

300

*Received October 2001: revised December 2001.

†Send requests for reprints to the author; Depto. Lógica y Filosofı́a de la Ciencia,
UNED, 28071 Madrid, Spain; e-mail: jpzb@fsof.uned.es

‡Financial support for this reseach was received from Fundación Urrutia Elejalde, from
The Spanish Government’s DGICYT research project PB98–0495-C08–01, and from
the Department of Economics of the Universidad Carlos III. Previous versions of this
paper were presented in the Seminar of Economic Methodology of Universidad Au-
tónoma de Madrid (November 1999), and in the Seminar ‘Theoretization and Experi-
mentation in Economics’ (Rovaniemi, Finland, December 1999); my thanks to Juan
Carlos Garcı́a-Bermejo, Uskali Mäki and Timo Tammi for inviting me to take part in
them. Hepful comments were made by Francisco Álvarez, José Ramón Álvarez-
Rendueles, Salvador Barberá, Miguel Beltrán, José Luis Ferreira, Shaun Hargreaves
Heap, Frank Hindriks, Javier Ruiz-Castillo, David Teira, and especially Juan Urrutia
and two anonymous referees.

Philosophy of Science, 69 (June 2002) pp. 300–323. 0031-8248/2002/6902-0008$10.00
Copyright 2002 by the Philosophy of Science Association. All rights reserved.

Scientific Inference and the Pursuit
of Fame: A Contractarian Approach*

Jesús P. Zamora Bonilla†‡
UNED, and Fundación Urrutia Elejalde. Spain

Methodological norms are seen as rules defining a competitive game, and it is argued
that rational recognition-seeking scientists can reach a collective agreement about which
specific norms serve better their individual interests, especially if the choice is made
‘under a veil of ignorance’, i.e., before knowing what theory will be proposed by each
scientist. Norms for theory assessment are distinguished from norms for theory choice
(or inference rules), and it is argued that pursuit of recognition only affects this second
type of rule. An inference rule similar to ‘eliminative induction’ is defended on the basis
of such a possible agreement. According to this contractarian approach, both the ex-
planation and the justification of scientific norms only need to refer to the preferences
of individual scientists, without assuming the existence of ‘collective’ points of view.

1. Introduction. Despite a long tradition of understanding the scientific
method as a matter of careful application of logical rules, it is now
commonplace to view methodological norms as conventions. One of the
philosophical approaches which contributed most decisively to the accep-
tance of this position was falsificationism. According to Popper, not only


       301

1. Some good surveys of the ‘economics of science’ are Stephan (1996), Hands (1997)
and Sent (1999).

the general rules of method had to be justified on the grounds of their
contribution to the aims of science, but their application to concrete cases
always needed some decision making, not determined by methodological
rules alone. In particular, the acceptance of ‘basic statements’ was a pro-
visional decision, potentially subjected to further criticism, but which was
conventionally settled in order to stop the actual process of testing (e. g.,
Popper 1959, sec. 11). Likewise, for Lakatos not only the acceptance of
basic statements was conventional in this sense, the commitment to a given
research programme was also a conventional decision: even under ap-
palling contrary evidence, defenders of a ‘degenerating’ programme could
rationally support it, if they were confident in a future solution of its
present anomalies (e. g., Lakatos 1977, sec. d4). Unfortunately, neither
Popper’s nor Lakatos’ views offered many insights about how to deter-
mine the rationality of those concrete decision making processes; instead,
both authors always presented this issue as if the problem of when to stop
testing a basic statement, when to abandon a research programme, and
so on, were a problem left to the judgement of the flesh-and-bone scientist,
rather than to the philosopher’s elucidation.

It is not strange that sociologically or psychologically minded authors,
following Kuhn (1962), took precisely the concrete processes of acceptance
of statements or practices as the topic which deserved more attention for
students of science. These authors have put forward an impressive number
of case studies intended to show that scientific decisions are the outcome
of ‘negotiations’ influenced by interests, prejudices, biases, and so on. Re-
searchers’ reference to general rules of scientific method seemed to play
only an ideological or rhetorical role, not justifying the epistemic value of
those statements on which a scientific consensus is eventually reached (see,
for example, Knorr-Cetina 1981, and Latour 1987).

