The esperable uberty of quantum chromodynamics

13552198(95)00006-2

The Esperable Uberty of Quantum Chromodynamics

Steven French*

Abstract-Within the philosophy of science there has been a great deal of rather vague talk about the ‘heuristic fruitfulness’ (or what Peirce called the ‘esperable uberty’) of theories. It is my aim in the present paper to add some precision to these discussions by linking this ‘fruitfulness’ to the satisfaction of certain heuristic criteria. In this manner the demarcation between ‘discovery’ and ‘pursuit’ becomes blurred. As a case study. I present the competition between the paraparticle and colour models of quarks in the late 1960s. I argue that the eventual appraisal of the latter as the more fruitful of the two was based on the incorporation of a particular symmetry principle, regarded as a heuristic guideline, rather than on non-epistemic factors concerning ‘cognitive resources’ and the like.

Introduction

This paper begins with a particular question: Why did physicists, in the late 1960s

and early 197Os, pursue the colour model of quarks, rather than the paraparticle

counterpart? From the purely historical point of view, the answer has some

importance, since the former model developed into quantum chromodynamics, while

the latter languished. However, I shall also attempt to draw some broader

methodological conclusions from this episode, particularly as regards the nature and

characteristics of theory ‘pursuit’.

One answer to the above question can be distilled from the view, currently enjoying

a wide degree of popularity, to the effect that theory choice in general is, to a

considerable extent, dependent upon essentially non-epistemic factors concerning, for

example, familiarity with the models and techniques employed. However, I shall

suggest that, first of all, in the general case, this response is tied to the positivist legacy

with regard to the domain of theory pursuit and fails to acknowledge the rich epistemic

structure of this domain. Secondly, I shall argue that in the particular case considered

here, such an approach simply cannot carry the weight it is forced to bear.

As an alternative, I shall press the view that it is the objective structural

*Division of History and Philosophy of Science, Department of Philosophy, University of Leeds, Leeds LS2 9JT. C-mail: [email protected]. Received IO August 1994: inJim form 2 February 1995.

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87

88 Studies in History and Philosophy of Modem Physics

characteristics of the models concerned that contribute to their heuristic fruitfulness,

or ‘esperable uberty’ as Peirce would have called it, and which lead to one

being pursued rather than the other. One such characteristic involves general,

well-established symmetry and invariance principles into whose framework the

model can be incorporated and I shall argue that it was this feature of the colour model

that accounts for the decision to prefer it to the paraparticle approach. Such principles

form the basis of one of a number of heuristic criteria that have been proposed as

providing a rationale of scientific discovery. By drawing on similar criteria in this

manner, ‘discovery’ shades over into ‘pursuit’, which, of course, should come as no

surprise to those who hold that extensive correspondences exist between successive

theories.

Colour versus Parastatistics

In 1964 the fledgling quark theory of hadrons was faced with a fundamental

difficulty, known as ‘the statistics problem’.’ It had been suggested, on various

grounds, that quarks should be assigned spin l/2. Therefore, according to the

well-established spin-statistics theorem (a cornerstone of quantum field theory)

quarks should be fermions and their overall wave-function should be antisymmetric.

However, although this worked well in the case of mesons, it failed in that of baryons

where the symmetric quark model had proven successful in classifying the baryon

spectrum. According to this model, the wave-function of the three-quark collective

of which the particle was composed should be symmetric under interchange of any

two quarks. This, then, was the problem: how could quarks be fermions and also form

aggregates with symmetric wave-functions?

A particularly elegant solution to this problem was proposed by 0. W. Greenberg,

who suggested that quarks be regarded as ‘parafermions’ of order 3.’ This would allow

them to possess wave-functions that were symmetric under permutation of any two

quarks, and also overall wave-functions that were antisymmetric. In this way the

requirements of the spin-statistics theorem were met, without having to give up the

empirically successful symmetric quark model. Greenberg’s solution was the

outcome of a line of research which he had been pursuing and which concerned the

theoretical possibility of particles described by ‘mixed symmetry’ wave-functions;

i.e. particles which are neither bosons nor fermions.

That the standard symmetric and antisymmetric combinations (giving Bose-

Einstein and Fermi-Dirac statistics, respectively) were merely the two simplest of

the set of possible eigenfunctions for an assembly of particles, was recognized by

‘See, for example, F. E. Close, An Introduction to Quarks and Purtons (London: Academic Press, 1979). ch. 5.

‘0. W. Greenberg, ‘Spin and Unitary-Spin Independence in a Paraquark Model of Baryons and Mesons’, Physical Review Letters 13 (1964), 598-602.

The Esperable Uberty of Quantum Chromodynamics 89

Dirac as early as 1926.3 He later wrote that, ‘It appears that all particles occurring

in nature are either fermions or bosons, and that only antisymmetrical or symmetrical

states for an assembly of similar particles are met with in practice. Other more

complicated kinds of symmetry are possible mathematically but do not apply to any

known particles.’ 4

The investigation into these alternative symmetry types was initiated by Gentile

in the early 1940~.~ Essentially he generalized the standard combinatorial approach

to quantum statistics to obtain a generalized ‘intermediate’ statistics, which

degenerated into the Fermi-Dirac and Bose-Einstein forms when the occupation

number equalled one or infinity, respectively. However, this approach was criticized

on the grounds that it violated the fundamental assumption of quantum mechanics

that every physically distinct state of an assembly of particles must correspond to

some unique ray in Hilbert space.6 It was precisely this assumption which Greenberg

rejected in his work.

The theory of parastatistics, as it came to be called, began to attract serious

theoretical attention again in the 1950s following Wigner’s demonstration that the

equations of motion obeyed by the operators in quantum mechanics do not uniquely

determine the standard commutation relations.’ The implication was that perhaps

more general commutation relations could be found that were also consistent with

the quantum mechanical formalism.

It was precisely this implication that Green drew in 1953 in an attempt to loosen

the rigid structure of quantum field theory in the hope of resolving some of the

problems with which it was beset. By imposing the fundamental requirement that any

quantization scheme would be regarded as satisfactory if it ensured the equations of

motion, he obtained a generalization of the existing methods of field quantization that

contained Bose-Einstein and Fermi-Dirac statistics as special cases.* It was then

shown that Green’s ‘parafields’ possessed statistical properties very different from

ordinary quantum fields’ and that the generalized quantization procedure from which

they were obtained was indeed consistent with the formalism of quantum

‘P. A. M. Dirac, ‘On the Theory of Quantum Mechanics’, Proceedings of the Royal Society (London) All2 (1926) 661-667.

“P. A. M. Dirac, Principles of Quantum Mechanics (Oxford: Oxford University Press, 1930; 1958), p. 211.

