What Is Structural Empiricism? Scientific Change in an Empiricist SettingAuthor(s): Otávio BuenoReviewed work(s):Source: Erkenntnis (1975-), Vol. 50, No. 1 (1999), pp. 59-85Published by: SpringerStable URL: http://www.jstor.org/stable/20012902 .Accessed: 17/09/2012 20:45

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OTAVIO BUENO

WHAT IS STRUCTURAL EMPIRICISM? SCIENTIFIC CHANGE IN AN EMPIRICIST SETTING

ABSTRACT. In this paper a constructive empiricist account of scientific change is put

forward. Based on da Costa's and French's partial structures approach, two notions of

empirical adequacy are initially advanced (with particular emphasis on the introduction

of degrees of empirical adequacy). Using these notions, it is shown how both the infor

mativeness and the empirical adequacy requirements of an empiricist theory of scientific

change can then be met. Finally, some philosophical consequences with regard to the role

of structures in this context are drawn.

Now, we daily see what science is doing for us. This

could not be unless it taught us something about reality; the aim of science is not things themselves, as the

dogmatists in their simplicity imagine, but the relations

between things; outside those relations there is no reality knowable.

Henri Poincar? (1905), p. xxi

1. THE PROBLEM

In this paper, I am concerned with presenting some suggestions towards

the development of a constructive empiricist view of scientific change. As is well known, Bas van Fraassen has advanced and developed a com?

prehensive research programme aimed at the formulation of a particular

(empiricist) interpretation of the scientific undertaking. As an alternative

conception to several antagonistic views (ranging from scientific realism to

versions of scepticism and relativism), his proposal constitutes perhaps one

of the best articulated empiricist conceptions in contemporary philosophy of science (for details, see van Fraassen 1980, 1985, 1989, and 1991).

Being well articulated is, of course, compatible with having its diffi?

culties. And I want to address here a point that, in the realism-empiricism debate, has received a massive attention in the realist side, but no compa? rable consideration in the empiricist camp (especially by the constructive

empiricist). The realist puts forward a challenge for the anti-realist claim?

ing that, in Putnam's words, 'the positive argument for realism is that it

^* Erkenntnis 50: 59-85, 1999.

l\ ? 1999 Kluwer Academic Publishers. Printed in the Netherlands.

60 OTAVIO BUENO

is the only philosophy that doesn't make the success of science a miracle'

(Putnam 1979, p. 73). Realism is thus taken as the best (and even the only)

explanation of the success of science, and at least according to Putnam,

this supplies a positive argument for realism - which is now known in the

literature as the 'no-miracles' argument. Given the importance of this ar?

gument for realism, it comes as no surprise that the constructive empiricist addresses the issue of the success of science brought by it. The difficulty

here, and this supplies the main motivation for the present proposal, derives

from the question-begging nature of the constructive empiricist's defensive

strategy regarding this argument. Indeed, the chief empiricist claim con?

sists in pointing out that there are limits to the demand for explanations, and that questions concerning scientific progress and the success of science

lie beyond these limits. Thus, claims the empiricist, there is no real point in answering the realist 'challenge'.1

It is plain that the empiricist has reasonable grounds for reaching this

conclusion. The problem is that these grounds are question-begging: they

rely on an assumption (about the limits to the demand for explanation) -

which is not shared by the realist proposal, but is typical of the empiricist view - in order to present a defence of empiricism. In other words, the

main strategy adopted by the empiricist against the 'no miracles' argument, based as it is on the limits to the demand for explanation, assumes from the

outset a feature that a realist is not willing to concede, namely, the existence

of such limits. And even if this feature were not simply assumed, but really

argued for, it would constitute a highly controversial issue in the debate.

So, the empiricist cannot claim that he or she is not required to explain the

predictive success of science if this feature is taken by the realist as the

very trait of science that an empiricist cannot account for!2

Of course, the no-miracles argument, for this very reason, is similarly

question-begging when adopted by the realist against the empiricist, given that it assumes, at least in some versions, a conceptual commitment that

clearly is not admitted by the empiricist: the establishment of the truth, or

approximate truth, of scientific theories on the basis of their empirical suc?

cess. As we shall see, this constitutes a weakness of the realist argument, at least if it were meant to turn the empiricist into a realist philosopher. So,

both the realist and the empiricist ground their cases on question-begging

strategies. The debate, thus, seems not to be advancing much.

My problem then consists in putting forward an empiricist non-question

begging answer to circumvent the realist's challenge. In order to do so, I

shall first briefly present, in Section 2, the general conceptual setting within

which I will be working, in terms of da Costa's and French's notions of

partial structures and quasi-truth. Using these tools, I shall consider next

WHAT IS STRUCTURAL EMPIRICISM? 61

the main elements involved in the presentation of an empiricist proposal of scientific change. In Section 3, I will put forward a notion of degree of empirical adequacy. In terms of this notion, I will consider, in Section

4, certain criteria of theory choice, acceptable to the empiricist, and a

particular pattern that describes some features of theory change in science.

These criteria and this pattern shall supply a non-question-begging an?

swer to the realist challenge at least in the following sense: in contrast to

the standard empiricist reply, they offer a positive, empiricist account of

theory change without assuming the existence of limits to the demand for

explanation. Of course, the existence of such limits is not denied (this is a

cherished empiricist idea after all). The point is simply not to use it against the realist, who will never grant it, nor will ever be satisfied with an answer

to his or her challenge in terms of it. Indeed, in claiming that there are such

limits, the empiricist is simply denying the point of the realist challenge. In

this respect, van Fraassen has unnecessarily adopted a too restrictive line

for dealing with this challenge, which prevented him of making a stronger case for constructive empiricism.

In my view, the empiricist can adopt a different strategy -

provided he or she also adopts the partial structures approach. The realist requires a positive account of theory change and an explanation of the success of

science, and claims that the empiricist cannot present either. The answer

to be advanced here is simply to outline, in terms of partial structures, an empiricist account of both. In this sense, the issues considered in this

paper lead to a stronger constructive empiricist proposal, one that examines

these two problems left behind by the original version - problems, I insist,

that according to the realist, the constructive empiricist could never take

into account. This, of course, enhances the empiricist case, extending the

programme to new domains. I intend then to draw, in Section 5, some

philosophical morals from the previous discussion, advancing structural

empiricism as a possible candidate to supply a distinct (and hopefully more

adequate) perspective on the issues under consideration.

In a future article, I shall illustrate the account advanced here with a

case-study, considering an actual example of scientific change. The aim of

the present paper is only to lay down the formal framework.

2. THE BASIC FRAMEWORK: PARTIAL STRUCTURES AND

QUASI-TRUTH

Throughout this piece, I shall be working within the conceptual setting determined by partial structures and quasi-truth, which was originally for?

mulated by Mikenberg's, da Costa's and Chuaqui's paper on pragmatic

62 OTAVIO BUENO

truth (see their 1986), and later extended to accommodate issues in the in?

terpretation of probability theory (da Costa 1986), in the logic of induction

(da Costa and French 1989), in the model-theoretic approach in the phi?

losophy of science (da Costa and French 1990), in theory acceptance (da Costa and French 1993a), as well as in the modelling of 'natural reasoning'

(da Costa and French 1993b), among others. I shall now present the main

tools supplied by this view.

The investigation of a particular domain A of knowledge can be viewed

as involving the determination of certain relations among its objects. As a

matter of fact the information with regard to these objects is in general

considerably 'incomplete', in the sense that it is unknown whether the

relations concerned can be applied to every (n-tuple of) object(s) of the

relevant domain. It is precisely this situation that the notion of a partial relation is meant to model. Indeed, as introduced by da Costa and French, a relation is partial in the sense that it is not defined for every object (or

w-tuple of objects) of a domain D under consideration. More formally, an

rc-place partial relation R can be viewed as a triple (Rx, R2, R3), where

Rx, R2, and R3 are mutually disjoint sets, with Rx U R2 U R3 = Dn, and

such that Rx is the set of rc-tuples that belong to R; R2 the set of n-tuples that do not belong to R; and finally R3 of those n-tuples for which it is not

defined whether they belong or not to R (note that when R3 is empty, R is

a normal n-place relation that can be identified with Rx; see da Costa and

French 1990, p. 255, note 2). Of course, in order to represent certain traits of our patterns of mod?

elling information, one needs more than partial relations: a convenient

(and corresponding) notion of structure is also required. Such a notion,

it is worth noting, is likewise conceived as encompassing the 'openness'

typical of our epistemic situation (in which we face, with considerable

frequency, 'incomplete' information).3 Moreover, its use in this context

is meant to highlight the particular role of structures in the process of

representing bits of empirical information - a point, as will be clear in

a moment, of particular relevance for my present purposes. Meeting these

demands, and based on this notion of a partial relation, it is natural to in?

troduce the concept of a partial structure. A partial structure is an ordered

pair (D, Ri)ieI, where D is a non-empty set (that represents the objects

employed in the syst?matisation of the relevant domain of knowledge A,

whose study one is concerned with), and (/?,-),-eI is a family of partial relations (in the sense just presented) defined over D.