But it should not be assumed that the presence of non-epistemic inter-
ests automatically invalidates the internal rationality of the process which
leads to the acceptance of those theories. As every student of economics
knows, ‘greedy’ private interests may produce , at least under some insti-
tutional settings, efficient public results, and perhaps something similar
takes place in the case of scientific research. In this vein, some epistemol-
ogists have recently employed economic-theoretical tools to show that
some possible institutional mechanisms make epistemic goals attainable,
not only ‘in spite’ of private interests and psychic biases, but even thanks
to them. For example, under some regimes of merit attribution the prob-
ability of finding a true solution to a scientific problem is higher than when
researchers directly pursue ‘truth’ instead of ‘merit’ (see Goldman and
Shaked 1991, Kitcher 1993, and Goldman 1999).1 One fundamental prob-


Ú .  302

2. In Zamora Bonilla (2000) and (forthcoming a) I have tried to show that some prev-

lem with these results is, however, that it may not be in the interests of
scientists to establish such merit attribution regimes; a ‘philosopher-
monarch’ (to use Kitcher’s expression) could force scientists to do so, if
he were really interested in promoting truth acquisition, but, in the absence
of such an external enforcement, perhaps researchers would prefer to work
under a different system of rules, one less efficient in the production of
objective knowledge, but more efficient in satisfying their own private
goals. Or perhaps they prefer to work without any kind of rules whatso-
ever!

In this paper, I will study first what systems of norms (and, in partic-
ular, what ‘merit attribution regimes’) would be chosen by the members
of a scientific discipline, were they given the chance of making this choice
by themselves and assuming they were ‘recognition-seekers’; and second,
what epistemic properties the resulting norms would be expected to have.
In order to approach these questions, I will not use a ‘general equilibrium’
model, but a different economic tool, ‘constitutional economics’-the study
of the collective choice of norms by rational agents. If scientists did not
obey any kind of rule while competing for ‘recognition’, then no researcher
would ever have a reason to accept a ‘rival’ theory, since the pursuit of
recognition is a zero-sum game (you can only win if others lose) and every
researcher would have permanently open the possibility of rejecting all
their competitors’ theories on the basis that ‘they are not verified enough’
(that this possibility exists is something we have to concede to falsi-
ficationism). So, if scientific research does exist, and if researchers are
recognition-seekers, then the game of science has to be played under some
rules, in particular, rules commanding the acceptance of certain proposi-
tions if certain circumstances obtain. Stated differently, the scientists’ de-
cisions about what statements to accept must be subjected to some recog-
nisible patterns, for if no such patterns existed at all, no ‘merit-seeking’
person would choose to enter the game of science, since she would not have
any way of knowing what to do in order to get her own theories accepted
by her possible colleagues. Therefore, I propose to consider the ‘negotia-
tion of scientific knowledge’ as a negotiation about the norms governing
the process of scientific research. The specific aim of this paper is to show
that recognition seeking scientists may have a preference for some specific
set of norms, and hence, that these preferences will count among the fac-
tors determining actual scientific norms.

Only a very limited type of norms will be analysed here: those stating
when a theory is so ‘good’ that it becomes compulsory to accept it (these
are what I will call ‘inference norms’). In particular, I will not study here
the norms defining what kinds of properties of scientific theories will count
as ‘epistemic virtues’; this problem is an extremely important one, and I
have devoted to it some other papers,2 but I have opted not to discuss it


       303

alent norms for the comparative assessment of scientific theories can be explained under
the assumption that the main ‘epistemic virtue’ preferred by scientists is what I have
called ‘empirical verisimilitude’. These papers are, therefore, a necessary complement
of the present one in offering a more complete theory about the constitution of scientific
norms.

