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Falsificationism and the structure of theories: thePopperKuhn controversy about the rationality of normal science

Jose Dez

Universitie of Barcelona/LOGOS Research Group, 08001 Barcelona, Spain

Abstract

Many controversies within philosophy of science have been attempted to be explained in terms of the metaphilosophical prescription/description distinction over the goal of philosophy of science. The aim of this paper is to show that the controversy between Popper andKuhn about the ir/rationality of Normal Science cannot be fully explained in these terms, not even if we also take the truth/problem-solving distinction over the goal of science into account. It is argued that, to gain full understanding of this controversy, it is necessary totake into account their differences regarding a topic apparently not involved in it, namely the structure of scientific theories. The con-clusion is that both Popper and Kuhn were descriptive/prescriptive at the same time in their attempt to make the rules of (a specific partof) scientific practice explicit, yet Kuhn did it better because he had a richer and more accurate idea of what scientific theories are.Although this work is mainly a piece of history of philosophy of science, it also aims at shedding some light on epistemological issues.If the conclusion is sound, it also shows how structural aspects of scientific theories may be relevant to the epistemology of science. 2007 Elsevier Ltd. All rights reserved.

Keywords: Falsificationism; Normal science; Rationality; Theories; Thomas Kuhn; Karl Popper

When citing this paper, please use the full journal titleStudies in History and Philosophy of Science

Though he is not a nave falsificationist, Sir Karl may, I

suggest, legitimately be treated as one. (Kuhn, 1970a, p.

14)

This passage is really astonishing. It is exactly like say-

ing: Although he is not a murderer, Sir Karl may, I sug-

gest, legitimately be treated as one. (Popper, 1983

[1956], p. xxxiv)

1. Prescription and description: making rules explicit

The aim of this paper is to show that, contrary to whathas been widely accepted, the controversy between Popper

and Kuhn about the ir/rationality of Normal Science can-not be fully explained in terms of the metaphilosophicalprescription/description distinction, not even if we alsotake the truth/problem-solving distinction over the goalof science into account. To gain full understanding of thiscontroversy, it is necessary to take into account their differ-ences regarding a topic apparently not involved in it,namely the structure of scientific theories. I begin withsome introductory remarks about the task of philosophyof science showing that, in the specific field relevant tothe controversy, description and prescription are not inopposition, and that, a fortiori, their alleged oppositioncannot explain crucial episodes of such controversy.Secondly, I introduce the main textual references of the

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Stud. Hist. Phil. Sci. 38 (2007) 543554

Studies in Historyand Philosophyof Science


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controversy and discuss their puzzling character. Third, Ipresent the main traits of Kuhns analysis of scientific the-ories in contrast to Poppers traditional axiomatic account.Finally, I show that, taking into account the different

notions of scientific theory they implicitly have in mind,the puzzling aspects of the controversy vanish and that,so understood, although Poppers falsificationism has aclear insight, his criticisms of Kuhns Normal Science aremisguided.

Analytic philosophy of science consists in analysing,among other things, two kind of entities: scientific con-structs (concepts, theories. . .) and scientific practices (test-ing, explaining. . .). Analysing scientific constructs isbasically a reconstructive/interpretative endeavour, whichhas to be evaluated both intrinsically and through the ben-efit of the reconstruction applied to other tasks, mainly theanalysis of scientific practices. For instance: a reconstruc-

tion of scientific concepts that does not allow one to saythat there is a(n important) sense in which scientific con-cepts remain the same throughout the evolution of a singletheory, is worse than another which does; a reconstructionof scientific theories which does not make room for the dis-tinction between normal and revolutionary changes isworse than another which does.

Analysing scientific practices consists basically in mak-ing its rules explicit. Every practice (argumentation, speak-ing a language . . .) is constituted by certain rules, andmaking these constitutive rules explicit is both descriptiveand prescriptive. For example, a specific grammar makes

the rules of a specific language explicit: it describes itsrules. But rules are constitutively normative.1 Thus,describing the grammar rules of, say, Spanish is at the sametime prescribing how people must/must not speak, that is,to distinguish between grammatically well formed(rule fol-lowing) and grammatically ill formed (non-rule following)utterances. In analysing practices, description (of the rulesthat constitute them) and prescription are not in oppositionbut two sides of the same coin.2 This task must be evalu-ated by historical/empirical data about practice perfor-mance, taking paradigmatic examples specially intoaccount.3 On the other side, the normativity that followsfrom making the constitutive rules of a practice explicit,that is, evaluating whether a particular performance is oris not in accordance with the rules, is compatible with leav-ing certain performance alternatives open. That is, thisnormativity does not imply a command of every possiblecourse of action, it simply rules out some courses as non-

rule-following and allows others. The rules of many prac-tices do not determine a unique course of action, but thisdoes not mean that they are not normative/prescriptive.

All this applies to scientific practices as well. Scientists

perform certain practices like testing, explaining, experi-menting, working within a theory, and so on. These prac-tices are constituted by their own rules, and philosophers ofscience try to make these rules explicit by analysing the cor-responding scientific practices. The analysis must be evalu-ated in the light of historical/empirical data about scientificpractice, taking paradigmatic examples specially intoaccount. For instance, if certain analysis of working withina theory implies that the first predictive failure amounts to(epistemically) throwing the whole theory away, then itenters into conflict with paradigmatic examples of good sci-entific practice like working within Newtonian theorywhen, before the discovery of Neptune, predictions about

Uranus trajectory didnt fit the data.As in the other cases, this endeavour of describing the

rules governing scientific practices has normative importand allows for evaluating some performances as good, thatis, rule-following (e.g. Lavoisiers mercury experiment),and some others as bad, that is, non-rule-following (e.g.phlogiston theorists attempt to face Lavoisier experimentpostulating negative mass). This normativity, whichexcludes certain courses of action, is, again, compatiblewith leaving some others open, that is, it may not uniquelydetermine what to do in a specific situation.

Scientific practices, though, have a peculiar character.

