on the relevant causal properties of the system
under consideration. So on the causal account, S is explained by a series of
statements the contents of which are causally dependent on each other (this series
would look like “we have situation X, in which S0 causes S1 to occur, which causes
S2 to occur, ..., which causes Sn to occur, which causes S to occur”). These accounts
bring with them the various problems associated with theories of causation, originally
pointed out by Hume (although Salmon has made some progress here). But at the
same time, they have a great deal of intuitive attractiveness: causal stories feel like
ordinary explanations from outside of science.

Recently, there has been a growing consensus among philosophers that both the
unficationist account and the causal account(s) are correct, in appropriate situations
in science (see especially (Salmon, 1989a) and (Godfrey-Smith, 2003)). This is probably
the right step forward. One of the strongest arguments against the DN and IS
models was essentially phenomenalistic- no examples could be produced from actual
science that had the forms Hempel described. Both the unificationist and the causal
accounts, on the other hand, have innumerable examples of explanations in their
support. In fact, one of the largest problems for each account is the great success
of its opponent in describing some (although neither can lay claim to all) explanations.
Short of labeling a large section of science “bad”, there is little option but for
the polemicists to concede to a plurality of accounts: sometimes, a proper explanation
is a specific causal story, at other times, a proper explanation involves fitting
the explanandum into a larger structure. Some philosophers (see (Salmon, 1989a),
(Hartmann, 2001)) have distinguished between the kinds of understanding achieved
in each case, arguing that the unificationist account produces global understanding,
whereas the causal account produces local understanding. Other philosophers (see
(Godfrey-Smith, 2003)) have avoided the complicating step of fragmenting explanation
by proposing a kind of contextualism for scientific explanation, in which different areas of science have different explanatory systems.

Pluralism seems correct, but leaves open the, essentially pragmatic, question of
distinguishing between explanatory contexts. To begin to answer this question, I turn
to a third major account of explanation, originally proposed by van Fraassen in his
(1977) and expanded in his (1980), which I will call the “pragmatic account”. The
pragmatic account has generally been considered unorthodox because it sidesteps
the debate between the causal and unificationist accounts entirely. At the same
time, and most interestingly, properly construed, neither the unificationist account
nor the causal account is inconsistent with the pragmatic account.1 Moreover, the
pragmatic account is intended to resolve exactly the same issue of determining what
kind of explanation is appropriate in a given context that faces the pluralist account.
The inspiration behind the pragmatic account is to consider what an explanation is
supposed to do: answer a why question. A proper understanding of explanation,
then, lies in an understanding of the logic of why questions and their answers2. Van
Fraassen suggests the following structure for a why question. A question can be
thought of as an ordered triplet consisting of the topic T, the contrast class X, and a
relevance relation R which the answer is expected to bear to T. R and X are usually
implicit in the context in which the question is asked, but to be clear, the question
“Why T?” is elliptical for “Why T as opposed to X, where the answer should bear R
to T”.

Van Fraassen does not specify constraints on R, a point on which he has been heav-ily criticized (see (Kitcher, 1989), (Kitcher and Salmon, 1987)). It seems, however,
in light of the move towards plurality, that by leaving R unspecified, van Fraassen
has proven something of a visionary, paving the way for the kind of contextualism
that Godfrey-Smith suggests3. Indeed, R could be a causal story, a fitting into a
unified framework, or something else entirely. Because the structure of the pragmatic
account already incorporates a pluralistic description of understanding in a natural
way that makes the relationship between the different elements of the pluralism clear,
I think it is valuable to adopt that structure as a way of speaking about explanation,
bracketing for a moment the acceptability of the account from which the structure
originates.4,5

There are two closely related questions that I would like to address in this paper.
The first is with respect to the compromise between the unificationist and causal
accounts. If we accept a pluralistic account, then we must accept that there are times
when a causal explanation is the best form to give, and similarly, there are times
when a unificationist explanation is best, because otherwise one kind or the other
would always be best, in which case we would be committed to a single account. But
if sometimes the causal form is better and sometimes the unificationist form is better,
the question immediately arises: when? There seems to be the danger of a free-for-all,
in which the decision to employ one form of explanation or the other is random. So
it seems important to understand the situations in which each form of explanation
is not only appropriate, but best. And distinguishing between explanatory contexts seems to be a pragmatic issue.