here, both because of space limitations, and because that discussion will
probably distract our attention from the analysis of the inference norms,
for this analysis will be the same no matter what epistemic virtues are
preferred by researchers. In order to perform our analysis, the following
assumptions about the members of a scientific community will be made:
first, that they have already agreed on what will count as an ‘epistemic
virtue’, although these criteria may be difficult to apply to concrete cases;
second, that they do not necessarily worry about the epistemic value of
proposed theories, even if they are wise enough to make an estimation of
that value; and third, that what they are really pursuing is the merit
of having devised a theory their colleagues explicitly recognise as ‘correct’.
The problem I will attempt to solve in this paper, with the help of a very
simple economic model, is whether the members of such a scientific com-
munity could reach an agreement on how to decide who must be taken as
the winner of the race for recognition.

The main conclusion that can be drawn from our model is that we can
decompose scientists’motivations into two different elements: epistemic
preferences and the pursuit of recognition. The first element can be used
to explain what counts for scientists as a cognitive virtue, and hence, to
explain the scale against which the scientific value of proposed scientific
hypotheses is to be measured. On the other hand, the ‘pursuit of fame’
will normally have no influence on the choice of this scale, but, instead, it
will determine which point on the scale is going to divide ‘acceptable’ hy-
potheses from ‘unacceptable’ ones. In this sense, the operation of the pur-
suit of fame provides the argument to fill the gap in falsificationism re-
ferred to in the first paragraph: the unsolved question of how scientists
actually determine when to conclude the testing of a scientific statement
in order to make a decision about its acceptability. Falsificationists would
probably deny that such a decision is necessary at all, but we can take as
an empirical fact about scientific research that countless statements (ab-
stract theories, general hypotheses, experimental laws, and so on) are ac-
tually accepted by scientists, and it seems reasonable to try to explain why
researchers behave the way that they do.

In the next section I will present the fundamental ideas of this contrac-
tarian approach, and justify its relevance for the study of scientific norms.
Section 3 introduces a classification of types of scientific norms in terms
of their role in the ‘persuasion game’; only a brief comment will be pro-
vided about each type of rule, since the rest of the paper will focus on


Ú .  304

inference norms. Section 4 will present the paper’s basic analytical instru-
ment, which is the ‘success function’, i.e., a function indicating the prior
probability each researcher has of producing a theory which surpasses a
battery of tests of predetermined strength. In Section 5, the properties of
some possible inference norms are studied. Section 6 shows how an agree-
ment about a norm can be reached even if the members of a scientific
discipline do not have identical preferences about the optimum rule.
Lastly, Section 7 summarises the main conclusions of the paper.

2. The Constitutional Approach to Scientific Norms. Norms are a contro-
versial topic in economic theory. Most economic models assume that the
relevant norms are given and simply study how agents will behave under
those norms; sometimes, the application of a new norm or the withdrawal
of an old one is suggested, as a way to enhance economic efficiency or
social justice, but it is almost always assumed that the State will have the
power (and the will) to implement such a change. This assumption leaves
a number of questions open; for example, how can we be sure that poli-
ticians will actually impose the most efficient norms, instead of those which
favour their own interests? Where do the criteria of social justice come
from? Why has the State the powers it has? And, in particular, since many
relevant norms are ‘social conventions’, not imposed by the State, the
question is simply why do these norms exist at all? Some authors have
denied that these questions may receive an answer which is ultimately and
solely based upon the assumption of egotistic maximisation of utility on
the part of individuals (see Elster 1989). Other authors, instead, have de-
fended the notion that norms can ‘emerge’ and ‘evolve’ as an unintended
result of the interaction of many individual decisions (e.g., Hayek 1973,
Sugden 1989), though their approaches have little in common besides,
perhaps, this conception of norms as ‘emergent’). Lastly, a third group of
authors have argued that rational and autonomous people have the ca-
pacity to negotiate and change the norms under which they live, indepen-
dently of the origin of the pre-existing norms; this is the ‘contractarian’
or ‘constitutional’ approach (see especially Brennan and Buchanan 1985,
and Vanberg 1994). I will not discuss here the pros and cons of these
competing approaches; it is enough to recognise that, in order to explain
the emergence of norms, it may be necessary to use some explanatory
mechanisms besides instrumental rationality and strategic reasoning; for
the ‘emergentist’ approach, this additional explanatory element would be
history, while for contractarians it is basically the autonomy of individuals,
as well as the moral stance of recognising this autonomy in other people
(see Buchanan 1991). I will try to apply this contractarian perspective to
the study of scientific norms, though other approaches may also be illu-
minating.