They are the paradigm (or at least, one prominent para-digm) of epistemic rationality, of coming to believe in arational way. And this does not simply follow from itsbeing constituted by rules, since there are many other prac-tices that are constituted by rules which are not rational inthe relevant sense, such as exorcism, tarot, chiromancy,astrology, and the like. Of course one can stipulate a senseof rational equating it with performing a practice accord-ing to its constitutive rules, and maybe it could even beuseful for distinguishing, say, rational astrology practitio-ners from irrational ones. But this is not the relevant senseat stake. Scientific practice is paradigmatically rational in asense in which other, also regulated, practices are not. Andthis specific rationality must rest in the specificity of theconstitutive rules of scientific practice. It is then an addi-tional task for philosophy of science to elucidate the sensein which the constitutive rules of scientific practice makesuch a peculiar practice a paradigm of rationality (although

1 This applies to any form of convention(cf.Lewis, 1969).2 Of course not every description involving the rules of a practice has normative import. One can, for instance, describe what practitioners believethe

rules are, and this has no normative import (although may have psychological/sociological import). The point, to repeat, is that, given a practiceconstituted by certain rules, making these constitutive rules explicit has normative import. Since making them explicit is also to describe them, we obtainthat description and prescription arein these casestwo sides of the same coin. One could object the use of the word description for referring to the activityof making rules explicit, precisely because this activity has normative import. But I want to keep it for stressing the analogy between logic or grammar and(part of) philosophy of science. Needless to say, the distinction description/prescription is perfectly disjoint when making constitutive rules of a practiceexplicit is not at stake.3 A problem: practitioners could, in principle, suffer of massive ill performance, therefore, evaluating the analysis is not merely checking whether it fits

the majority. Some complications arise here.

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this does not mean that we have to constrain our task ofmaking the rules explicit with a preconceived notion ofrationality4).

These considerations apply to part of the PopperKuhn

debate about the ir/rationality rationality of normal science(NS). The thesis I want to defend is that some aspects ofthis controversy cannot be fully explained in terms of theprescriptive/descriptive distinction, nor even plugging inin addition the truth/problem-solving one, and that suchaspects cannot be fully understood without taking intoaccount something which apparently was not involved inthe controversy, namely the different views on the natureand synchronic structure of scientific theories they hadimplicitly in mind. That is, both Kuhn and Popper attemptto make the rules of certain scientific practice explicit, bothare descriptive/prescriptive in the aforementioned sense;but Kuhn does it better (that is, fits better paradigmatic

historical examples), and he does so because he is implicitlyrunning a better interpretation of the constructs implicitlyinvolved, namely, scientific theories.5

One could object here to the very idea of this project that,since Kuhn rejects that scientific practice is constituted byrules, one cannot see his work as making constitutive rulesexplicit and,a fortiori, his controversy with Popper as a dis-agreement regarding such rules.6 For example:

The determination of shared paradigms is not, however,

the determination of shared rules . . . Anyone who has

attempted to describe or analyze the evolution of a par-

ticular scientific tradition will necessarily have sought

accepted principles and rules of this sort. Almost cer-

tainly, as the preceding section indicates, he will have

met with at least partial success. But, if his experience

has been at all like my own, he will have found the

search for rules both more difficult and less satisfying

than the search for paradigms . . .As a result, the search

for a body of rules competent to constitute a given nor-

mal research tradition becomes a source of continual

and deep frustration. (Kuhn, 1970d [1962], pp. 4344)

Normal science can be determined in part by the direct

inspection of paradigms, a process that is often aided

by but does not depend upon the formulation of rulesand assumptions. Indeed, the existence of a paradigm

need not even imply that any full set of rules exist. (Ibid.,

p. 44)

Scientists work from models acquired through educa-

tion and through subsequent exposure to the literature

often without quite knowing or needing to know what

the characteristics have given these models the status

of community paradigms. And because they do so, theyneed no full set of rules. Paradigms may be prior to,

more binding, and more complete than any set of rules

for research that could be unequivocally abstracted

from them. (Ibid., p. 46)

Contrary to appearances, I dont think these passages arein tension with the above characterisation of the analysis ofscientific practice as making the rules of such practice expli-cit. There are two readings of the word rule involved here.In the strong reading, it refers to a set of quasi-mechanisedprocedures that one can explicitly be taught in practice-learning.7 This is the sense in which the late Wittgenstein

famously denied that to learn a language is to learn a setof such rules and claimed, instead, that to learn a languageconsist better in capturing similarities among groups of par-adigmatic examples. This is the sense used by Kuhn in thesepassages, who explicitly mentions Wittgensteins move atthe beginning of the chapter. In this sense, according toKuhn (and to me) normal science does not reduce to a setof rules; in normal science the ability to capture similaritiesamong paradigms/exemplars plays a more important andessential role. It is in this sense that normal science is notguided by rules but by paradigms. But this is not the sensein which I stated above that scientific practice, like any otherpractice, is constituted by rules. In this weaker sense, forinstance, trying to apply the same symbolic generalisationsto cases which one finds similar to paradigms, is one of therules that constitute normal science, and not reducible toany set of rules in the first, stronger sense.8

2. Popper and Kuhn on the ir/rationality of normal science

Which are the aspects of the controversy that are betterunderstood as caused by their implicit disagreements onthe structure of theories? What might be called the possi-bility conditions for the rationality of NS. If Popper wereright, NS could not be rational, NS would be irrational in

principle. If Kuhn (and Lakatos) is (are) right, NS maybe perfectly rational (and as a matter of fact,9 it is almostalways rational). The parts of the controversy I deal withare then confined to these, so to speak, transcendental

4 Of course one could always try to imposedifferent rules, yet this is not to analyse a practice but to changeit.5 Of course this does not need to coincide with either Popper or Kuhn self-description of their task in general, and of their controversy in particular, since

they may be metaphilosophically misguided (as, if I am right, they partially are).6 I owe this criticism to an anonymous referee.7 For instance, to learn the syntax of a formal language, for example the rules of well formed formulae in, say, propositional logic. But there are very few

interesting real life examples, if any, of such rules and practices; maybe chess-moving or following driving regulations, which of course are only part ofthe more complex practices playing chess and driving, really real life and not rule-guided in this first sense.8 Just as playing chess or driving are constituted by rules in this weak sense which are not reducible to sets of rules in the stronger sense. One might

now object that then the thesis that scientific practice is constituted buy rules is very weak. And it actually is, but not totally empty; it simply emphasisesthat scientific practice is a practiceand, like any other practice, analysing it consists in making explicit what the practice consists in. If someone objects thatin this weak sense it is better not to use the word rule, I would be happy with some other more adequate term.9 But, importantly, not in virtue of the definitionof NS (see the last section).

