On the Nature and Roles of Formalism in Economics

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Tony Lawson and His Critics
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Edward Fullbrook (ed.) (2009) Ontology and Economics: Tony
Lawson and His Critics; Routledge, London and New York
Featuring: Tony Lawson
Bruce Caldwell, Bjørn-Ivar Davidsen, John B. Davis, Paul Downward, Bernard
Guerrien, Geoffrey M. Hodgson, Bruce R. McFarling, Andrew Mearman, David
Ruccio, Irene van Staveren, and Jack Vromen
Contents
Edward Fullbrook
Introduction: Lawson’s Reorientation
Tony Lawson
Introduction
Bruce Caldwell
Lawson Response
Some Comments on Lawson’s Reorienting Economics: Same
Facts, Different Conclusions
History, Causal Explanation and ‘Basic Economic Reasoning’
Bjørn-Ivar Davidsen
Lawson Response
Critical Realism in Economics – a different view
Underlabouring for Substantive Theorising
John B. Davis
Lawson Response
The Nature of Heterodox Economics
Heterodox Economics and Pluralism
Paul Downward, and
Andrew Mearman
Lawson Response
Reorienting Economics Through Triangulation of Methods
Triangulation and Social Research
Bernard Guerrien
Lawson Response
Irrelevance and Ideology
The Mainstream Orientation and Ideology

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Geoffrey M. Hodgson
Lawson Response
On the Problem of Formalism in Economics
On the Nature and Roles of Formalism in Economics
Bruce R. McFarling
Lawson Response
Finding a Critical Pragmatism in Reorienting Economics
Ontology or Epistemology?
Ruccio, David
Lawson Response
(Un)Real Criticism
Ontology and Postmodernism
Staveren, Irene van
Lawson Response
Feminism and Realism – A Contested Relationship
Feminism, Realism and Essentialism
Vromen, Jack
Lawson Response
Conjectural Revisionary Ontology
Provisionally Grounded Critical Ontology
Chapter 12
On the Nature and Roles of Formalism in Economics
Response to Hodgson
Geoffrey Hodgson and I have debated numerous issues over the years (not least the
nature of old institutionalism and how its contributions are best interpreted), mostly in
seminars or over a drink or two. Whether we agree or disagree, I find that Hodgson’s
views are always interesting and usually very substantial. The issue of formalism
seemingly opens up a new area of debate between us. In characteristic style
Hodgson’s various contentions in his current piece are wide-ranging, thought
provoking and backed up by numerous authoritative sources. Thus, it is necessary to
do quite a bit of work to show why I nevertheless think Hodgson fails to make too
much of a case against my position.
Hodgson’s main thesis is that my critique of mainstream mathematical modelling
is overly restrictive in the way I imagine models to be useful. Formalistic models can

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provide insight in numerous ways that I fail to contemplate, and Hodgson is
concerned to indicate some of these.
This topic of the alternative roles for formalistic models is actually something I
explore at length in Economics and Reality. Its consideration takes Hodgson to
discussions of methods of abstraction, theoretical isolation, heuristics, and so forth, all
issues on which I have previously found a need to say much, but which do perhaps get
too little coverage in economic methodology in general. As it happens, I believe that
much of what Hodgson has to say on these issues cannot be sustained. But his
commentary does provide an opportunity to give my take on these neglected issues a
further airing, and perhaps to develop them further.
There is a further related, if ultimately secondary, issue I should also address.
Overall, I think there is a danger that Hodgson’s contribution conveys the (false)
impression that I am opposed to formalism per se. This is such a misunderstanding
that I need first to get it out of the way before addressing the central topic here, the
manner in which formal models might usefully be employed.
Orientation to formalism
Whatever Hodgson’s intention, it seems to me likely, as I say, that the dominant
impression conveyed by his piece is that my stance is somehow an anti-mathematics
one. Hodgson does not attribute such an orientation to me directly; in brief asides,
indeed, he even acknowledges that this is not an accurate statement of my position.
However, he pursues several lines of argument that, I fear, will mostly encourage the
uninformed reader to suppose that I am after all opposed to the use of mathematical
formalism per se. Little could be further from the truth. Rather I am opposed to the
abuse of mathematical formalism, and such abuse is, I believe, typical of the situation
in much of modern economics.
What line of argument of Hodgson’s do I have in mind? At the start of his
commentary Hodgson reproduces a passage by Mark Blaug of which I have
previously made much use. In it Blaug suggests that “Modern economics is sick”,
noting that “Economists have converted the subject into a sort of social mathematics
in which analytical rigour is everything and practical relevance is nothing” Mark
Blaug (1997, p. 3))
Now the reason I quote this passage is simply that I both agree with it, and I find it
significant because Blaug once seemed sympathetic to the mainstream. However,
Hodgson asserts that Blaug and I make different evaluations, with my position being

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“more radical”. My own view, though, is that, to the contrary, Blaug’s position is
simply a summary of a critical assessment that I have spent much time defending.
Indeed, I would describe my own position on the use of mathematics as anything but
radical; it is simply informed by an appreciation of mathematics. I neither support its
universal application in economics as an a priori stance nor its universal rejection as
an a priori stance. Rather I recognise that all tools, including mathematical ones, are
limited in their scope of application (I believe that the appreciation of a tool is bound
up with an awareness of its limitations), and that the relevance of mathematics in any
specific application depends on the context-specific merits of the case.
I am perplexed, therefore, to find that Hodgson portrays me as an extremist on
such matters1:
“In regard to formalism, many economists take the extreme view that it is the
only means by which economics becomes rigorous and scientific, and thus the
dominance of formalism is a positive sign of success. Lawson takes a position near
the opposite extreme. He argues that formalism is justified in 'rare' circumstances
only, where local closure exists (or is approximated). I propose that both attitudes
to formalism are flawed […].
And Hodgson ends with the following plea2
“The pressing agenda issue for further discussion and enquiry in this area is to
explore the inadequately explored middle ground between the unacceptable
extremes of unreflecting worship (and at least expectational) denial of formal
models and methods”
1 In this way, Hodgson claims the middle ground for himself without having to do the
ontological groundwork. Thus having noted these supposed extremes Hodgson associates
himself with “middle ground solutions” on such matters, and connects this back to his original
reference to the passage from Mark Blaug:
“I suggest that the problem with formalism is not the general inappropriateness of formalism
itself, but it is the problem identified by Blaug in the quotation at the beginning of this article.
Blaug sees the kind of formalism in modern economics as 'an intellectual game played for its
own sake' rather than for its use in explaining and engaging with the real economic world.
Blaug complains that in modern economics 'analytical rigour is everything and practical
relevance is nothing'. Again the solution here is not necessarily to confine formalism to the
very rare conditions of actual or approximated closure, but to bring concerns for practical
relevance to the fore. Formal techniques should become the servants rather than the masters
of scientific enquiry”
2 In a recent presentation at the Cambridge Realist workshop this passage is revised to read
as follows:
“We need to investigate the inadequately explored middle ground between unacceptable
extreme stances that either treat mathematics as the sine qua non of theory, or practically
exclude it in all but 'rare' cases. I advocate this middle ground position, not because central
areas are intrinsically or universally superior to extremes, but because the extremes in this
case jointly downplay the necessary interpretative structure of any formal theory”

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Hodgson’s talk here of extremes is misleading if not incoherent. At one supposed
extreme is the view that formalism “is the only means by which economics becomes
rigorous and scientific”; at the other is the view that the use of “formalism is justified
in ‘rare’ circumstances only”. Clearly, such views need not even be incompatible let
alone opposite extremes. Of course, I have argued extensively against the former view
that formalism is essential to science or rigour. But one could (mistakenly) hold to
such a view (that formalism is after all essential to science), conclude that formalism
has but limited application to the social realm, and infer thereby that a scientific
economics has limited scope.
As I say, this is not my position (my own position to the contrary is that a science
of economics is entirely feasible whatever the scope for formalism3). But it is
logically feasible, and indeed is accepted by many hermeneuticists and others who do
accept the implicit conception of science in question, but reject its relevance to the
study of society (see Lawson, 1997, chapter 10).
In truth the (mainstream) view that formalism “is the only means by which
economics becomes rigorous and scientific” is just a mistake, not an extreme view or
form of practice. The real sense in which the mainstream is extreme lies in its
insistence that we all must always adopt mathematical deductivist methods of a
certain sort, irrespective of how explanatorily successful they are (in potential or
practice). If there is an opposite extreme to this it is the insistence that such
formalistic methods be always rejected irrespective of how explanatorily successful
they are. I doubt anyone accepts such a position.
Why then does Hodgson suggest that I am at an opposite extreme to the
mainstream? I have to admit to being unsure about this. Perhaps I have just not
expressed myself with sufficient clarity.
It is true that, in attempting to identify conditions under which certain methods of
mathematical deductivist reasoning are guaranteed, I have suggested that they seem
3 Thus in Reorienting Economics I write:
“For many modern economists, in fact, mathematical deductive reasoning is regarded as
essential to science. It follows, for this group, that to relax the existing emphasis on
mathematical methods is effectively to give up on the possibility of economics as science.
One reasonable response to this line of reasoning is to question why economics has to be a
science. Many critics indeed have rejected the possibility of economics as science. But in fact
this is not my orientation. To the contrary, my concern is more with the recovery of
economics as science. Ontology helps us better understand the nature of science, and, as
we shall see, to appreciate that mathematics is not essential to it. To suppose that scientific
practice reduces to, or even necessitates, mathematical formalism is once more erroneously
to universalise a priori a special case (in this case a particular form of scientific practice) as
we shall see in due course” (Lawson, 2003, pp.xx-xxi).

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rarely to have come about in the social realm. But this is a long way from an a priori
rejection of formalism, from an insistence that formalistic methods be rejected
irrespective of how explanatorily successful they are.
Actually, it may be useful if I elaborate a bit on this issue. For although it seems to
me that the orientation I adopt is reasonable, Hodgson actually interprets it as setting
limits to what he calls “my claim of anti-dogmatism”. Perhaps this explains his
misunderstanding. Let me briefly elaborate.
Dogmatism and identifying the conditions of closures
First, I must examine what is meant here by dogmatism, or dogma. I do use the
term dogma in Reorienting Economics, though only occasionally. In fact, I use it
twice, in each case to describe the doctrine, advanced by mainstream economists
without grounds, that certain sorts of methods only should always be followed.
Thus the preface to Reorienting Economics I write:
“Rather, the primary object of my criticism is as stated. In its most general
formulation, my opposition is directed at any kind of a priori dogma. The realist
approach I defend is contrasted with any kind of ungrounded insistence that certain
methods only, or almost only, should be followed” (Lawson, 2003).
and in chapter 7 I write:
“Rather the opponent is the advocate of any form of a priori dogma. In the context
of modern economics specifically, the primary target is […] the current
mainstream a priori insistence that formalistic modelling is the only proper, and a
universally valid, method for modern economics, along with its effective
prohibition on alternative approaches.”
No doubt dogma and dogmatism have various meanings. But it is surely clear that
in using it to describe mainstream practice I am here simply taking dogma to be
doctrine that is not defended but accepted on authority as unquestionable. Dogmatism
as I am interpreting the practice, then, is just the act of accepting dogma, that is, of
adhering to something on the basis of authority alone and treating it as beyond
question or criticism4. Clearly, it is something similar to Guerrien’s notion of ideology
discussed elsewhere in the current volume.
4 Can it be doubted that the practice of mathematical-deductivist modelling is treated this way
in the academy? I suspect Frank Hahn captures the ruling sentiment well when he insists of