‘G. Gentile, ‘Osservazioni sopra le statistiche intermedie’, II Nuovo Cimenro 17 (1940). 493-497. ‘D. ter Haar, ‘Gentile’s intermediate statistics’, Physica 18 (1952), 199-200. ‘E. P. Wigner, ‘Do The Equations of Motion Determine the Quantum Mechanical Commutation

Relations?‘, Physical Review 77 (1950), 711-712. *H. S. Green, ‘A General Method of Field Quantization’, Physical Review 90 (1953), 270. Several later

results in the first quantized theory were anticipated by Okayama (T. Okayama, ‘Generalization of Statistics’, Progress of Theoretical Physics 7 (1952), 517-534) and Green’s generalized commutation relations were independently discovered by Volkov (D. V. Volkov, ‘On the Quantization of Half-Integer Spin Fields’, Soviet Physics JETP 36 (1959). 1107-I 111).

91. E. McCarthy, ‘Physical Properties of Particles Obeying General Statistics’, Proceedings of the Cambridge Philosophical Society 51 (1955), 131-140.

90 Studies in History and Philosophy of Modern Physics

mechanics. lo The only problem, noted by Volkov” for example, was that there did

not seem to be any evidence for the existence of paraparticles in nature.

As a graduate student, Greenberg was also interested in the possibility of

alternatives to Bose-Einstein and Fermi-Dirac statistics’* and in 1962 demonstrated

that parafields are not ruled out by the spin-statistics theorem.13 In 1964 he and

Messiah formulated a consistent first-quantized theory of paraparticles, in the context

of a rigourous examination of the Symmetrization Postulate (SP). This is assumed

by all the usual formulations of quantum mechanics and requires, broadly speaking,

that all particle states be either symmetric (bosons) or antisymmetric (fermions).14

They noted that this condition was much stronger than that implied by the quantum

mechanical indistinguishability of particles of the same species. This is expressed in

terms of the Indistinguishability Postulate (IP), which states, informally, that particle

permutations are not observables. Greenberg and Messiah then demonstrated that SP

is a sufficient but not a necessary condition for IP” and that the arguments typically

employed to insert the former into the quantum mechanical formalism are, in fact,

ad hoc in character. In particular, they argued that particle indistinguishability, as

expressed by IP, allows for the possibility that states of an assembly of particles could

correspond to a so-called ‘generalized’ ray within Hilbert space. (The state vectors

then lie in a sub-space of dimension greater than one.) Within the latter framework,

they argued, particles with wave-functions that were not purely symmetric or

antisymmetric were theoretically permitted. Finally, they concluded their paper by

noting that many experiments designed to test SP were actually tests of the weaker

IP and that the statistical character of certain kinds of particles was unclear.

The first quantized approach was further clarified and simplified by Hartle and

Taylor, who demonstrated that the most important theorems of ordinary quantum

mechanics could also be established within paraparticle theory.16 In particular, they

showed how the ‘generalized’ rays could be eliminated and the usual connection

between states and rays restored by moving to a sub-space of lower dimension and

using the one-dimensional ray belonging to such a sub-space to label the mixed

symmetry states. Stolt and Taylor then brought this line of development around full

“T. Kibble and J. Polkingbome, ‘On Schwinger’s Variational Principle’, Proceedings of rhe Royal Society (London) A243 (1957). 2.52-263.

“Op. cit., note 8. %ivate correspondence. 130. W. Greenberg, G. F. Dell’Antonio and E. C. G. Sudarshan, ‘Parastatistics: Axiomatic Formulations,

Connection with Spin and TCP Theorem for a General Field Theory’, in F. Gursey (ed.), Group Theoretical Concepts and Methods in Elementary Particle Physics (London: Gordon and Breach, 1964).

140. W. Greenberg and A. M. L. Messiah, ‘Symmetrization Postulate and its Experimental Foundation’, Phgical Review B136 (1964). 248-267.

The difference between SP and IP can be expressed thus: the former is a restriction on the states for all observables, whereas the latter is a restriction on the observables for all states.

16J. B. Hartle and J. R. Taylor, ‘Quantum Mechanics of Paraparticles’, Physical Review 178 (1969). 2043-205 I.


circle by establishing the equivalence between the first quantized formalism and

parafield theory.17

The history of parastatistics provides an interesting example of the role of

surplus mathematical structure in generalizing a particular theoretical formalism.”

Certain elements of this structure, regarded initially as mere theoretical possibilities,

may then be accorded ontological reference. In the case of paraparticles, it appeared

to be the case that this theoretical possibility was physically realized in Greenberg’s

application of the theory to the statistics problem facing quark theory. However.

the price of this resolution was the introduction of three new labels assigned to

each quark. These labels were subsequently interpreted as representing a new

threefold degree of freedom and in 1965, Han and Nambu introduced the three-triplet

quark model, which suggested that each quark came in three ‘colours’.” These

then provided the extra degrees of freedom by which quarks could have spin l/2

yet also possess symmetric wave-functions under interchange of any two. Thus,

the colour model also reconciled the symmetry characteristics of quarks and

their composites and appeared to be observably equivalent to its paraparticle rival?

The rest, as they say, is history (albeit a complex and very interesting history).”

The three-triplet model with colour went on to become the core of the theory

of quantum chromodynamics, now accepted as the best theory of the strong nuclear

forces currently available. Paraparticle theory, on the other hand, languished and

although some further theoretical work continues to be done, it is now generally

regarded as being outside of the mainstream.‘*

The question then arises: Given that, at the time, there were no experimental

“R. H. Stolt and J. R. Taylor, ‘Correspondence Between the First- and Second-Quantized Theories of Paraparticles’, Nuclear Physics 19B (1970). l-19. They established a one-to-one correspondence between parafields and first quantized paraparticles of finite order by means of the place permutation operators, there being no analogues of the particle permutation operators in the second-quantized formalism. This followed an earlier suggestion by Landshoff and Stapp (P. V. Landshoff and H. P. Stapp, ‘Parastatistics and a Unified Theory of Identical Particles’, Annals of Ph&s 45 (1967). 72-92). It should be noted that Kamefuchi and Ohnuki had also been following their own group theoretical investigation of the wave functions of indistinguishable particles and obtained a highly generalized formalism by translating certain field theoretic results concerning many particle systems into the language of quantum mechanics (see, for example, S. Kamefuchi and Y. Takahashi, ‘A Generalization of Field Quantization and Statistics’, Nuclear Physics 36 (1962) 111-206; S. Kamefuchi and Y. Ohnuki, ‘On Quantum Mechanics of Identical Particles’, Annals of Physics 57 (1970), 543-578; Y. Ohnuki and S. Kamefuchi, Quanrum Field Theory and Parastatistic~ (Springer, 1982)).

‘%ee M. L. G. Redhead, ‘Symmetry in Intertheory Relations’, Synrhese 32 (1975), 77-l 12; see pp. 106107. Further details of the history of parastatistics are given in S. French, ‘Identity and Individuality in Classical and Quantum Physics’, Ph.D. thesis (University of London, 1984).

‘%4. Y. Han and Y. Nambu, ‘Three-Triplet Model with Double SU(3) Symmetry’, Physical Revirn 139B (1965) 1006-1010.

