

Isolation Is Not Characteristic of
Models
Till Grüne-Yanoff

Modelling cannot be characterized as isolating, nor models as isolations. This article
presents three arguments to that effect, against Uskali Mäki’s account of models. First,
while isolation proceeds through a process of manipulation and control, modelling
typically does not proceed through such a process. Rather, modellers postulate assump-
tions, without seeking to justify them by reference to a process of isolation. Second,
while isolation identifies an isolation base—a concrete environment it seeks to control
and manipulate—modelling typically does not identify such a base. Rather, modellers
construct their models without reference to concrete environments, and only later seek
to connect their models to concrete situations of the real world. Third, Mäki argues
that isolation employs idealization to control for disturbing factors, but does not affect
the factors or mechanisms that are supposed to be isolated. However, models typically
make idealizing assumptions about the factors and mechanisms that are the focus of inves-
tigation. Thus, even the product of modelling often cannot be characterized as isolation.

1. Introduction

With his isolation account, Uskali Mäki made an important contribution to the
philosophy of science, and in particular to the philosophy of economics. In a series
of publications, Mäki (1992, 1994, 2004a, 2004b) has characterized isolation as a
distinct method of theorizing, and has convincingly shown its usefulness for the expli-
cation of certain cases of economic theorizing.
In some recent publications, however, Mäki (2005, 2006, 2009a, 2009b) has sought

to extend his isolation account to function as an explication of what scientific models
are, and how they function. Although he focuses largely on examples from economics,
Mäki clearly intends his account to have wider applicability. In this article, I argue

CISP574854 Techset Composition Ltd, Salisbury, U.K. 5/9/2011

Till Grüne-Yanoff is at the Helsinki Collegium of Advanced Study. Correspondence to: Helsinki Collegium of
Advanced Study, P.O. Box 4, 00014 University of Helsinki, Finland. E-mail: till.grune@helsinki.fi

International Studies in the Philosophy of Science
Vol. 25, No. 2, June 2011, pp. 1–19

ISSN 0269-8595 (print)/ISSN 1469-9281 (online) © 2011 Open Society Foundation
DOI: 10.1080/02698595.2011.574854

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against this account of models as isolations. Like Mäki, I also focus on economic
models.
Beyond the specifics of Mäki’s account, my argument may be of interest to a

wider audience. A number of influential philosophers of science, among them
Nancy Cartwright, Michael Strevens, and Robert Batterman, have suggested that
models explain by representing only those factors that make a difference to the
occurrence and essential character of the explanandum (cf. Weisberg 2007a).
Mäki’s account of models as isolations spells out certain views that defenders of
such a minimalist model account seem to share. An in-depth discussion of
Mäki’s account may therefore also elucidate some of the issues that the minimalist
account faces.
I start by recapitulating the main features of Mäki’s isolation account in Section 2.

Section 3 summarizes Mäki’s attempts to characterize models as isolations. Against
this characterization, I address instances in which models and isolations diverge. In
Section 4, I argue that while isolations commence from a base, gradually eliminating
certain features from it, models do not start from such a base. In Section 5, I argue that
the process of eliminating or sealing-off, characteristic of isolation procedures, is not
the common modelling process. In Section 6, I point out that models often idealize
their very targets, and thus do not offer a ‘neutral’, isolating setting. Addressing
these three questions, I conclude that Mäki’s isolation framework cannot function
as a general account of models and modelling. Instead, I argue in Section 7 that
Mäki’s account of isolation should be seen as a sufficient (albeit not necessary)
criterion of model success. Section 8 concludes.

2. Isolation as a Form of Scientific Theorizing

In the early 1990s, Mäki described a form of scientific theorizing that had not received
proper attention from philosophers of science. He termed this form of theorizing iso-
lation, and characterized it as follows:

Theoretical or ideal isolation . . . is manifest when a system, relation, process, or
feature, based on an intellectual operation in constructing a concept, model or
theory, is closed from the involvement or impact of some other features of the situ-
ation. (Mäki 1992, 325)

Thus, isolation is a process that leads from a base to an isolated product. These three
aspects are central to the notion of isolation.
First, isolation is a process, an ‘intellectual operation’ that consists in ‘constructing’

and in ‘closing off from’. This process, Mäki suggests, is analogous to scientific exper-
imentation. An experimenter causally intervenes in a process occurring in the world,
and thus closes off the target entity from causal interferences of other entities. Yet while
the experimenter causally manipulates real entities, the theoretical isolator manip-
ulates representations (Mäki 1994, 151).

1
Mäki therefore conceives of theoretical iso-

lations as thought experiments, as opposed to laboratory experiments: ‘isolation takes
place in one’s ideas, not in the real world’ (Mäki 1992, 325).

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Yet Mäki also sees the limitations of this analogy: ‘The theoretical method of iso-
lation involves an imitation of a limited portion of the logical structure of experimen-
tal research capable of material isolation’ (Mäki 1996, 443). While they differ on
ontological grounds and epistemic powers, experiments and theoretical isolations
share the same logical structure. But what are the properties that characterize this
logical structure of isolation?
Isolation proceeds via two procedures. The act of omission excludes the impact of

some factors by neglecting them in the representation. The act of idealization distorts
the impact of some factors, by changing a parameter in the representation to a differ-
ent value, typically to zero or infinity. Idealization thus yields a deliberately false rep-
resentation (Mäki 1992, 324). To engage in idealization requires that one represents
the idealised element, and that one knows that this element could be more accurately
represented—even if the exact form of this more accurate representation is not spelled
out.
Mäki addresses the procedural aspect of isolation explicitly when discussing Ronald