Such structures can be employed as basic components in the under?

standing and modelling of certain features of scientific activity, in particu? lar with regard to the use of models in certain branches of science (see da

WHAT IS STRUCTURAL EMPIRICISM? 63

Costa and French 1990, and da Costa and French 1997). But they have a

second, more 'formal', function as well. They can be employed in order to

formulate a particular notion of truth, that extends Tarski's account, leading to the characterisation of the concept of quasi-truth. As a matter of fact,

partial structures display here nearly the same role that the formal concept of interpretation (viewed as a total structure) has in the usual Tarskian

semantics: if truth is defined depending on an interpretation, quasi-truth is defined depending on a partial structure.

The connections between truth and quasi-truth, however, are still tighter. The whole strategy of defining the latter consists in introducing an 'inter?

mediary' kind of structure, so that the former can be employed. Indeed,

given that Tarskian semantics was constructed only for total structures, it

is necessary that a total structure be obtained from a partial one through a process of 'filling in' its partial relations. Such 'filled in' structures are

called normal structures. More formally, given a pragmatic structure A =

(D, Ri, P)ieI, we say that the structure B = {Df, R?)ieI is an A-normal

structure if the following conditions are met: (1) D = D'\ (2) every con?

stant of the language in question is interpreted by the same object both in

A and in B; and (3) each R? extends the corresponding partial relation R?, in the sense that each R?, supposed of arity n, is defined for all n -tuples of elements of Df (that is, the Rf3-component of R[ is empty). Notice that,

although each R? is defined for all w-tuples over Dr, it holds for some

of them (the R[x-component of R[), and it doesn't hold for others (the

/^-component). As a result, given a partial structure A, there may be too many A-normal

structures. Suppose that, for a given n-place partial relation R?, we don't

know whether Rta\.. .an holds or not. One way of extending Rt into a full

R[ relation is to look for information to establish that it does hold, another

way is to look for the contrary information. Both are prima facie possible

ways of extending the partiality of R?. But the same indeterminacy may be

found with other objects of the domain, distinct from a\.. .an (for instance, does R[b\.. .bn hold?), and with other relations distinct from Rt (for exam?

ple, is Rjb\.. .bn the case, with j ^ il). In this sense, there are too many

possible extensions of the partial relations that constitute A. Therefore, we

need to provide constraints to restrict the acceptable extensions of A.

In order to do that, we need first to formulate a further auxiliary notion

(see Mikenberg, da Costa and Chuaqui 1986). A pragmatic structure is

a partial structure to which a third component has been added: a set of

accepted sentences P, which represents the accepted information about the

structure's domain. (Depending on the interpretation of science which is

adopted, different kinds of sentences are to be introduced in P: realists will

64 OTA VIO BUENO

typically include laws and theories, whereas empiricists will tend to add

certain laws and observational statements about the domain in question.) A pragmatic structure is then a triple A = (D, Rt, P)ieI, where D is

a non-empty set, (/?,-)/ / *s a family of partial relations defined over D, and P is a set of accepted sentences. The idea, as we shall see, is that P

introduces constraints on the ways that a partial structure can be extended.

Our problem now is, given a pragmatic structure A, what are the nec?

essary and sufficient conditions for the existence of A-normal structures?

We can now spell out one of these conditions (see Mikenberg, da Costa and

Chuaqui 1986). Let A = (D, Rt, P)ie? be a pragmatic structure. For each

partial relation R?, we construct a set M? of atomic sentences and negations of atomic sentences, such that the former correspond to the rc-tuples which

satisfy Ri, and the latter to those n -tuples which do not satisfy Rt. Let M be

U/ /M/. Therefore, a pragmatic structure A admits an A-normal structure

if, and only if, the set M U P is consistent. (For further discussion, see

Bueno 1997, Section 3.1, and Bueno and de Souza 1996.) It is plain that such a normal structure is constructed in order to present

an interpretation of the language that was fixed in the (relevant) context.

This was, to some extent, the strategy devised by Tarski to formulate, in

a rigorous way, the concept of truth: the latter is defined in a structure.

One finds the same feature in the formulation of the concept of quasi truth. One says that the sentence a is quasi-true in a pragmatic structure

A = {D, Rh P)ieI, according to the A-normal structure B = (D\ R?)ieI,

if a is true in B (in the Tarskian sense). If a is not quasi-true in S according to B, one says that a is quasi-false (in S according to B). Of course, if

we are dealing only with full structures, Tarski's definition is obtained as

a particular case. In this sense, quasi-truth provides a generalisation of

Tarski's account.4

With these definitions, one can then proceed to consider, from a com?

prehensive viewpoint, several problems in the philosophy of science. I in?

tend now to examine one of them, using the present framework to enhance

the empiricist case.

3. EMPIRICAL ADEQUACY: ITS DEGREES AND CHARACTERISATIONS

In order to present an empiricist answer to the no-miracles argument, I

shall adopt a strategy that can be divided into two parts. The first step consists in formulating a convenient notion of empirical adequacy, that

allows, in particular, the introduction of degrees of empirical adequacy. Based on this, I shall then propose a model of scientific change, compatible

WHAT IS STRUCTURAL EMPIRICISM? 65

with the main theses of constructive empiricism, and with this model at

least part of the realist challenge can be met - or so I shall argue. In an empiricist setting, the concept of empirical adequacy is of para?

mount importance. The very aim of science, in van Fraassen's view (see

1980, p. 12), is presented in terms of it. Assuming the semantic approach to

science, according to which the analysis of scientific theories should focus

on the study of their models (instead of their linguistic formulations),5 van

Fraassen asserts that the empirical adequacy of a theory T depends on

three model-theoretic components (see 1980, p. 64): (1) a particular theo?

retical model of T, (2) certain empirical substructures of this model (that is, 'candidates for the direct representation of observable phenomena', which

are in fact substructures, in the model-theoretic sense, of the structures

provided by T), and (3) the appearances (or structures 'described in ex?

perimental and measurement reports'). The first two components come, of

course, from the theory side; the third, from the experimental one. They are linked, at least in this characterisation, by an isomorphism between

the appearances and the empirical substructures of a particular theoretical

model. In van Fraassen's own words: 'the theory is empirically adequate if it has some model such that all appearances are isomorphic to empirical substructures ofthat model' (1980, p. 64).

Elsewhere, I have discussed in detail certain criticisms of van Fraassen's

formulation (Bueno 1997). These criticisms (see, for instance, Su?rez

1995) are based on the claim that there are scientific contexts (in Su?rez's

case, the construction of the first model of the Meissner effect in super?

conductivity, the so-called London model) in which a theory is taken to be

empirically adequate despite the presence of relations in the phenomena that have no counterpart in the theoretical models. In order to circumvent

these critiques, two further characterisations of empirical adequacy, en?

tirely compatible with constructive empiricism, have been suggested (see Bueno 1997, Sections 3 and 4). The point of recalling them here is simply that these characterisations allow the introduction of degrees of empirical

adequacy, a notion that shall be crucial, as we will see, for the problem under consideration.