J. Dez / Stud. Hist. Phil. Sci. 38 (2007) 543554 545


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aspects of the rationality in NS. I wont deal with the con-ditions for NS to be actually rational, nor with any aspectof inter-paradigmatic or trans-revolutionary rationality.10

Since this controversy is well known, I shall emphasise

only the most striking passages, beginning with the aston-ishing two which head this paper:

Though he is not a na ve falsificationist, Sir Karl may, I

suggest, legitimately be treated as one. (Kuhn, 1970a, p.

14)

This passage is really astonishing. It is exactly like say-

ing: Although he is not a murderer, Sir Karl may, I sug-

gest, legitimately be treated as one. (Popper, 1983

[1956], p. xxxiv)

and continuing with Poppers complaints about Kuhns(and Lakatos) incapacity for understanding his ideas:

[Kuhn] attended my William James Lectures at Harvard

in 1950 . . . But it seems clear that he does not fully

remember what happened during these lessons. (Ibid.,

p. xxxii)

Kuhn, early in his career, formed a theory of my views

which became his paradigm of Popper. . .Kuhn formed

this paradigm before he ever read any of my writings. . .

But, as we have learnt from Kuhn, paradigms are not

given up so easily. (Ibid., p. xxxiv)

Lakatos has read almost everything I have written. After

being my pupil, he was my colleague and after my suc-

cessor at LSE. Yet I have to warn the reader that he

has not understood my theory of science. (Popper,

1974, p. 999)

There must be some noise in the controversy thatexplains the difficulties for understanding one another. Itis true that Popper said from the very beginning (togetherwith, and besides, his conventionalism on observationalstatements) that theories cannot conclusively be provedfalse, that there always are possible strategies for eludingthe refutation, etc. But at the same time he says things like:

scientific theories are inventions to be eliminated if they

clashed with observations. (Popper, 1963, p. 61)

the falsity of a theory can be inferred from empirical evi-

dence, and this inference is a purely deductive one.

(Ibid., p. 72)

it must be possible for an empirical scientific system to

be refuted by experience. (Popper, 1958 [1934], p. 18)

I am going to propose that the empirical method shall be

characterized as a method that excludes precisely those

ways of evading falsification which, as my imaginary

critic rightly insists, are logically possible. (Ibid., p. 20)

the uncertainty of refutation (which I pointed out) must

not be taken too seriously (as I have pointed out too).

(Popper, 1983, Introduction to 1982 edition 1)

Etcetera. There is something that makes Poppers state-ments and qualifications hardly coherent, or in need of fur-ther articulation, to say the least. He says he is not a na vefalsificationist, but what is he then?

Sir Karl is not, of course, a naive falsificationist. He

knows all that has just been said and has emphasised

it from the beginning of his career. Very early in his

LSD he says that . . .no conclusive disproof of a theory

can ever be produced . . .. Statements like this display

one more parallel between Sir Karls view of science

and my own, but what we make of them could scarcely

be more different. For my view they are fundamental. . .

For Sir Karls, in contrast, they are an essential qualifi-cation which threatens the integrity of his basic position.

Having barred conclusive disproof, he has provided no

substitute for it, and the relation he does employ

remains that of logical falsification. Though he is not a

naive falsificationist, Sir Karl may, I suggest, legitimately

be treated as one. (Kuhn, 1970a, p. 14)

Popper needs something to articulate (some of) his ideasbetter. This something is what Kuhn (and Lakatos) has(have), and what makes that the same statements sounddifferent, as Kuhn acknowledges:

our intentions are often quite different when we say the

same things. Though the lines are the same, the figures

which emerge from them are not. (Kuhn, 1970a, p. 3)

The conflict clearly emerges in a topic they both explicitlydisagree about, namely the value of NS:

I admit the existence of what Kuhn calls NS, but I dont

admit the evaluation behind the term normal: It is not

only that I dislike it, but I also believe that it became

important just very recently and it is, in my view, a dan-

ger for science. (Popper, 1974, p. 1145)

the normal scientist, as Kuhn describes him, is a personone ought to be sorry for . . . He has been taught in

a dogmatic spirit: he is a victim of indoctrination.

[. . . And his attitude] a danger to science and, indeed,

to our civilization. (Popper, 1970, pp. 5253)

Why is the normal scientist so dangerous? Because, accord-ing to Popper, Kuhns normal scientist has been indoctri-nated, is dogmatic, acritic and, to sum up, such scientistcontinues epistemically attached to the theory/paradigmeven when empirical tests show evidence against it. Thisis the core of Poppers charge, an activity like this cannotbe rational in principlesince rationality amounts to the dis-

10 Regarding the former, cf. the last paragraph of the last section; about the latter, although I think Kuhn has many insights (cf. Kuhn, 1977), theirelaboration is, to me, totally led astray by his ideas on incommensurability.



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position to critically revise our beliefs when contra-evi-dence is found.

There are more textual references of a similar kind, but Ithink that these suffice for realising that something goes

wrong in this controversy. Something that, firstly, cannotbe explained in terms of the prescriptive/descriptive distinc-tion since, as we have seen: (i) Popper attributes to Kuhnan evaluation of the phenomenon; and (ii) although Kuhndoesnt like to use normative terms, he talks of the differentsignificance he and Popper attribute to NS, connoting hispositive evaluation of the phenomenon. And it couldhardly be otherwise, since we saw that, terminological pref-erences aside, both Popper and Kuhn are analysing a pieceof scientific practice constituted by certain rules and, inattempting to make such rules explicit, both are performinga normative/descriptive task. And secondly, somethingwhich cannot be explained in terms of the truth/problem-

solving distinction either, since their different evaluationof NS does not follow from their theses on the goal of sci-ence. A friend of problem-solving may or may not believethat refutations oblige us to (epistemically, see below)abandon the paradigm/theory;11 and a friend of truthmay or may not believe that refutations are (epistemically)compatible with the preservation of (the core of) theories/paradigms (more on this below, Section 4). Therefore nei-ther the prescriptive/descriptive distinction nor the truth/problem-solving one suffice here. There must be somethingelse involve and we have to look for it elsewhere.