Coase’s methodology. He interprets Coase’s rejection of the neoclassical tradition as
‘blackboard economics’ as rejecting too high a degree of vertical abstraction—i.e. as
too high a degree of isolating universal aspects of things from their particular features.
But Mäki observes that Coase himself employs vertical abstractions: after all, he wrote
about the nature of the firm, not the natures of particular firms. To make sense of
Coase criticism, Mäki acknowledges ‘that the term “abstraction” in the vertical
context designates two different concepts, namely the level of abstraction and the
process of abstraction’ (Mäki 1998, 15; emphasis in original). In a process of abstrac-
tion, a theorist moves from detailed knowledge of particular phenomena to vertically
abstract notions of these phenomena. Coase, Mäki notes, performed a large number of
case studies on industrial structure and behaviour, hence documenting the detailed
knowledge from which he then derives his vertical abstraction.
Second, isolation commences from a base, closing off ‘the involvement or impact of

some other features of the situation’ (Mäki 1992, 325; my emphasis). By ‘base’ I here
mean any description of an environment that the isolation seeks to manipulate and
control. This may be a description of the actual world. For example, Mäki interprets
Coase as first establishing case studies of real firms, and then isolating certain features
from these detailed description. Here, through isolation, a ‘situation is simplified by
removing items from the actual situation’ (Mäki 2004b, 1725).
Alternatively, a base may be another level of theory or quasi-theory. For example,

Mäki (1996) postulates the existence of three ‘hypothetical levels of thought’:
general folk views, folk economics, and scientific economics. The entities in all three
of these levels remain the same, ‘entities with which economists and others are familiar
on the basis of ordinary experience’ (Mäki 1996, 434). Yet when moving from one level
to the next, these entities are modified and rearranged. By moving from the general
folk view to folk economics, ‘emotions are excluded in favor of rational deliberation.
Making love is excluded in favor of making money’ (Mäki 1996, 435). By moving from
folk economics to scientific economics, properties of these entities are ‘selected’,
‘abstracted’, ‘idealized’, ‘projected’, or ‘aggregated’ (Mäki 1996, 435). Thus, an instance

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of the general folk view would be a base for folk-economic isolation, and an instance of
folk economics would be a base for a scientific-economic isolation.
Furthermore, even within the realm of scientific economic theories, bases of iso-

lation can be found. When discussing debates and changes in economic theorising,
Mäki (2004a) suggests that debate and change can often be reinterpreted in terms
of isolation and re-isolation. Thus a critic may suggest a new theory in which the
focus of isolation of a prior theory is shifted towards another feature, or in which
the isolation is narrower than in the prior theory. The prior theory then is the base
of isolation. The new theory is developed from it by a process of omission or
idealisation.
Whether a description of phenomena or a theory, what is relevant is that the base

has a higher degree of complexity, with the interaction of various entities, so that
there is something to be isolated from. Additionally, this base must be, in some
sense, represented. Isolation is a manipulation of representations (Mäki 1994, 151);
hence not only the result of the isolation is a representation, but also the base from
which isolation starts.
Third, isolation yields a product, ‘a concept, model or theory’ that is appropriately

isolated. In laboratory experiments, a target entity is shielded from the causal interfer-
ences of other entities, yielding a material isolation. Theoretical isolations, in contrast,
yield a representation in which some entities are ‘sealed off’ (Mäki 1992, 321) from the
influence of everything else.
Conceptually, two kinds of isolation products can be distinguished. An abstraction

is ‘a universal . . . isolated from particular exemplifications’ (Mäki 1992, 322). For
example, a theorist may abstract from the linear form of the functional equation
q ! a + bp, instead choosing q ! f(p) for a theoretical representation. Mäki therefore
calls abstraction vertical isolation. A horizontal isolation, in contrast, isolates while
keeping the level of abstraction constant. For example, a theorist may isolate the influ-
ence of p on q from other influences by representing it in the form q ! f(p) instead of
q ! f(p, p’, p", . . .). Notably, only horizontal isolation corresponds to isolation in
experiments, while vertical isolation is merely realizable as a manipulation of
representations.
Mäki carefully distinguished the isolation process, which may involve idealisation,

from the product of isolation. When isolating a factor F from intervening factors
G1, . . ., Gn, one may either omit or idealize the operations of the Gi, but not the oper-
ation of the factor F itself. This way, one makes false claims about the Gi; but the
purpose of the theoretical process—to isolate the operation of F—remains intact.
Idealisation thus is a procedure applied to entities one isolates from, but not to entities
that one intends to isolate (Mäki 1992, 328); and idealization is used as an auxiliary
technique for generating isolation, yet it is not part of isolation itself (Mäki 1992,
325). Thus the product of isolation—the isolated factor—is never idealized.
Mäki originally developed the isolation account in order to support a realist

interpretation of economic theories (Mäki 2009a, 70–72). The core of this argument
is isolating theories are representations of the world that partially resemble the world,
and hence are true. Assuming that (i) theories consist of separable elements, and

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(ii) the world is partitioned into the aspects some of which resemble the theory
elements, one can say that the partial resemblance consists in a resemblance of
certain aspects of the world—in particular causal factors active in the world (Mäki
1994, 149–152). Assuming further a correspondence notion of truth, this resemblance
between aspects of theory and world allows Mäki to say that ‘an isolating theory or
statement is true if it correctly represents the isolated essence of the object’ (Mäki
1992, 344).