3.1. Partial Isomorphism and Quasi-Empirical Adequacy

The first formulation is based on the concept of partial isomorphism (as

suggested in French and Ladyman 1999; see also Bueno 1997). Roughly

speaking, a partial isomorphism is an isomorphism between partial struc?

tures. As I have noticed in Section 2, a partial relation R is characterised as

an ordered triple (R1, R2, R3). Thus, in order to formulate an isomorphism between two partial structures M =

(D, Ri)i l and M' = (Df, R?)ieI,

66 OTAVIO BUENO

one should consider the main features of the three components that con?

stitute each partial relation. Here is a tentative proposal: given two partial structures M = (D, Rt) and M' =

(D', R[) (where Rt = {Rx, R2, R3)

and R? =

(R'x, Rf2, R'3), for some / e I, are, for instance, binary partial

relations), one says that the function /: D -> Df is a partial isomorphism between M and Mf if (i) / is bijective, and (ii) for every x and y e D,

Rjxy o R[lf(x)f(y) and Rfxy *> R,2f(x)f(y). (In particular, when

Rf and Rf3 are empty - in other words, when we are considering total

structures -, one has the standard notion of isomorphism.) As I have mentioned, an interesting feature of partial structures consists

in the 'openness' they provide for the consideration of certain issues; in

particular, with regard to the very representation of the phenomena. As

Suppes (1969a) has stressed a long time ago, phenomena are by no means

simply raw data, but are constructed as certain kinds of structures (called

by him 'models of data'), based on involved strategies of statistical mod?

elling (see also van Fraassen 1985, p. 269). More recently, Woodward and

Bogen have introduced a further sophistication into Suppes's framework,

highlighting a demarcation between models of data and models of phe? nomena. The latter, as opposed to the former, are not so theory-dependent, are more stable, and from Woodward's and Bogen's viewpoint, are really the items to be explained by scientific theories (for details, see Bogen and

Woodward 1988, and Woodward 1989; a particularly witty discussion of

their views, in the context of the distinction between factual and repre? sentational beliefs, can be found in da Costa and French 1997, Chapter

4). A characterisation of these models of phenomena based on partial struc?

tures can also be presented; the result is the hierarchy of partial models of

phenomena (see Bueno 1997, Section 4). In rough terms, it is a hierarchy of partial structures, conceived to represent empirical information, such

that each level contains 'more' information than the previous one. It can

be outlined as the following hierarchy of partial structures:6

S* = (Dk, Rkl, Rk2, Rk3i ? Rkn)

Sk-l =

(Dk-li R(k-l)l> R(k-l)2> R(k-l)3> > R(k-l)n)

S3 = (?3, R31, /?32, R33, > R3n)

S2 =

{D2, Rl\Rl2, R23, -, R2n

S\ = (^i, /?n> R\2, R\3, ? ̂lw>

WHAT IS STRUCTURAL EMPIRICISM? 67

In this hierarchy, each R?j is a partial relation - thought of as a structure

of the form {RXj, Rfj, R3j),

where Rjj represents the n-tuples that belong

to Rij, Rfj, those that do not belong to Rij9 and

R3j, the ones for which is

not defined whether they belong or not to Rtj - such that, for every level

of the hierarchy, that is, for every /, 1 < / < k, card(/?? ) > card(/?^+1) ).

(Given that, by hypothesis, RXj U /??. U

Rfj =

Df, and supposing that

we are considering only finite relations,7 it follows that either card(Rj- <

card(Rxi+ly) or

card(R2j) <

card(R2i+l)j); this feature expresses, from an

intuitive point of view, the growth of the information regarding R?j.) Thus, at each level, partial relations R that were not defined at lower

levels (whose elements belong thus to R3) come to be defined; their ele?

ments, depending on the particular case, belong either to the domain of R

(i.e., to Rx) or to the complement of R (that is, to R2). The partial structures

that constitute this hierarchy can be extended to normal total structures. In

some contexts, these structures are then compared to scientific theories in

their test; in others, and perhaps more frequently, theories are compared to 'intermediate' levels of the hierarchy, which are constituted by partial structures. In the latter case, theories are constructed so that the determina?

tion of still 'unknown', 'higher' relations in the hierarchy can be naturally

adjusted to their conceptual frame, in order to guarantee their empirical

adequacy. This hierarchy of structures constitutes the partial models of

phenomena? We can now return to the issue of empirical adequacy. Under this set?

ting, a theory T is said to be quasi-empirically adequate if it has a theoret?

ical model MT such that, for a certain level /, 1 < / < k, of the hierarchy of partial models of phenomena (represented by S? =

{Di, Rij)iej), there

is a partial isomorphism between St and the empirical substructures E =

(Df, R?j)ieJ of MT; that is, for some i, 1 < / < k, there is a bijective

function f'.Di ? D' such that, for every x and y e Dt, RJjXy

^>

R?ljf(*)f(y) and

Rfjxy o

R,2jf(x)f(y). Notice that, in this character? isation, the three main elements (mentioned above) involved in an em?

piricist view of empirical adequacy, are clearly represented. As opposed to van Fraassen's proposal, however, the main relation between empirical substructures and the appearances (models of phenomena) is not an iso?

morphism, but a partial isomorphism. Moreover, an explicit reference to

a specific level of the hierarchy is required, and this introduces in turn an

interesting relativisation of the judgements of empirical adequacy.

68 OTAVIO BUENO

3.2. Quasi-Truth and Empirical Adequacy

Still considering the hierarchy of partial models of phenomena, we can

examine the concept of empirical adequacy from a different perspective. A theory T (thought of, in conformity to the semantic approach, as a

family of mathematical structures S)9 is empirically adequate if there is

an empirical substructure E of certain structure 5 such that t (the set of

sentences associated with S) is quasi-true in St (a partial structure found

at the level /, 1 < i < k, of the hierarchy of partial models of phenomena) with regard to E; i.e., ? is a structure that is an S?-normal model of t.

One should note that, in order to present this second proposal, given some formal requirements of the concept of quasi-truth, (1) the domain

of Sj has to be the same as that of E, and (2) the relations in E have

to 'extend' those of S?. In any case, as this tentative characterisation of

empirical adequacy makes plain, within the context of partial structures

and quasi-truth, there is an equivalence between a theory 'saving the ap?

pearances' and being 'empirically adequate', just as might be expected within an empiricist framework. This result also holds, of course, within

constructive empiricism, though for a slightly different reason (see van

Fraassen 1980, Chapter 3). An interesting feature of the formulation of empirical adequacy in terms

of quasi-truth consists in the fact that certain traits of the latter can be natu?

rally transferred to the former. In particular, if a theory is quasi-true, it will

remain as such, in its original domain, independent of the vicissitudes of its

further extensions; empirical adequacy would be, thus, similarly preserved - and this, as we will see in a moment, is a crucial point.

3.3. Empirical Adequacy in Degrees

The last step now consists in formulating the notion of 'level of empiricali

ty ' : it is the number associated with each particular level of the hierarchy of

partial models of phenomena. As we saw, given the cardinality condition

stressed above, this hierarchy models certain aspects of the empirical in?

formation at our disposal. For each level / of the hierarchy, 1 < / < k, the

level / + 1 is meant to contain further empirical information than the level

i. Thus, in the partial isomorphism characterisation of empirical adequacy

presented in Section 3.1, given the indexical reference to the specific level

of the hierarchy, the higher such a level is, the 'more' empirically adequate a theory will be. This suggests a kind of 'degree' of empirical adequacy -

something which is striking throughout scientific practice. One should

therefore add this indexical condition to the definition of empirical ade?

quacy, which results in the following tentative characterisation: a theory T is more quasi-empirically adequate than T' if (1) T and Tf are quasi

WHAT IS STRUCTURAL EMPIRICISM? 69

empirically adequate, and (2) the levels / and V of the hierarchy of partial models of phenomena

- with regard to which respectively T and T' are

quasi-empirically adequate - are such that / > /'. The idea is that a theory

is more quasi-empirically adequate than another if it takes into account

'more' empirical information than its rival (which is represented by the

condition that / > /') Of course, this account of the degrees of empirical adequacy assumes

the 'comparability' of the hierarchies of the partial models of phenomena associated with each theory. Is this a reasonable assumption? Thus far, I

have not been concerned with the particular content of the theories under

comparison. Nonetheless, this assumption seems to demand something on

this line. In the present work, I do not intend to consider and contrast the?

ories from altogether distinct domains of knowledge (such as evolutionary

theory and statistical mechanics), but those that, in a reasonable sense,

could really be taken as 'rival' (for they cover the same domain). After

all, the whole point of presenting this proposal concerning the degrees of

empirical adequacy comes from the need of developing some criteria of

theory choice in an empiricist framework; presumably, the theories to be

chosen are in conflict with each other. Based on such criteria, the empiri? cist could (at least in principle), and against the sceptic, choose between

rival theories. This explains the very strategy underlying, and the role

of, the employment of the notion of degrees of empirical adequacy in an

empiricist account of scientific change: it can help theory choice.