As I said, I think we have to look for it in a field appar-

ently not involved in the controversy. As far as I can see,the only way to fully understand this controversy is takinginto account the different conceptions of scientific theoriesthey implicitly hold. We will have now a brief look on theseconceptions and see later how they help with understand-ing the otherwise intractable aspects of this controversy.

3. The structure of theories and normal science

My thesis is that Popper cannot articulate his viewbecause he lacks a good reconstruction of essential aspectsof the synchronic (hence diachronic too) nature of theories.

And he thinks that Kuhns NS is a danger for (scientific)rationality because he misunderstands Kuhn when Kuhnsays that there is no logical force involved in refutation,that (epistemically) we can keep the same theory after ref-utations/anomalies and that to abandon a theory is not amatter of logic.12

As is well known, Poppers view of (the synchronic nat-ure of) scientific theories is the axiomatic traditional one: atheory is basically a mere conjunction of statements, withno fine grained structure, where every statement has the

same weight;this is a rocky view of theories with no differ-ence betweenmore essential/centralandless essential/centralconstituents. Then, upon this view, every change is alike.

Kuhns (and Lakatoss) interest in the history of science

allows him (them) to emphasise a fact that, yet almost obvi-ousonce one pays attention to it, is extremely important fora correct analysis of scientific practice, namely that scientifictheories are enduring entities: they change preserving theiridentity for a while, passing through different stages/ver-sions, until they die, that is, until they are replaced by anew one. If theories, diachronically considered, are endur-ing entities then, synchronically considered, they must benon-compact entities: they must have parts which are notessential in the sense that their change is compatible withthe survival of the theory; and other parts which are essen-tial, whose change amounts to the death of the theory.

When, after several (and sound) charges of imprecision,

Kuhn makes his original notion ofparadigmmore preciseby the new concept of disciplinary matrix, he says of thefirst component, the laws:

. . .symbolic generalisations [like f = ma . . .] are not so

much generalisations as generalisation-sketches, sche-

matic forms whose detailed symbolic expression varies

from one application to the next. For the problem of

free fall, f = ma becomes mg = md2s/dt2. For the simple

pendulum, it becomes mg sinh= md2s/dt2. For cou-

pled harmonic oscillators it becomes two equations,

the first of which may be written m1d2s1/dt

2 + k1s1=

k2(d + s2s1). More interesting mechanical problems,

for example the motion of a gyroscope, would display

still greater disparity f = ma and the actual symbolic

generalisation to which logic and mathematics are

applied. (Kuhn, 1970c, p. 465; cf. also Kuhn, 1970d

[1962],Postscriptum, p. 155 and Kuhn, 1970b, p. 272)

The most general symbolic generalisations (like f = ma,which are not proper laws but schemes of laws and there-by empirically empty/irrefutabletaken in isolation) are sup-posed to apply, in different specific versions, to allexemplars and are essential to the theory/matrix; whereas

the different specifications of these general principles,which apply only to specific applications/exemplars, arenot essential since they can change without putting theidentity of the theory into risk. Analogously, some of theseexemplars, the paradigmatic ones, are essential in the sensethat they cannot be questioned without putting the identityof the theory into risk (for example planetary motions),whereas others are not essential since they can go in (forexample ties) or out (for example light) with no dangerfor the identity of the theory. (Something alike may happen

11 Actually, from a problem-solving perspective, ifthe failure is not massive and the paradigm continues to work quite well in a vast number of othercases, it might be more rational to try to solve the anomaly while preserving the (nucleus of) the paradigm than to abandon it building a new one, since thelater may imply a (perhaps temporal) lost of problem-solving capacity.12 To be fair, Kuhn didnt help very much, perhaps because he was not conscious yet that part of the controversy was driven by their differences about the

structure of scientific theories.



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with the other two components of the disciplinary matrices,models and values, although we wont focus on them here).

The essential/accidental distinction applied to the com-ponents of scientific theories is obviousonce one pays atten-tion to and emphasises the fact that theories, like manyother natural and cultural entities, endure. What emergesfrom these considerations is a picture of theories such that,at a single moment, a theory can be represented as a (tree-like) net with a nucleus/core (of laws, principles, and so on)at the top from which different lines of specific laws/princi-ples open out downwards in order to account for differentspecific phenomena. For example, in the case of ClassicalMechanics (in a specific moment of its history, see below),something like the tree-like net inFig. 1.13

This net-like structure represents a single theory in aspecific moment/period of its life. Normal science, that is,

intratheoreticchange, is the evolution of a theory throughdifferent stages, a succession of such nets preserving thenucleus (constituted, basically, by some very generallaws/principles and some paradigmatic exemplars). Andrevolutionary science, that is, intertheoretic change, is thesubstitution of (the last stage of) one theory-evolution by(the first stage of) another (which is compatible with somethings being preserved through the revolution,14 yet thesethings cannot be the whole nucleus).

Ill use D-theory for referring to theories diachronicallyalong their whole history, and S-theory for referring totheories synchronically as the components/stages of D-the-ories. We can then summarise the (idealised) kinematics ofscientific change in Fig. 2. A certain D-theory D-T1 (e.g.Classical Mechanics) is constituted along its history by asequence of n S-theories S-T11, S-T

21;. . . ; S-T

n1 which share

the same nucleus. This sequence, D-T1s life, correspondsto a period of normal science. When, after a crisis, changesaffect the nucleus, then we dont have normal science any

more but a revolution, after which a new D-theory D-T2(e.g. Relativistic Mechanics) comes out in its first versionS-T12, a new period of normal science starts with other S-theories S-T22, S-T

32, . . . as improved versions all sharing

the new nucleus, until the new crisis and revolution.

Though some complexities arise here, what we have seen,even so simplified, suffices for showing how these differentconceptions of the structure of scientific theories mayaccount for the intriguing aspects of the controversy I havepointed out.

4. Rationality, refutation and S-falsificationism

Poppers correct insight is that rationality implies thatwhen there is a predictive failure we cannot be epistemi-cally15 indifferent, we must do something. And this is cor-rect irrespective of whether we believe that sciences goalis truth or only problem-solving. But he stated this idea

many times (see the quotations above) in these simplisticfalsificationist terms:

(FALS) Theories must be (epistemically) abandoned

when refuted.