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Now, of course, in suggesting that the dogmatic stance of modern mainstream
economists be rejected I do not want to imply that all doctrines can always be
meaningfully challenged5. And I am well aware that in acting at any point in time it is
practically impossible to subject all beliefs that condition an action to critical scrutiny
at that moment. But I do believe that everything that can be challenged should be
treated as open to critical scrutiny in principle whether or not the latter is
forthcoming. And I certainly believe the mainstream insistence that methods of
mathematical formalism be everywhere utilised ought to be open to question and
criticism by all. As I say, it is the mainstream refusal to consider the possibility that
formalistic methods may actually be limited in their scope of legitimate application
that I have suggested is dogmatic.
However, Hodgson suggests that my pointing to such limitations reveals the limits
of my anti-dogmatism in practice. How does he reach this view? He writes:
“In these passages [by Lawson] at least two features are emphasized. The first is a
strong, sincere and repeated claim of anti-dogmatism concerning whether or not
mathematics can or should be used. But he lays down criteria for its use, including
the requirement of (approximated) local closure. As a result of these criteria, the
specific measure of his own anti-dogmatism, in practice rather than in intention, is
how far he would admit that open systems might appear (or be approximated) in
reality. Lawson argues that his critical realist perspective suggests at the outset that
they are ‘limited’ or even ‘rather rare’. Accordingly, the ontological arguments in
Lawson’s critical realism lead him right away to expect that the possibilities for
formalism are highly restricted. This sets limits on his anti-dogmatist stance,
despite his pronounced antidogmatist intentions. Although Lawson imposes no
absolute normative ban on the use of mathematics, his arguments limit its
legitimate use to ‘rare’ circumstances only”
Hodgson’s logic here is not compelling. Let me momentarily leave aside the
seemingly emotive topic of the use of formalistic methods in economics. As I say, I
am opposed to dogmatism in the form of any authoritative assertion that only one set
of research methods can ever be used in economics. Suppose, though, that having
any suggestion that the reliance on formalism may be problematic that it is "a view surely not
worth discussing" (Hahn, 1985, p.18). In fact, Hahn later councils that we should "avoid
discussions of ‘mathematics in economics’ like the plague and give no thought at all to
methodology" (Hahn, 1992a; see also Hahn 1992b).
5 Hodgson seems to suppose that I believe the contrary, but does not say why. Of course I do
not. I believe that I have sense experiences that are of a real world in which I live (not, for
example, that I am fooled into supposing this is the case by some evil demon that is sending
false signals directly to my brain). Yet I do not know how to subject this belief to critical
scrutiny.

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made this declaration, I also make the suggestion that the conditions under which, say,
electron accelerators or stethoscopes are useful in economic research rarely crop up.
Would Hodgson maintain that I am thereby once more setting limits to my otherwise
anti-dogmatic stance? I doubt it. Certainly I hope not. For in such examples it is
surely clear enough that it is neither I, nor my arguments, that limit the use of electron
accelerators or stethoscopes to ‘rare’ socio-economic situations; rather it is the world,
the nature of social reality, that sets the limits to the conditions under which the tools
in question are useful. Seeking to identify or theorise these conditions has nothing per
se to do with dogmatism or anti-dogmatism6.
The point is that the mathematical methods used by economists are themselves just
tools. My claim is merely that the conditions in which they are useful seem not to
have occurred much in the social realm.
I may be quite wrong in this assessment. But that does not yet set limits to my
anti-dogmatism. It would be dogmatic of me, perhaps, if I used this assessment to
advise that formalistic methods be everywhere excluded from the economist’s
toolbox. But I have never suggested this. My position is always that all methods (that
anyone seriously proposes) be retained to some degree, not least because even
ontological arguments seeking to uncover their spheres of usefulness are fallible.
For example I write in Reorienting Economics:
“In so concluding I am not at all suggesting that formalistic modelling methods
should not exist among the battery of options available. All knowledge is fallible,
including ontological theorising. And even accepting the ontological perspective
systematised and defended in the chapters, which follow, there may yet be some
(greater) scope of application for methods of mathematical modelling than so far
uncovered. But just as significantly, although ontology can provide some
directionality to social theorising, one of its most useful functions, and perhaps its
primary one, is actually to open up analysis. This is precisely its role here. My
aim with the discussion of this chapter is not to narrow down the range of
methodological options by attempting to prohibit a particular method. Rather it is
to widen the range of possibilities through criticising the fact that, and manner in
which, the particular method in question is currently and unthinkingly
universalised” (Lawson 2003, chapter 1)7.
6 A radical constructivist might demur, but Hodgson declares himself a realist in the same vein
as myself.
7 Or as I write elsewhere in the same book:
“The last thing I wish to do is support any efforts to prohibit forms of activity, or limit the range
of methodological options.
I do not deny that I am rather pessimistic about the prospects of significant success
with mathematical methods in economics. In the light of the conception of social ontology

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The surprising aspect of all this is that Hodgson’s assessment of my position is
thought to carry plausibility. To the extent that it is, I suspect it has more to do with
some rhetoric that likely misleads. Consider the final sentence of his passage
reproduced above. Here Hodgson writes:
“Although Lawson imposes no absolute normative ban on the use of mathematics,
his arguments limit its legitimate use to ‘rare’ circumstances only”.
I have already noted that it is not my argument but the nature of social reality that
serves to limit the legitimate use of any methods. The point to which I want to draw
attention here, though, is the first part of the sentence: “Although Lawson imposes no
absolute normative ban on the use of mathematics”8, and in particular Hodgson’s use
of terms like “imposes” “absolute” and “ban” which seem create a smell of
dogmatism. Even use of the term “normative” in this context adds to this effect (it is
difficult to imagine a non-normative ban) 9.
defended in the chapters below, along with the assessment made of the ontological
presuppositions of formalistic modelling methods, I find it not at all surprising that these latter
methods have fared somewhat poorly. But in acknowledging my pessimism, I do not oppose
a share of resources being used in endeavours to study social material mathematically.
Amongst other things, all knowledge is fallible, as I have already stressed, so that, in
particular, the grounds of my pessimism may yet prove erroneous. Rather, the primary object
of my criticism is as stated. In its most general formulation, my opposition is directed at any
kind of a priori dogma. The realist approach I defend is contrasted with any kind of
ungrounded insistence that certain methods only, or almost only, should be followed. Such
an insistence seems especially unfortunate when, as currently, the methods laid down
persistently perform rather badly, whilst that unhappy performance can be explained (Lawson,
2003, pp. xix-xx).
8 Whether or not Hodgson is conscious of the fact, by the very act of (unnecessarily) denying
that something applies to me he is conjuring up the possibility that it might, or that something
similar might. If I started a sentence with the words “Although person X is not an absolute
imbecile (or, say, philosophical novice)…” the nature of the expectation/impression I would
be seeking to convey is clear. Similarly it is easy to (or rather it is difficult not to) take
Hodgson to be suggesting that I impose at least a partial ban on the use of mathematics. And
this affects the way in which the remainder of the sentence – “his arguments limit its
legitimate use to ‘rare’ circumstances only” -- is received.
9 We might also consider the first part of the passage in question. Here Hodgson writes (with
emphasis added by me):
“In these passages at least two features are emphasized. The first is a strong, sincere and
repeated claim of anti-dogmatism concerning whether or not mathematics can or should be
used. But he lays down criteria for its use, including the requirement of (approximated) local
closure. As a result of these criteria, the specific measure of his own anti-dogmatism, in
practice rather than in intention, is how far he would admit that open systems might appear
(or be approximated) in reality”.
It is the emboldened terms that I wish to draw to attention. I assume Hodgson means “closed”
and not “open” in the last sentence. In any case I do not seek to lay down criteria under which
something may be used. Rather I seek to identify conditions under which success with the
methods in question are guaranteed. That is all. It is these, in my assessment, that may rarely
figure in the social realm.

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Now I hope it is clear that I am not in a position to impose anything, whether or not
I want to; that I would not like to be in such a position; and even more to the point I
want nothing banned, whether absolutely or partially. Such sentence constructions
mislead and I fear hinder serious argument.
It is true that I argue that regularities (real or imaginary) of the form “whenever
event (or state of affairs) x then event (or state of affairs) y” (or stochastic near
equivalents) are a necessary condition if formalistic deductivist methods of the sort
economists seek are to be utilised. Systems in which these regularities occur I refer to
as closed. But I seek to identify the conditions under which such event regularities are
guaranteed. I may be wrong in my analysis. And in any case, my analysis does not
preclude the possibility of their occurring in other conditions. So however we look at
it I am hardly laying down criteria for the use of mathematical deductivist methods,
merely trying to understand something about the conditions of their likely successes,
if any.
Basically I am trying to help clarify the nature of the situation in modern
economics. Whether I speculate that closed social systems are more likely, or less
likely, or just as likely, in the future than in the past, this hardly counts as an
“admission”, and again clearly has no bearing on my position vis-à-vis dogmatism.
Successful econometrics?
Now if in Reorienting Economics, I observe that examples of successful
deductivist, including econometric, modelling seem not to have occurred especially
often in the social realm, I do not contend that there could never be any limited
success stories. Indeed, I suggest possible examples of past successes. However,
presumably because he reads me as seeking to banish the use of econometrics,
Hodgson seems to regard this as a logical slip. Let me quickly indicate why this too is
not the case.
Very briefly, the reason my noting a (conceivably) successful econometric exercise
is not a logical slip is simply that there is nothing in the conception I defend that
suggests that a closure (or indeed any configuration) could not occur. I may yet be
committing an empirical mistake; I may have assessed the econometric contribution
to which I referred in an overly positive manner. But this has nothing to do with the
logic of my overall argument.
Remember that a closed system is simply one in which an event regularity of sorts
occurs. In particular, a closure is not the same as, and cannot be reduced to, the
closure conditions. Closure conditions are sufficiency conditions, those that guarantee

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an event regularity; they are not strictly necessary for it. In principle, an event
regularity could even emerge by accident, with differing causal factors underpinning
any set of found-to-be-correlated events10.
More to the point, remember too that in perhaps all ‘applied’ or empirical contexts
where measurement is involved (including the well-controlled experiment), the
relevant form of closure is a stochastic one (see Lawson, 1997, p. 76) not a
deterministic one. A stochastic closure is a system in which a regularity occurs,
connecting or covering a set of random outcomes or ‘variables’. Specifically a
regularity holds between the conditional mean value of any one ‘variable’
(conditional upon the realised outcomes of the others) and the realised values of the
remaining ‘variables’. Notably, such a scenario can include a stochastic component
capturing not only any measurement error but also the effects of any relevant factors
or conditions that are unobserved (or otherwise excluded from explicit analysis).
Clearly if the conditional distribution of the latter component (and so of the
dependent or response variable) is small, the regularity involved, because closely
approximating a deterministic regularity, will, if successfully identified, and non-
spurious, be useful for predictive purposes. It was such a stochastic closure that (for
particular reasons set out in Reorienting Economics) I was presuming had been
(unusually) uncovered in the econometric exercise to which I referred.
Hodgson recalls that in a seminar discussion somewhere, I referred to a local closure
being ‘approximated in reality’, facilitating the use of econometrics. Unfortunately, I
do not remember the occasion or context. But I assume that if I made such a remark, I
had in mind a stochastic closure closely approximating (or constituting a stochastic
near-equivalent of) a deterministic one. The standards of approximation will be those
laid down by econometricians.
I admit that I do not expect social reality to throw up very often such conditions as
guarantee stochastic closures of this sort (that are not completely spurious11, and
10 Of course, as I discuss in Reorienting Economics, the latter scenario is unlikely. But
however unlikely, such a situation remains logically feasible; it simply does not follow that a
closure, even a deterministic one, could not occur if generally operative causal mechanisms
are not all explicitly accounted for.
11 Of course, this has not prevented econometricians producing thousands of models. But we
all know that, especially with time series analysis, if we experiment by running very many
regressions (some econometricians run literally tens of thousands of regressions on a given
data set), exploring all imaginable functional forms (or data transformations), it is usually
possible to find a within-sample relationship that is close fitting by conventional criteria,
whatever the latter may currently be. In this case, a stochastic closure of sorts is identified.
But I do not suppose anyone believes many of the results (in the form in which they are
presented, whether or not they are published). The theory and assumptions behind the
methods of statistical inference employed to identify the relationship are repeatedly
contravened (rendering the interpretations typically attached to such empirical results invalid).