201nsofar as all three-triplet models have the same consequences with regard to hadron spectroscopy, the two models may be regarded as experimentally equivalent. (For further discussion, see Greenberg and Nelson, note 23 (below), pp. 84-88.)

“A. Pickering, Consrrucfing Quarks (Edinburgh: Edinburgh University Press, 1984). ‘*See Ohnuki and Kamefuchi, op. cit., note 17.


grounds for choosing one model over the other, 23 why was the colour model actively

pursued and developed, while the paraparticle model was not?

Familiarity and Opportunities-in-Context

One possible answer is that paraparticle theory was simply too obscure, too

complex and too ‘out of the ordinary’ for most physicists.24 This suggestion springs

from the view that it is primarily the sociological and psychological, rather than the

epistemic, virtues of theories that provide the driving force behind theory choice,

understood here in the broad sense to also include theory pursuit. Thus, scientists will

prefer to work on, or pursue, those models that they are familiar with, using the

mathematical tools and techniques that they learnt in graduate school. Pickering, for

example, attempts to explain the dynamics of scientific practice, ‘. . . in terms of the

contexts within which researchers find themselves, and the resources which they have

available for the exploitation of those contexts’,2’ a position which he characterizes

as ‘opportunism-in-context’.26 More fully, his answer to the question with which I

began this paper is that, ‘Each scientist has at his disposal a distinctive set of resources

for constructive research. These may be material-the experimenter, say, may have

access to a particular piece of apparatus-or they may be intangible-expertise in

particular branches of experiment or theory acquired in the course of a professional

career, for example. The key to my analysis of the dynamics of research traditions

will lie in the observation that these resources may be well- or ill-matched to partic-

ular contexts. Research strategies, therefore, are structured in terms of the relative

opportunities presented by different contexts for the constructive exploitation of the

resources available to individual scientists.“’

Similarly, Giere, while attempting to give an account of scientific decision-making

which embraces both epistemic and non-epistemic values, gives a number of

illustrations of the role of one particular form of the latter: a scientist’s ‘cognitive

resources’ ? These generate potential scientific interests and include, for theoreticians

at least, the models with which the scientist is familiar. By familiarity Giere does not

mean ‘ . . just an abstract, intellectual familiarity. I mean the ability, even the skill,

*‘Op. cit., note 19, p. 1010; 0. W. Greenberg and C. A. Nelson, ‘Color Models of Hadrons’, Physics Reforrs 32 ( 1977). 69- 12 1.

‘See, for example, Pickering, op. cit., note 21, pp. 94-9.5. In private correspondence Pickering notes that, on this point, he relied upon Nambu who described Greenberg’s work as ‘very formal’ and that he was perhaps too sweeping in describing parastatistics as ‘obscure’. Nevertheless he maintains that the choice to pursue colour was made in purely contingent terms regarding the routine techniques that could be applied.

250p. cit., note 21, p. 11. 26‘The opportunism-in-context model of the dynamics of practice is the primary explanatory device of

CQ, .’ (A. Pickering, ‘Knowledge, Practice and Mere Construction’, SocialStudies ofScience 20 (1990). 682-729; see p. 712.)

270p. cit., note 2 1, p. 11. 28R. N. Giere, Explaining Science (Chicago: University of Chicago Press, 1988), p. 213-221.


to work with the models, to apply them in new cases, to use them in calculations,

and so on.“9 Thus one might argue that the physicists of the 1960s were simply

unfamiliar, in Ciere’s sense, with the paraparticle model and preferred the Han and

Nambu approach because they possessed the particular skills that enabled them to

work easily with it.

I do not find this kind of account plausible, either in general or in this particular

case. I do not find it plausible in general because it suggests a view of science

according to which the ‘internal’, epistemic, constraints on theory construction and

choice are so weak that ‘external’ factors must be invoked in order to account for the

decisions of the scientific community. I believe this view is mistaken and is the result

of a somewhat superficial perception of the ‘internal’ constraints within the

framework of which theories are developed and pursued. A closer look at the actual

practice of scientists reveals that there are more constraints upon this practice than

generally supposed.3” The ‘extemalist’ or ‘sociological’ programme can be

understood as a reaction to the positivistic tendency in philosophy of science, which

focused on acceptance and justification to the exclusion of heuristics and pursuit. The

apparent lack of ‘internal’ constraints in these latter domains led to the perception

that there exists a methodological vacuum which, it was thought, could only be filled

by ‘external’ considerations of cultural contexts, research resources, and the like.

There is no such vacuum, however, since heuristics and pursuit have a rich, internal

structure which is worth exploring, as recent investigations have attested.“’

I do not find this kind of account plausible in this particular case for the following

reasons. The paraparticle model had been in circulation for some months prior to the

publication of Greenberg’s 1964 papeP and, as I have indicated in the brief history

above, the idea of a generalized form of quantum statistics had been around for quite

some time. It is certainly notable that the textbook on which generations of physicists

cut their quantum mechanical teeth-Dirac’s Principles-specifically mentioned this

possibility. Furthermore, at the heart of parastatistics lies group theory, a fundamental

part of quantum mechanics as applied to high energy physics and certainly well known

to physicists at that time. (It is worth noting that Greenberg gave two lectures on

parastatistics at a NATO Advanced Study Institute summer school in 1962.” The

“Ibid., pp. 213-214. “‘Cf. P. G&on, ‘Multiple Constraints, Simultaneous Solutions’, in A. Fine and .I. Leplin (eds),

Proceedings of the 1988 Biennial Meeting of rhe Philosophy of Science Association. Vol. II (East Lansing, MI: PSA, 1988), pp. 157-163.

“Perhaps the most well-known collection of studies in this area is T. Nickles (ed.), Scientijc Dtscoverx. Logic and Rufionalify (D. Reidel, 1980) and T. Nickles (ed.), Scientijc Discovery: Case Studies (Hingham, MA: D. Reidel, 1980); but see also H. R. Post, ‘Correspondence, Invariance and Heuristics’, Studies in Hisfory and Philosophy of Science 2 (1971), 213-255, and S. French and H. Kamminga (eds), Correspondence. Invariance and Heuristics: Essays in Honour of Heinz Post (Dordrecht: Boston Studies in Philosophy of Science, Kluwer, 1993).

“A preprint of the Greenberg and Messiah work is cited in A. Galindo and F. J. Yndurian, ‘On Parastatistics’, II Nuovo Cimenro 30 (1963). 1040-1047.

‘j0ne of these lectures was subsequently published as Greenberg, Dell’Antonio and Sudarshan, op. cif.. note 13.


school had, as its principal theme, the application of group-theoretical methods to

elementary particle physics and was attended by, among others, Glashow, Salam and

Nambu.34) Thus, there was little that was fundamentally new or unfamiliar

mathematically in paraparticle theory and this was particularly true of the ‘cleaned

up’ version presented by Hartle and Taylor. This disposes of the claim that the theory

was ‘obscure’ or ‘unfamiliar’ and was not pursued for that reason.