And he complained against Kuhns NS because he thoughtthat NS violates this rationality condition.

It is my claim that, properly understood, NS does notviolate this rationality condition. The key is to realise thatthe occurrence of theories makes FALS ambiguous. It isthen normal that confusion and misunderstanding arisein the debate: one, Popper, says he (roughly) endorsesFALS, and the other, Kuhn, says he doesnt; but at thesame time they both say they accept part of what the otherwants to mean, and so on. As we have seen Kuhn feels thatthe same words sound different. Why? In brief: they wereequivocating over the term theory. If we disambiguateit, we have

f=m(s/t)"

s-dep. forces (s/t)'-dep. forces

dir. dep. inv. dep. frict. forc.

m(s/t)"=-kx sq. inv. m(s/t)"=

-(s/t)'mgsin

m(s/t)"= m(s/t)"=

-mgsin G(mm'/s2)

Fig. 1.

S-T11 S-T1

2 .. S-T1n S-T2

1 S-T22 ..

.. ..

D-T1 D-T2

Normal science Revolution Normal science

Fig. 2.

13 What follows is a Sneedianstructuralist presentation of these Kuhnian ideas, which Kuhn himself recognised as an accurate precisification of (this partof) his thinking (cf.Kuhn, 1976, 2000). This graph shows only the net of laws, it should be completed with the associated applications, models, values, etc.This is an informal presentation, but it can be made fully precise using the structuralist tools; for an early structuralist precisification of Kuhns ideas (cf.Stegmuller, 1973, Ch. XIX, and 1979); for a later one with more standard structuralist apparatus (cf.Balzer, Moulines, & Sneed, 1987, Ch. 5, and Balzer &Moulines, 1998).14 For instance in the Classical to Relativistic revolution, the idea that for bodies to change their state of motion energy is needed.15 Epistemically, since this is compatible with continuing to use the refuted theory for practicalreasons as long as we dont have better alternatives, or

when we have an epistemically better one but the former is simpler and works quite well in certain domains (e.g. geocentrism for navigation, ClassicalMechanics in vast number of cases, etc.).



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(D-FALS) D-theories must be (epistemically) aban-

doned when (their last stage is) refuted.

(S- FALS) S-theories must be (epistemically) abandoned

when refuted.

D-FALS is false, it has no rationality import (irrespec-tive of whether sciences goal is truth or merely problem-solving). As Kuhn showed, there is no purely logicalreasonfor abandoning one D-theory and starting another (inLakatosian terms, for abandoning the core instead of keep-ing addressing the refutation to the protection belt). Thisis not matter of logic but of confidence failure; scientistsdont trust the theory any more as the frame for tryingto solve the anomalies. Just as, following Stegmullers anal-ogy,16 there is no (formal) logic involved in the decision ofbuilding a new house instead of continuing trying to fix theleaks. Yet according to Kuhn there is a lot of non-(for-mal)logic rationality: you can be rational or irrational indoing it, but the criteria have nothing to do with (formal)logic.17

S-FALS is true (irrespective of whether sciences goal isproblem-solving or truth), and keeps all of Poppers correctinsight.And Kuhn endorses it: in NS, when we have a prob-lem/anomaly, we (epistemically) must do something, wecannotbe (epistemically) indifferent, we mustchange/aban-don the S-theory and build a new one. Either preservingthe core, that is, building a different S-theory stage of thesame D-theory (changing the protection belt, in Lakatosianterms); or trying a different core, that is, building a different

S-theory with a new core opening thereby a new D-theory.Nothing in logic obliges us to do the later better than theformer and this is perfectly compatible with any sensiblenotion of rationality. Yet, logic does oblige us to do eitherthe former or the later, and Kuhn totally agrees with this

(remember that, among the former, there is room for theredescription of facts/observations, changing some con-stants, changing some very specific laws, applying newmeasurement methods, postulating new applications, andso on18).

There is a curious passage that could seem a refutationof my claim that Kuhn endorses S-FALS, a passage inwhich Kuhn says that in NS it is not the theory but the sci-entist what is tested:19

when engaged with a normal research problem, the sci-

entist must premise current theory as the rules of his

game. His object is to solve a puzzle . . . [If his conjec-

ture] fails, only [his] own ability not the corpus of cur-

rent science is impugned. In short, though tests occurfrequently in normal science, these tests are of a peculiar

sort, for in the final analysis it is the individual scientist

rather than current theory which is tested. (Kuhn,

1970a, pp. 45)

This cannot mean, literally, that in NS the entity which isthe target of an empirical test is not a scientific constructbut a human being. They key is to realise that what scien-tists have to do in NS is to solve puzzles/anomalies. And ananomaly is something that does not fit with the current the-ory. Hence the current theory, the current D-theory, has aproblem; that is, its last current S-theory has a problem.And the fact that Kuhn clearly states here (as everywhereelse) that normal scientists task is to try to fix these prob-lems shows uncontroversially that according to him thenormal scientist cannot remain (epistemically) indifferentwhen confronted to an anomaly. Normal scientists musttry to solve the problem. This is their task in NS, whichin our jargon is tantamount as saying that they have tochange the current S-theory by another one that solvesthe anomaly.20 Thus the current S-theory must be (episte-mically) abandoned, which is what S-FALS states. Sincewe are in NS it must be replaced by another S-theory ofthe same current D-theory; in NS the scientist mustpremise

the (nucleus of the) current (D-)theory. Of course in doingso the normal scientist may fail, and in this sense it is him,not the premised D-nucleus, that is challenged.