Tony Lawson and His Critics
12
employing econometricians own context specific assessments of acceptable
approximations); and nor do they seem frequently to have occurred. That is why, as
Hodgson also notes, I am able to provide very few examples of apparent successes.
But if they occur, or more to the point, if I assess (fallibly) that they have occurred,
this per se says nothing about the logic of my overall argument
Notice, too, that the position I am defending, despite Hodgson’s suggestion to the
contrary, in no way encourages the current emphasis on formalistic modelling, even in
respect to econometrics. The situation of modern econometrics is not that
econometricians are everywhere manipulating criteria whereby stochastic closures
might be said to be close approximations to deterministic ones, in order that the
current heavy emphasis on formalism wrongly appears justified. Rather this heavy
emphasis continues in the absence of widespread successes as measured by these
(conventional) criteria, and indeed in the absence of any other apparent justification.
So, in sum, I hope it is clear that by my giving some qualified support for a particular
econometric exercise (whether or not the support is warranted in this particular instant),
I am thereby neither revealing a logical inconsistency in my argument nor supporting
the current emphasis on formalism.
But equally, to return to the broader theme (and as my support for the particular
exercise just discussed further illustrates), I am nowhere opposing the use of formalism
per se either. As I have repeatedly stressed, my objective in my critical assessments of
the state of modern economics, is to understand why certain research methods have
generally failed or occasionally (seemingly) proven successful. Whatever else my
project may entail, it has nothing to do with seeking to narrow down the range of
research practices on offer. Ultimately, indeed, as I have argued earlier, my findings in
fact support just the opposite stance, of expanding the options available and recognised
as viable.
In addition,, the right hand side ‘independent’ variables are usually not at all those that can
reasonably be claimed to stand in the causal history of the dependent variable. Most telling of
all, perhaps, is that as soon as new observations are obtained, previously ‘identified’
relationships of this sort are almost uniformly found to break down.
Econometricians, of course, know all this (even if they continue with their project on
grounds other than realisticness or believability – see Vromen, this volume). Edward Leamer
(1978), for example, talks of the inconsistencies in the theory and practice of econometrics,
and of the ‘priests’ who produce the theory to inform econometric practice, and the ‘sinners’
who misapply the theory in practice. He even notes that these are the same people on
different occasions. He notes too that “Sinners are not expected to avoid sins; they need only
confess their errors openly” (Leamer, 1978, p. vi). He further notes that, where realisticness is
the issue, "hardly anyone takes anyone else's data analysis seriously" (1983, p. 37).

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Previous Statements
Perhaps the reader unfamiliar to my contributions will suspect that there is no
smoke without fire, that the overall or basic position I am here accepting is so far
from that seemingly attributed to me by Hodgson, that I must myself be saying things
now that are inconsistent with the broad message of previous contributions. In case
this is so, I hope I can be permitted to reproduce here a few (of the very many)
relevant passages.
In Reorienting Economics I write:
“Let me elaborate a little on my orientation to formal modelling. Although parts of
this book, and most specifically chapter 1, are critical of the way formal modelling
methods are taken up in modern economics, I hope by now the highly conditional
nature of my criticism is apparent. It is not, and has never been, my intention to
oppose the use of formalistic methods in themselves. My primary opposition,
rather, is to the manner in which they are everywhere imposed, to the insistence on
their being almost universally wielded, irrespective of, and prior to, considerations
of explanatory relevance, and in the face of repeated failures” (Lawson, 2003, p.
xix).
Elsewhere in a paper in the Journal of Economic Methodology I am just as explicit.
Here I write (in response to comments by Julian Reiss):
“My argument is not at all an anti-mathematics one; and it never has been. I have
only ever criticised the way (certain) mathematical methods tend to be used in
modern economics”12 (Lawson, 2004, p. 337; emphasis in the original).
12 The broader passage forming the context in which the passage in the text is set reads as
follows:
“Notice, too, that I do not suggest that the methods of mathematic-deductive modelling which
mainstream economists wield can never have an appropriate application. To the contrary, I
suggest in Reorienting Economics that the perspective I adopt can identify the sorts of
conditions in which success is likely and so explain such successes as occur (see e.g. p. 20).
And nor do I suppose that mainstream economists do nothing but mainstream economics;
indeed I expressly deny that this is so (see e.g. p. xxi) [….]
Let me […] [stress] that I fully agree that ‘there is no necessary link between mathematics and
bad practice’. Indeed, I cannot emphasise my agreement with this statement too strongly. My
argument is not at all an anti-mathematics one; and it never has been. I have only ever
criticised the way (certain) mathematical methods tend to be used in modern economics.
Indeed it is precisely the belief that mathematics ought not to be applied without due care and
consideration, coupled with a conviction that in modern economics it too often is so, that
explains the direction of much of my writing. If you like, my concern is that much of economic
modelling appears somewhat analogous to a violin being used as a drumstick. To suggest
that this may be “bad practice” is in no way to devalue the violin, or to deny it a place in the
orchestra.

Tony Lawson and His Critics
14
After a lengthy discussion of my views on the use of mathematics in economics I
summarise my position as follows:
“In short, I do not denigrate the use of mathematics. I do, though, believe that
the sorts of mathematical-deductivist methods mainstream economists mostly use
presuppose an implicit worldview that is not especially typical of social reality. I
also suggest that many of the widely acknowledged failures of the discipline arise
just because these methods are being applied in conditions for which they are not
especially appropriate. In consequence, in Reorienting Economics I argue for a
more pluralistic orientation to social theorising, and spend time demonstrating that
alternatives methods of relevance do exist. In this I do not suggest that formalistic
methods be excluded for the methodological options on offer. But I do insist that
methods of mathematical-deductivist reasoning (like any other tools) have limits to
their usefulness, and that this be recognised and respected. However, I see this as a
pro-, rather than an anti-, mathematics position” (Lawson, 2004, pp. 337-339).
I hope I have said things with sufficient clarity, not to mention repetition, to dispel
any worry that I am somehow opposed to the use of mathematical formalism as an a
priori disposition.
The roles of formalistic models in economics
I turn, then, to the matter that I take to be Hodgson’s central concern, the manner in
which models can be useful to social illumination. Unfortunately, before we can get to
points of substantive disagreement, there are, even here, one or two important issues
of interpretation on which Hodgson does not get me right.
In developing his comments on how models can be used Hodgson suggests that I
supposedly commit the mainstream error of viewing models as somehow mappings
onto, or in correspondence with, reality13:
Nor do I limit mathematics to deductivist modelling. Actually if what economists do is
mathematics, it is a form of applied mathematics; it is the application of mostly already worked
out mathematical systems And if it is ever appropriate to “associate” a method with an
ontology I see no reason to suggest that some mathematical methods could not be
associated with a causalist ontology.
If I do not, then, limit mathematics to methods of deductivist modelling I do contend that the
sorts of modelling methods mostly utilised by modern economists are deductivist in nature
[…] (Lawson, 2004, pp. 337-8; emphasis in the original)
13 In a revised version of Hodgson’s paper presented at the realist workshop on November 14
2005, the relevant passage is formulated as follows: “Lawson suggests that logical or
mathematical constructions, if they are to be of relevance or use, must be some kind of map
of reality at the level of ongoing events. In one passage Lawson […] writes of the importance

Tony Lawson and His Critics
15
“[Lawson] seems to suggest that logical or mathematical constructions, if they are
to be of relevance or use, must be some kind of map of reality at the level of
events. For example Lawson (2003, p. 22) writes of the importance of a ‘ “fit” with
reality’ ”.
I do write on the idea of models as mappings of, or as corresponding to, reality. But I
defend precisely the opposite position to that which Hodgson imputes to me. What I
actually write is the following:
“It seems likely that [many] […] economists are in effect holding, if implicitly, to
conceptions of knowledge and truth as relations of identity or, more generally,
correspondence14. Certainly the widespread use of the terminology of economic
models is consistent with this – as if the latter are somehow smaller, scaled down,
or otherwise simplified, versions or mappings of the original. Economists
frequently talk of ‘mappings’ in connection with their modelling, often remarking
that any map drawn to a scale of one-to-one would be as complicated as whatever
it is supposed to represent, and thereby useless. From this perspective it follows
that because of the complex nature of social reality any feasible mapping is never
isomorphic. In consequence, the argument seems to run, all models are inevitably
distortions; true models or theories are most unlikely to be obtained.
Whether or not any economist holds to this line of reasoning completely (or
explicitly), or would express things quite so starkly, it is worth considering this
position here anyway as an obvious point of reference. And it should be apparent
from everything that has gone before that any conception of knowledge and truth
along the lines indicated, i.e., as relations of correspondence between discourse and
extra-discursive reality, is profoundly misleading” (Economics and Reality chapter
17, p. 238).
Rather than employing the misleading imagery of mappings in my argumentation,
I refer over and again to the ontological preconditions of formalistic-deductivist
methods, and question whether they hold in the social realm. Rarely do I use the word
‘fit’, and where I do it is clear that this is precisely my meaning in using the term.
Even the passage to which Hodgson explicitly refers is followed by one indicating
that ‘fit’ is to be interpreted in terms of the presence of ontological preconditions:
“But ‘fit’ with reality matters too. The problem with the mainstream stance is that
the ontological preconditions of its formalistic methods appear to be not only not
ubiquitous in the social realm, but actually rather special occurrences. If we knew
of a ‘“fit” with reality,’ suggesting that all theory has to somehow correspond with the real
world”
14 This conception is presumably influenced by the positivistic conflation of knowledge with
direct experience and reduction of reality to events and states of affairs given in experience.

Tony Lawson and His Critics
16
both that social life was everywhere atomistic, and also that for any type of outcome
we could effectively isolate a fixed set of causes (treating all other causal processes
as a kind of stable, non-intervening or homogeneous backdrop), we would have
grounds for feeling confident in the emphasis that mainstream economists place on
the sorts of deductivist methods they use. However, our best ontological analysis
suggests that closures are a special case of social ontology, whilst our a posteriori
experience is that this special case seems not to come about very often at all”
(Reorienting Economics, p. 22)
Actually I use the word ‘fit’ twice in Reorienting Economics. In the other instance I
indicate precisely what I mean:
“As a result the possibility of a lack of ontological fit (a mis-matching of the
presuppositions of these modelling methods with [the nature of] those features of
social reality being investigated) does not arise. Yet, as I say, methods of
mathematical-deductivist modelling, like all methods, do have ontological
presuppositions. And my assessment, simply stated (and defended below), is that
these preconditions of mathematical-deductivist methods appear not to arise very
often in the social realm” (Reorienting Economics, p. 12).
Heuristic and internal critique
An equally surprising assertion made under this head is that I concentrate my
critique on econometrics15 and in doing so fail to consider whether formalistic models
might be used for heuristic purposes or as vehicles for internal critiques. As much of
the discussion below is about, and draws upon, my account of heuristic as set out in
Economics and Reality I will not add anything on this topic for the moment. But I
should perhaps say something at this point about internal critique.
Now an internal or immanent critique (which I actually discuss fairly extensively
in Economics and Reality) proceeds by way of working from certain internally
accepted features of a project or paradigm, and pointing out that they lead to
15 Hodgson thus writes:
“Much of Lawson’s discussion of formalism concerns econometrics. He gives insufficient
attention to other applications of mathematical techniques, which serve primary purposes
other than the prediction or explanation of measurable variables. Such additional applications
of formalism include (a) heuristics and (b) internal critiques. I shall address each of these in
turn”
As it happens, in Economics and Reality I address very many different ways in which it might
be thought that mathematical modelling can contribute to social illumination. Only one of the
chapters (chapter 7) focuses on econometrics. Chapter 9 deals explicitly with defences that
accept some goal other than tracking measurable variables, and, unsurprisingly, I do there
discuss the possible heuristic role of formalistic models at some length (see below).