2

This of course is a non-standard use of the correspondence notion of truth, as it
yields the theory to be true (by resembling an isolated essence), while at the same
time it is also false (in its statements about idealized entities). Consequently, Mäki dis-
tinguishes two truth concepts, where a theory making only true statements expresses
‘the whole truth’, while a theory making true statements about the intended isolated
objects is ‘nothing-but-true’.
The use of isolation as a defence of realism makes substantial ontological assump-

tions about the relation of isolating theory and parts of the real world. I will therefore
call it the essential account. In particular, it claims that the factors and causal mechan-
isms represented by a successful isolating theory are real, in the partition that the
theory proposes. Whether one can hope to find such ontological assumptions to
hold in the social realm seems largely an open question (cf. Reiss 2009).
Such concerns may have motivated Mäki in the early 1990s to develop the isolation

concept in a more formally characterized way, less reliant on an essentialist ontology.
This account characterizes isolation through the three properties of the theory con-
struction process discussed in this section, namely isolation base, procedure, and
product. It is used as a theory of how economists theorize: their ways of theorizing
is influenced by how they believe their theories relate to the world, but is independent
of how their theories relate to the world. Isolation then becomes a meta-theoretical
framework that helps organize and understand the development of a particular
theory (Mäki 2004a). In this usage, the framework spells out what properties make
a theory an isolation, and how it influences scientists’ theorizing choices. To dis-
tinguish this account from earlier essential isolation, I call it formal isolation.

3

Based on this formal account, Mäki argues that isolation is a method of theorizing
that has particular centrality in the sciences. It includes abstraction as a special form of
isolation; and because idealization is a means for isolation, isolation holds primary
status over idealization (Mäki 1992, 332–333). Yet throughout Mäki’s earlier work
(Mäki 1992, 1994, but also 2004a), isolation is presented as one method of theorizing
among many.
In recent publications, Mäki has disavowed the procedural aspects of the formal

account. Instead, he defends a minimalist account by claiming what matters is the
product—that is, that the model is an isolation—and not that the modelling is ident-
ifiable as an isolation process from an isolation base.

I take theoretical isolation to be a central characteristic of an important class of
models, akin to isolation in material experiments . . . What the two procedures
share is the goal or function of closing a system by neutralising a number of
factors that are not included in the isolated system. This outcome is essential for

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isolative modelling, while the precise way in which isolations are implemented is
inessential. (Mäki 2009b, 31; emphasis added)

4

One might be sceptical about such a minimalist notion, on the grounds that intuitive
notion of isolation includes a procedural aspect, and requires a connection to a base.
From such a point of view, to claim that a theory is an isolation, and to link it to
material experiments is flatly contradicted by the consecutive claim that such a
theory is not the result of any specific isolation process.
I will not press this intuition here. Instead, I take the minimal account as an alterna-

tive to the formal account in the following analysis. The arguments in Sections 4 and 5
against isolation as a characteristic feature of modelling then apply only to the formal
account, while the arguments presented in Section 6 apply to both.

3. Models as Isolations and Modelling as the Process of Isolation

In more recent publications, Mäki (2005, 2006, 2009a, 2009b) has proposed the
isolation account not only as a meta-theory of one mode of theorizing, but as a
general account of economic modelling. Crucially, Mäki has conceived of his
account as universal: every model is fruitfully explicated as an isolation. In particular,
isolation supposedly characterizes the representational function of models, their
relation to experiments and their truth.
Mäki’s account of models as isolations and surrogate systems (MISS account)

distinguishes between the representative and resemblance aspects of representation,
and embeds models in a pragmatic context that includes the modeller’s purposes,
audiences, and commentary. More specifically, a model is an object used by an
agent as

a representative of some target system R for purpose P, addressing audience E,
prompting genuine issues of resemblance to arise; and applies commentary C to
identify and align these components. (Mäki 2009b, 32)

Of these characterizing elements, the notion of representative is most relevant for the
present purpose. A model is a representative of some target in the sense that it stands
for that target as its surrogate. A model functions as a surrogate for a target in the sense
that instead of seeking to acquire information about target R by examining R directly,
one examines the properties of the model, thus hoping to indirectly acquire infor-
mation about R.
For a model to fulfil the function of a surrogate of R, the model must resemble the

target system R in suitable respects and sufficient degrees.
5
Yet Mäki has argued that a

model being a representation of R does not require resemblance. Rather ‘it only
requires issues of resemblance to potentially arise’ (Mäki 2009b, 32). This requires
that model shave the likely capacity to resemble, and that ‘irrelevant resemblances
do not count’.
Mäki has contrasted models as surrogates with models as substitute systems. A model

is a substitute system, if it does not raise issues of resemblance at all. This may be the
consequence of model users focusing their attention merely on examining the

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properties of the model without any interest in the resemblance aspect of represen-
tation. The model then

becomes a substitute system, a freely floating subject of inquiry, unconstrained by
any concern as to how it might be connected to real-world facts. It substitutes for
the real system rather than serves as its surrogate. (Mäki 2009b, 36)

Thus, the issue of resemblance is central to Mäki’s MISS account. It is here that the
notion of isolation comes in, as it explains how models resemble their target
systems.

Models represent the target systems as far simpler, as devoid of most of those prop-
erties and causal facts, highlighting or focussing on just a small fraction of them. I
have attempted to capture this feature of models by saying (following Marshall and
other economists) that they isolate a fragment of their target systems. (Mäki 2006,
10; emphasis added)

The issue that the representative function of models raises is that of partial resem-
blance, explicated as the isolation of certain features of the target by the model.
Isolation thus becomes one of the central tenets of the MISS account.
Mäki has explored the relevance of the isolation notion for the understanding of

models and modelling further by suggesting an analogy between models and
experiments. Models, he argued, are constructed to create ‘a simple and controlled
mini-world in contrast to the complex and uncontrolled maxi-world’. The way they
are constructed proceeds via manipulation: ‘a system of entities is manipulated in
order to accomplish effective isolations of a limited set of properties and causal
relations from the rest of the world’ (Mäki 2005, 306). The only difference between
experiments and models lies in what exactly is manipulated:

While material experimentation employs causally effected controls, theoretical
modelling uses assumptions to effect the required controls. Assumptions are used
to neutralise, in the model worlds, the involvement of other things by assuming
them to be constant, absent, of zero strength, negligibly small, in a normal state,
within certain intervals, and so on . . . The structure of experimentation, involving
controls and isolation, is the same, while what is different is the way these controls
and isolations are effected: by way of thinking and assuming, and by way of material
or causal manipulation. (Mäki 2005, 308–309)

Mäki thus drew on his earlier analogy of material experiments and theoretical iso-
lations to characterize models. Models are a special kind of theoretical isolation,
and modelling is a special kind of theoretical isolating.
Lastly, Mäki argued that models can be true if they are isolations. They can be true,

he said, by isolating a real causal force, and showing its characteristic way of function-
ing (Mäki 2006, 14). This reading is further supported by another article, where Mäki
stated:

Economists can be philosophical realists about their models even though these
describe imaginary situations . . . This is because it is possible that the mechanisms
in operation in those imaginary situations are the same as, or similar to, those in
operation in real situations. (Mäki 2009a, 79)

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The diagnosis that economists can be realists about some parts of their models
clearly presupposes that these models are isolations, and may be successful iso-
lations. So Mäki embraces the view that economic models (by and large) are
isolations.
To conclude, Mäki characterized models as isolations and modelling as isolating. By

appealing to this characteristic of models, he strives to answers the question what
models are, how they can be true, and how to understand their use. Against this, I
will argue that models and the practice of modelling in economics often do not go
well together with Mäki’s isolation account.

4. Lack of Base

The first aspect in which models and isolations differ is what they are constructed
from. Intuitively, and in accord with Mäki’s formal account, an isolation is an iso-
lation from something else. This is obvious in material isolations. Experimenters
commonly believe that the same causes are at work in their experiments as in
the relevant parts of the real world, because they take the ‘stuff’ of the real
world and examine it under controlled conditions in the laboratory. An experimen-
tal asset market, for example, includes real human actors, but has them trade only
a small number of stocks, with a given budget, for a limited time, in specified
channels of communication under certain information. But beyond this general
relation to the world through using its material, experimenters typically identify
the specific base or bases from which their experiments isolate. Take the following
example:

Our immediate objective in the present series of experiments was to determine
whether agents would actively trade an asset when all investors faced identical uncer-
tain dividend payout schedules. The previous cited asset experiments pay different
dividends to different investors on the grounds that investors have different oppor-
tunity costs. But if this is so, subject agents ought to have their own homegrown
differences in opportunity cost (as in field environments). Consequently it is an
open question whether artificially inducing different dividend values on subject
investors is a necessary condition for observing trade. (Smith, Suchanek, and
Williams 1988, 1122; emphasis added)

Vernon L. Smith, Gerry L. Suchanek, and Arlington W. Williams here identify two
bases from which their experiments isolated: previous experiments and field environ-
ments. Furthermore, they identify the specific feature exhibited in both bases, from
which their experiment isolates: different dividends to different investors. Because
almost all actual asset markets exhibit this feature, they do not need to specify any con-
crete instance of it; while they are much more specific about the alternative laboratory
experiments that exhibit this feature.
To have a base, then, an isolation at least needs to refer to those properties that it

seeks to isolate from. Genuine experiments do this by listing all the factors that are
explicitly controlled for—the assumption being that any non-listed factors are the
same as in the base. Only then is there a reason to assume that experiments treat

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the same ‘stuff’ as found in the target system, and only then might there be reason to
have more confidence in experiments than e.g. in ‘merely formal’ simulations (cf.
Morgan 2003, 231; Guala 2005, 215).
Yet theoretical models in economics often lack such a base. Economic modellers

commonly do not refer to the relevant property of such a base when constructing a
model; nor do they refer to such a link once the model has been constructed.
Thomas C. Schelling gives a good illustration of this when describing how he came
to develop his famous chequerboard model. As he recounts in a recent note, he was
interested in how people’s interactions led to unintended consequences, for example
spatial patterns resulting from ‘preferences about whom to associate with in clubs,
classes, or ballparks, or at dining tables’. After searching the sociological literature,
he concluded ‘I found nothing I could use, and decided I’d have to work something
out for myself’ (Schelling 2006, 249). This ‘working out’, alas, was entirely devoid of
references to the specific properties of those clubs, classes, or dining tables, in particu-
lar to properties that the model isolated from.
Instead, Schelling ‘experimented’ with pen and paper, with copper and zinc pennies,

and finally with tokens on a chequerboard. The experiments consisted of defining one-
or two-dimensional spaces, randomly distributing symbols, coins or tokens over it,
and then letting them ‘move’ according to some predefined rule. The moves yielded
robust patterns that interested Schelling: ‘I experimented with different sizes of
“neighbourhoods” . . . and got results that fascinated me . . . We kept getting the
same kind of results, and the dynamics were intriguing’ (Schelling 2006, 250). It
becomes clear from this quotation that Schelling did not isolate his model from any
base. First, it is obvious that he did not have any concrete urban space in mind
when he constructed the model. But that may be too strong a criterion, as Smith
et al. (1988) in the above example do not refer to concrete asset markets either. Yet
unlike them, Schelling does not refer to any properties of actual city types, either—
there is no reference to data or the result of data analysis, nor to background knowl-
edge of any form. Schelling may of course have used such background knowledge in
his modelling choices—but the degree to which he did remains mere speculation, as
he chose not to document it anywhere. The real world, with its concrete neighbour-
hoods or generalizable observations about urban environments, is thus not the base
for the chequerboard model, at least not in any detectable way.