4. A MODEL OF SCIENTIFIC CHANGE: A PARTIAL STRUCTURES

APPROACH

Taking into account the framework just presented, based on partial struc?

tures, quasi-truth and the degrees of empirical adequacy, I shall now in?

dicate a possible (and definitely partial!) model of theory change from an

empiricist point of view.

4.1. Main Features of the Model

The first feature to be stressed consists in the use one can make of the

degrees of empirical adequacy in order to represent certain elements of

'empirical' progress. If the degrees of empirical adequacy grow when we

move from the theory T\ to T^, a kind of 'advance' at the empirical level

will have taken place, given that, from the characterisation just presented of these degrees, T^ takes successfully into account 'more' empirical in

70 OTA VIO BUENO

formation than 7\ (remember that in the hierarchy of partial models of

phenomena, one has that card(/??.) > card(/?^+1) .))

It might be pointed out that the notion of empirical adequacy adopted in this context is problematic. Indeed, when claiming that there are degrees of empirical adequacy, it is assumed that empirical adequacy is relativised

to the data at our disposal - in other words, to the level of the hierarchy of

partial models of phenomena that one considers (and thus if one ascends

to higher levels in the hierarchy, 'more' information would be considered).

Now, empirical adequacy is a 'modal' notion, concerned not only with

actual data, but with possible (future and past) ones as well. So, to re?

strict the characterisation of (the degrees of) empirical adequacy to actual

information seems to be not only an oversimplified assumption, but an

unacceptable one!

This is, of course, an interesting point. However, it is not incompatible with the characterisation presented here. The fact that we are taking into

account actual data by no means implies that these are the only ones that

should be considered, but only that they are those that (at least up to the

moment) can in fact be. From a theoretical perspective, we cannot deny that the claim of empirical adequacy involves a commitment to data of the

most varied features (from past to future ones), as well as to the fitting of

the particular theory under investigation to them. This is acknowledged by van Fraassen himself (see, for instance, 1980, p. 69). If we have focused

on actual data, this is just a matter of perspicuity; opening up, in particular, an important conceptual resource for empiricism (the degrees of empirical

adequacy and their consequences for theory change). It does not reflect any commitment to a restrictive (and definitely unbearable!) 'non-modal' view

of empirical adequacy.

Having said this, let us return to our model. Its first feature consists

in supplying certain tools for modelling 'empirical' progress. This kind

of progress is represented by the construction of theories with increasing

degree of empirical adequacy; and this feature, in turn, is characterised by

increasing the level of partial models of phenomena being considered. Of

course, within an empiricist setting this progress can naturally be expected to be accounted for, based as it is on the very empiricist aim of science -

empirical adequacy. It turns out however that further theoretical features

can also be described, and to this point I shall now turn.

In what respects can an empiricist make sense of theoretical progress? Could this be sensibly reduced to empirical progress? If so, given that the

latter seems to be reasonably accounted for by an empiricist view (at least

adopting the partial structures framework suggested above), the former

would have been ipso facto settled. Of course, the realist would claim that

WHAT IS STRUCTURAL EMPIRICISM? 71

this reduction is plainly unacceptable; after all, theoretical features brought

by science seem to go beyond the observational level. Indeed, perhaps the main claim underlying the no-miracles argument boils down to the

'novel predictions' issue: the only way, or so goes the realist's argument, to explain the predictive success of a theory T in describing certain phe? nomena not used in its construction, is to suppose, according to realist's

standards, that T is true (or approximately true). And so, the realist claims, this kind of 'theoretical' progress cannot be accounted for by the empiricist

proposal. As opposed to this, I shall argue for a double-headed claim: (1) the

realist does not supply a minimally acceptable answer to this problem (ac?

cording to his or her own standards!); and (2) to the extent that this problem can be 'settled', the empiricist

- at least one of a structural persuasion (as constructive empiricism definitely is)10

- can of course 'settle' it.11

Before arguing for these claims (respectively, in Sections 4.2 and 4.3), I wish to spell out briefly the sense of theoretical progress which is in

question here. Besides the novel predictions issue (which is taken by some

authors as the main point in the present dispute; see Brown 1994, Chapter

1), it involves other issues as well, such as simplicity, unification, concep? tual syst?matisation, and theoretical understanding. But all these features

can be accounted for in an empiricist setting: they constitute pragmatic

aspects of science (in van Fraassen's reading, for instance), lacking an

epistemic dimension. If we (or the relevant community) adopt them, that is

only, or can be explained as involving exclusively, a human predicament. So our problem concerns novel predictions only.12 And it is to this that I

shall now turn.

4.2. Problems for Realism13

The realist claims that he or she is able to account for (successful) novel

predictions in science. In fact, if theories are true, or approximately true

(as his or her position maintains), then it is natural that they have true

consequences. Part of the problem here however consists in arguing for

such a conditional. Viewed as an argument for realism (as, of course, the

realist intends it to be), it is blatantly question-begging, as several authors

(e.g. Laudan 1981, Fine 1984, and Boyd 1984) have already pointed out.

After all, it has to assume the truth (or approximate truth) of theories in

order to present the (putative) explanation of their predictive success -

the very point at issue in the debate! Of course, an empiricist could not

simply grant this much: according to empiricism, (quasi-)empirical ade?

quacy, and not truth, is advanced as the main epistemic aspect of science.

But even if the empiricist granted this point, the realist would not be in a

72 OTAVIO BUENO

better position. For then, he or she would simply be arguing inductively from the truth of the (observational) consequences of a theory to the very truth of the theory

- and that is simply fallacious, as we all know, from

the perspective of classical deductive logic. For the argument would then

run as follows: If theories are true (or approximately true), they have true

consequences; and they actually have true consequences; hence they are

true (or approximately true). It is worth remarking that some realists, after noticing the invalidity of

the 'no-miracles' argument, simply reject, in contrast to Putnam's initial

presentation of it, that it should be taken as establishing realism. Rather, it is claimed - but not really argued for - that the argument only supplies some plausibility for this view (see Worrall 1989, p. 142). Given that it

is not logically valid, not surprisingly, the most the realist asserts is that

it has a 'psychological force' (Worrall 1989, p. 142). This is, of course, a major concession for anti-realism, given that the argument has initially been taken by some realists (such as the early Putnam) as the 'ultimate

argument' for realism.

Therefore, from the realist's viewpoint, the basic ingredient of his or

her putative explanation of the success of science hangs on the notion of

truth, or at least approximate truth. Let me first briefly consider the latter.

As is generally acknowledged, until now no undisputed theory of approx? imation to truth has been devised. (Even realists themselves acknowledge this point; see Boyd 1990, p. 216.) And even if someone had proposed one

(presenting thus an acceptable characterisation of truth approximation), it

would by no means imply that the problem of novel predictions would

have been solved. In fact, approximately true theories are not (necessarily) true ones, and might have false consequences. So, the alleged fact that

a particular theory T is approximately true seems not to be enough to

guarantee that an acceptable explanation of its predictive success will be

presented; after all, T can be false, and from a false theory one can draw

both true consequences and false ones as well. What kind of explanation would have been formulated then? In order to circumvent this, the realist

needs a stronger notion: truth simpliciter.

However, even the employment of the notion of truth faces cumbersome

difficulties in this context. In fact, as Brown has pointed out (1994, Chapter

1), truth does not seem to be either a necessary or a sufficient condition

for the predictive success of scientific theories. False theories (such as for

instance Fresnel's) can have, and usually have, true consequences (even novel ones!). On the other hand, even granting the truth of a particular the?

ory T is not sufficient for appropriately explaining its predictive success,

WHAT IS STRUCTURAL EMPIRICISM? 73

given that, as is well known, several assumptions are added to T in order

for it to make these very predictions.

Therefore, in neither case (adopting truth or approximate truth), the

realist seems to have supplied good answers to the problem under consid?

eration. One wonders whether an alternative could be articulated.