Tony Lawson and His Critics
17
problems, inconsistencies, or limits elsewhere within the project or paradigm,
conceived on that projects own terms16.
As I say, Hodgson advances the idea that formalistic models might be used for
making internal critiques. Now in the context of modern mainstream economics no
one could presumably fail to recognise this, simply because the mainstream is
everywhere couched in terms of mathematical formalism. The insistence on
mathematical deductive methods is the essence of that project. The possibility, to
which Hodgson points, arises just as a consequence of the mainstream problematic
insistence on formalistic methods17. Indeed, as most mainstream contributions
advance by precisely addressing perceived (internal) weaknesses, or inconsistencies
or limitations of preceding contributions, most mainstream contributions themselves
constitute or contain internal critiques. There is no great insight here.
Of course, heterodox economists will likely employ formalistic models for
purposes of seeking more destabilising critiques than will mainstream economists
themselves. And I do not at all want to belittle their achievements on their own terms.
Why then do I not join in (more than I do18)? The answer is simply because I do not
think such critiques lead to any necessary advance in terms of illuminating the world
in which we actually live. Mostly they lead to the internal shoring up of an irrelevant
conceptual system. And even when a framework is radically transformed or replaced,
it almost always is so by an equally irrelevant alternative formalistic system. Witness
the recent turn to evolutionary game theory, agent based modelling, complexity
theory, and so forth, following the demise of general equilibrium analysis and the like.
Does anyone really suppose that these providing advances in understanding social
reality? Some commentators do seek to interpret such developments as examples of
mainstream pluralism. But in spirit they are no such things. And at the methodological
level, in particular, they are quite the opposite. At best they are manifestations of the
mainstream flexibility to move from one highly questionable mathematical
conception to another.
Is there no scope for progress via internal critique involving formalistic methods?
It seems to me that the best bet for those keen on internal critiques utilising formal
models is precisely to keep plugging away in the hope that mainstream practitioners
16 Thus it is not clear that Hodgson’s examples – those that reveal that models are based on
restrictive or unwarranted assumptions - are after all critiques of this form.
17 Moreover, certain critiques that do not at all require mathematical models for a point to be
made are often put in that form just in order to get a hearing. Hodgson references Sraffa’s
contribution. But Sraffa’s essential point is that the meaning/interpretation of an integral
element of a system will (or can) depend on the system as a whole. He made the same point
to Wittgenstein (in the context of language systems - and causing Wittgenstein to significantly
rethink his position) but without the need/constraint of using mathematics to convey his
message. Moreover, in the latter case Sraffa seems to have had the more persuasive impact.
18 I have engaged in this sort of activity myself a good while ago. See for example, Lawson
1981

Tony Lawson and His Critics
18
eventually grow tired of shoring up existing, or seeking new, formalistic systems (for
I doubt that the options by way of formalistic systems will run out), and are willing to
turn to something else. But I am not optimistic it will happen.
Is there any better alternative way to proceed? If the problem is that by making an
internal critique of (elements of) one mathematical-deductivist approach, mainstream
economists merely readjust it or invent an alternative one, the surest way to make real
progress, it seems to me, is to orient the internal or immanent critique at features
common to (or presupposed by) the variety of mathematical-deductivist methods or
projects associated with mainstream economics. It is to carry out an immanent
critique of the mathematical-deductivist approach to social theorising itself. This
anyway has been my approach.
Mainstream economists recognise that event regularities are required (or need to be
posited) if their methods are to have application (see e.g. Maurice Allais, 1992, p. 25).
It is widely recognised that such regularities (whether deterministic or stochastic)
rarely emerge in the social realm. What I have shown is that such regularities, if they
are to be guaranteed, require conditions (a closed world of isolated atoms) that are
rather unlikely to hold in the social realm. Thus methods that presuppose them (if
success is to be guaranteed) are questionable, and the reason for the continuing failure
of a project that insists on them is evident.
This is indeed an internal or immanent critique just because (or to the extent that)
in footnotes, introductions, public speeches, rhetorical asides, and so forth,
mainstream economists talk in a manner that presupposes worldviews according to
which social reality is anything but closed and atomistic. The problem is an apparent
lack of awareness that their methods prohibit the sorts of theorising that conforms to
their implicit broader perspectives.
Still here I am straying rather from the issue. Hodgson seems to suggest that I fail
to notice, or consider the possibility, that mathematical-deductivist methods can be
used for purposes of internal critique in the context of modern economics. My
response is to observe that no one could fail to recognise this possibility, for it mostly
exists just because that project is itself intrinsically mathematical. My worry, though,
is that the sorts of critiques possible will likely leave this overall and unhelpful
mainstream emphasis or orientation (as opposed to specific mainstream examples)
untouched. It is for this reason that I have adopted an alternative approach that reveals
the limitations of the mainstream deductivist project as a whole. Of course, there is
more to effecting change than getting it right (irrespective of whether or not my
arguments are correct). If Hodgson believes that continually chipping away via
internal critiques employing mathematical methods will prove more effective in the
long run, whatever the intellectual case, then let him chip away (also see John Davis’

Tony Lawson and His Critics
19
commentary in this volume and my response). For reasons I have given, though, if a
more realistic economics is the objective, I am not optimistic that the outcome will be
worth the effort.
Points of Substantive Disagreement
Now that the main misunderstandings at least have been cleared out of the way I
can turn to those of Hodgson’s comments that, in part at least, do point to some real
substantive differences between us.
A central plank of Hodgson’s critique is the charge that the distinction I draw
between methods of abstraction and theoretical isolation does not hold. Or rather
Hodgson claims “the distinction is, at least in prominent practical instances, difficult
to sustain”. I believe, to the contrary, that the distinction (elaborated below) is very
easy to sustain, and that it is vital to social analysis that we do sustain it.
Why does Hodgson single out this particular issue? The answer is not totally clear
to me. Hodgson notes that I regard abstraction as both unavoidable and useful but
that I am rather wary of the method of theoretical isolation, associating it implicitly
with the mainstream. I think Hodgson’s goal is to persuade that the sorts of methods
that I advocate (and more especially abstraction) face essentially the same problems
as those confronting the mainstream. In other words, Hodgson seems to be working
on two fronts. On the one hand he wishes to suggest that formalistic methods can be
more useful than I allow. On the other hand he wishes to convey the impression that
any alternative methods that I have advocated share any difficulties that can be
associated with formalism.
I say this because I notice that his discussion of these matters is preceded by a
commentary on my own critique of the mainstream insistence on using mathematical-
deductivist methods. Specifically, Hodgson notes my criticism of the mainstream
turns on their reliance on methods that presuppose a closure, in order to analyse open
systems. Hodgson clearly hopes to undermine this critique. And his strategy in this
entails seeking to persuade the reader that methods that I advocate also presuppose a
closure. For if the latter were the case, Hodgson seems to suppose, then my critique
of the mainstream would be seen to be unsuccessful, at least in the sense of my failing
to propose anything better. Hodgson notes that I distinguish the method of theoretical
isolation from abstraction and that I associate closures mostly with the former. At the
same time I emphasise that abstraction allows us to investigate open as well as closed
systems, and, specifically, that it does not force us to treat open systems as though
they are closed. Thus Hodgson perceives a need to undermine the distinction between
abstraction and theoretical isolation.

Tony Lawson and His Critics
20
Now, curiously enough, if my assessment of Hodgson’s motivation is correct here
he does not actually need to seek to dissolve the distinction between methods of
theoretical isolation and abstraction. For I do not deny that closures of some sort are
often important to the (dialectical sort) of explanatory analysis that I have often
emphasised. However, I do find that the closures that have proven most relevant are
not of the sort that mainstream economists tend to seek. Mainstream economists are
interested in closures of causal sequence, those (if any) in which one (set of) event(s)
or state(s) of affairs stands in the causal sequence of another (for example, household
disposable income standing in the causal history of household expenditure patterns).
The sort I think are typically more useful to explanatory social analysis are (a subset
of) closures of concomitance (see Lawson, 2003), and specifically those that hold
when specific features of a domain of reality share a similar causal history and so can
be expected to turn out roughly the same (when the price of postage stamps increases
in London it also does so in Cambridge; the amount of rain that falls in a square metre
of my front garden on any given day, is much the same as falls in the same area in my
back garden (and in my neighbour’s).
Moreover, for mainstream economists the goal of seeking closures is to predict and
thereby control. In contrast, closures are of most use to the very different sorts of
(dialectical) explanatory procedures I defend precisely when they unexpectedly break
down, when the stretch of reality under consideration in fact ceases to be closed (to
support an event regularity). There is much to be said here (see especially chapter 4 of
Reorienting Economics). Certainly the methods I believe to be most useful to
explanatory analysis are very different to the deductivist modelling efforts of the
mainstream.
If Hodgson really wants to suggest otherwise it is here he ought to pitch his
critique. But he does not. Instead he notes my positive exploration of the method of
abstraction. As I say, I can only suppose it is because he thinks that he can somehow
undermine my own explanatory emphasis by showing that abstraction and theoretical
isolation cannot be easily rendered distinct that it is here he concentrates his attack.
Because I believe the distinction that Hodgson’s attempts to dissolve is nevertheless
vital to social analysis (if not actually the one Hodgson best needs to attack) I must
now defend it anyway. This is the focus of the discussion that follows.
Abstraction and Theoretical Isolation
Before turning to the details of Hodgson’s criticism I should recall what I take the
distinction between abstraction and theoretical isolation to be.

Tony Lawson and His Critics
21
I interpret abstraction, here as always, according to its traditional meaning of
focusing upon certain aspects of something to the (momentary) neglect of others. It is a
process of focusing on some feature(s) of something(s) while others remain in the
background. For example, in considering the ability of copper to conduct electricity
well I may focus upon its atomic structure and thereby abstract from its colour, texture,
malleability, and so on. It follows that there is always something that is abstracted
from. That which is abstracted from is the concrete. One significant purpose of
abstraction is to individuate one or more aspects, components, or attributes and their
relationships in order to understand them better.
Hodgson notes that in referring to the method of theoretical isolation I draw on the
work of Uskali Mäki. This is correct; the method is not one I myself defend or have
sought to develop. Let me then restate the conception of it I set out in Economics and
Reality, which makes reference to Maki’s (1992) conception, and seems to be
Hodgson’s notion. There I write of it:
“According to Mäki, [the method of theoretical isolation] is a method ‘whereby a
set of elements is theoretically removed from the influence of other elements in a
given situation’ (1992: 318). Mäki adds that ‘In an isolation, something, a set X of
entities, is “sealed off” from the involvement or influence of everything else, a set
of Y entities; together X and Y comprise the universe" (ibid.: 321). Of course, even
in experimentation no such isolation occurs literally, only physical re-arrangement.
But the aspect of all this that I find most problematic is Mäki's notion of theoretical
or ideal isolation, an apparently ‘traditional forceful procedure ... in economics’
wherein no material re-arrangement is involved at all. Rather ‘a system, relation,
process, or feature ... is closed from the involvement or impact of some other
features of the situation’ by way of ‘an intellectual operation in constructing a
concept, model or theory’ (ibid: 325). In fact, Mäki goes further and distinguishes
‘internal’ and ‘external isolation’: ‘In an internal isolation, one isolates a system
from influences coming from within the system, while external isolation closes a
system from influences that have sources which are external to the system’. Mäki
adds that both ‘internal and external isolation are relevant in economics’ (ibid.:
326)” (Lawson, 1997, pp. 131-2)
The distinction before us is easy enough to grasp. To abstract is to focus on aspects
of something whilst not assuming the non-existence, or non-impact, of features not
focussed explicitly upon (that are abstracted from). To theoretically isolate is
precisely to treat those aspects not focussed upon as non-existent, or at least as sealed
off, as having no systematic influence.
The difference between the two is easily demonstrated if we consider an aspect of
some team game, say football or hockey, on television. Suppose, we see on the

Tony Lawson and His Critics
22
television screen a player, say a footballer, running with the ball down the side of the
pitch, towards the end at which the opponents goal is situated. If we are abstracting
we will be interpreting this footballer’s actions in a manner that takes into account the
fact that supporting players on the same side will be moving in the same direction,
and defenders of the opponents’ team will be facing up to make a challenge. If instead
we treat these other players as somehow sealed off from the action, as momentarily
non-existent, then we are using the method of theoretical isolation. Clearly this creates
a different world to the actual one addressed via abstraction. In the isolationist’s world
as described, if scoring is the player’s objective all he or she has to do is take the ball
to the goal and kick it between the two posts. There will be no opposition, because all
other players not focussed upon are assumed to have no impact.
A sports example such as this is useful because the game is clearly an internally
related whole. The parts, the various movements of individual players, only get their
meaning from the whole, so that any attempt to interpret one bit whilst ignoring the
rest must fail if it is meaningful at all. I throw in the TV screen just to get the
abstractionist and the isolationist to focus on the same part.
Clearly abstraction, but not theoretical isolation, will be relevant wherever the
whole is not just the mechanical sum of parts. Composers, surgeons, artists as well as
social theorists deal with internally related wholes. As such abstraction, not
theoretical isolation, will be the appropriate method of analysis.
Now it should be clear, although it is worth emphasising it anyway (not least
because this may be a source of the confusion), that these two methods, though
distinct, are not strict alternatives. Because the world in which we live is so complex,
abstraction is always involved. It will be so even where an isolationist approach is
adopted (indicating that the presumption of ‘isolation’, or being sealed off, can only
ever be a relative one). For example, in considering the sports game above, in the
scenarios of both the abstractionist and the theoretical isolationist, the causal force of
gravity is presupposed, but abstracted from. That is, in each case gravity is not
mentioned or analysed but accepted as acting; it is not assumed to be sealed off or
inoperative; in neither case are the players treated as being propelled into outer
space19.
In contrast the method of isolation has very restricted conditions under which it is
relevant or anyway useful. The paradigm case is provided by a situation of controlled
laboratory experiment. Here a mechanism is physically insulated from countervailing
19 In other words, in cases where isolationist methods are adopted, and it is assumed that
some factor X operates in isolation, it will be clear from the context of analysis that some (and
which) factors are being treated as operative but unmentioned as opposed to being sealed
off.