6

Rather, Schelling developed first a paper-and-marks, and later a coin-and-chequer-
board system because (a) they offered an interesting interpretation (allowing one to
interpret elements as ‘blacks’, ‘whites’, and ‘neighbours’), and (b) they allowed interest-
ing manipulations (‘moving them around’, ‘deciding where one can go’). It was the
formal properties of the representation device that gave rise to the properties of the
surrogate system, and not any explicit link to a real-world base.
Schelling’s chequerboard model is considered by many to be an exemplary case of a

good theoretical economic model (Sugden 2000; Aydinonat 2007). Of course, it
cannot stand for all of the many different kinds of models employed in economics
or the sciences more generally. But because many economists consider it an important
model worth aspiring to, it is sufficiently significant an example to pose a problem for

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Mäki’s account. Furthermore, Mäki himself analyses this model and admits that it does
not have a base:

Schelling’s Commentary does not go far enough beyond such possibilities to allow
him to state that the mechanism isolated by his model is actually in operation and
responsible for a segregated pattern. The model isolates a possible mechanism.
(Mäki 2009b, 38)

Mäki suggests that Schelling’s model isolates a social mechanism, but admits that the
accompanying commentary leaves it open whether such a mechanism exists in any
real-world situation. In Mäki’s analysis, all that Schelling claims is that it is possible
that this mechanism is in operation in some real-world situation. This implies,
however, that in the model construction process no situation or type of situations
was identified in which this mechanism was in operation, and from which this mech-
anism was consecutively isolated.
Thus, taking Schelling’s description as a typical case rather than an aberration,

models are distinct from isolations: while experiments (and hence material isolations)
necessarily start from a (concrete) base, models do not necessarily do so.
If isolations commence from a base, as intuition and Mäki’s early account suggest,

then models differ from isolations in this way. Models are typically constructed
without reference to a base. Unlike experiments, and pace Mäki, they are not the
result of ‘stripping’ or ‘sealing off’ elements of a base. In model construction, and
sometimes in model use, there is a conspicuous absence of any base from which
they could have been isolated.

5. The Lack of Process

The second aspect in which models and isolations differ is the process by which they
are constructed. Intuitively, and in keeping with Mäki’s formal account, isolations
are constituted by isolating processes. This is obvious in laboratory experiments.
By some detectable causal intervention, an environment is controlled, an impulse
given, a reaction channelled in certain ways. Through such interventions, exper-
iments are clearly distinguished from quasi-experiments (also called natural exper-
iments) or observation studies. Scientific actions without such a process of
consecutive interventions would not be considered controlled experiments. Similarly,
it seems, with theoretical isolations: why speak of isolation if an isolation process is
lacking?
Indeed, Mäki suggests that modelling proceeds through the manipulation of entities

in a way structurally similar to isolation in experimentation:

Assumptions are used to neutralise, in the model worlds, the involvement of other
things by assuming them to be constant, absent, of zero strength, negligibly small, in
a normal state, within certain intervals, and so on. (Mäki 2005, 308)

In the words of Mäki’s earlier publications, thought experiments are performed
through idealisation and omission processes: ‘the vast number of items is excluded
. . . neglected . . . omitted . . . nullified’ (Mäki 1994, 149–151), ‘modified’ and ‘purified’

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(Mäki 2005, 306). One finds a particularly clear expression of this idea in Mäki’s analy-
sis of Coase’s methodology.

The Coasean research process involves changing levels of vertical abstraction, while
Coase might argue that this does not happen in blackboard economics which sticks
to a high level of vertical abstraction without an ongoing process of abstraction.
(Mäki 1998, 15)

A process of abstraction or vertical isolation thus involves changing levels of
abstraction.
This implies that states of the representation previous to the final model must

be existent in some form. To neutralize a property, there must be a suggestion of
the variable’s non-neutral state. To change it into a stable state, there must be some
trace of its dynamics. To neglect something, a hint of its possible existence is required.
Mäki here acknowledges both that the presence of such processes may have important
epistemic consequences for models, and that different modelling methodologies can
be distinguished by the presence or absence of such processes.
Yet in most practices of theoretical modelling in economics, such processes and

sequences of changes are notably absent. Take Schelling’s case. It gives no evidence
of the modeller neutralising, changing, or neglecting anything. No levels of abstraction
different from the proposed models are documented. Rather, Schelling sticks with one
level of abstraction of the chequerboard.
The contrast to the practices of those not involved in modelling may make this point

clearer. Those scientists go through the processes of data measurement, data clean-up,
data refinement, and the construction of ‘data models’ or ‘phenomenological laws’. In
their papers, they extensively document how they proceeded, and what the sequence of
changes is. Most theoretical modellers in economics, however, do no such thing. Their
papers commonly lack any evidence of how they arrived at their models. In the rare
cases where modellers speak about their modelling practice, they say something like
Schelling: they start with an ‘idea’, they played around with a formal system, they
used the system as a stand-in for the idea. What they do not report is that they
developed the system in a number of stages, changing an initially complex system
into something simpler and more isolated. Thus, modelling practice lacks detectable
processes of manipulation that seem so characteristic of isolation.
Some authors have argued that the lack of isolation or abstraction processes is

characteristic of scientific models generally. Weisberg (2007b; see also Godfrey-
Smith 2006) illustrates how models as indirect representations contrast with direct
theoretical representations. When developing his famous predator–prey model,
Vito Volterra did not proceed by identifying patterns and structures of a real-world
phenomenon, working out which of these properties are essential and which ones
can be abstracted away. Rather, he proposed a completely abstract mathematical
system as a possible object of study for the Mediterranean fish population, without
ever having studied the actual fish populations before (Weisberg 2007b, 14). Volterra’s
differential equations are thus an exemplary case of modelling. In contrast to this,
direct theoretical representations identify patterns in data, and develop these patterns