4.3. An Empiricist Proposal

In what respects can the empiricist succeed where the realist's expectations seem to have led him or her too far? With this question, we finally reach

the second item mentioned above: whether the empiricist can successfully

examine, and perhaps even 'solve', our problem - at least to the extent that

the latter can be 'solved' at all. In a slightly different context, van Fraassen

himself has put forward some suggestions that might be adopted in the for?

mulation of an empiricist model of scientific change. Before proceeding, I wish to consider them briefly as the motivation for the proposals to be

advanced in the sequel. 'New theories', van Fraassen notices, 'are constructed under the pres?

sure of new phenomena, whether actually encountered or imagined' (1989,

p. 228). Such phenomena, he adds, are new in the sense that there is

no room for them in the models of the accepted theory. What kinds of

conceptual moves (or theoretical changes) are then open to the empiricist? At least two: (i) in order to guarantee empirical adequacy, 'the existing theoretical framework is widened so as to allow the possibility of those

newly envisaged phenomena' (p. 228), and (ii) as a way of retrieving infor

mativeness and empirical import, the theoretical framework is 'narrowed

again, to exclude a large class of the thereby admitted possibilities' (p.

228). Both moves reflect, of course, the empiricist disposition to preserve two basic theoretical virtues: empirical adequacy and informativeness. The

preservation of these virtues constitutes one of the main constraints of the

empiricist theory of scientific change. With regard to informativeness, there is an obvious sense in which it

is obtained and preserved (not exactly as a theoretical virtue, but more

as an 'empirical' one): in the hierarchy of partial models of phenomena the higher the level one considers, the 'more' information is loaded. It

is natural to represent empirical progress, as I have already remarked, in

terms of an ascent in this hierarchy. This comes from the phenomena's

side; but something can be said from the theory's side as well. Indeed, the introduction of degrees into the concept of empirical adequacy allows

one to grasp the informativeness supplied by a theory with regard to the

phenomena to which it is quasi-empirically adequate. The higher its degree of quasi-empirical adequacy is, the 'more informative' the theory will be.

74 OTA VIO BUENO

Such a degree, of course, constitutes a comparative matter, depending both

on the rival theories developed in a specific domain (in particular, on their

quasi-empirical adequacy), and on the more or less 'incomplete' nature of

the information supplied by the hierarchy of partial models of phenomena

(represented by the particular level being considered). So much for informativeness. With regard to empirical adequacy, theory

change can be achieved, for instance, in the following way. Suppose that

our empirical information with respect to a certain domain of knowledge A is represented by a particular level i of the hierarchy of partial models of

phenomena (which is a partial structure of the form S? = (D?, Rij)ie?jej,

where D? is a non-empty set, and Rtj a family of partial relations). As

I have suggested above, the empirical adequacy of a theory T involves, from an intuitive viewpoint, the existence of an empirical substructure E of

some theoretical model MT that extends 5/ into a normal (total) structure.

It may happen, however, that new information about A is obtained, so that

one should now take into account a higher level of the hierarchy, let us

say, S,-+i. In this case, empirical adequacy may have been lost, and a new

theory (that can of course be constructed by changing part of the previous

one) has to be devised. This new theory, Tf, would then have to account

for 'more' information than T, meeting in this respect the informativeness

requirement too. On the other hand, Tf will be constructed in order to

provide an appropriate model of the phenomena, and in order to do so, it

will have to be empirically adequate. This picture is meant to consider only local, particular changes of sci?

entific theories. How might one consider, within this framework, a global

process of theory change (in which a series of local changes is performed)? How might one describe some of its features in an empiricist setting? For

the empiricist, this problem will be thought of as a matter of theory uni?

fication. According to van Fraassen, the process of unification is mainly one of correction, rather than of conjunction, as some realists claim (see van Fraassen 1980, pp. 83-87). The central idea is that, in some cases, in

the process of modelling and explaining the phenomena, one can end up with far better results if theories from (even prima facie) distinct domains

are simultaneously used. In these circumstances, one of the theories pro? vides constraints and corrections for the other, whereas the other supplies

more specific information about certain objects than the first, accounting thus for the relevant phenomena in a more appropriate way.14 Similarly,

theory change is a process in which more encompassing theories (that is,

those capable of accounting for phenomena at the highest levels of the

hierarchy of partial models) are selected. But, of course, besides these

'vertical' developments (restricted, as it were, to a specific hierarchy of

WHAT IS STRUCTURAL EMPIRICISM? 75

partial models), one can also find 'horizontal' ones, in which the same

theory is able to account for phenomena depicted in distinct domains (i.e., found in different hierarchies of partial models).

One point should be made in this context. As the empiricist notices

(see van Fraassen 1985, pp. 280-81, and van Fraassen 1989, p. 192), there

exists a delicate tension between, on the one hand, informativeness and

explanatory power of a theory T, and, on the other hand, its credibility and the possibility of T being true. In fact, as van Fraassen points out,

the former vary inversely with the latter. More comprehensive theories,

for instance, have more ways of being false than less comprehensive ones.

And this offers an argument (for empiricism) to the effect that acceptance of a theory does not require belief in it: there are reasons for acceptance

(informativeness, for example) that are not reasons for belief.

I mention this point because, as opposed to the empiricist view, the

realist claims that if T successfully predicts new phenomena, its credibility and the possibility of its being true should increase. Is this really so? Even

if it were, what gains would one have with this move? As I have already

remarked, false theories may generate true (novel) predictions. So, despite the increase in jH's credibility, T can end up being false! On the other

hand, from the empiricist point of view, loosely speaking, novel facts are

accounted for by T when, in a particular model of T, there is room for

them; that is, they are allowed by T - and this is what opens up the possi?

bility of T being employed in explaining them. According to empiricism, there is therefore no mystery nor any miracle in this process. If a theory T has successfully taken into account a new phenomenon, this means that

there is a partial isomorphism between the hierarchy of the partial models

of phenomena (in which the phenomenon under consideration is repre?

sented) and the empirical substructures of T. (Such a phenomenon is new

in the sense that it is not represented in the hierarchies of phenomena that

were used in the construction of T.) As opposed to realism, the putative truth of T is not required in order to understand this process, but only an

appropriate notion of empirical adequacy. The point here is that scientific change can be understood in terms of the

comparison between theory and evidence, and so it is possible to 'reduce'

the former to the latter (where the empiricist view is particularly strong). Thus when the realist claims that a theory Tf is to be accepted instead of

T, because Tf entails new phenomena, and such phenomena are true, the

empiricist will simply point out that it suffices that such phenomena be

representable in the hierarchy of partial models of phenomena, and that a

partial isomorphism holds between them and the empirical substructures

of T'. So even if we are considering hierarchies of phenomena that have

76 OTAVIO BUENO

not been used in the construction of T (novel facts), the empiricist strat?

egy in order to take them into account is the same as the one adopted in the standard case (in which one is simply concerned with the (quasi-)

empirical adequacy of T'). In other words, for the empiricist, there is

nothing epistemically new about new phenomena. Let me present this point in a different way. Suppose that a realist argues

that, in theory change, it is not simply the case that a new theory T ex?

tends the partial relations that represent the empirical information about a

domain, but rather that new relations are advanced, and T entails that such

relations in fact hold. Using quasi-empirical adequacy, the empiricist can

accommodate this as follows. If T was successful in explaining some new

relations, (i) such relations have been represented in a convenient hierarchy of partial models of phenomena, and (ii) T has to be quasi-empirically

adequate with regard to the information about the domain of knowledge

represented in this hierarchy. Thus, new types of phenomena can be ac?

counted for by the empiricist, with the introduction of quasi-empirical

adequacy and the hierarchy of partial models of phenomena.15

Adopting a different strategy, the realist may then claim that T is suc?

cessful in certain predictions because it has apprehended the underlying 'structure' of the phenomena. A fundamental difficulty here consists in

how to establish this claim. Does the 'structure' of the phenomena go be?

yond the set-theoretic structures we devise to represent them? If so, what

would the notion of 'structure' in this context be? If not set-theoretical,

how could one argue for the 'sameness of structure' between theory and

world? As opposed to this, from an empiricist point of view, T was suc?

cessful because it has certain heuristic features, represented by some of its

models, that allow the explanation of the phenomena. The 'sameness of

structure' can then be viewed straightforwardly as a partial isomorphism between empirical substructures and partial models of the phenomena (see

also French and Ladyman 1999, and Bueno 1997), and one is not required to go further than comparing them in order to explain the success of a

particular theory. Nonetheless, the empiricist will insist, the explanatory

power of a theory, as opposed to the realist's intention, by no means has

an epistemic dimension, but only a pragmatic one (see van Fraassen 1980,

pp. 87-9).