Tony Lawson and His Critics
23
features in order to be empirically identified: an event regularity is generated
correlating the triggering of the mechanism and its unimpeded effects. Once more
abstraction will be involved. We may momentarily concentrate on the ‘isolating’ of
the mechanism, then on the triggering of it, then on some of its effects. We may at all
times abstract from, colour, smell, sound, cost of apparatus, and so forth; but then
again we may not: it all depends on the context.
Of course, the controlled experiment represents a physical not a theoretical
isolation. But a theoretical isolation is a process of imagining what would occur if a
physical isolation could be achieved. A theoretical isolation is indeed a thought
experiment. And where physical conditions are such as to inhibit in principle (as
opposed to providing practical difficulties for) the physical isolation of certain
features, then it seems that the method of theoretical isolation is without utility.
For example the interconnectedness and mutual constitution of the numerous
different features of social reality are such that it is impossible to experimentally
isolate individual components, such as money, firms, or markets, and examine how
they so operate when isolated from each other and from everything else. Equally, it is
meaningless to theorise these features as if sealed off from the influence of each other
and everything else. Of course, stated explicitly, this all seems obvious. Nevertheless
such isolationist procedure dominates the specific methodological practices of modern
economics.
If it seems clear enough that abstraction and theoretical isolation are indeed rather
distinct (albeit not strict alternatives), I must now turn and examine how Hodgson
argues to the contrary. There are essentially three strands to Hodgson’s endeavour.
First, seemingly accepting that closure is presupposed by the employment of methods
of theoretical isolation, Hodgson seeks to associate closure with abstraction too.
Second, drawing on Schelling’s (1969) analysis of ‘racial’ segregation, Hodgson
seeks to show that the use of heuristics, clearly presupposing the method of isolation,
is equivalent to the process I describe under the heading of abstraction. Third
Hodgson claims that the distinction I draw between the methods of abstraction and
isolation is too vague to be of practical import. Let me run through each of these
charges in turn indicating why I believe each to be unsustainable.
1) Abstraction and closure
How first does Hodgson argue that abstraction presupposes closure? In truth, he
does not; that is, he does not provide an argument. Rather he asks the question:

Tony Lawson and His Critics
24
“If abstraction is necessary, and it involves the limitation of the sphere of
consideration and the exclusion of additional relations or disturbing forces, then
doesn’t this too imply the assumption of a closed system?
And he gets Stephen Nash to answer it for him:
“Stephen Nash (2004) has recently argued in the affirmative, suggesting that Lawson too
must assume conditions or forms of closure”
Hodgson adds nothing to this, though he perhaps believes that his case is bolstered
through his suggesting that I use the distinction (between abstraction and theoretical
isolation) as a form of protection:
“[Lawson] uses this distinction to protect his argument against the objection that
his method of abstraction also implies the assumption of closure; he argues that
abstraction does not imply closure but isolation does”
Now whatever else Stephen Nash (2004) does or does not do, as far as I can see he
nowhere mentions abstraction, let alone argues that it presupposes a closure. Nash
does suggest that the explanatory method I advance presupposes closures (something
I have already acknowledged above), but fails to draw a distinction between closures
of concomitance and closures of causal connection and so to appreciate that it is the
former variety that are significant for the explanatory approach I defend. He further
fails to note that (perceived) closures are significant precisely when they beak down.
But this is all beside the point. The topic of abstraction is not addressed.
If there is no argument advanced either by Hodgson or by Nash, there is seemingly
none (here) to which I must determine a response. And to the point it should be very
clear from all that has gone before that of course abstraction does not imply closure.
At least it does not if by abstraction we mean focussing on a part of a whole whilst
leaving the rest of the whole momentarily out of focus, and if by closure we mean, as
I do throughout, a system supporting an event regularity. Clearly, abstraction can be
applied to all types of systems, to those that support strict event regularities, to those
that support partial ones and equally to those seemingly not supporting any. It can be
applied to matters that are real or fictitious. If I talk only about the horn (or white
colour, or billy-goat beard, or lion's tail, or cloven hoofs) of a unicorn, I am
abstracting in the context of discussing a fiction. To say of the social system, or of any
specific part of it, that it is fundamentally open is to abstract. To suggest that
abstraction presupposes closure is simply to misunderstand one or other or both of the
two terms.
2) The use of heuristics is equivalent to the method of abstraction

Tony Lawson and His Critics
25
A second point of difference between us concerns the way in which Hodgson
believes that formalistic models might serve as heuristic devices. Once more Hodgson
is concerned to connect abstraction to theoretical isolation. The latter method is
closely connected to the notion of heuristics as used in economics, and this seems to
account for Hodgson’s concern to relate the latter in turn to abstraction. Here the
analysis gets more interesting. Hodgson writes:
“The purpose of a heuristic is to identify possible causal mechanisms that form
part of a more complex and inevitably open system. Heuristics can be useful
without necessarily making adequate predictions or closely matching existing data.
Their purpose is to establish a plausible segment of a causal story, without
necessarily giving an adequate or complete explanation of the phenomena to which
they relate”
It is this belief that appears to ground Hodgson’s suggestion, which I am disputing,
that the use of heuristics and abstraction are closely related if not equivalent, that
“heuristics relate to the very process of abstraction that Lawson himself highlights”
Hodgson’s contention that the ‘purpose of a heuristic is to identify possible causal
mechanisms’, is, I believe, simply wrong (at least if I am interpreting him correctly, a
matter to which I return in due course). It may well be the case that heuristics can be
useful for some yet-to-be-explicated purposes ‘without necessarily making adequate
predictions or closely matching existing data’. But their contribution is not ‘to
establish a plausible segment of a causal story’. Rather any usefulness they posses, or
so I shall argue, can stem only from the fact that a plausible segment of a causal story
has already been established20.
However, I realise that this last claim is likely to be contentious; that others too
will likely be uncomfortable with it. So let me defend it at length. It is in the context
of suggesting that heuristics achieve the same outcome as abstraction that Hodgson
refers to Schelling’s (1969) model of ‘racial’ segregation (to illustrate his argument).
This latter focus is useful in that, unlike many economic contributions, Schelling’s
analysis does indeed seem to carry insight and be somewhat persuasive. This, no
doubt, is why Hodgson draws upon it. So eventually below I run through my
argument referencing Hodgson’s example of Schelling as is relevant.
20 In other words, I am suggesting that any insight attached to a formal model is typically not
the result of the modelling or heuristic exercise itself but derived first in a different context. For
a mainstream economist, the overriding objective is to produce a mathematical model.
Obviously, modellers are uncomfortable with the charge of irrelevance, so attempts will be
made to render models as realistic as possible; real insights will be tagged on wherever
feasible. But as I say, I believe the real insights are typically independent of, and indeed
achieved prior to, the construction of the mathematical model.

Tony Lawson and His Critics
26
Heuristic and the method of successive approximation
First, though, I should establish the meaning of the term heuristic. Of course,
specific categories can be made to mean anything we want them to. But all have a
context, and most have a history. The term heuristic originally meant something like
“serving to find out”. How the latter is interpreted does vary according to context. In
education it usually relates to a system in which pupils are trained to find out things
for themselves. In philosophy and science it most commonly means a rule of thumb
that has been found to be useful in making progress towards solving a problem. A
heuristic computer program is one that begins with only an approximate method of
solving a problem within the context of some goal, and then uses feedback from the
effects of the solution to improve its own performance.
It is worth emphasising that in all such cases, the heuristic (the method, system or
whatever) is observed to work; it is found successfully to serve some process of
finding out. If something new is proposed as a heuristic device there is presumably an
expectation at least that it will serve its intended purpose.
The way the term heuristic is usually employed in economic methodology is bound
up with developing theories by way of relying on assumptions or conceptions
believed to be false21. Heuristic assumptions are often said to be those that are used to
simplify the analysis as a first step with the expectation (or perhaps, with hindsight,
with a knowledge) that the picture is to be (or has been) rendered more realistic
through complicating it at a later stage.
Such a process of gradually complicating the picture with the aim of making it
more realistic is presumably what Hodgson has in mind when he notes that “heuristic
models […] are literally unrealistic” and he writes that Schelling’s “model is simply a
heuristic step along the road towards that more complete end”. In a later version of
his paper (presented at the Cambridge Realist workshop in November 2005) Hodgson
also refers approvingly to Musgrave (1981) who in fact provides the classic statement
of the step-wise procedure in terms of heuristic devices or assumptions:
“[A scientist] may wish to develop ... a theory in two stages: in the first stage he
takes no account of factor F, or ‘assumes’ that it is negligible; in the second stage he
takes account of it and says what difference it makes to his results. Here the
21 This is the conception shared by others who work in this field. For example, Steve Keen
recently considers heuristics emphasising clearly that “A heuristic assumption is one which is
known to be false, but which is made as a first step towards a more general theory”

Tony Lawson and His Critics
27
‘assumption’ that factor F is negligible is merely a heuristic device, a way of
simplifying the logical development of the theory. Let us call such assumptions
heuristic assumptions” (1981, p. 383)
It is thus easy to see how the method of theoretical isolation “whereby a set of
elements is theoretically removed from the influence of other elements in a given
situation” (Maki, 1992, p. 318) relates to the making of heuristic assumptions in
economics. For both advanced knowing that significant causal influences (and
perhaps other significant features) are omitted.
The stepwise approach of moving from initial conceptions of isolated features to a
more realistic or complete theory is often referred to as the method of successive
approximation, particularly when there are (possibly many) more than two steps
involved. It is something I discuss explicitly in Economics and Reality, where I look
at the practice of accepting certain sorts of believed-to-be-false assumptions as a
“heuristic device in a step-wise process of moving from simplified or ideal
conceptions to others of greater complexity and so, it is supposed, realisticness”
(Lawson 1997, p. 127). What is required here is some analysis of heuristic
assumptions interpreted as unrealistic claims, and how they serve to facilitate theory
development.
Hodgson himself does not give any analysis of why, or when, a conception
regarded as unrealistic might be illuminating. He does, though, appear to suggest that
it might be provided by Robert Sugden’s (2000) account of ‘credible worlds’, which
also makes reference to Schelling’s (1969) contribution. Sugden’s idea is that if a
model captures a ‘credible counterfactual world’ we apparently have some inductive
warrant for its relevance to our world. Hodgson writes:
“Robert Sugden (2000) asks probing questions concerning the role and
‘realisticness’ of this and other heuristic models in economics. These heuristic
models have the paradoxical claim that they are literally unrealistic yet they seem
to illuminate important aspects of reality. Using the Schelling model alongside
George Akerlof’s (1970) famous article on the ‘market for lemons’, which again
claims to establish meaningful propositions about the world on the basis on an
admittedly unrealistic model, Sugden (p. 28) describes these models as ‘credible
counterfactual worlds’ that give ‘some warrant for making inductive inferences
from model to the real world”
Now inductive inferences concerning states of affairs are problematic at the best of
times. But even overlooking this, we are entitled to ask: what does it mean to talk of
‘credible counterfactual worlds’? It appears to be accepted that worlds such as that
described by Schelling could not come about. So in what sense are they credible? We