Hence, in both normal science and revolutionary science(RS), when we proceed to an empirical test what is tested iswhat we use to make the prediction, and this is the wholetheory. To be more precise, what is tested is at least onebranch of the theory-net including both top-nuclear andbottom-specific parts which, remember, cannot be testedindependently of each other. What is different in NS andin RS is what scientists are ready to do after a negativeoutcome. As we have seen, NS is characterised by the(implicit) rule of trying to solve negative tests addressingthe changes to the bottom-specific parts preserving the

16 Cf.Stegmuller (1973)(for a related, yet different ancestor of this analogy, see also Post, 1971).17 This is not exactly inter-paradigmatic theory choice/evaluation (cf. Kuhn, 1977), since in theory choice the options already exist to be compared. The

rationality related to the choice between continuing to reforming the old paradigm or starting a new one has to do with plausibility conditions and whatKuhn calls crisis phenomena. These plausibility conditions are vague and hard to systematise but, although Kuhn speaks often in quite psychologicalterms, they provide the only possible notion of rationality applicable in this case, as we realise when we think in the building-a-new-house analogy: ifthings start to gotoobadly, it is irrational to keep fixing the house; as it would be irrational to build a new one after the first leak (with lot of vagueness inbetween, true, but vagueness is a different issue).18 An aside: facts/observations may very well be theory-laden, but not by the same theory-laws that try to explain/predict them. Sometimes they are laden

through non-nuclear connections with other theories (e.g. optics in the case of the telescope and Venus phases), sometimes by a presupposed theory inthe nucleus (e.g. kinematics in mechanics) (cf. Lewis, 1970; Hempel, 1970 and 1973; Sneed, 1979 [1971]; Lakatos, 1970 and Dez, 2002) for the origin of thedistinction between the conceptual part of the theory that describes the facts (concepts whose determination does not presuppose the laws of the theory)and the conceptual part that explains data so described as a different distinction from the traditional observable/theoretical one.19 I thank Stephan Hartmann for pointing this out to me.20 Of course this is an idealisation, since as Kuhn insists many times we can never fix all the anomalies, paradigms/disciplinary matrices do have always

anomalies.



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top-nuclear unchanged (the Lakatosian negative and posi-tive heuristics), whereas RS consists in addressing changesto the nucleus. The kind of activity scientists are ready todo after a failure test is quite different. Normal scientists

have to find out a way of fixing the anomaly withoutchanging the nucleus, which amounts to different aimsand needs different abilities to the ones needed in RS. I takeKuhns statement to be a peculiar way of emphasising thisdifference in attitudes and abilities, connoting that in NSthe (nucleus of the) D-theory is not put into question,but premised. Yet of course there is one S-theory literallytested in NS and, if unsuccessfully, scientists are (epistemi-cally) obliged to change it. This is the only interpretation ofthe passage compatible with other parts of Kuhns work.Therefore, Kuhn is not denying S-FALS, quite thecontrary.

Another challenge to my interpretation21 comes from

the many places in which Kuhn says that theory replace-ment is exclusive of revolutionary science, or even that[p]aradigms are not corrigible by normal science (Kuhn,1970d [1962], p. 122). Moreover, Kuhn insists many timesthat normal science, unlike revolutionary science, is cumu-lative, but how could it be so if, as I maintain, theories aresubstituted during normal science? The key is to insist thattheory is ambiguous, it can refer to either S-theories or D-theories. My whole point is just that when Kuhn says suchthings, as when he explicitly argues against falsificationism,he is referring to D-theories. Paradigms are not corrigibleby normal science in the sense that what constitutes the

paradigm/disciplinary matrix is the nucleus, and thenucleus, as we have seen, is preserved during normal sci-ence; actually, the preservation of the nucleus is whatdefines normal science. But if we take at a certain momentthe nucleus together with the whole set of complementaryassumptions, laws, and soon, what we obtain is (in ourterms) a complete S-theory, that is, a specific version ofthe paradigm/disciplinary matrix in a specific moment.And these things are replaced during normal science. Notin their nuclear part, of course, but in their non-nuclearcomponents. Kuhn devotes the full Chapter III of Thestructure to the different kinds of activities developed dur-ing normal science. The main ones are: improving theexperiments/measurements and the experimental/measure-ment apparatus; determining or making more precise somephysical constants; identifying new phenomena as similarto familiar ones; improving the form of existing laws;applying existing laws to new phenomena (for exampletides); developing new laws relating new phenomena toold ones (for example hydrodynamics); and, we can add,even sometimes throwing away some phenomena (for

example light). In our terminology, all this consists in mod-ifying the non-nuclear parts of the S-theories, that is, insubstituting a specific S-theory by another which sharesthe nucleus with the former. Of course Kuhn does not

express this in these terms;22

the whole point of this paperis that reconstructing him in this way we understand himand this part of his controversy with Popper better. Thisis the sense in which Kuhn (rightly) endorses S-FALS,yet (rightly too) not D-FALS. Intra-paradigmatic changeis S-theory replacement, which is compatible with leavingthe (essential part of the) paradigm unchanged. And thisis how normal science may be cumulative (and as a matterof fact it isoftencumulative), because the commonnucleus is what theoretical content depends on. Since thiscommon core is what is not preserved in revolutionary/inter-paradigmatic change, such change, according tohim, does not allow comparison by content and, as a con-

sequence, revolutionary science is not cumulative (all thisdepends on additional, and highly controversial theses oncontent and meaning that I will not discuss here).

It is worth stressing that, as I have already said, nothingin this interpretation depends on whether we believe thatthe goal of science is truth instead of merely problem solv-ing. Maybe one could say, along the lines of Feyerabendsproliferationism, that logic alone doesnt entitle us tochange the D-theory, but that logic plusthe thesis that sci-ence aims at truth (not only at problem-solving) does, sincethe more the proliferation of theories the higher thechances for truth; hence this issue would not be indepen-

dent of theses about sciences goal. But things are not so.It is true that the greater the proliferation the higher thechances for truth, but the key question is: the greater theproliferation of what? Of D-theories or of S-theories? If sci-ence aims at truth, after a refutation the truth may lie inprinciple in a different D-theory as well as in a different

S-theory of the same D-theory. That is, the falsehood ofan S-theory may lie in the top, core, D-essential, generallaws/principles, but it may lie in the bottom, more specific,D-non essential ones as well, and since neither top nor bot-tom laws/principles can be tested in isolation, refutation doesnot entitle us to modify the former rather than the latter,even if the goal of science is truth. Maybe science aimingat truth makes a case for proliferation, but the whole pointis that even regarding truth, proliferation of different S-ver-sions of the current D-theory is as rational as proliferationof (incipient) new D-theories.23

To summarise: Popper attributes to Kuhn the thesesthat science often behaves non-FALS and that this is goodfor science, whereas for him it is a danger for science andeven to our civilisation. Yet, because of the ambiguity of

21 I owe this criticism to an anonymous referee.22 Although he has agreed with a very similar way of re-presenting his ideas (cf. Kuhn, 1976, 2000).23 Feyerabend doesnt accept the distinction between S-theories and D-theories (cf. Feyerabend, 1970, 1975, 1977), since he considers that, given the

widespread theoretical interrelations, every change infects everywhere. But, again, if Kuhn is right, and we think he is, it is simply false that all parts of thetheories are equally interconnected with every other. The whole point of Kuhn we are emphasising here is that they are not, that we can distinguish degreesof interaction. And again, Kuhns reconstruction fits historical data better than Feyerabends.