Having said this, we can now consider one of the most delicate prob? lems in the realism-empiricism debate: how is the choice between empir?

ically equivalent theories to be performed? One of the advantages of the

present account is that, with the notion of degree of empirical adequacy, a new light can be cast on this issue, at least from the empiricist point of

view. As is well-known, realists claim that empirically equivalent theories

WHAT IS STRUCTURAL EMPIRICISM? 77

should be chosen on two grounds, either because there are certain theo?

retical virtues that discriminate them, or because they can be differently

supported by the same evidence. Van Fraassen, on the other hand, argues that no such a choice is required, but if a theory happens to be chosen, no epistemic consideration is involved, but only pragmatic. Now, with the

notion of quasi-empirical adequacy, and the degrees thereof, the empiricist can say something more. If a theory is quasi-empirically adequate, it takes

into account only some phenomena (up to a certain level of the hierarchy of partial models of phenomena). The phenomena found at higher levels

are not (necessarily) meant to be accommodated. Thus, given two quasi

empirically adequate theories, there may be empirical differences between

them - indeed, this is precisely the point of introducing the idea that a

theory can be more empirically adequate than another - and in this way, the

choice to be made is still based on empirical grounds. Therefore, the role

of empirical factors in theory choice according to constructive empiricism can be extended, and this enhances the empiricist case.

Thus, with the introduction of an appropriate notion of empirical ad?

equacy, the empiricist seems to be able to put forward an account of sci?

entific change: there are empirical criteria for theory choice - formulated

in terms of the degrees of empirical adequacy -, and a pattern of theory

change - articulated in terms of the interplay between the two main em?

piricist requirements: empirical adequacy and informativeness. The idea

is that the empiricist selects theories with a greater degree of empirical

adequacy and which are more informative. Both features are formulated

with reference to the hierarchy of partial models of phenomena: the higher the level we consider, the more informative and the more empirically ad?

equate a theory will be (supposing, of course, that we have managed to

construct such a theory). So, these features, having been presented in terms

of their degrees, stand together, and this is a fact that the empiricist can

explore. Indeed, a theory which is more quasi-empirically adequate than

another will be more informative as well, given that it takes into account

more information found in the hierarchy of the partial models of phenom? ena. In this sense, there is no clash between quasi-empirical adequacy and informativeness (at least with regard to the level of the hierarchy of

phenomena considered).16 However, as we have seen, and as van Fraassen

has pointed out, there is a clash between informativeness and truth, but this

only supplies a further argument against realism.

As I remarked in the introduction, one of the aims of the present paper was to present a non-question-begging answer to the realist's challenge, that is, the claim that realism is the only account that does not make the success of science a miracle. The answer to this challenge suggested here

78 OTAVIO BUENO

is to advance an approach to scientific change in empiricist terms; an ap?

proach in which science's success is explained in terms of the structural

interconnections between empirical substructures and the hierarchy of par? tial models of phenomena. Moreover, this answer is not question-begging in the sense that, in contrast to van Fraassen's standard reply to scientific

realism (see 1980, pp. 23-5), it does not rely on the existence of limits

to the demand for explanation (an aspect that the realist will never grant

anyway), but actually suggests an account of scientific change according to empiricism.

However, there is still an issue to be examined concerning the cognitive status of the present view, and I shall consider it now.

5. AN ALTERNATIVE: STRUCTURAL EMPIRICISM

In what sense can the suggestions outlined here be deemed empiricist! A

straightforward answer derives from the fact that they are entirely compat? ible with the main features of constructive empiricism.17 But there is more

than that. The empiricist idea that new theories are brought by new phe? nomena finds its place in the present proposal, given that as new empirical information is brought to higher levels of the hierarchy of partial models of

phenomena, in order to preserve empirical adequacy, new theories have to

be formulated. On the other hand, the dynamics of theory change, and here

comes the informativeness constraint, presents a degree of continuity that

is obtained due to the fact that quasi-truth, and thus empirical adequacy, as I have mentioned in Section 3.2, are preserved under theory extension.

The idea is that informativeness is a fairly 'stable' item in the development of scientific theories.

So, both requirements formulated by the empiricist, empirical adequacy and informativeness, are satisfied.18 But there is a third feature that must

also be stressed: the special role assigned to structures. Let me begin by

quoting van Fraassen again:

The important point for us here is that this claim of adequacy too is in the first instance

a structural claim. To be matched are two models, a data model and a theoretical model.

The matching in question may be as simple as an embedding or partial isomorphism, or

it may need to be some measure-theoretic refinement thereof to allow for approximation.

But is in any case a mathematical relationship, and therefore purely structural. The claim

of adequacy is in the first instance a claim about how two structures are structurally related.

(1997, p. 524)

Thus, the strategy outlined above (in Section 3.1) of characterising em?

pirical adequacy in terms of partial isomorphism is acknowledged by van

Fraassen himself as a sensible (empiricist) proposal. The chief claim, none

WHAT IS STRUCTURAL EMPIRICISM? 79

theless, consists in pointing out the basic 'structural' feature of the concept of empirical adequacy: 'a claim about how two structures are structurally related'. (And this feature, of course, is also found in the formulation of

empirical adequacy via quasi-truth, put forward in Section 3.2.)

My main point in suggesting an empiricist model of scientific change is the result of extending this explicit trait of constructive empiricism

-

its emphasis on structures - to the problem of the dynamics of scientific

knowledge. This dynamics, as I have argued in Sections 4.1 and 4.3, both

at the 'local' level of the comparison between theory and phenomena (in which judgements of quasi-empirical adequacy are of paramount impor?

tance), and at the 'global' level of theory change (in which informativeness

and scope are crucial), can be represented in terms of the formulation of

ever more comprehensive structures.19 Being, on the one hand, disentan?

gled from certain metaphysical assumptions typically found in realism

(with regard, for instance, to the notion of truth),20 and sticking, on the

other hand, to the employment of particular structures (in perfect agree? ment to the constructive empiricist stance), it seems appropriate to call the

present approach structural empiricism. To some extent, and immodestly

put, it is nothing but constructive empiricism brought to self-consciousness -

however, it still is, and this should be stressed, constructive empiricism.

Finally, from an empiricist perspective, at least in the structural version

suggested here, the problem of theory evaluation and theory change is

primarily considered as being based on the comparison of certain struc?

tures (except perhaps for some pragmatic features): partial models of the

phenomena and empirical substructures with regard to empirical adequacy, and families of partial models of the phenomena and distinct empirical substructures (coming from rival theories) in the case of theory choice.

But then the problem arises: what about the relation between these models

of the phenomena and the world? Or between the structures of a theory and the world? Structural realism comes up with a bold claim:

The structural realist simply asserts, in other words, that, in view of the theory's enor?

mous empirical success, the structure of the universe is (probably) something like quantum mechanical. (Worrall 1989, p. 163.)21

This is the point where, usually, empiricism and realism diverge, and their

structural versions present no exception. The main idea for the structural empiricist is, as always, that we don't

need to stick our necks out so much. We can go on and understand the phe? nomena of scientific change and empirical success, as I have been outlining here, without holding this kind of 'metaphysical' claim. The structures

that matter for the understanding of these phenomena are set-theoretical

80 OTAVIO BUENO

(empirical substructures and partial models of the phenomena). And these

are enough.

Having spelled out the formal framework of structural empiricism, the

next step consists in showing how it can be applied to understand real cases

from the history of science. Although this is an issue to be explored in a

future paper, I hope that enough has been said in order to convey the main

formal ideas to be employed in such applications, spelling out in particular the role of quasi-empirical adequacy, of the hierarchy of the partial models

of phenomena, and of partial structures in theory change. Despite its ten?

tative character, the present proposal seems enough to suggest, as opposed to the rather abrupt realist claim, that an empiricist treatment of certain

issues surrounding scientific change can in fact be formulated. Thus, if the

success of science happens in fact to be a miracle, the realist will not be in

a better position than the empiricist to complain.