Tony Lawson and His Critics
28
surely need to know this if Hodgson’s reference to Sugden is to help us understand
when or why some conceptions that are acknowledged as unrealistic remain useful.
It so happens, as I say, that in Economics and Reality I set out an analysis of
possible heuristics and related issues that can make sense of all this. This is something
to which I now need to return. Let me give a brief summary.
The method of successive approximation and heuristic assumptions
In Economics and Reality, in fact, I argue that two conditions are essential (though
by no means sufficient) to the success of this method of successive approximation
(relying on heuristic assumptions as interpreted by Musgrave and others). These are:
1) “that the factors considered in ‘isolation’ be real causal factors, structures and/or
transfactually acting mechanisms or tendencies; and
2) that the effects of the factors so considered in ‘isolation’ combine or interact
mechanically” (Lawson, 1997, p. 129)
These conditions, and the need to satisfy them, are easily grasped. Basically the idea
is to move from an understanding of a part of a causal story to an understanding of
more, or of all, of it.
This requires, first, that the features (treated as) isolated in thought be causal
mechanisms and that the nature of the causal parts, or individuals, viewed in isolation as
a first step, are not knowingly portrayed incorrectly. In other words, it is essential that
the intentional fictionising concerns not the manner of acting of the parts considered
separately (in isolation) but only the (heuristic) assumption of their acting in isolation
from (some) other factors affecting the total outcome.
Of course, this requirement, in its turn, presupposes that the way a causal mechanism
operates as it is found in reality is the same as it would operate in ‘isolation from (some)
other factors affecting the total outcome’ (or under the conditions assumed in the
heuristic exercise).
Notice too, that this requirement rules out the vast majority of theoretical
conceptions that are bound up with modern mainstream formalistic modelling.

Tony Lawson and His Critics
29
A second condition that must typically be satisfied if we are successfully to utilise
the method of successive approximation (or heuristics), that is if we are to achieve an
understanding of the whole by way of considering the workings of parts considered in
isolation, is that the effects of the different parts or causal elements can be aggregated,
that is combined additively or mechanistically. In contrast, if there are, say, emergent
powers of the more complex entity or whole irreducible to those of its parts considered
separately, then it is not clear that it is especially useful to proceed by seeking to
understand (or speculating about) how each part might act in isolation.
Notice too, that to make sense of the first condition (that the way a causal
mechanism operates as it is found in reality is the same as it would operate in isolation
from (some) other factors affecting the total outcome) we need the notion of
transfactuality. Something is said to be acting transfactually when it is having its
effect whatever the actual outcome. Gravity is pulling my computer keyboard to the
floor even as my desk acts to counteract this force and leave the keyboard at rest
(relative to myself) in front of me. In other words, the keyboard does not need to be
dropped in an experimental vacuum for gravity to have its effect. Similarly, the
aspirin acts to offset my headache even if my noisy environment and heavy drinking
countervail its effects and leave my head in a worse state. Such factors as gravity and
the aspirin, when triggered, act not counterfactually but transfactually. We can talk
not just of how they would (counterfactually) act in different non-actual but ideal
circumstances, but also of how, when triggered, they are continually transfactually
acting, whatever other forces are in play. The category of a tendency is reserved for
the effects of forces that are acting transfactually, i.e., whatever the actual outcome22.
It is when a mechanism is insulated from countervailing factors that (as in a well
controlled experiment) its tendencies and the outcome produced coincide.
Although advocates of the method of successive approximation, or the making of
heuristic assumptions, typically do not identify the two noted conditions for the
method of successive approximation to be successful, they can be seen to be built into
their illustrations. Consider the classic exposition of Alan Musgrave, concerning
Newton’s analysis of inter-planetary motion:
22 Notice that the point of a controlled experiment is to insulate some real causal factor (in
order to better empirically identify, or, just as commonly, to empirically verify [or not], the
manner in which a mechanism works). Significantly, however well the mechanism is insulated
(and insulation will rarely, if ever, be perfect) knowledge of the mechanism’s workings will
often allow us to say that, and how, it will operate outside the experiment, in the open system
of complex interacting reinforcing and countervailing forces. Clearly it is because many
mechanisms act transfactually that we can successfully apply knowledge achieved in the
(controlled) experiments, where event regularities are produced, to conditions where event
regularities are absent; for the result achieved apply first and foremost to transfactual
tendencies not to highly restricted and rare event regularities.

Tony Lawson and His Critics
30
“When Newton sought to discover what his theory predicted about the solar
system, he first neglected inter-planetary gravitational forces by ‘assuming’ that
there was only one planet orbiting the sun. He proved that, if his theory was
correct, the planet would move in an ellipse with the sun at one of its foci. This
assumption was not a negligibility assumption: Newton knew that planets would
sometimes have detectable gravitational effects on one another. Nor was it a
domain assumption: Newton was not saying that his theory only applied to one-
planet solar systems. You miss the point if you object that Newton's assumption is
false, because our system has more than one planet. You also miss the point,
though less obviously, if you object that the consequence of Newton's assumption
was false, because planets do not move exactly in ellipses. The consequences
drawn from heuristic assumptions do not represent the precise predictions of the
theory in question; rather, they are steps towards such precise predictions”
(Musgrave, 1981, p. 383).
Clearly, the method of successive approximation is found to be successful in the
case of Newton's analysis of inter-planetary motion, both because it is real
(gravitational) tendencies that are so considered (in isolation), tendencies that
seemingly operate transfactually whatever else is going on, and also because
gravitational tendencies do appear to combine mechanically.
Equally clearly, however, the conditions in question, and in particular the
requirement that causes combine mechanically, do not hold in general. Perhaps their
lack of universality is most readily apparent if we think of chemical reactions and
combinations. But mechanistic combining is hardly typical of social phenomena either.
For example the network of social relations so central to social life cannot meaningfully
be broken down into parts with some bits treated as though existing in isolation before
others are eventually added back in. It makes no sense at all to treat any feature in
isolation from another to which it is essentially related. In studying family behaviour,
say, it is clearly quite irrelevant to study conceptions of parental mechanisms apart from
conceptions of the nature, including needs, of children or the mutual relationship in
which parents and children stand. Equally, it is incoherent to consider the situation of
landlords/ladies in isolation from (conceptions of) tenants, or conceptions of employers
in isolation from those of employees, and nor does it make sense to consider capitalist
firms, markets and money in isolation from each other, and so on.
Pure and Applied Explanation

Tony Lawson and His Critics
31
There is a further point I want to pull out from all this, one that can perhaps be
made in the clearest way if I first distinguish pure from applied modes of explanation.
Briefly put, pure explanation is concerned with identifying and understanding causal
mechanisms; applied explanation is concerned with working out how already known
mechanisms conspired to bring about some concrete real world event or state of
affairs (see e.g., Lawson, 1997, chapter15). For example meteorologists pretty much
know the separate causal mechanisms that govern weather patterns; much of the pure
explanatory component has been done. Each day, though, at least in the UK (and
probably everywhere else after some novel weather pattern has been experienced) an
applied explanatory endeavour is initiated: the object becomes to explain the pattern
of behaviour just experienced utilising an understanding of causal mechanisms
already available (and drawn upon in explaining every other day’s weather patterns).
Now the point of drawing attention to this latter distinction here is to emphasise
that, to the extent that the method of successive approximation, or the making of
heuristic assumptions as understood here, have relevance at all in scientific
methodology, it is as a component of applied, not pure, explanation. The method in
question can be put to work only after the pure-explanatory work has been done. For
example, the heuristic assumption that only causal mechanism X is in play (or need be
considered), albeit as a first step, presupposes that causal mechanism X has already
been uncovered.
Thus in Musgrave’s analysis, Newton’s goal is not to construct a theory of
gravitational forces. This he already possessed. Rather the purpose (we are
informed23) was to show in a stepwise manner how his theory could ultimately
correctly predict inter-planetary movement.
Grounding counterfactuals
The reason I draw attention to this distinction is to indicate that it is only after a
causal hypothesis of interest is obtained, that is after the pure-explanatory stage, that it
may be legitimate for counterfactual insights concerning it to be generated. In other
words, a statement about a tendency that is transfactually in play will often license a
subjunctive conditional about what would have happened at the level of the course of
events if the system had been insulated from the activities of (some) other actually
operative mechanisms, or indeed if it had been in any other state.
23 Actually, I am not so sure of Musgrave’s explanation of Newton’s intentions (see below),
even if, as in this case, the conditions for method of successive approximation to be
successful appear to be satisfied.

Tony Lawson and His Critics
32
How we obtain our understanding (or hypotheses) of causal mechanisms of interest
is itself a complex process that I discuss at length elsewhere (see especially, Lawson
2003, chapter 4; but also see my responses to Caldwell and Ruccio in this volume).
Contrast explanation will often be important (operating under a logic of analogy and
metaphor amongst other things). But it may be merely that we abduct insights
obtained in other spheres (as I think may be the case of Schelling’s analysis - see
below).
Now I think it is this overall framework or understanding that Sugden is edging
towards with his notion of “credible counterfactual worlds”. If a mechanism does act
transfactually it licences a hypothetical statement about how things might be in a
different world. Descriptions of the different worlds to our own may be more or less
realistic. There is a sense in which alternative worlds seem more credible if the only
unrealistic aspect is the absence of actual mechanisms, as opposed to claims about
how identified mechanisms do, or could, actually work. This, I suspect, is the basis
for Sugden regarding such a counterfactual world as in some sense credible, despite
never being expected to occur.
But if it is, notice that it is not the fact of “ ‘credible counterfactual worlds’ that
give ‘some warrant for making inductive inferences from model to the real world”, as
Hodgson, following Sugden, puts it. Rather it is a prior understanding of the real
world that licences subsequent claims about certain counterfactual ‘worlds’ appearing
credible.
Notice too, that no matter how insightful a counterfactual analysis of this sort
might be, a comprehensive understanding of the causal process under study cannot
typically be captured or conveyed in this manner. Rather, to obtain a full (and indeed
ultimately practically useful) understanding of the situation, tendency statements must
be interpreted as categorical and indicative, to the effect that, if triggered, a
mechanism is really in play whether or not its effects are fully manifest.
In other words, to focus only on actual outcomes in counterfactual scenarios (real
or impossible) is typically to miss the main insights available. For if a mechanism
licensing a focus on ‘credible counterfactual worlds’ is indeed operative, then it is it is
having its effects anyway (transfactually); there is a tendency continuously in play in
our actual world, whatever the outcome. And this can be acted on. For example policy
can consequently be devised to reinforce or countervail such a tendency as required.
The dominant-mechanism special case
Of course, if a domain of reality is such that a causal mechanism focussed upon
(and treated as acting in isolation as a first theoretical step) is not only stable but