As for the idea that, broadly speaking, ‘political’ or, more generally, ‘cultural’

factors were at work here, it needs to be pointed out that, at this stage of the game,

both models were equally speculative. There simply was no dominant context, either

theoretical or cultural, which could force the choice of one over the other. Finally,

underlying my objections to the ‘extemalist’ account, lies the suspicion that scientists

are rather more flexible than this approach gives them credit for. And in this case,

given what has been noted above, it would not have taken much of a re-tooling of

their ‘cognitive resources’ for them to become familiar enough with paraparticle

theory to develop it further, if it had been worth it, epistemically speaking.35 This is

not to dismiss out of hand the reports of scientists themselves regarding the relative

obscurity or unfamiliarity of different techniques, theories or approaches.36 The point

is rather that the role played by such concerns is considerably less significant than

that played by ‘non-sociological’ considerations having to do with the objective

structure of the models involved.

From the Problematic of Knowledge to the Problematic of Practice: a Response

It has been claimed, by Pickering himself and others3’ that the approach to the

dynamics of practice, which was criticized above, has been substantially refined in

recent years. 38 The changes have proceeded at both the global and local levels.

Globally, Pickering has shifted away from the ‘interest theoretic’ approach

340. W. Greenberg and E. P. Wigner, ‘Group Theoretical Methods in Elementary Particle Physics’, Physics Tpday April (1963), 62-65.

‘Jumpmg ahead a little, ‘t Hooft’s renormalization of gauge theory was initially regarded as very difficult to understand, if not impenetrable, but was eventually generally accepted (op. cit., note 2 1, pp. 177-181).

‘%ee, for example, Giere, op. cif., note 28, pp. 214-218. Parastatistics was referred to as ‘an unattractive possibility’ (R. H. Dalitz, ‘Symmetries and the Strong Interactions’, Proceedings ofrhe 13th International Conference on High Energy Physics (Berkeley: University of California Press, 1967), pp. 215-234; p. 232) and Greenberg himself refers to the familiarity of the colour model (private correspondence).

“Pickering, private correspondence; T. Nickles, ‘How to Talk with Sociologists (or Philosophers)‘, Social Studies of Science 20 (1990), 633-638.

381n their reply to Nickles’ response to their critique of Consrructing Quarks (P. Roth and R. Barrett, ‘Deconstructing Quarks’, Social Studies of Science 20 (1990). .579-632), Roth and Barrett wonder if Pickering has merely refined his earlier views or actually abandoned them (P. Roth and R. Barrett, ‘Reply: Aspects of Sociological Explanation’, Social Studies of Science 20 (1990), 729-745; p. 730). Pickering himself regards the framework in which his more recent work is couched as ‘marking a significant break’ from the earlier ‘sociology of scientific knowledge’ background of CQ (A. Pickering, ‘From Science as Knowledge to Science as Practice’, in A. Pickering (ed.), Science as Practice and Culture (Chicago: University of Chicago Press, 1992) pp. l-26).


associated with the Edinburgh school. According to that approach, as I indicated

above, ‘closure’ within scientific practice-that is, the achievement of consensus-is

to be understood in terms of interests, which both drive practice and serve as standards

against which the products of that practice might be assessed.“’ This, Pickering now

claims, is not a terribly perspicuous way of looking at things, given the complexity

of actual scientific practice. Instead, he advocates the elaboration of new conceptual

frameworks that are no longer bound to employ resources inherited from the concern

with science-as-knowledge, but can develop their own set of concepts that relate more

directly to science-as-practice.

A fundamental element of such frameworks relates to the ‘patchiness’ or

‘multiplicity’ of scientific culture, which is made up of ‘. . all sorts of bits and

pieces-material, social, conceptual-that stand in no necessary unitary relation to

one another.‘40 As Pickering acknowledges, this last is something that has been

particularly emphasized by Hacking and indeed he accords Hacking a place of

prominence in his review of these developments.4’ The above problem of ‘closure’

is now resolved, not in terms of interests, but in terms of the incorporation of these

disparate elements, or ‘bits and pieces’: ‘To successfully engineer an association of

disparate cultural elements is, then, a nontrivial achievement that can itself be taken

as the explanation of a degree of closure in scientific practice, of a limit where practice

can rest (temporarily, at least).‘42

This, then, might be advanced as a response to my comments concerning

constraints above.43 It is the difficulty of ‘fitting together’ these diverse elements that

effectively constrains scientific practice, on this view. At one level, this is entirely

uncontroversial: who today would deny the difficulty in bringing theory and

experiment together? The importance of approximations and idealizations is now

generally accepted and has further emphasized the complexity of the interrelation-

ships between at least two of Pickering’s ‘bits and pieces’.

But on another level, the contention is highly debatable. Hacking, for example, has

alleged that there is ‘patchiness’ and multiplicity not only between elements of

scientific practice but within them. Thus he has claimed that there is no ‘theory’ of

the electron, for example, but rather a disparate collection of disconnected and

unrelated models: there is no common core, only a common lore.44 The inference then,

is that within this particular bit of practice there is, in fact, no ‘closure’ at all, in the

sense of consensus as to the most appropriate model to employ. What commonality

%ee Pickering, op. cit., note 38. 4oIbid., p. 8. 4’I. Hacking, ‘The Self-Vindication of the Laboratory Sciences’, in A. Pickering (ed.), Science as

Practice and Culture (Chicago: University of Chicago Press, 1992). 42A. Picketing, ‘From Science as Knowledge to Science as Practice’, in A. Pickering (ed.) Science as

Practice and Culture (Chicago, ILz University of Chicago Press, 1992, pp. l-26; p. 9). “Cf. Pickering’s comments on Galison, in A. Pickering, ‘Knowledge, Practice and Mere Construction’,

Social &dies of Science 20 (1990). 682-729; p. 727, footnote 46. 441, Hacking, Representing and Intervening (Cambridge: Cambridge University Press, 1983).


that exists is provided by the acceptance of the existence of the electron as a

manipulable tool, which, of course, forms the heart of Hacking’s ‘entity realism’. I

do not find Hacking’s pluralism plausible, but to engage it fully would take me far

beyond the limits of the present work. Suffice to say that on this account,

manipulability of a given entity is mediated by a set of low-lying causal laws (this

is particularly emphasized in Cartwright’s account, which is taken to mesh with

Hacking’s); but then the obvious suggestion that can be made in response is that it

is these that form the common core.

It is with precisely this latter level of theories and models that I am concerned here

and there is little indication in the general exposition of this ‘shreds and patches’

approach, as Nickles terms it,45 as to how the successful engineering of these disparate

material, social and conceptual resources can impose constraints at this level. Perhaps,

then, we should look at the more localized changes in Pickering’s view. Before doing

so, however, it is worth recording that, as Pickering himself notes, this shift away from

the interest theoretic approach has not gone uncontested by adherents of the latter,

who have pressed the point that it is interests that determine a unique closure out of

the many possible closures made possible by the above engineering of resources.46

Again it would take me far outside the scope of the present discussion to enter into

the details of this debate.