NOTES

* I wish to thank Steven French, Newton da Costa, Jos? Chiappin, Caetano Piastino,

Val ter Bezzerra, Bas van Fraassen, Stathis Psillos, James Ladyman and Mauricio Su?rez

for discussions and correspondence on the topics examined here. Its inspiration arose while

reading an illuminating work of James (see Ladyman 1998), to which I am clearly indebted.

I also have a very special debt to Chiappin, whose work (see his 1989) and discussions were

crucial for the development of these proposals. Of course, the present ideas could only have

arisen within Newton's and Steven's most interesting framework (being also dependent on

their help and support), which does not mean that they (or any of the others) agree with the

points formulated here.

An earlier version of this paper was presented in the 1996 Annual Conference of the

British Society for the Philosophy of Science (held in Sheffield, from 11 to 13 of Septem? ber), and I wish to thank the comments I received there, in particular, from Anna Maidens,

Adam Morton and Jason Grossman. Finally, thanks are also due to two anonymous referees

for their helpful comments and suggestions on an earlier version of this work.

1 For the constructive empiricist 'defensive' strategy and a discussion of Putnam's point,

see van Fraassen 1980, pp. 23-5; 31^40. 2

Van Fraassen also advances the 'Darwinist analogy' between the 'survival' of scientific

theories and of certain species: only those theories that are empirically successful, similarly

to those species that are well fitted, survive. Thus, from his viewpoint, there is no miracle

in the success of current scientific theories (see van Fraassen 1980, pp. 39-40; see also

van Fraassen 1985, pp. 262-63). I don't take this as a strong argument against the realist

position, but roughly as a statement of certain traits that an empiricist answer to the realist

challenge would present. 3

It should be pointed out that the fact that partial relations and partial structures are partial

is due to the 'incompleteness' of our knowledge about a given domain, and as we shall see,

this feature is to be explored by the empiricist (with further information about this domain,

a partial relation may become total). Thus, the partialness modelled by the partial structures

approach is not understood as an intrinsic, ontological 'partialness' in the world - an aspect

WHAT IS STRUCTURAL EMPIRICISM? 81

about which the empiricist will be glad to remain agnostic. We are concerned here with an

'epistemic', not an 'ontological' partialness. 4

Someone may claim that, because quasi-truth has been defined in terms of full structures

and the standard notion of truth, there is no gain with its introduction. In my view, there

are several reasons why this is not the case. First, it should be noticed that quasi-truth is weaker than truth: a sentence which is quasi-true in a particular domain - that is, with

respect to a given partial structure A - may not be true if considered in an extended domain.

After all, there might be distinct A-normal structures that extend the partial relations in

A in a different way. As a result, we have here a sort of 'underdetermination' - distinct

ways of extending the same partial structure - which makes the notion of quasi-truth

especially appropriate for the empiricist case. (On the other hand, if a sentence is true,

trivially it is quasi-true.) Second, one of the points of introducing the notion of quasi-truth, as da Costa and French have argued in detail (see their 1989, 1990, 1993a, and 1993b), is

that, in terms of this notion and the concept of partial structure, a formal framework can

be advanced to accommodate the 'openness' and 'partialness' typically found in science

and, in particular, in scientific practice. Moreover, it is possible to formulate the notion

of quasi-truth in a different way, independently of the standard notion of truth, and still

preserving all its features (see Bueno and de Souza 1996). So, the standard notion of truth

is dispensable in the characterisation of quasi-truth. For additional discussions of some

logical and philosophical aspects of the concept of quasi-truth, further arguments for its

introduction, and details on the partial structures approach, see also da Costa, Bueno and

French (1998), da Costa and French (1997), and Bueno (1997). * For a discussion of the semantic approach, see for instance Suppes (1961) and (1969a),

Sneed (1971), Ludwig (1978), Suppe (1977), pp. 221-30, van Fraassen (1980), pp. 41-69, van Fraassen (1989), pp. 187-89; 217-32, and Suppe (1989), pp. 3-20. 6 I wish to mention that the idea of this hierarchy found its inspiration in a particularly

stimulating paper by Matthias Kaiser (see his 1991). 7

Otherwise, one can simply impose that, for every /, 1 < / < k, Rf. D R7-,n

8 Further conditions that should be met by these structures will not be considered here

(for details, see Bueno 1997, Section 4). 9

Notice that van Fraassen has been quite cautious at this level. Indeed, he has identified

the presentation of a theory (not the theory itself) with the specification of a family of

structures, its models (see, for instance, van Fraassen 1980, p. 64). This, in fact, is an

important move, given that from his viewpoint, theories are to be thought of as those kinds

of entities that might be true or false (something models are not meant literally to be) - a basic condition, anyway, in order to develop a semantic analysis of them (see, for

instance, van Fraassen 1989, p. 192). Nevertheless, pressed by the urgency of liberating the philosophical reflection on science from the 'tragedy' (as he puts it) resulting from the

linguistic-oriented analysis of the structure of a scientific theory, he is sometimes lead to

make the bolder identification of a theory with its models (see van Fraassen 1989, p. 222). Of course, a delicate question to be raised in this context consists in examining the

meaning of the term 'model' adopted here. Within Suppes's view, as is well known, the

notion of model in science and in logic is not altogether distinct (see his 1961); van

Fraassen seems to agree (see 1980, p. 44; but compare with p. 65). The issue is subtle,

depending in particular on the strategies of axiomatisation being employed, both in logic and in science. Unfortunately, however, I do not have space to pursue this point here. 10 In fact, van Fraassen's commitment to the employment of structures in the examination

of certain problems in the philosophy of science is clear enough. For instance, he claims:

82 OT?VIO BUENO

'A scientific theory gives us a family of models to represent the phenomena. But it rep?

resents the phenomena as fragments of a larger and simpler structure - the world as it is

according to the theory, if you like. These models are mathematical entities, so all they have is structure, the only thing they can represent is structure. There is nevertheless a

right and a wrong in representation' (van Fraassen 1997, pp. 528-29). I shall briefly return

to this point in Section 5, below. 11 The realist, also of a structural kind (see Worrall 1989, and Ladyman 1998), would then 'settle' it as well, but with several metaphysical additions that an empiricist would not be

able to grant. 12

Notice that to focus the discussion on novel predictions is in fact a concession to the

realist, who usually takes those predictions to provide crucial support to a scientific theory. 13

There is, of course, a voluminous literature on the realism versus empiricism debate,

and my point here is not to enter into details of this debate, but simply to re-emphasise in

the present context some well-known problems for the realist. 14

Van Fraassen mentions an illuminating case: 'How could we have a successful physiol?

ogy that does not take into account the effect of gravity which requires tensing of different

muscles in different postures? One might contemplate teaching one theory of gravity to

physiologists and another to astronomers. But at some point, someone will have to devise

an account of the behaviour of the complex system consisting of a man in a space suit

walking on the surface of the moon' (van Fraassen 1980, p. 86). 15 It may be claimed that, from the realist perspective, to say that a theory is quasi

empirically adequate supplies no explanation of the fact that it has produced novel pre?

dictions. But since this point assumes a realist view, it is simply question-begging. 16 It should be noticed that I am not claiming that informativeness is a criterion for empir?

ical adequacy (although it certainly is a criterion for theory choice). And even if it were such a criterion (for empirical adequacy), this would not supply any help for the realist,

since it still would not be a criterion for truth. Indeed, the information we are concerned

here, being related to the hierarchy of partial models of phenomena, is empirical, and the

usual empiricist underdetermination argument is enough to warn us that, from the fact that

a theory is empirically adequate, we cannot conclude that it is true.

17 Notice, in particular, that the proposal suggested here is articulated in terms of a seman?

tic notion (quasi-truth) which, as we saw in Section 2, generalises the Tarskian concept

of truth and coincides with it if we only consider full structures. Now, van Fraassen's

conception also draws on Tarski's account in order to provide a semantic interpretation

of science. In this way, the present view generalises constructive empiricism (CE) by

providing a more 'open-ended' empiricist framework, but it is also compatible with the

main traits of CE, since both views lead to the same results if we restrict our consideration

to full structures. In particular, the present account avoids instrumentalism in the same way

that CE does: roughly speaking, by formulating scientific theories in such a way that they

can meaningfully receive truth-values. For further details, see Bueno (1997). 18

For an elaboration of the notion of empiricism adopted in the present context, see van

Fraassen (1994), and van Fraassen (1995). 19 An original elaboration of this process (stressing its structural components) and a vivid

illustration (in the case of the mathematical development of classical mechanics) can be

found in Chiappin (1989). For the notion of structure adopted in the present context, see

da Costa and Chuaqui (1988).