Tony Lawson and His Critics
33
dominating of other causal factors (and especially if all mechanisms in play do
combine mechanistically) it is likely that event patterns that the theory predicts are
recognisable in the outcomes actually achieved. But where this is so, the method fares
well not because false claims are providing insight in some mystical fashion, but
because the conceptions of mechanisms acting in relative insulation from
counteracting others are not that unrealistic after all (and so barely qualifying as
heuristics). Of course, it was in part to deal with such scenarios that I introduced the
notion of demi-regularities or demi-regs24
In other words, isolationist methods appear most legitimate and insightful (though
their ability to actually add much is questionable) precisely in situations where a
causal mechanism is so dominant it is (momentarily) effectively insulated from the
countervailing effects of other factors. That is, methods of theoretical isolation are
legitimised and express reality in a recognisable fashion precisely on occasions where
the isolation is not merely ‘theoretical’ but effectively actual. Needless to say, to
suppose that such occasions licence the ubiquitous reliance on such methods is to
overlook the rarity of the former.
An example of such a special case is the celestial patterning addressed by Newton
and referred to by Musgrave. Indeed, I suspect that Newton was as much concerned to
explain a demi-reg (the approximate ellipse traced out by the paths of many planets) as
to launch a project of successive approximation (in conditions where the mathematics
of dealing with the movements of more than two planets had yet to be developed, and
indeed was achieved only after Newton’s death). The celestial pattern arises because of
rather peculiar conditions that hold in the case of the planets, in that both their intrinsic
states as well as the extrinsic forces acting upon them are, in relevant respects,
sufficiently stable, at least over the time period with which most people are usually
concerned, i.e., over human life-spans. Properly interpreted, Newtonian mechanics
posits theories of how bodies (tend to) act; celestial phenomena function merely as
evidence of the postulated tendencies. Thus, if the intrinsic or extrinsic states of the
planets in our solar system were not so stable but were to change in some way, perhaps
a massive meteor were to pass through the solar system, then such a mechanics would
entail a consequent disruption of the familiar celestial phenomenal patterns.
24 Which in Economics and Reality I characterised as “a partial event regularity which prima
facie indicates the occasional, but less than universal, actualization of a mechanism or
tendency, over a definite region of time-space” (see also Reorienting Economics, chapter 4).
In Lawson 1997 I suggested that a demi-reg:
“[…] indicates the likely effects of a causal mechanism that frequently but not uniformly are
actualised over a particular region of time-space. The patterning observed will not be strict if
countervailing factors sometimes dominate or frequently co-determine the outcomes in a
variable manner. But where demi-regs are observed there is evidence of relatively enduring
and identifiable tendencies in play”

Tony Lawson and His Critics
34
The point is that although the celestial example is spectacular in nature, it represents
a relative rarity in constituting a spontaneous demi-reg of its sort. No doubt it is
precisely its spectacular nature that accounts in some part for the general failure from
Laplace onwards to realise that the situation is relatively uncommon, to appreciate that
the celestial demi-reg, or near closure supporting it, is far from being indicative of the
phenomenal situation that can be expected to prevail more or less everywhere. This
failure, in turn, appears to be largely responsible for the widespread, if tacit, acceptance,
formerly in philosophy, and currently in the social sciences in particular, of a ubiquity
of constant conjunctions of events in nature, and thus of the doctrine of the actuality of
‘causal’ laws. It no doubt also encourages the idea that methods of theoretical isolation,
or of successive approximation, or of heuristics and such like, have ubiquitous
relevance, when in fact conditions under which they are relevant, certainly as they are
formulated in modern mathematical-deductivist economics, appear to be circumscribed
indeed25.
Schelling
We are finally in a position to interpret the contribution of Schelling. And we can
now appreciate that Schelling’s analysis can be expected to be insightful if it captures
a real mechanism that operates transfactually, that is, that produces tendencies
towards ‘racial’ segregation, whatever else is going on.
As I understand Schelling’s (1969) analysis, the basic idea is as follows.
In a context in which
1) individuals perceive themselves as belonging to one or other of two mutually
exclusive and exhaustive groups and
2) (at least a significant number of) individuals prefer not to be located in a
situation where they are dominated or overwhelmed by members of the ‘other’
group, and
3) space that can be occupied is confined or restricted, or where grouping of some
kind must (for whatever reason) occur
there will be a tendency towards (some) segregation.
25 Perhaps too it a focus upon the rare (if sometimes rendered prominent) scenario, wherein
some mechanism dominates others (so that that treating it as if acting in isolation is not so
different from treating it realistically) that most encourages Hodgson in his view that “the
distinction (between theoretical isolation and abstraction) is, at least in prominent practical
instances, difficult to sustain”.

Tony Lawson and His Critics
35
I doubt this was ever news. Indeed, do we not all experience situations in which a
tendency of this sort is so dominant that it is even actualised. I certainly have, and
regularly. My earliest memories include glimpses of physical education lessons in
primary school where the teacher regularly asked the class of about 30 children to form
four or so groups. Invariably, as I recall, the groups were wholly male or wholly female
but not mixed. Today, I cannot but notice that in my workplace (Cambridge) coffee
room, the ‘support staff’ invariably avoid sitting next to ‘academic staff’ except on
occasions (such as outside of lecture term) when the number of academics present is
much reduced (and indeed no greater than the number of support staff).
Schelling’s contribution, I think, is to suggest that the mechanism in question –
basically a preference not to be dominated by perceived ‘others’ in a confined space – is
relevant to understanding racial segregation in the US, at least at a certain moment and
place in history. He points out that for purposes of the US census individuals are (or
were) classified as white or as black, and that many at least view themselves in this
fashion. Now to the extent that a majority (and perhaps almost all) individuals prefer
not to be overwhelmed by others of a different ‘colour’, and there is a restricted area in
which some population is located, we have reason to expect a tendency to racial
segregation.
Schelling suggests several more concrete claims that seem likely realistic and
consistent with his basic more abstract conception. Thus he mentions mechanisms
whereby “Whites may prefer to be among whites and blacks among blacks” (p.489);
or “whites may prefer the company of whites, while blacks don’t care” (p. 489) or
whereby “Whites and blacks may not mind each other’s presence, even prefer some
integration, but” [where there is] […] a limit to how small a minority either colour is
willing to be” (p. 489).
Schelling, though, does not develop an ontology of transfactual tendencies as set
out above. Instead, he writes as though countervailing factors are absent and
tendencies in play will all be realised (as outcomes or movements). For example:
“Whites and blacks may not mind each other’s presence, even prefer some
integration, but, if there is a limit to how small a minority either colour is willing to
be, initial mixtures more extreme than that will lose their minority members and
become one colour; those who leave may move to where they constitute a
majority, increasing the majority there and causing the other colour to evacuate”
(p. 489)
Clearly, this passage is easily rewritten in terms of tendencies and greater
contingency (‘tend to lose’ in place of ‘lose’, etc). When it is, it is this revised

Tony Lawson and His Critics
36
formulation in terms of tendencies that licenses the passage as written (not the other
way round).
Of course it may be that Schelling believes that ‘colour preferences’ dominate all
countervailing factors. If so then his formulation might be accepted as it is, as a claim
intended to be realistic with respect to the real world.
Schelling and counterfactuals
Alternatively, the implicit claim that only ‘colour preferences’ are effective (or that
they dominate) can be interpreted as a heuristic assumption. Proceeding on this
interpretation seems legitimate, although the point of it is not clear. The language of
tendencies conveys all the insights that could be so expressed (and indeed more). The
aim could be to do as Musgrave suggests and add in complicating factors bit by bit.
But then we would need to know that the effects of Schelling’s mechanism, and of
those yet to be identified, aggregate in a mechanical fashion. I see no reason to expect
this and Schelling reveals no inclination to proceed in this fashion.
Instead, Schelling continues by imagining yet more concrete or detailed scenarios
that conform not at all to the world in which we live or to one we could reasonably
expect to occur. He constructs fictitious set-ups (e.g., “a line along which blacks and
whites […] have been distributed in equal numbers and random order” [p. 489]), and
assumes that individuals can move freely [and repeatedly move] according to fixed
rules, identical for everyone, without costs or countervailing forces of any kind, and
so forth.
I am not at all sure that this additional analysis provides any insight other than to
the very specific properties of the very particular set-ups or ‘models’ considered. Any
understanding concerning the real world is already contained in the analysis of
tendencies. What is going on is that the concern with modelling for its own sake at
this point takes over.
Interestingly enough Schelling (1969) does not actually construct any
mathematical model as such. As a result, Hodgson’s claim that Schelling’s
contribution is a demonstration of the benefits of “a formal heuristic” is erroneous
from the outset. Still there is little doubt that the just discussed assumptions
introduced by Schelling facilitate or encourage a mathematical modelling approach.
And it is also clear that whatever the precise nature of Schelling’s own early piece it
eventually stimulated many papers of a more formalistic kind.

Tony Lawson and His Critics
37
The point to emphasise, though, is that these later papers, or modellers, did not
generate the insights we associate with Schelling, but rather they drew upon them in
an attempt to legitimise their modelling endeavour. Any new insights obtained
concerned merely the properties of the (increasingly complex and unrealistic)
formalistic models. Assumptions are made just to get certain desired patterns or
results (elegantly) to emerge26.
If I am correct in my analysis of all this the question that clearly arises is “why
bother?” Why the interest in models for their own sake? The answer, of course, is the
situation I have been actively attempting to counteract throughout much of my
writing: the widespread idea that mathematical modelling is in itself a necessary
feature of any respectable economic theorising.
Heuristics and causal mechanisms
Let me at this stage return to Hodgson’s particular critique. It will be remembered
that according to Hodgson: “The purpose of a heuristic is to identify possible causal
mechanisms that form part of a more complex and inevitably open system”. I have
shown that, to the contrary, the heuristic assumptions can go to work in economic
methodology only after causal mechanisms of interest have already been identified or
at least hypothesised. Schelling (1969) I have suggested illustrates just this.
After setting out his own outline of Schelling (1969) Hodgson adds:
“I have suggested above that heuristics are appropriate if they successfully abstract
an important causal mechanism in reality. Accordingly, heuristics relate to the very
process of abstraction that Lawson himself highlights. But Lawson suggests that
heuristics are isolations rather than abstractions. So here I must return to Lawson’s
(1997, p. 236) attempted distinction between isolation and abstraction, as quoted
above. According to him, the key difference is ‘between leaving something
26 At this point I am minded once again of Frank Hahn’s awakening to the nature of this sort of
state of affairs (even if Hahn mistakenly supposes that those who recognise it more
immediately are disposed to being anti-mathematics [as opposed to being anti- the abuse of
mathematics]):
"[…] there is [...] a lesson which has only gradually been borne in on me which perhaps
inclines me a little more favourably to the "anti-mathematics" group.
The great virtue of mathematical reasoning in economics is that by its precise account of
assumptions it becomes crystal clear that applications to the "real" world could at best be
provisional. When a mathematical economist assumes that there is a three good economy
lasting two periods, or that agents are infinitely lived […] everyone can see that we are not
dealing with any actual economy. The assumptions are there to enable certain results to
emerge and not because they are to be taken descriptively" (Hahn, 1994, p. 246).

Tony Lawson and His Critics
38
(temporarily) out of focus and treating it as though it does not exist’. Again take
the Schelling model as an example. Schelling himself accepts that bigoted racists
exist, yet he leaves them out of his model. The purpose of the model is not to
excuse or deny racism, but the more severe forms of racism are deliberately
removed. Nevertheless, the model is extremely and worryingly persuasive”
Here Hodgson seems to make the same mistake as before. Let us be clear. Where a
causal mechanism is in play we can focus momentarily upon it, and leave
countervailing factors and so forth aside. If the causal mechanism is of a sort that it
will have these effects whatever the context, i.e., whatever the relations in which it
stands to other causal structures, then clearly it follows that the way it would operate
in isolation is equivalent to the way it will operate as we find it in the real world. In
such a scenario, it is not illegitimate, and there may be some utility, if, as a first step
to an analysis, we adopt the heuristic assumption that the causal factors left out of
focus do not exist, or are sealed off. This will clearly be especially the case if the
omitted factors appear insignificant compared to the factor on which we focus.
But to describe this situation with the words: “heuristics are appropriate if they
successfully abstract an important causal mechanism in reality” is to get things the
wrong way round. A correct statement is rather of the sort that “heuristics are
appropriate (if at all) where an isolatable causal mechanism has already been
abstracted”. And from this it does not quite follow, as Hodgson would have it, that
“Accordingly, heuristics relate to the very process of abstraction that Lawson himself
highlights”. Rather it follows only that the appropriate use of heuristics depends (like
everything else) on the very process of abstraction that I highlight.
The heuristic, in the given context, is the assumption that factors out of focus have
no effects, that they can be treated as sealed off or non- existent, that the mechanism
in focus is acting in (relative) isolation. It is thus indeed the case that “heuristics are
isolations rather than abstractions”.
In the second part of the passage Hodgson writes that although Schelling ignores
factors such as ‘bigoted racists’ Schelling’s “model is extremely and worryingly
persuasive”
I myself am not sure how useful it is to treat Schelling’s mechanism as a heuristic
first step, as I have already indicated. But whether or not it is useful to do so, any
insight to Schelling’s analysis arises only because it first captures a case (albeit a
special one) of a mechanism that can be regarded as realistic. Why any persuasiveness
thereby imparted should be worrying I do not know. Moreover, the consequences of
some individuals holding racist views are likely incorporated anyway; certainly