Attempting to understand the contextual relationships between the causal and
unificationist account leads to the second question: can the pragmatic account be
modified to resolve the pragmatic issues raised by a pluralist view of explanation, and
if so, how? Van Fraassen’s decision to leave the class of possible relevance relations
unspecified presents two major issues. The first is that, without any constraints on R,
the pragmatic account is open to trivialization (Kitcher and Salmon, 1987), since one
could present a relevance relation Rtrivial such that any true statement Strue (or, even
worse, a false statement) bears Rtrivial to the topic in question. The natural response
to this concern is that Rtrivial, although conceptually acceptable, would never arise
in a real context, or at least, it would never arise in a scientific context. Which leads
to the second issue with van Fraassen’s account (and subsumes the first): there are
many contexts in which why questions can be asked. Only some of these contexts are
scientific (see the introduction to (Salmon, 1989b) for examples), in which case one
would expect the relevance relations to have a certain set of possible forms. So now
it is important to ask what relevant relations are scientific and which explanatory
contexts call for which elements of this, now limited, set of relevance relations. Note
here that there is a temptation to be prescriptive about which relevance relations are
scientific. I believe it is a mistake to succumb to this temptation. Instead, I want
to be careful to ask what relevance relations do arise in mainstream science, and in
what contexts, as opposed to asking which should arise, since this second path comes
dangerously close to undermining the pluralistic view.

Now I can state the question that this paper is intended to begin to answer: When
do why questions asked in scientific contexts have unificationist relevance relations,
when do they have causal relevance relations, and how should the relationship between
the two sets of contexts be understood? Before I continue, there are two notes.
First, I am going to immediately limit the question by replacing “scientific contexts” with “the contexts of particle physics”. Secondly, I have specified two kinds of explanation.
There may be others; I would be contradicting myself if I said there were not.
However, it is well established that at least sometimes causal relevance relations are
important and sometimes unificationist ones are. Even if this is not an exhaustive
list, it is a useful first step to understand the relationship between these two already
acceptable explanatory accounts. The discovery of additional relevance relations in
science would not reduce the value of this work, it would only suggest new avenues
towards completing it. I will come back to both of these limitations in the concluding
remarks of the paper, in an effort to understand how my results generalize.

In order to address this question, I will consider a special class of theories that
have gained prominence in high energy and condensed matter physics over the course
of the last 30 years. The motivation for choosing these theories, called Effective
Field Theories (EFTs), is that they provide an excellent case study for two things: a)
they allow one to relate distinct energy scales (or length scales)6 in a well-defined way,
which, I will argue, is crucial to understanding the contexts in which the unificationist
and causal accounts are each most successful, and b) they offer an extra-philosophical
way of distinguishing between which causal features of a system are the “relevant”
ones, a problem that has plagued the causal account from its beginning, and which I
will come back to often.

Based originally on work on coupling constant renormalization by Kenneth Wilson
as early as 1965, EFTs appeared in their first instantiations when, in 1979,
Steven Weinberg adapted Wilson’s renormalization techniques to relativistic systems
and combined them with Appelquist and Carazzone’s decoupling theorem. Wilson’s
renormalization technique originated with straightforward “cut-off” renormalization,
where one would resolve infinite results in Quantum Field Theory (QFT) by chang-ing the bounds of integrals from infinity to some finite value  and then redefining
parameters in the theory to eliminate references to  before letting it go to infinity
again. Unfortunately, there were cases when one could not consistently take the limit
of  ! 1 (called nonrenormalizable theories), so this method sometimes resulted
in theories that were dependent on the value of . Initially, these results seemed
unphysical, since predictions of nonrenormalizable theories were dependent on the
choice of an arbitrary constant.

Wilson’s contribution was to develop a way of understanding how those predictions
varied with the choice of a cut-off. Specifically, he developed a way, called
the renormalization group (RG), of describing how coupling constants would have
to change as one changed the cut-off so that the predictions made by nonrenormalizable
theories would remain the same for different choices of the cut-off. The idea
was that one could then measure a coupling constant under known circumstances,
fix its value for some cut-off, and then vary the cut-off to obtain other predictions.
Joined with the decoupling theorem, Weinberg showed that the RG produced some
very powerful results: since phenomena at different energy scales could be shown to
be dissociated from each other, varying the cut-off to below the energy required to
produce some particles in a theory dynamically (essentially limiting the ontology of
the theory) produced new, phenomenological theories that, although only applicable
at relatively low energies, were much easier to use than their more complicated high
energy counterparts.

The way in which EFTs have been conceived has changed fairly drastically since
Weinberg’s first paper. First, nonrenormalizable theories became physically acceptable,
as low energy approximations to (potentially unknown) high energy theories.
This drastically increased the size of the possible theory space, since renormalizability
had been a constraint since early work on quantum electrodynamics. Secondly,
and more interestingly, many physicists have come to think of successful high-energy theories (including the Standard Model, which is currently the closest thing to a “final
theory” in physics), even when renormalizable, as EFTs for even higher energy
theories. Some philosophers and many physicists have begun to wonder, in light of
the EFT program, whether the idea of a final theory is sensible, or at least, if research
into such theory is worthwhile, since it may never be clear if the most “fundamental”
theory known is actually final, or just an approximation valid only at appropriate
energy scales. In fact, the EFT techniques have been used to argue that fundamentality
is an arbitrary attribute. If one cannot be certain about whether the highest
energy theory known at any given time describes the smallest distance interactions
possible (as the EFT program may suggest, although this interpretation remains contentious),
and if high energy theories only offer partial information about low energy
phenomena (as emergence suggests), the primacy of higher energy theories required
to define fundamentality properly is undermined.