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FALS, this charge is misguiding. I am not saying that Pop-per attributes to Kuhn the negation of both D-FALS andS-FALS, since he didnt distinguish between them. Butthe effect was the same, he attributed to Kuhn a general,

or global, anti-FALS thesis. If we distinguish them, Ithink it is clear that Kuhn never defended an anti-S-FALSthesis (a real danger for science, true, if not to our civilisa-tion), though he diddefend an anti-D-FALS thesis, whichis perfectly correct, completely coherent with any sensiblenotion of rationality and not dangerous for science at all.In brief: since Popper didnt have in mind the distinctionbetween S-theories and D-theories, he (i) could not articu-late his non-nave falsificationism, and (ii) could not seethat NS persistence is compatible with FALS-rationalityproperly understood. Since Kuhn did have this distinctionimplicitly in mind, he could articulate better the samefacts and see that the persistence of NS is perfectly coher-

ent with FALS-rationality properly understood. In ourterms, coherent not with D-FALS, which is false, but withS-FALS, true and never questioned (at the epistemic level)by Kuhn. If I am right, then, this implicit equivocation onthe notion of theory causes the puzzling aspects of thecontroversy and looking at it we can remove the perplexityKuhn himself confesses to feeling:

our intentions are often quite different when we say the

same things. Though the lines are the same, the figures

which emerge from them are not. That is why I call what

separates us a gestalt switch rather than a disagreement

and also why I am at once perplexed and intrigued about

how to explore the separation. (Kuhn, 1970a, p. 3, my

emphasis)

All this has to do with possibleNS-rationality, that is, itshows just that, contrary to Popper, NS may be rational.Which are the criteria for NS actually being rational isanother, related but different issue, an issue that has todo with the connections (both lawful/formal and empiri-cal/applicative) between successive S-theories stronger thanmerely preserving the theory-core. It is worth emphasisingthat NS is not actually rational merely by definition ofNS.24 What defines NS is, basically, the persistence of cer-tain formal-and-applicative nucleus, plus certain models,values and practices associated with it. But, although as amatter of fact scientists do this kind of activity almostalways (and as a group, probably always) rationally, thenotionof NS does not exclude the possibility of an irratio-nal normal scientist, nor even of an irrational normal scien-tific community. For instance, if they continue workingwithin what has become, in Lakatosian terms, a clearlydegenerate research programme (that is, post-Lavoisierphlogiston chemistry, post-Keplerian geocentric astron-omy, and the like). It is true that this irrationality is hardto evaluate at present, since the conceptual possibility that

a degenerate research programme regenerates andbecomes progressive again is always open, and then it can-not command what to do in a certain moment. But whyshould it? Maybe overall it is evaluable, as Lakatos

stressed, only ex post facto. But this is compatible with,so to speak, local evaluations when the research pro-gramme is pretty degenerate at a certain moment. Even ifthe posterior regeneration is conceptually possible, it seemsperfectly plausible to say that, at the moment of such adegenerate stage, it is irrational to continue working in it(again, the house-leaks analogy applies). Of course muchmore has to be said regarding the criteria for progressive/rational NS, and Kuhn and Lakatos didnt say very much,but what they did suffices for seeing that there is a genuinesense in which NS is rational (when it is).25

5. Conclusion

If the hypothesis defended is sound, their implicit differ-ences on the notion of scientific theory is what explains thenoise in the PopperKuhn controversy, why the samethings sound different in both mouths, why they seemedto misunderstand each other. In a sense, they actually mis-understood each other, since the meaning of their statementsabout the relation between theory testing, theory abandon-ment and rationality depends on the implicit reading oftheory, which was different. Once this, apparently unin-volved element is made explicit, then Kuhn is right andPopper is (partially) wrong in their descriptive/prescriptiveendeavour. And this is so independently of whether sci-ences goal is truth or merely problem-solving. The argu-ment is transcendental in a sense: this interpretationprovides understanding of certain parts of the polemicsand I know no other way of providing such understanding.Neither the prescriptive/descriptive dichotomy, nor thetruth/problem-solving one can. Nor can the statement/non-statement distinction, contrary to what Stegmullersuggests. Even someone like him, the first who approachedKuhns ideas in the vein I have presented here, misaddress-es this controversy. Evaluating Poppers criticisms ofKuhns normal science, and after correctly emphasising

that Kuhns normal science essentially presupposes the dif-ference between very general central/core principles andmore specific non-central laws, regarding falsificationismhe says:

As a mathematical structure a theory is immune to fal-

sification as a consequence of the fact that it is not the

kind of entity that make sense to say that it has been

refuted, as it wouldnt make sense either to say, for

instance, that a [algebraic] group has been refuted . . .

The common assumption of all Kuhns opponents is

the statement view, according to which theories are

24 Of course the rationality of NS does follow from the definition ofgoodNS, but this is of course an additional definition (see below).25 Maybe this sense is weaker than Poppers rationality, but as I said at the beginning, philosophy of science has to elucidate the kind of rationality

characteristic of the rules that actually constitute scientific practices, not to misinterpret the rules guided by a preconceived notion of rationality.



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classes of statements . . .The notion of theory [presup-

posed by] Kuhn in his description of normal science

can be adequately precisified only within the framework

of the non-statement view of theories. Kuhn himself has

contributed to the confusion conceding too much to hispopperian opponents, admitting for instance, that a the-

ory must be testable in principle. (Stegmu ller, 1973, Ch.