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to organize, simplify (and hence isolate) hypotheses. As typical examples of such direct
theoretical representations, Weisberg suggests Mendeleev’s periodic system and
Darwin’s theory of coral reefs. Thus Godfrey-Smith and Weisberg suggest the lack
of an abstraction or isolation process as the central characteristic of modelling, and
hence agree with my diagnosis that models and isolations diverge in this respect.
It is possible, though, that modellers proceed through such an isolation process, yet

do not report it. Then Mäki’s claim—that theoretical modellers isolate in a way similar
to experimenters—may still help one understand models and modelling better. Yet
there are further reasons to doubt this analogy.
In experiments, the process of controlling and isolating itself has an epistemic func-

tion. Experimental manipulation processes are highly restricted by the causal proper-
ties of the manipulated materials: liquids cannot be heated beyond their boiling
points, animals endure only limited toxic doses, and people react to opponents only
if they know of their existence. Experimenters’ attempts to heat a medium, reach a
drug dose level, or create an interactive environment are frequently frustrated,
because the causal properties of the materials resist such manipulations. Such failed
manipulations, occurring in the isolative process, are important sources of learning
for experimenters, and are frequently reported as such. Crucially, such failures not
only tell us about research strategy or experimental design, but also about properties
of the actual materials experimented with.
In contrast, modellers do not report such epistemic gains from the process of mod-

elling. This is not surprising. Models, in Mäki’s view, are representations. But represen-
tations are established, first, by constructing an artefact, second, by declaring this
artefact to be a representation of a target, and third, by establishing some connection
between the artefact and the target (Knuuttila and Voutilainen 2003). In this order of
construction, the target imposes no constraints on developing the artefact: the mod-
eller can imagine any object, property or relation at her whim. Thus the construction
process of theoretical models cannot reveal any actual constraints of the real world, but
only discovers the implications of the model’s assumptions. Hence modelling does not
offer the same opportunities of learning as experimenting.
To use the above example again, Schelling’s choice of a chequerboard was not con-

strained by his intention to model certain spatial dynamics. He could have later found
out that the dynamics produced by this model were not interesting or relevant for his
epistemic purposes. But there was nothing in the model construction process that
would have prevented him from choosing the chequerboard, or setting up the rules
in the way he did; and hence, there was nothing he could have learned about the
world in this process.
Thus, while experimenting involves negotiating actual constraints of the real world,

modelling does not involve such constraints. This is an important disanalogy between
experimenting and modelling, and puts into further doubt Mäki’s claim that modellers
isolate in ways similar to experimenters.
To conclude, models and experiments differ with respect to the processes of their

construction. Experiments are constructed through consecutive steps of causal
manipulation and control. In contrast, modelling does not commonly involve such

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a process. Indeed, some philosophers of science consider it a central characteristic of
models that they are not constructed by such a process from any base.

6. Inseparability of Isolation and Idealization Q1

The criticism advanced in Sections 4 and 5 rests on Mäki’s formal isolation account,
which stresses the procedural aspect of isolation. This interpretation is supported by
(i) Mäki’s claim of an analogy between isolation and experiments, and (ii) intuitions
derived from standard uses of the term isolation. Yet in recent publications, Mäki has
disavowed such a procedural understanding of isolation. Instead, he now defends a
minimal models-as-isolations position. According to this position, models are iso-
lations because they ‘close a system by neutralizing a number of factors that are not
included in the isolated system’ (Mäki 2009b, 31). What matters for the characteriz-
ation of models as isolations are the model results, not the modelling processes.
This leads to the question what a characterization of models as the product of iso-

lation implies, and what such a characterization would explicate. For the sake of argu-
ment, let’s assume that the concerns of Sections 4 and 5 are irrelevant. Does Mäki’s
models-as-isolations account then still give a characterization of what models are in
terms of the models’ properties themselves? I argue that it does—but that unfortu-
nately, this positive characterization is at odds with the reality of modelling.

7
I will

argue for this claim in the remainder of this section. In the next section, I will then
show that instead it should be seen as a normative characterization of models.
Idealization, in contrast to isolation, falsifies its objects: to idealize an object X

means to (consciously) make false claims about it; to isolate the same object
X means that one may make false claims about X’s environment, etc., but not about
X itself. Idealization, in Mäki’s account, is therefore a means of the isolation
process, but it is not part of the isolation result. If idealizations and isolations were
not clearly delineated, Mäki would have to admit that isolations also make false
claims about the world, putting his defence of realism in doubt. He therefore insists
that idealized representations are elements of the excluded field, and not the isolated
one (Mäki 1992, 328). Against this claim, I will argue that the core of a model—what is
reasonably assumed to be its isolating elements—is often and indeed usually contami-
nated with various idealizations.
The distinction between isolation and idealization quite intuitively applies to the

interpretation of experimental results. Experiments take entities of the real world
and examine them under controlled conditions. In successful experiments, the
assumption goes, such controls will not affect the workings of the causal powers
under investigation. In asset market experiments involving human agents, for
example, we commonly assume that limiting the number of stocks, or changing
their dividends, will leave unchanged the agents’ ability to maximize utility under
constraints. The experiment can thus examine the workings of this causal capacity
under changing conditions. To apply these experimental results to the real world,
the experimental conditions need not be identical to those of the real world. Rather,
the experimental conditions may diverge from those of the target situation—i.e.