The relevant feature of EFTs with respect to scientific explanation, however, is
that they allow one to link theories at different energy scales to each other in a
very well-defined way, via RG calculations. It has been suggested (see (Hartmann,
2001)) that the different explanatory accounts I have singled out lend themselves to
different kinds of descriptions of nature. Hartmann argues that the causal account
(at least Cartwright’s version) tends to rely on models, which focus on the relevant
causal properties of a system, bundling extraneous material into conceptual shortcuts7.
Unificationist accounts, on the other hand, rely on complete theories, since the
robustness of an explanation is directly tied to the number of disparate phenomena
that can be shown to fit together. Hartmann only cites a tendency here, and although
there is evidence to support his pattern, it seems reductive. However, his approach
does highlight a crucial difference between the two relevance relations: causal expla- nations do focus only on the parts of a system directly relevant to the phenomena
being explained, since the kinds of “stories” prescribed by the causal account only
involve direct causal relationships, and unificationist explanations do gain robustness
if the structure on which they rely is as encompassing as it can be.
In the context of particle physics, the RG offers a way of relating these cases, by
allowing one to rigorously isolate the relevant particle interactions for any given energy
level. By appeal to the EFT program, the causal and unificationist accounts can
be seen as appropriate for different ends of a spectrum of related scenarios. And since
energy levels translate directly to experimentation- the cut-off of a theory has to be
larger than the energy of the particles used in experiments if the theory’s predictions
are to be accurate- explanatory context can be reduced to experimental context. Low
energy explanations, with irrelevant interactions (causal powers) removed lend themselves
to causal explanations, whereas high energy theories unify many interactions
into a single framework, lending themselves to unificationist explanations. In order
to explain a phenomenon, then, one needs to specify the energy scale at which she
is interested in the explanation. I will argue that all phenomena have characteristic
energy scales- essentially the range between when they emerge from underlying
structures as individual particles with distinct causal properties, and when the become
subsumed into still larger structures- at which they are important, and at which
causal explanations are best. For energy scales higher than a phenomenon’s characteristic
scale, unificationist accounts are better. By understanding the relationship
between these energy levels, a why question can be made to be specific enough to
define explanatory contexts rigorously and to determine which explanatory account
is appropriate.

1.2 Overview
My goal is to make this paper accessible to a mixed audience of physicists and philosophers,
which is not necessarily simple. To accommodate varied backgrounds and interests,
I will structure this paper in the following way. I will focus on arguments
that are immediately relevant to my thesis, giving enough background in the body of
the paper to give a relatively inexperienced reader a heuristic sense of the structures
of the theories I am discussing. In addition, for readers unfamiliar with the physics
(or readers familiar enough to question some of my generalizations) and interested
in more mathematical detail, I include several appendices containing some of the
calculations and derivations I gloss over in the body of the paper.
That said, the structure of the remainder of this paper will be as follows. In
chapter 2, I will give a full description of the physics behind the EFT approach,
starting from a basic knowledge of quantum mechanics. This chapter is admittedly
a detour from the philosophical arguments in the paper, but I have found that most
philosophers with whom I have discussed this work are unfamiliar with EFTs. I will
try to make it both brief and complete, to keep from going too far afield, but so that
a reader with no familiarity with QFT will have an informed perspective from which
to evaluate the arguments I make in the rest of the paper. Chapter 3 is a review of
the literature on the philosophy of EFTs. Chapter 2 is purely on the techniques used
by physicists, with as little interpretation as possible. But to understand the salient
philosophical features of the techniques, it is important to discuss how they have
been interpreted in the past. The idea is to complement and inform my discussion of
the pure physics with the philosophical interpretations, again with a mind towards
grounding the arguments of the subsequent chapters.

In chapter 4, I describe the unificationist and causal accounts of explanation. I
offer an example of how each can used in physics, and then I cite the main conceptual
concerns associated with each. In doing so, I argue that the domains in which the two accounts seem most successful complement each other. I also try to show that
the language of EFTs can be used to limit the domains of each account in a way
that avoids their main difficulties. In section 4.3, I build on the observation that
the domains of the causal and unificationist accounts seem to be complementary,
and discuss the pluralist account that this suggests in greater detail. Here I argue
that the domains of the accounts can be separated in high energy physics, again
by appeal to the language of EFTs. Finally, in chapter 5, I discuss the pragmatic
account, proposing several modifications intended to a) resolve the major problems
that have been associated with it, and b) adapt it to describe the pragmatic aspects
of a coherent pluralist account. All of what I argue in this paper is specific to particle
physics, in which the distinctions that I think are important for understanding the
pluralist account are particularly clear. In section 5.3, I explore how these ideas may
generalize to areas of science in which distinctions between explanatory contexts may
be less explicit.