WHAT IS STRUCTURAL EMPIRICISM? 83

20 Moreover, as we have seen in Section 4.2, despite the use of the concept of truth, the

realist view does not actually solve the problem about novel predictions it has set out to

solve. 21

For a critical examination of Worrall's proposal, see Psillos (1995).

REFERENCES

Bogen, J. and J. Woodward: 1988, 'Saving the Phenomena', The Philosophical Review 97,

303-52.

Boyd, R.: 1984, 'The Current Status of Scientific Realism', in Leplin (ed.) (1984), pp. 41-82.

Boyd, R.: 1990, 'Realism, Approximate Truth, and Philosophical Method', in Savage (ed.)

(1990), pp. 355-91. (Reprinted in Papineau (ed.) (1996), pp. 215-255.) Brown, J.R.: 1994, Smoke and Mirrors: How Science Reflects Reality, Routledge, London.

Bueno, O.: 1997: 'Empirical Adequacy: A Partial Structures Approach', Studies in History

and Philosophy of Science 28, pp. 585-610.

Bueno, O. and E. de Souza: 1996, 'The Concept of Quasi-Truth', Logique et Analyse 153

154, pp. 183-199.

Chiappin, J. R. N.: 1989, Duhem's Theory of Science: An Interplay Between Philosophy

and History of Science. Ph.D. thesis, University of Pittsburgh.

Churchland, P. M. and C. A. Hooker (eds.): 1985, Images of Science: Essays on Realism

and Empiricism, with a Reply by Bas C. van Fraassen, The University of Chicago Press,

Chicago, da Costa, N. C. A.: 1986, 'Pragmatic Probability', Erkenntnis 25, 141-62.

da Costa, N. C. A., O. Bueno, and S. French: 1998, 'The Logic of Pragmatic Truth', Journal

of Philosophical Logic 27, 603-620. da Costa, N. C. A. and R. Chuaqui: 1988, 'On Suppes' Set Theoretical Predicates',

Erkenntnis 29, 95-112.

da Costa, N. C. A. and S. French: 1989, 'Pragmatic Truth and the Logic of Induction',

British Journal for the Philosophy of Science 40, 333-56.

da Costa, N. C. A. and S. French: 1990, 'The Model-Theoretic Approach in the Philosophy of Science', Philosophy of Science 57, 248-65.

da Costa, N. C. A. and S. French: 1993a, 'Towards an Acceptable Theory of Acceptance: Partial Structures and the General Correspondence Principle', in French and Kamminga

(eds.) (1993), pp. 137-58. da Costa, N. C. A. and S. French: 1993b, 'A Model Theoretic Approach to "Natural

Reasoning" ', International Studies in the Philosophy of Science 7, 177-90.

da Costa, N. C. A. and S. French: 1997, Partial Truth and Partial Structures: A Unitary

Account of Models in Scientific and Natural Reasoning, unpublished book, University of

S?o Paulo and University of Leeds, in preparation. Dalla Chiara, M. L., K. Doets, D. Mundici and J. van Bentham (eds.): 1997, Logic and

Scientific Methods, Kluwer Academic Publishers, Dordrecht.

Fine, A.: 1984, 'The Natural Ontological Attitude', in Leplin (ed.) (1984), pp. 83-107.

French, S. and J. Ladyman: 1999, 'Reinflating the Semantic Approach', forthcoming in

International Studies in the Philosophy of Science.

French, S. and H. Kamminga (eds.): 1993, Correspondence, Invariance and Heuristics:

Essays in Honour of Heinz Post, Reidel, Dordrecht.

84 OT?VIO BUENO

Freudenthal, H. (ed.): 1961, The Concept and the Role of the Model in Mathematics and

Natural and Social Sciences, Reidel, Dordrecht.

Kaiser, M.: 1991, 'From Rocks to Graphs - The Shaping of Phenomena' Synthese 89,

111-33.

Ladyman, J.: 1998, 'What is Structural Realism?', Studies in History and Philosophy of Science 29, 409-424.

Laudan. L.: 1981, 'A Confutation of Convergent Realism', Philosophy of Science 48, 19

49. (Reprinted in Leplin (ed.) (1984), pp. 218-49.) Leonardi, P. and M. Santambrogio (eds.): 1995, On Quine, Cambridge University Press,

Cambridge.

Leplin, J. (ed.): 1984, Scientific Realism, University of California Press, Berkeley.

Ludwig, G.: 1978, Die Grundstrukturen einer physikalischen Theorie, Springer, Berlin.

Mikenberg, I., N. C. A. da Costa, R. and Chuaqui: 1986, 'Pragmatic Truth and Approxi? mation to Truth', The Journal of Symbolic Logic 51, 201-21.

Papineau, D. (ed.): 1996, The Philosophy of Science, Oxford University Press, Oxford.

Poincar?, H.: 1905, Science and Hypothesis, Dover, New York.

Psillos, S.: 1995, 'Is Structural Realism the Best of Both Worlds?', Dial?ctica 49, 15^6.

Putnam, H.: 1979, Mathematics, Matter and Method, Philosophical Papers, volume 1,

second edition, Cambridge University Press, Cambridge.

Savage, C. W. (ed.): 1990, Scientific Theories, Minnesota Studies in the Philosophy of

Science, vol. 14, University of Minnesota Press, Minneapolis.

Sneed, J.: 1971, The Logical Structure of Mathematical Physics, Reidel, Dordrecht.

Stapleton, T. J. (ed.): 1994, The Question of Hermeneutics, Kluwer Academic Publishers,

Dordrecht.

Su?rez, M.: 1995, 'How Theories Save Phenomena: A Case Against "Embedding"',

unpublished manuscript, London School of Economics.

Suppe, F.: 1977, 'The Search for Philosophic Understanding of Scientific Theories', in

Suppe (ed.) (1977), pp. 1-232.

Suppe, F.: 1989, The Semantic Conception of Theories and Scientific Realism, University

of Illinois Press, Urbana.

Suppe, F. (ed.): 1977, The Structure of Scientific Theories, second edition, University of

Illinois Press, Urbana.

Suppes, P.: 1961, 'A Comparison of the Meaning and Uses of Models in Mathematics and

the Empirical Sciences', in Freudenthal (ed.) (1961), pp. 163-77.

Suppes, P.: 1969a, 'Models of Data', in Suppes 1969b), pp. 24-35.

Suppes, P.: 1969b, Studies in Methodology and Foundations of Science, Reidel, Dordrecht,

van Fraassen, B.C.: 1980, The Scientific Image, Clarendon Press, Oxford,

van Fraassen, B. C: 1985, 'Empiricism in the Philosophy of Science', in Churchland and

Hooker (eds.) (1985), pp. 245-308. van Fraassen, B.C.: 1989, Laws and Symmetry, Clarendon Press, Oxford,

van Fraassen, B. C: 1991, Quantum Mechanics: An Empiricist View, Clarendon Press,

Oxford,

van Fraassen, B. C: 1994, 'Against Transcendental Empiricism', in Stapleton (ed.) (1994),

pp. 309-35.

van Fraassen, B. C: 1995, 'Against Naturalized Empiricism', in Leonardi and Santambro?

gio (eds.) (1995), pp. 68-88. van Fraassen, B. C: 1997, 'Structure and Perspective: Philosophical Perplexity and

Paradox', in Dalla Chiara et al. (eds.) (1997), pp. 511-30.

Woodward, J.: 1989, 'Data and Phenomena', Synthese 79, 393-472.

WHAT IS STRUCTURAL EMPIRICISM? 85

Manuscript submitted July 1, 1997 Final version received August 28, 1998

University of Leeds

School of Philosophy L52 9YT Leeds U.K.

Worrall, J.: 1989, 'Structural Realism: The Best of Both Worlds?', Dial?ctica 43, pp. 99

124. (Reprinted in Papineau (ed.) (1996), pp. 139-65.)