Tony Lawson and His Critics
39
Schelling does not examine or distinguish the various grounds for preferences
regarding racial segregation, so there is no reason to suppose that bigotry is excluded.
Now I am well aware that I have only provided an interpretation of what is going
on and that it is open to contestation. But I do believe I have set out a defence of a
framework that can render coherent the various issues before us. Certainly, I do not
find much that is coherent in Hodgson’s few criticisms; and nor actually am I aware
of an equally coherent alternative framework provided elsewhere. Hodgson is very
wide of the mark indeed when he suggests that I do not consider the possible heuristic
value of formal models, and that I ignore the role of context. At the very least, I think
we must accept that if there is insight to be gained from treating formal models as
heuristic devises the case for this has yet to be made. If Hodgson feels compelled to
establish this point I think he must first do a bit more work. In any case there is
nothing here to encourage the view that abstraction is the same as theoretical
isolation.
An alternative interpretation
Let me, though, add a qualification to all this. For many reasons it is vital to be
charitable in debate, and perhaps there is a more charitable reading of what Hodgson
is saying. The preceding discussion does seem to me to be the most accurate reading
of Hodgson, in that he writes that the “purpose of a heuristic is to identify possible
causal mechanisms”, and that the “purpose [of heuristics] is to establish a plausible
segment of a causal story, without necessarily giving an adequate or complete
explanation of the phenomena to which they relate”, and so forth. And I did want to
respond to what seems to be the most comprehensive as well as accurate
interpretation of Hodgson’s position. But it is possible that Hodgson is simply
suggesting that when we make heuristic assumptions and consider features as if in
isolation it is important that those features treated as isolated be real causal
mechanisms. That is, it is feasible that Hodgson is not at all suggesting that heuristic
is somehow bound up with the process of identifying a causal mechanism but rather
that heuristic (to be successful) needs to be is employed in an analysis in which a
mechanism has already been identified.
If this is the correct interpretation of his position, Hodgson has seemingly
expressed himself rather misleadingly, but at least this would be a claim on
Hodgson’s part that seems sustainable.
However, the nature of my response is still much the same (albeit I could perhaps
have made it significantly shorter). Specifically, it remains the case that it is an

Tony Lawson and His Critics
40
achieved understanding of the actions of a transfactually-active causal mechanism that
licences the subjunctive conditional or counterfactual, that sets the boundaries of, and
illuminates, ‘credible counterfactual worlds’; it is not the other way round. And
fundamentally, it still does not follow that theoretical isolation or “heuristics relate to
the very process of abstraction” in the sense of being much the same thing.
For sure, to consider a transfactually active mechanism as if it were isolated from
countervailing factors involves abstraction. But to assume thereby that this method of
isolation, or the use of heuristics involved, is the same as abstraction (even if the
focus is a scenario of a single dominant mechanism in operation), is simply a mistake.
Abstraction, as earlier noted, is involved in theorising both the real and the fictional,
the open and the closed and equally both the isolated and non isolated; indeed it is a
part of all forms of conceptualisation or theorising. To conclude that because
abstraction is involved in some special case it thereby reduces to, or is somehow
intrinsically bound up with, that special case is a conflation that simply does not bear
considering further.
So, in short, we can see that, whichever way Hodgson is arguing it, the distinction
between abstraction and theoretical isolation cannot be dissolved and in fact
(especially given the apparent rarity of the conditions in which the latter is likely
useful) remains vital to successful explanatory endeavour.
3) The distinction drawn between abstraction and theoretical
isolation is insufficiently precise.
Hodgson’s third charge is that the distinction I draw between abstraction and
theoretical isolation is insufficiently precise. I hope, though, that is by now clear that
this is not so, and that I have said enough to demonstrate that the two methods are
indeed irreducible one to the other. Still let me go through Hodgson’s last strand of
argument to illustrate this one more time.
Hodgson considers a case in which some factor X (trade with other nations) is
ignored (in an analysis of the workings of a national economy), and questions whether
ignored meaning being-not-mentioned (abstraction) is not the same as ignored
meaning treated-as-having-no-influence or not-existing (theoretical isolation)
He writes of the former (abstractionist) scenario:
“Surely, some verbal statement would be required, acknowledging the existence of
international trade, explaining its omission from the current discussion, and
suggesting that further work must be done to incorporate it into the analysis. But

Tony Lawson and His Critics
41
this is also the kind of necessary qualification that we should expect from the best
presentations of heuristic models”
Actually, I think it is typically only in the case of theoretical isolation that mention
of specific omissions is warranted. Analysis never starts from complete ignorance;
much is always taken for granted but remains unstated. As I noted earlier, most social
theorists take gravity as given (they abstract from it) in social analysis, but rarely
acknowledge or explain that omission. If in contrast they wanted to assume its effects
were absent or sealed off, this would most certainly warrant a mention, and an
explanation. For under such a heuristic assumption our planet (if indeed there was one
at all) would be very different indeed.
In similar fashion, when an economist discusses aspects of an economy such as the
UK, its trade with other nations might not get a mention (be abstracted from); but it
would nevertheless be presupposed. The focus may be on the workplace, say on
improving work security, or on gender mainstreaming in employment strategy. In
each such case trade may not be mentioned (it may be abstracted from); because most
social theorists take for granted the fact that the UK is a trading nation. But if trade
were assumed away, rather than treated as a background causal factor, this once more
would certainly warrant a mention and an explanation. For life in the UK, under such
an assumption, would be very different indeed to life in the UK as we currently know
it27. There is no support here for the thesis that abstraction and theoretical isolation
cannot be distinguished.
Hodgson continues:
“On the other hand, it would be impossible to mention all the things that we have
left out of the account. In this sense all theory is ‘temporary’. But do such
unmentioned omissions amount to treating some causal linkages as though they do
not exist? If this were the case, then every theory, including non-formal, discursive
theory, by Lawson’s criteria is a failure. Once we try to apply Lawson’s criteria,
then their insufficiency and vagueness become apparent, and his attempted
distinction between abstraction and isolation is revealed as highly problematic”
27 Any resulting analysis would be extremely different. This absence would mark most of the
UK’s internal economic institutions, as well as the sorts of political activities undertaken. All
goods, including technology, would be home produced. Competition would presumably be
internally generated. International pressures affecting security at work policies would be
absent. The economy would not (need to) be part of trading blocks. Presumably factors like
the European Employment Strategy would have no impact. There would be no scope for
policies like export-led growth or import quotas. There is no obvious reason why movements
in world commodity prices would have any impact, etc, etc.

Tony Lawson and His Critics
42
The first two sentences here are surely correct. But it does not at all follow that to
not mention a causal linkage is thereby, of necessity, to treat it as not existing, or as
being sealed off. As I say, it is not at all the case that a social analysis that neglects to
mention the gravitation is necessarily operating thereby under the assumption that
gravity does not exist. That is one reason abstraction is so useful.
In short, it is clear that there is nothing in all this that in any way threatens the
distinction between abstraction and theoretical isolation or renders it ‘highly
problematic’. It may well be that the method of isolation is found to have little utility.
But the distinction in question, between the practice of not focusing on something and
assuming its effects are somehow absent or sealed off, remains as clear and vital to
social theorising as ever.
Concluding Comments
Despite the emphasis that mainstream economists place on methods of
formalistic modelling (or perhaps because of it), they make relatively few attempts to
justify their orientation. This is surely a significant absence leading in and of itself to
an impoverishment of the discipline, whatever else might be going on. Hodgson’s
spirited intervention to make a substantial defence of forms of formalistic modelling,
and/or the manner in which mathematical-economic models might fruitfully be
interpreted or utilised, is thus to be welcomed. He performs an important service. For
reasons given, however, I am not convinced by Hodgson’s efforts so far. But
knowing Hodgson, I suspect he will persevere further in this, and I am confident we
will all be the better for it, whatever may be the conclusions that are reached along the
way.
Addendum
At the end of 2006, after I had completed the foregoing response to his Post-
Autistic Economic Review piece, Geoffrey Hodgson kindly presented me with a copy
of his new book Economics in the Shadows of Darwin and Marx. It contains a revised
longer version of his PAE Review paper. In this longer version, Hodgson expands
some of his arguments and adjusts some of his rhetoric. But I find nothing in it to give
me reason to revise or qualify anything written above.

Tony Lawson and His Critics
43
However, Hodgson does introduce one seemingly new line of argument in his later
text. There is an extra section tagged on asking whether economists should be allowed
to embrace false assumptions. This contains an additional criticism of me:
“Lawson (2002, p. 76) warns against false assumptions, proposing that if they are
allowed ‘it is clearly possible to derive any conclusions whatsoever – true ones or
false ones – simply by deductive logic’. The argument is wrong. If I make the
(false) assumption that ‘the economy consists of just two goods’ then there is no
way we can deduce from that proposition alone that the economy consists instead
of four, five or a million” (Hodgson, 2006, p. 128).
But my argument is not wrong. What is wrong is Hodgson’s representation of it.
The first sentence in this passage makes reference to the claim (by me) that a specific
suspect practice (allowing false assumptions) makes it feasible for the modeller to
generate any conclusions. The contention ridiculed in the third sentence is that any
specific suspect model can be used to generate any conclusions. The mistake,
Hodgson’s not mine, is to suppose that the latter contention follows from the former.
Let me be clear. I do point out that if false assumptions are allowed, then for any
conclusion X, I can always find some allowable set of assumptions Y, from which X
can be deduced. For example if (to use Hodgson’s construction) the desired
conclusion X is “the economy consists […] of four, five or a million [goods]”, then I
can assume 1) the number of goods in the economy is the same as the number of days
in a week; and also 2) the number of days in a week is four, five or a million. The
desired result follows by deduction. But if the suspect practice in question (of
allowing assumptions thought to be false) allows me to generate any result, it does not
at all follow that once I specify some particular model H (e.g. ‘the economy consists
of just two goods’) that any conclusion (such as X) can be drawn it. Hodgson’s charge
simply rests on a non-sequitor.
In Lawson (2002), I do give illustrations. In fact, at the point where Hodgson
paraphrases me I write:
“Now if, and once, falsity (in this broad sense) of assumptions is allowed, it is
clearly possible to derive any conclusions whatsoever -- true ones or false ones --
simply by deductive logic. Thus suppose I want to deduce the (apparently true)
proposition that ‘all ravens are black’. One way I might do it is by including in my
assumptions, the propositions: "all ravens are vegetables" and "all vegetables are
black". Clearly my desired conclusion follows by deductive logic. In similar
fashion if I want to deduce that "agent X does Y", I need only assume (i) that a
situation prevails in which it is rational (in a specific sense) for a situated agent X
to do Y, along with the assumption (ii) that X always acts rationally in the

Tony Lawson and His Critics
44
specified sense. The assumptions about the situation and human capabilities and
their exercise need not be realistic, merely facilitating of mathematical modelling
tractability. What could be more trivial and more pointless?”
Of course, my focus in the paper in question is specifically on strategies of
mathematical-deductivist modelling. It is in this context that I look at the
consequences of the practice of allowing assumptions considered by everyone to be
false. The reason I do so, it should be clear, is precisely that, given the nature of social
reality, the mainstream insistence on a formalistic modelling orientation regularly
necessitates the reliance on such accepted-as-false assumptions. My point is that
because the construction of such assumptions is considered legitimate practice (i.e.,
the restriction of being realistic is removed), the mainstream ‘theorist’ or modeller can
always find some way of generating a particular desired result28.
In any case, I hope it is now clear enough that in Lawson (2002) I am, at the
relevant stage of the discussion, not at all concerned with the properties of any
specific model29. As I say, the mainstream insistence on a formalistic modelling
strategy in economics requires that a reliance upon thought-to-be-false assumptions be
an allowed practice. I am merely pointing out how easy it is to generate any desired
conclusions once such a practice (that Hodgson seems to be encouraging) is
sanctioned, and questioning the value of such activity30.
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28 The specific challenge for formalistic modellers in economics is to start from ‘results’ widely
accepted as plausible and to work back to assumptions relating in effect to a closed world of
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