At the local level, Pickering now recognizes that opportunism-in-context is not an

exhaustive model of scientific practice, but covers only the goal-formation phase.

Thus, it leaves a gap between the formation of goals and their achievement and it is

within this gap that Pickering claims a notion of ‘resistance’ to practice can be

articulated.47 An example of this resistance in the material world, say, would be the

failure of a particular experimental technique.48 A dialectic of resistance and

accommodation can then be articulated which leads Pickering to a form of ‘pragmatic

realism’ that ‘... recognizes that the production and transformation of scientific

knowledge in accommodation to resistance is inseparable from a larger process of

the production and transformation of complex and heterogeneous forms of life.‘49

More importantly, from the point of view of the criticisms developed above,

Pickering also recognizes that the understanding of goal-formation offered by the

opportunities-in-context model was crude and sketchy.50 The formation of a research

450p. cif., note 31, p. 633. 46A. Pickering, ‘From Science as Knowledge to Science as Practice’, in A. Pickering (ed.) Science as

Practice and Culture (Chicago: University of Chicago Press, 1992). 47A. Pickering, ‘Knowledge, Practice and Mere Construction’, Social Studies of Science 20 (1990).

682-729. 48Pickering gives the example of Morpurgo’s attempt to search for quarks using a liquid-suspension

method (ibid., pp. 694-697). In an analysis of the development of quaternions, he argues that resistance can arise within purely conceptual practice also (A. Pickering and A. Stephanides, ‘Constructing Quaternions: On the Analysis of Conceptual Practice’, in A. Pickering (ed.), Science as Practice and Culture (Chicago: University of Chicago Press, 1992)).

@Op. cit., note 47, p. 688. ‘Orbid., p. 693.


goal involves a process of modelling that is inherently open-ended and it is here that

Pickering appeals to the substantive claims made by the ‘shreds and patches’ approach

and noted above: the open-endedness of this modelling process is managed in practice

through the bringing together of a plurality of elements. ‘Goals situate themselves

at the intersection of projections of multiple cultural elements.‘5’ These cultural

elements are not projected independently of one another, but are brought into

coherence, which Pickering views as a constant ‘telos’ of practice. Once a state of

coherence has been achieved, between, say, experimental procedures and conceptual

models, practice can rest and we move from a dynamic to a static phase in which

findings are reported and conclusions justified.

Again, at one level this all seems uncontroversial (at another, when one considers

the particular details of this move to coherence, it is not, of course). Where the kind

of account being suggested here and Pickering’s approach differ, however, is in his

claim regarding the contingency of goal-formation: ‘I believe that one can see an

underlying general structure to goal-formation in science, and that modelling and

coherence are important concepts in unravelling that structure. But I do not think that

one can offer causal explanations of goal-formation on this basis. To the contrary,

there seems to be an ineradicable element of chance here. There is an explanatory

gap that I cannot see how to bridge between possessing a given range of resources

and assembling them into a coherent goal.‘52 Here he gives the example of Zweig’s

fundamental move of regarding the fundamental representation of the SU(3) group

as referring to quarks, rather than purely mathematical entities, a move which

Pickering claims cannot be understood or justified at all in terms of the context and

resources available at the time. All that we can say by way of explanation is that ‘it

just happened’ .53

This, I think, is simply wrong. Between the neurophysiology and the conceptual

advance lie the heuristics! Zweig’s move can be understood, I think, in terms of

Redhead’s notion of supplying a physical interpretation for surplus mathematical

structure within a theory, noted earlier. 54 This is connected with Post’s heuristic

guideline of ‘Adding to the Interpretation’ (closely related to ‘Taking Models

Seriously’): ‘We take a hitherto incompletely interpreted part of the abstract

formalism of the theory, and give it a tentative interpretation of our own. at some

level.‘“’ Dirac’s interpretation of negative energy states can be understood in exactly

the same way. Once again, further elaboration would take us too far from the central

thrust of this essay, although it is interesting to note Pickering’s appeal to what is

nothing more than a form of the ‘flash of genius’ view! (And again, he is misled by

“Ibid, p. 684. ‘*Ibid., p. 684. 531bid., p. 721, footnote 16. 540p. cit., note 18. “Op. cit., note 31, p. 241.


an explanatory lacuna, which one can see doesn’t actually exist once heuristics is

taken into account.)

Let us ask, then, is there anything in the above ‘refinement’ of Pickering’s views

which would cause us to revise our dismissal of his account as incapable of accounting

for the preference of the colour model over parastatistics? The answer, I think, is no.

The later work really is only a refinement of the earlier and Pickering’s notions of

the patchiness of scientific practice, of coherence and resistance and his form of

pragmatic realism, either do not impact on my thesis at all or do so only in deeply

problematic ways (such as Hacking’s projection of this patchiness to the conceptual

level taken on its own). In particular, the essential idea of ‘opportunism-in-context’

remains, regarded as illuminating the episodes discussed in Construcring Quarks

although not capturing their richness. 56 The new image of scientific practice that

emerges from Pickering’s later work underpins rather than undermines the earlier

(ibid.), and my criticisms stand.57

Another Example: Dirac versus Schriidinger Models of the Nucleus

To further drive home the point that was being pressed before we embarked on the

above digression, let us take as another example, Giere’s case of the ‘young theorist’

who decides to pursue Dirac (relativistic) models of the nucleus rather than

Schrodinger (nonrelativistic) ones. 58 As the names suggest, members of the latter

family are characterized by some form of Schrodinger’s equation, with suitably

approximate interaction potentials obtained by ignoring or down-playing relativistic

effects, whereas the former are all based on the Dirac equation with relativistic effects

included. Whilst admitting that it was new experimental data that led to a resurgence

of interest in the Dirac approach, Giere notes that not all the scientists involved were

convinced of the usefulness of such models as applied to medium-energy interactions.

At this point, Giere claims, non-epistemic considerations must come into play and

he argues for the importance of ‘acquired cognitive resources’ in such situations, in

particular those that refer to the scientists’ ‘ familiarity’ with the model concerned.

As noted earlier, a theoretician’s familiarity with a particular conceptual element, such

as a model, is not to be regarded as abstract, but rather in terms of a particular skill

of applying and extending the model to new situations. Experimentalists typically

share many of the same cognitive resources with the theoreticians, but in addition

possess a wide range of skills necessary for working with the material elements of

j60p. cit., note 47, p. 692. 570f course, it might be argued that it is quite irrelevent whether or not Pickering has changed his

position: given the wide ranging influence of CQ it may still be viewed as a worthy target (cf. P. Roth and R. Barrett, ‘Reply: Aspects of Sociological Explanation’, Social Studies of Science 20 (1990). 729- 745; pp. 73&73 1 and 741). As should by now be clear, my contention is that although his view has changed in certain respects, the more significant elements, which were criticized previously, remain.