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may be idealisations—because the successful experiment tells us about the operation
of this power in isolation.
A model, however, isolates not by manipulating material entities, but by manipulat-

ing representations. Every part of the model is such a representation—i.e. both iso-
lated as well as idealized features—which are pinned down through some form of
description, be it mathematical, graphical, or through prose. Thus there is no prima
facie reason to believe that a model correctly represents a certain mechanism. It all
depends on the assumptions of that model, and on how the world really is.
Of course, if the model corresponds well with our ontological convictions, we may

have good reasons to believe that this model indeed isolates a certain power or mech-
anism. For example, a physicist who models the motion of a falling body might dis-
regard the effect or air resistance on that body. Depending on what kind of body is
modelled, such a model may give a good approximation of the body’s falling, or
not. But independently of whether the model is true or false in this sense, the modeller
might maintain that the model correctly isolates gravitational forces, and that the
idealization of no air resistance has no effect on the operation of this isolated
factor. The modeller can rest her argument on the conviction that gravity and air
resistance indeed are two separate forces, and that theoretically neutralizing the
effect of the second has no effect on the first.
It is a lot harder to make such an argument in the social sciences, because there are

few ontological convictions to rest it on. As an example, take the completeness
assumption of expected utility theory. Wherever modern microeconomics refers to
the utility function, it implicitly assumes the completeness of the underlying prefer-
ence ordering. The main micro-concepts, from standard demand functions through
Nash equilibrium to social welfare functions, depend on completeness. Yet it is clear
that actual preference orderings are often incomplete Q1.
In Mäki’s reading, completeness is an idealizing assumption to isolate the causal

influence of preferences on choice. Preference incompleteness is a strongly disturbing
causal factor in decision-making, Q1as it adds features of information search, and judge-
ment processes. The completeness assumption adds an excessively powerful mental
capacity to the model in order to remove these extra real-world features from the
model. This isolation allows investigating microeconomic phenomena in the
absence of such disturbances (cf. Mäki 2009a, 78–79).
I have three reasons to doubt such a reading. First, completeness is constitutive of

utility models in a way that e.g. disregarding air resistance in a model of falling bodies
is not. Standard utility functions are not defined for incomplete preferences. Thus, the
completeness assumption not only removes disturbing influences on a factor of inter-
est, but partially constitutes the representational means by which this factor can be
studied in the first place. Without completeness, we would loose many of the
central micro-concepts, and we would not be able to express results as conditions
on the utility function.

8
The whole representational framework of microeconomic

theory would break down. This is not the case when modelling falling bodies. Neglect-
ing air resistance is not to overlook something Q1constitutive of our representation of

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falling bodies. Rather, it is more convenient, serves our scientific purposes better and
makes solving equations possible or easier.
Second, because completeness is constitutive of utility models, there is no way to de-

isolate the model. Demand functions, Nash equilibrium and social welfare functions
are all based on utility functions that are continuous, continuously differentiable,
and unique up to linear transformations. Most of the interesting results of theoretical
microeconomics are conditional on properties of these utility functions, like being an
increasing function, being quasi-concave, or being homogeneous of degree 1 (Mas-
Colell, Whinston, and Green 1995, 46–50). If completeness were relaxed, the utility
function is not defined any more, and we would have no way of knowing whether
an (incomplete) utility function would satisfy these properties or not. Again, this
differs notably from the physics example. It is imaginable that the effect of air resist-
ance cannot be exactly specified, and that without disregarding it, we would not be
able to solve the equations describing the motion of a body. But clearly, we have a
good idea how such a de-isolated equation would look like, even if we cannot fully
specify the disturbance’s strength and direction. For an incomplete utility function,
by contrast, we do not have such a similarly good idea at all.
Third, our ontological convictions are of little help in the case of incomplete utility

functions. True, we have folk intuitions about preferences; but our (hedonistic) folk
intuitions about utility are not reflected in the (ordinal) utility notion used in econ-
omic theory. This ordinal notion is a functional representation of complete prefer-
ences under uncertainty, and the properties of this measure (like being continuous
or quasi-concave) cannot be understood through intuitive folk notions. Yet this
makes it hard to understand what a complete utility function isolates from: we do
not have intuitions about a separate power or force that preference incompleteness
exudes. Thus, there is no way to separate the two functions, and hence no way to
know whether the causal influence of preference incompleteness could in principle
be isolated.

9
Instead, we are forced to admit that in our standard micro-models, com-

pleteness is inevitably linked with the derived results. It is an idealization of decision-
making itself, necessary to make the study of it possible Q1under the currently standard
representational framework.
The preceding example is by no means exceptional Q1. Philosophers of science have

pointed out that models involve idealizing assumptions not only for the purpose of
isolating certain objects, properties, or relations, but also for the purpose of handling
modelling relations. Such idealizations can take the role of derivation facilitators (Alex-
androva 2005). They facilitate derivation of model results (e.g. continuity of a distri-
bution, differentiability of a function). Yet such a continuity or differentiability
assumption idealizes elements not only of the excluded field but also of the isolated
field. Or they may take the role of tractability assumptions (Hindriks 2006 Q2). A tractabil-
ity assumption imposes simplifying conditions Q1without which a problem cannot be
solved. Yet again, it is often properties of elements of the isolated field that must be
idealized in order for the problem of interest to remain tractable. Finally, Cartwright
has argued that many model settings over-constrain the causal power of interest—they

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constrain it to a narrower set than those permitted by just the assumptions necessary
to ensure that there are independent causes at work (Cartwright 2007).
To conclude, idealizations are not restricted to the excluded field of model elements.

For a number of reasons, it is common to find the very core elements of models—
those that the models Q1are purportedly intended to isolate—to be idealized, too.
Thus, models not only nullify, neutralize, and purify, they are also augment, bias
and pollute. This makes it doubtful that even a narrow focus on the result of modelling
is adequately characterized by the isolation account.