IX, 2d)

According to our interpretation, this explanation istotally misguiding. The statement/non-statement differenceon the nature of theories hasnothingto do withthiscontro-versy about falsificationism. One could present both thePopper and Kuhn accounts in eitherway. Though Kuhnsideas are better presented in a non-statement manner, wecan perfectly make sense of the distinction between S-theo-ries and D-theories within the statement view. The reason

why the statement/non-statement difference does notaccount for the PopperKuhn controversy over falsifica-tionism is that, though literally speaking theories recon-structed in a non-statement manner, that is, as sets ofmodels, are not the kind of entity of which truth and false-hood are predicable, nevertheless they carry a statementassociated with them, the so-called theorys empirical claim,which asserts that certain empirical systems are embedda-ble into the models. Andthisstatement is of course suitableof truth/falsehood. This suffices for referring to the refuta-tion of the theory in the sense relevant to the controversyanalysed here.

What I propose is then, in Kuhns terms, like a gestaltchange: if you read things in the proposed way, payingattention to their implicit disagreement on the nature andstructure of scientific theories, then you see what hap-pened and you understand certain passages that, other-wise, are hardly understandable.26 The only author Ihave found that, if I understand him well, is relatively closeto this interpretation is Worrall (2003). He correctlyemphasises the presence of a Duhemian ancestor in Kuhnstheses, namely the idea that the minimum testable unit inscience consists always of a central theory together with aset of auxiliary assumptions, and that in some cases thecentral theory breaks down into a core component togetherwith a series of more specific assumptions. This fact has theconsequence that [t]he falsity of the central theory doesnot

follow from the falsity of the empirical conclusion (ibid., p.73), and therefore

if the empirical consequence entailed by some initially

accepted theoretical system turns out to be false, then

it would be just as dogmatic to arguein the way thatPoppers rhetoric seems to endorsethat it must be

the central theory or the core theory within the central

theory that is false, as it would be to argue that the fault

cannot be with the central theory but instead with some

auxiliary. (Ibid.)

Kuhns anomalies are, then, at least in the simplest case,

falsifications of overall theoretical systems that [in NS]

scientists regard as likely to be resolved by replacing that

theoretical system with another one that shares the same

central theory and differs only over some auxiliary or

instrumental assumption. (Ibid., p. 77)

According to Worrall this shows the sense in which, in hiscontroversy with Popper about falsification and normalscience, reason lies on Kuhns side. Other differencesaside,27 I find this quite congenial with the general idea be-hind the interpretation I have defended here. In particular,with the theses that (i) it is essential to pay attention to thedifferent essentiality of the different components of whatis tested, and (ii) Kuhn rightly rejected D-FALSyet always accepted S-FALS.

To conclude, one might protest that all this interpreta-tion is an unacceptable deflationary view of the part ofthe controversy at stake. If things are as I say, reason lies

too obviously on Kuhns side, and for too obvious reasons.Well, these reasons may very well seem obvious to us,familiar as we are with diachronic aspects of science andtheir synchronic implications. Yet, it was not obvious atthat time at all; to me, one of Kuhns major contributionswas precisely to point out these almost obvious facts andextract from them a more complex, more accurate andmore useful picture of what D-theories and S-theoriesare28 (though often in a not very precise way, it is true).

I want to emphasise again that these conclusions areexplicitly confined to the possible rationality of NS which,as we have seen, if Popper were right would be irrationalin principle. NS may be rational because it satisfies the min-imum possibility condition for rationality, namely whentesting goes wrong we cannot acritically, dogmatically

26 One can then raise the following question: had Popper entertained and acceptedthe distinction between S-theories and D-theories, would he haveaccepted that (*) the step from one S-theory to another S-theory of the same D-theory preserving the nucleus is compatible with his (non-na ve)falsificationism? Answer: if he accepted that the nuclear laws/principles cannot be tested in isolation (as he probably did), then he should have accepted ( *)(but, who can tell what Popper would actually had done?).27 This diagnosis, Worrall says, is reinforced if we take into account two new features that Kuhn added to Duhem which are connected with Kuhns

insistence on the importance in science of commitment to tradition (p. 78): (i) often it is not clear for scientists which specific auxiliary assumptions arethe best for completing the central theory; (ii) the central theory is often associated with a heuristics. I think Worrall is right in emphasising these facts, towhich I have not paid enough attention; yet I also think that this does not undermine the core of the interpretation defended here.28 The same could be said about Lakatos, upon a certain reading of him, since it is not clear to me that his research programmes always fit the profile of

our D-theories (cf. 1977). Sometimes they do, but sometimes he seems to refer to more coarse grained entities, including more than one D-theory,something in between Kuhns D-theories andLaudans research traditions (cf. 1977). But, as the many references to him in the text show, I think that hisessential point against Poppers nave falsificationism and his sophisticated alternative is along the same lines we have outlined here for Kuhn.



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and dangerously remain epistemically indifferent, we areepistemically oblige to change the S-theory. Regardingother parts of their controversy, like incommensurability,comparability, intertheoretic progress, realism and sci-

ences goal, I have not said anything and nothing in whatI have said implies that Kuhn does better than Popperthere.29 Indeed, I believe that in some of these topics Kuhnis wrong, or at least less right than Popper. But this is a dif-ferent issue. My only thesis here has been that, contrary toappearances, an essential part of their otherwise intractabledisagreements in their controversy about the possible ratio-nality of NS is explained and solved when we focus on theirdifferent conceptions of what scientific theories are. If I amright, though the goal of this paper is mainly historical, itwould also show that a better reconstruction/interpretationof scientific constructs allows for a better analysis (descrip-tive and prescriptive at the same time) of scientific prac-

tices. And, as a consequence, that analysis of structuralaspects of scientific constructs is necessary for approachingsome epistemological issues.

Acknowledgements

Research for this work is part of the research projectsHUM2005-03469/FISO (Spanish Ministry of Science andEducation) and BFF2002-10164-E (European ScienceFoundation). The main idea was first presented in a Span-ish version inDez (1998). This paper is a substantial elab-oration of this ancestor, thanks to a sabbatical stay, Spring

2005, at the Centre for the Philosophy of Natural and So-cial Sciences, London School of Economics; I want tothank the CPNSS for the stimulating atmosphere and theSpanish Ministry of Science and Education for the finan-cial support. I also want to thank Roman Frigg, StephanHartmann, Carl Hoefer, Lefteris Farmakis, Salvador Lo-pez, Ulises Moulines, Ana Rosa Perez and Mauricio Suar-ez for their comments on previous versions of this paper.

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