“Op. cit., note 28, pp. 216-218.


scientific practice. The upshot is that, ‘The question whether the Dirac or the

Schrodinger approach is correct seems to have played little role in these decisions.‘59

Now, if by ‘correctness’, truth, in the correspondence sense, is meant, then of

course I would agree with this last point since the decisions were made in the context

of pursuit, rather than acceptance. (Indeed, I would claim that, contrary to the

traditional view, theories are not accepted as true in the above sense, but that is another

story.) However, even granted that a young researcher, eager to publish and act in

her best short term professional interest, might prefer to work with that model with

which she was more familiar, the question arises as to how this familiarity was

obtained in the first place. Giere attributes the original impetus for working on these

models to a combination of the authority of the advisor and the student’s theoretical

interests. However, one must go back even further and ask, what was it about that

particular model that made it seem worth pursuing to the advisor and attractive to the

student, even before it gained any predictive success? The answer, I would hazard,

lies with certain objective characteristics of the model, such as, in this particular case,

those that cause it to satisfy the requirement of Lorentz invariance. There is, I trust,

little need to emphasize the fundamental importance of this requirement, embedded

as it is within Special Relativity, itself supported by a variety of epistemic

considerations. Indeed, we get a hint of this in the theorist’s responses as recorded

by Giere6’ and he himself notes the crucial importance of subsequent predictive

success in maintaining interest in this kind of model.

In response, it might be asked why anyone bothers with the non-relativistic theory.

Again, I would point to objective features of the model: those that confer upon it a

certain mathematical simplicity giving rise to greater computational tractability. In

this case the model is regarded as an approximation, useful where relativistic

processes are not extensively involved in the interactions concerned. The importance

of such considerations has long been emphasized: Redhead, for example, has

delineated the nature and stressed the importance of such ‘impoverished models’.”

And, of course, given their pragmatic value, the greater computational complexity

associated with the alternative, and the justification of the approximation concerned

in terms of what is understood to be going on in the domain under consideration, the

employment of such models may be entirely rational. “Nevertheless, as Giere himself

notes, ‘No nuclear physicist seems to doubt that, in principle, the correct model of

the nucleus would be a relativistic model based on the Dirac equation.“” The reason

for such lack of doubt, of course, lies with the success (ultimately empirical) of Special

Relativity and here we see a well-regarded invariance principle-such regard being

59ibid., p. 218. mIbid., p. 211. 6’M. L. G. Redhead, ‘Models in Physics’, British Joumal for the Philosophy of Science 31 (1980).

145-163. 62For more on this latter point, see N. C. A. da Costa and S. French, ‘A Model Theoretic Approach to

“Natural Reasoning” ‘, International Studies in the Philosophy of Science 7 (1993). 177-190. “Op. cit., note 28, p. 184; my emphasis.


grounded, I stress again, in the empirical success of a particular theory-being

invoked to establish overarching criteria of ‘correctness’ for those models associated

with another. This observation is fundamental to my account.

Paraparticles versus Colour Again

Let us return to the case of paraparticles versus colour. An alternative explanation

of the physics community’s preference in this example centres on the fertility or, as

Peirce called it, the ‘esperable uberty’, of the colour model. The central idea here is

that this model possessed a greater capacity for generating new lines of development

than paraparticle theory, which was, heuristically, comparatively sterile. In the

competitive atmosphere of elementary particle physics, the heuristic deficiencies of

the parafermion model consigned it to a theoretical backwater, whereas the potential

fecundity of colour led to its being eagerly seized upon and exploited by the theorists.

However, in order to explore this suggestion further, I need to consider in greater

detail what it is about a model that confers upon it this fertility or ‘esperable uberty’.

Fertility

The, typically Peircean, phrase ‘esperable uberty’@ originally referred to the

‘expected’ or ‘hoped for’ ‘fruitfulness’ or ‘fertility’ of the various forms of reasoning,

deductive, inductive and abductive.65 As one moves from the deductive, through the

inductive to the abductive, one loses security but gains ‘uberty’. Similarly the products

of reasoning, such as the theories and models of science, are commonly accounted

to possess a certain fertility, some to a greater degree than others. However, there has

been little in the way of detailed analysis of this notion, particularly as regards its

‘esperable’ aspect, by means of which, of course, it plays a role in theory pursuit.

There is, as McMullin has noted, some ambiguity in talking of the ‘fertility’ of a

theory.66 It could refer to the actual success a theory has in opening up new avenues,

dealing with problems and anomalies, etc., or it could designate the potential of a

theory for future development. Accordingly he distinguishes between ‘proven’

fertility, or ‘P-fertility’ and ‘untested’ fertility, or ‘U-fertility’. This distinction

generates, in turn, two forms of theory appraisal: there is ‘epistemic’ appraisal, which

is concerned with the truth-value of the theory and which involves an estimate of the

P-fertility of the theory; there is also the ‘heuristic’ appraisal of a theory, which is

concerned with the as-yet unexplored heuristic possibilities inherent in a theory and

“C. S. Peirce, ‘To F. A. Woods, On “Would Be”‘, Collected Papers of Charles Sanders Peirce Vol. VIII (Cambridge, MA: Havard University Press, 1966), pp. 246248.

65T. A. Sebeok, (1983). ‘One, Two, Three Spells UBERTY’, in U. Eco and T. A. Sebeok (eds), The Sign of Three: Dupin, Holmes, Peirce (Bloomington: Indiana University Press, 1983), pp. I-10; p. 1.

“E. McMullin, ‘The Fertility of Theory and the Unit for Appraisal in Science’, in R. S. Cohen et al. (eds), Essays in Memory of Imre Lakatos (Hingham, MA: D. Reidel, 1976), pp. 395-432; p. 400.


which involves such questions as, ‘what is its research-potential for the future? How

likely is it to give rise to interesting extensions? Does it show promise of being able

to handle the outstanding problems (inconsistencies, anomalies, etc.) in the field? Is

it likely to unify hitherto diverse areas or perhaps open up entirely new territory?‘h7

In similar fashion, Chalmers understands the ‘degree of fertility’ of a theory as the

set of opportunities it provides for future development and argues that, ‘Objective

opportunities for future development will exist within a programme whether or not

scientists realise it and whether or not those opportunities are taken advantage of. With

respect to a particular programme, one research policy or set of suggestions or hints

may be more appropriate than an alternative in the light of the objective opportunities

that do in fact exist. An important property of a research programme, then, will be

its degree of fertility, the extent to which it offers opportunities for future

development, the number of new avenues it opens UP.‘“~

However, neither McMullin nor Chalmers specify what features of a theory give

rise to these ‘objective opportunities’ for further development. What is required is

an answer to the question: What is it about the structure of a given theory that gives

rise to such opportunities, that, in short, makes the theory more fertile than its

competitors?”