7. Isolation as a Success Criterion

If modelling cannot be properly characterized as an isolation process, and models
cannot be properly characterized as isolations, Mäki’s framework may still be relevant
for models as a criterion of success. In other words, while models may often not be
isolations, what makes a model a good model is that it successfully isolates. This per-
spective needs to be specified further, but I believe that in it lies the central contri-
bution of Mäki’s framework to the discussion of models Q1.
A model may successfully isolate either in the substantial or the formal sense. In the

substantial sense, a model is successful if it ‘resembles the target while meeting the
pragmatic constraints’ (Mäki 2009b, 35), where the pragmatic aspects concern in
what ways and for what purposes the resemblance is necessary. I have no doubt that
if a model satisfied these properties, it would be a good model: it would make a sig-
nificant contribution to our knowledge about the world.
Yet this substantial success criterion only clarifies the metaphysics of success. It does

not give any indication of how Q1how a model must be (in contrast to what the model–
world relationship must be) in order to be a successful model. As a success criterion,
substantial isolation is thus more of philosophical than of methodological interest.
However, one finds a more ready criterion of success in a property of the model

alone, and not a property of the model–world relationship: namely, Mäki’s claim
that ‘the model must have a likely capacity to resemble’ (Mäki 2009b, 32–33; my
emphasis). Mäki does not explicate what he means by this capacity, and does not
discuss the issue further. I suggest that we find a partial explication of this capacity
in Mäki’s formal account of isolation: the absence of idealizations in the isolated
field is a crucial condition for the model’s capacity to resemble.
If elements of the isolated field are idealized, they are intentionally falsified in ways

that make them unlikely to resemble anything in the real world. Yet keeping idealiz-
ations out of the isolated field is hard, whether due to the need to keep the model tract-
able, or its results derivable, or due to Q1the simple fact that modellers have to construct
something concrete, with some kind of structure, where they simply do not know what
an appropriate structure may be. Nevertheless, modellers (and model users) are able to
see whether elements of the isolated field are idealized: they simply need to check
whether deliberately false assumptions are made about the object, property or relation
to be isolated. Hence absence of idealizations in the isolated field is a necessary (if not
sufficient) condition for isolating real factors. Many models fail to satisfy this

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condition, and the success or failure of the model to meet this Q1condition is detectable.
So it makes for an important success criterion if the goal is to construct models that
have a capacity to resemble.
While the separation of isolation and idealization constitutes an important part of a

sufficient criterion for the success of models, it is not a necessary condition. Mary
S. Morgan and Margaret Morrison (1999), Robert Sugden (2000), Mauricio Suárez
(2004), Tarja Knuuttila (2008), and Till Grüne-Yanoff (2009) have all offered accounts
of how models can be epistemically successful, without having to isolate parts of the
world. Given these alternative accounts, one can learn from models that are not iso-
lations. Formal isolation is not a necessary criterion for the success of models.
Rather, it is a success criterion only for those models that are intended to isolate.

8. Conclusion

In this article, I have argued against Mäki’s attempt to characterize models as iso-
lations. First, I showed that modelling differs from the process of isolation. This
served to distinguish models from isolations according to many standard interpret-
ations of isolation, and shows that Mäki must develop his non-procedural notion
further if he wants to defend his models-as-isolations account. Second, I argued
that models often make idealizing assumptions about the very factors they are
intended to represent or investigate. Because the isolation notion centrally relies on
the distinction between isolation and idealization, this served to show that models
often create an augmenting, biasing and polluting environment, and do not offer a
‘neutral’, isolating setting. Finally, I proposed that Mäki’s account of isolation
should be seen as a sufficient (albeit not necessary) criterion of model success. This
leaves an important role for isolation. But it insists on isolation being just one
method among many – in modelling just as in other forms of theorizing. It therefore
cannot be a universal characterization of models. Modelling is not isolating, and
models are not isolations.

Acknowledgements

Earlier versions of this article were presented at the INEM (International Network for
Environmental Management Q4) conference in Madrid, September 2008, and at the
workshop Models, Mechanisms, and Interdisciplinarity in Helsinki, November
2008. I thank the participants for valuable criticisms and in particular Tarja Knuuttila,
Uskali Mäki, and two anonymous referees of this journal for very helpful comments.
The usual disclaimers apply.

Notes

[1] Because there are material models, theoretical isolation may consist in the manipulation of a
real entity that functions as a representation. In most social sciences, however, material models
are insignificant.

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[2] Note that when speaking about an ‘isolated essence’, Mäki refers to the way the world is parti-
tioned, not about the way representations are isolated. Thus, he acknowledges the substantial
ontological claim he is making.

[3] A related distinction can be found in McMullin (1985, 255). He distinguishes between ‘con-
struct idealizations’, where the simplification is worked on the conceptual representation of the
object, and ‘causal idealization’, where the simplification is worked on the problem situation
itself.

[4] For an in-depth comparison of Mäki’s three concepts of isolation, see Grüne-Yanoff
(forthcoming).

[5] In personal communication, Mäki clarified that there is no conceptual difference between his
term ‘resemblance’ and the more commonly used term ‘similarity’.

[6] This lack of reality base is often diagnosed in economic models. About Lucas’s ‘model
economy’, for example, Knuutilla says: ‘the assumptions made are patently artificial in the
sense that it is difficult to imagine how they could have been drawn from the economic
reality’ (Knuutilla 2009, 63).

[7] There is, however, an alternative and much weaker reading. The above quotation may be read
as a merely intentional characterization: modellers intend to close a system. Such a character-
ization would point not to a property of the model, but merely to a property of the modeller.
This would jeopardize any intersubjective criterion for the explication or assessment of models
and modelling practice. I think it is worthwhile to resist such a reading, and ask for a stronger
characterization of models and modelling. I also think that Mäki would want to resist such a
reading.

[8] Recently, axiomatic representations of incomplete preferences as sets of utility functions have
been developed (Dubra, Maccheroni, and Ok 2004). However, it is unclear what sort of
demand functions, equilibra concepts or welfare functions could be derived from such rep-
resentations; it is only clear that these notions would be significantly different from the exist-
ing ones, and that the properties defined for unique functions do not apply to sets of
functions.

[9] In particular, robustness analysis would not be of help here. Analysing the robustness of model
results under varying assumptions requires varying these assumptions. But as I argued, com-
pleteness is constitutive of many other microassumptions, and hence cannot easily be varied
without affecting the whole set of model assumptions.

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