In a work which seeks to map out some of the internal constraints mentioned

above,70 Post has drawn on a wealth of examples from the history of physics to identify

certain heuristic criteria that furnish a rationale (although not a logic7’) of scientific

discovery. In particular, he argues that ‘There is a series of restrictions . . . which

render the activity of the scientist constructing new theories essentially different from

that of a clueless rat trying one trapdoor after another (a remark probably also applying

to any actual rat).‘72 Such restrictions are essentially ‘theoretic’ in nature, in the sense

that they involve an ‘internal’ analysis of the theory in question. One such restriction,

or heuristic criterion, concerns those symmetry and invariance laws that play a

fundamental role in modem physics: ‘. . the new theory should conform to those

“Ibid., pp. 423424; cf. Post’s distinction between the ‘dividends’ and the ‘bonus’ of a theory, where the former is understood as its strict logical consequences and the latter as ‘further suggestions’ (op. cir.. note 31, p. 241).

68A. F. Chalmers, ‘Towards an Objectivist account of Theory Change’, Brifish Journal for the Philosophy of Science 30 (1979), 227-233; p. 229; see also A. F. Chalmers, ‘An Improvement and a Critique of Lakatos’s Methodology of Scientific Research Programmes’, Methodology and Science 13 (1980), 2-27; and A. F. Chalmers, Science and its Fabrication (Minneapolis, MN: University of Minnesota Press, 1990), pp. 116120.

69‘Clearly the task of formulating a criterion of theory promise is a crucial one’ (L. A. Whitt, ‘Theory Pursuit: Between Discovery and Acceptance’, in A. Fine, M. Forbes and L. Wessels (eds), Proceedings of1990 Bienniul Meeting of the Philosophy of Science Association Vol. I (East Lansing, MI: PSA, 1990). pp. 467483; p. 467).

‘(Feyerabend describes it as ‘brilliant’ and ‘ . a partial antidote against the view which I try to defend’ (P. Feyerabend, Against Method (London: New Left Books, 1975). p. 61, footnote 17).

“The difference may be denoted, although not, perhaps, clarified by Ryle’s distinction between ‘Procrustean’ and ‘canonical’ rules (G. Ryle, ‘Why are the Calculuses of Logic and Arithmetic Applicable to Reality?‘, in Collected Papers Vol. II (New York: Barnes and Noble, 1971). pp. 226233: pp. 230-23 1).

‘*Op. cit., note 31, p. 218.


general laws, invariance or conservation principles, that have been confirmed without

exception either in the [existing] theory, if any, or in other theories, not necessarily

overlapping the new theory.‘73 I wish to suggest that this criterion, among others, plays

a crucial role in answering McMullin’s questions above and therefore in ‘heuristic’

appraisal, or theory appraisal from the point of view of pursuit. The features of a

theory, or model, which lead to its appraisal as satisfying this criterion are precisely

those that generate the ‘objective opportunities’ for further development. In the case

of the competition between the colour and parastatistics quark models, the former

satisfied an important invariance principle, whereas the latter did not. More

specifically, the colour model could be incorporated into a gauge theoretical

framework; the paraparticle model could not, and suffered for it.

Gauge Invariance

Classical electromagnetism is said to be ‘gauge invariant’ in the sense that the

empirical consequences of the theory are unaffected by certain transformations, which

vary from one space-time point to another, applied to the potentials (whose derivatives

express the electric and magnetic fields). In quantum electrodynamics-generally

acknowledged as one of the most (empirically) successful theories in the history of

physics-the electron and photon fields can also be transformed in this manner,

without changing the physical predictions of the theory. Notably, the existence of the

photon simply falls out of such a gauge invariant theory of electromagnetism.

In the 1950s the physicists Yang and Mills attempted to develop a gauge invariant

field theory of the strong interactions that was directly modelled on quantum

electrodynamics.74 (Th e role of analogy here is particularly important.) The

Yang-Mills approach was also applied to the weak interactions, with the attendant

speculation that it might be possible to effect a unification with electromagnetism.

This speculation acquired the form of a serious possibility with ‘t Hooft’s 1971

demonstration of the renormalizability of the Yang-Mills gauge theory, allowing

physicists to make calculations in the theory to arbitrarily high orders of

approximation. ” Enormous theoretical effort was expended in deriving predictions

from the various unified theories of the weak and electromagnetic interactions then

on the market. The experimental observation of the neutral current was taken to

confirm the Weinberg-Salam model and provided gauge theory with a solid

experimental grounding.76

731bid., p. 226. 7‘?here is, however, a conceptual difference between the gauge invariance of electrodynamics and the

non-Abelian gauge symmetries of the Yang-Mills approach in that the latter involve the description of different events at the same location, whereas the former involves the redescription of the same event at the same location; see Redhead, op. cit., note 61.

750p. cit., note 21, p. 180. 761bid., pp. 181-195.


With the problem of renormalizability resolved,” theorists returned to the

possibility of constructing a gauge field theory of the strong interactions and their

interest focused on the SU(3) group of quark colours as the appropriate gauge group.

Thus quantum chromodynamics was born. As Pickering notes, this was regarded as

’ . a highly desirable theory, at least in the eyes of field theorists, providing as it did

a field-theoretic understanding of the successes of the [quark/] parton model.‘7X

Fruitful lines of application of quantum chromodynamics soon opened up and,

following the November 1974 discovery of the ‘J-psi’ particle (the famous

‘November Revolution’), the theory ‘... rapidly came to dominate theoretical and

experimental perspectives on strong-interaction physics.‘79

The history is now well known. What is important from our point of view is that

the colour model was able to be gauged whereas the parastatistics theory was not.*”

This fact is acknowledged by Greenberg himself, who also gives a nod of the head

in the direction of the ‘opportunities in context’ approach: ‘The SU(3) color theory

became more popular than the parastatistics version because (a) the former is more

familiar and easy to use, and (b) up to now nobody has been able to gauge the

parastatistics theory, while the gauging of the SU(3) colour theory gives quantum

chromodynamics. Let me be explicit, the two theories are equivalent quantum

mechanically, but they are apparently not equivalent from the standpoint of quantum

field theory.‘*’ It is left open as to which factor carried more weight.

The Heuristic Power of Symmetry

As McMullin notes, the opportunities offered by a fertile theory are to be found

‘ . . . primarily in the model associated with the theory, a postulated explanatory

structure whose elements are capable of further imaginative development.“’ The

colour model possessed greater opportunities for development because it could be

gauged. The parastatistics model could not and was therefore comparatively sterile.

On this basis, the ‘uberty’ of the former was indeed ‘esperable’, once the

renormalizability of the Yang-Mills gauge theories had been established. (In so far

as the Han-Nambu model can be regarded as a reformulation of the paraparticle one,‘j

“It has recently been argued that renormalization is not a suspiciously ad hoc manoeuvre, as some philosophers have believed, but is an example of a general heuristic strategy of ensuring that reliable results are preserved through future changes in the theory by confining the unreliable parts (A. Rueger, ‘Independence from Future Theories: A Research Strategy in Quantum Theory’, in A. Fine, M. Forbes and L. Wessels (eds), Proceedings of 1990 Biennial Meeting of the Phi1osoph.v of Science Ascocimion Vol. I (East Lansing, Ml: PSA, 1990), pp. 203-2 I I).

“Op. cit. note 21, pp. 227-228. 790p. cit., note 21, p. 310. ‘“See the discussion in Greenberg and Nelson, op. cit., note 23, p. 88. 8’Greenberg, private correspondence. “Op. cir., note 66, p. 427. ‘“Strictly speaking the paraparticle and colour models have the same states only in certain cases, which

depend on the choice of observables in the former (op. cit., note 23, p. 85-87).


this episode supports Redhead’s point that when you mathematically reformulate a

theory, you may get more out of it heuristically speaking.)84

It is, perhaps, one of the more noteworthy features of modem physics that symmetry

principles have come to play this heuristic role. 85 Nonetheless, invariance criteria are

not infallible, as the case of parity conservation so clearly indicates.86 The selection

of which particular symmetry principles are to serve as heuristic guidelines is not,

of course, determined a priori (recall Post’s statement of this criterion of heuristics

above).87 As science progresses, certain of these principles are so elevated and

ultimately experiment must play a crucial role in this rise to prominence, although

the exact nature of this role may not be clear and the interconnections between theory,

symmetry principle and experiment may be tortuous and entangled.s* We learn what

principles of invariance to apply in discovery and pursuit by noting which are well

supported and incorporated into our most successful theories. In a sense, what we have

here is the importation of criteria of ‘P-appraisal’ into the realm of ‘U-appraisal’, thus

calling into question the impermeability of McMullin’s distinction: ‘The

study of the structure of existing houses may help us in constructing new

houses.“’ Note, however, that this importation proceeds from one (local) domain

of inquiry into another and essentially piggy-backs on the structural analogies

between the two.

Finally, despite the enormous success of quantum electrodynamics,” gauge

invariance itself was not immediately successful as a fundamental guide in the

construction of new field theories in the weak and strong nuclear domains, as is well

known. It was not until renormalization was demonstrated with regard to the latter

that it acquired this status and it was at this point that interest began to wane in the

paraparticle model. Since the domains of the electromagnetic, weak and strong

interactions were not seen as overlapping, the original importation of gauge

invariance into the latter two was essentially analogical but the success of the analogy

then provided the drive underlying attempts to unify all three. Much more needs to

NM. L. G. Redhead, ‘Symmetry in Intertheory Relations’, Synrhese 32 (1975). 77-l 12. “A classic discussion is given in E. P. Wigner, ‘Invariance in Physical Theory’, Proceedings of fhe

American Philosophical Society 93 (1949), 521-526; for a more recent account of the role of symmetry arguments in science, see B. van Fraassen, Laws and Symmetry (Oxford University Press, 1989). and for more on the heuristic role of symmetry principles, in particular, see Redhead op. cit., note 84, p. 105).

86Post, op. cit., note 31, ‘ the superlaws of symmetry are as liable to empirical revision as other laws of physics having a less obviously intuitive character’ (see also Redhead, op. cit., p. 105).

*‘Cf. van Fraassen: ‘Symmetry arguments have that lovely air of the a priori, flattering what William James called the sentiment of rationality. And they are a priori and powerful; but they carry us forward from an initial position of empirical risk, to a final point with still exactly the same risk. The degree of emtrical fallibility remains invariant’ (op. cit., pp. 260-261).

Thus, as Galison notes (op. cit., note 30, p. 161), the first grand unified gauge theory, based on the SU(5) model, met a number of theoretical and invariance requirements but its prediction of proton decay was not borne out. This is construed as a further argument against the ‘extemalist’ view and the claim that physics is automatically self-authenticating.

*‘Post, op. cit., note 3 1, p. 2 1 I. ?See Post, ibid., p. 227.

The Esperable Uberty of Quantum Chromodynamics I OS

be said here;” suffice it to say that unification, or the possibility thereof, also figures

among the ‘objective opportunities’ for development.

Discovery and Pursuit

In Laudan’s words, pursuit is the ‘nether region’ that lies between discovery and

acceptance. 92 What I have tried to do here is to offer the beginnings of a map or guide

to the topography of this area in the context of a particular historical example. By

arguing that the heuristic framework in terms of which discovery is understood can

also serve to underpin those appraisals that are involved in pursuit, the distinction

between the two has obviously become blurred. Indeed, given the problem of theory

individuation and of deciding where one ‘theory’ ends and another begins in the

sequence of developments, it is hard to see how any such distinction could be

maintained.

Theories and models do not spring up, inductively, from the humus of observation

and experiment, nor do they simply ‘pop’ into existence out of the heads of scientists.

Rather, they emerge from their predecessors according to certain guidelines. (This

is true even for those which lie on either side of a supposed revolutionary divide.)

The content of these guidelines may itself be supplied by these (successful) pre-

decessor theories, as I have indicated above. Nor are theories terminated abruptly

when just any modification is made. It seems odd to say that when Hartle and Taylor

modified Greenberg and Messiah’s formulation of parastatistics, they constructed a

new theory. A more plausible claim is that they merely simplified and made more

accessible the existing theory and this activity can be counted part of the development

of the latter. Yet obviously some modifications result in new theories, else how would

these theories emerge from their predecessors? (How would the notion of a distinct

predecessor even make sense?!) The distinction between ‘developmental’ modifica-

tions and ‘constructive’ ones is fine and acute, but I shall leave it for further discussion.

Returning to the supposed distinction between discovery and pursuit, the

conclusion to be drawn from this is that scientists use a select set of heuristic

guidelines both for theory construction, in the sense of ‘discovery’ and for theory

appraisal, in McMullin’s sense of appraising the ‘U-fertility’, or what Peirce would

call, the esperable uberty, of the theory.‘”

Acknon~ledgemenfs-I would like to thank Andy Pickering and Jim Cushing for helpful comments on an earlier draft of this paper. Needless to say, the responsibility for both the views expressed and any errors made is entirely mine.

“Ibid., pp. 226 and 249. “L. Laudan, ‘Why was the Logic of Discovery Abandoned?‘, in T. Nickles (ed.), ScientiJic Discovery.

Z_o,$c and Rationality (Hingham, MA: D. Reidel, 1980), pp. 173-183; p. 174. sThus, paraparticle theory was constructed by generalizing the standard formalism of particle statistics,

following a guideline, which Post designates as ‘enlarging the domain of a theory’ (op. cit., note 31, p, 242). Although it was not gauge invariant, the theory did satisfy the invariance principles ‘built into’ this standard formalism.

The esperable uberty of quantum chromodynamics

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