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The most important aspects of constitutional economics that should be
taken into account are the following:

a) Though every norm may in principle be subjected to constitutional
analysis, attention has mainly been paid to ‘fundamental’ norms,
in the sense of rules which define basic liberties, or, more fre-
quently, in the sense of norms which regulate the process of choos-
ing other, ‘lower-level’ rules.

b) The evolution of a game played under definite rules can be more
or less predictable, because people, once the rules are established,
tend to be pulled more or less automatically by their interests, and
because there is usually a limited set of strategies open to each
individual. However, the adoption of a concrete system of rules
(like the emergence of a certain institution) is, in comparison, much
more difficult to predict, because people must devise those rules in
the first place. Constitutional economics does not attempt to sur-
vey all ‘possible’ systems of norms in order to determine which one
is ‘optimal’; it simply tries to analyse specific types of rules (for
example, some voting mechanisms), so as to inquire about their
properties.

c) In order to assess social states or economic outcomes, constitu-
tional economics does not employ any normative criterion other
than the free agreement of individuals. Neither must a definition
of social justice or economic welfare be imposed ‘from above’, nor
is there any need of ‘aggregating’ individual values or preferences.
‘Right’ outcomes are simply those deriving from the application of
‘right’ norms, and these are just the norms that people have actu-
ally chosen, provided that the choice has been unanimous, well
informed, and free.

d) A fundamental distinction is made between the choice of norms
and choice under norms; the latter amounts to ‘playing a game’,
which can obviously be extremely competitive; the former, instead,
consists in deciding which game to play. As long as norms are ex-
pected to be in force for a long time, and to apply to many different
situations, it would be very risky for individuals to insist on the
collective adoption of a rule which just happened to be favourable
to them in their present situation, since it may easily cease to be
so as soon as circumstances change. In this sense, the choice of
norms is made ‘under a veil of ignorance’, and ‘impartial’ rules—in
the sense of warranting a satisfactory gain to anyone in a wide set
of conceivable circumstances—will tend to be chosen (cf. Rawls
1971). Impartiality is also warranted by the fact that the chosen
norms must be unanimously accepted among the members of a


Ú .  306

group, at least as long as people have the opportunity of joining
another group if they do not like the chosen rules.

The relevance of these aspects of constitutional economics to the anal-
ysis of scientific norms is easily understood. In the first place, when sci-
entists ‘negotiate’ the content of a communication, or the acceptance of a
hypothesis, or the use of a piece of equipment, they have to take into
account not only their own interests, or the interests of the people they
are negotiating with, but also the justifiability of their decisions before
their colleagues. For example, if my experiment has produced a result that
contradicts a prediction of your theory, we can ‘negotiate’ how I am going
to present that result, but our colleagues would not allow that I simply
decide to conceal it—if they happened to discover the terms of our ‘ne-
gotiation’. So, even if it were in my interest to diminish the impact of my
discovery on your theory (e.g., because of the favours you have promised
to me in exchange), I could not do it unless I provided an argument in-
dicating why the result is not so damaging, and this argument must show
that my stated decisions follow some patterns which are accepted as gen-
eral principles of argumentation among our research community. The
norms studied in this paper are just this kind of ‘patterns of justification’,
particularly those that can be used in turn to justify the acceptability of
‘lower-level’ patterns.

In the second place, I will not try to present an ‘optimal’ set of scientific
rules, i.e., one defining the best possible game for scientists to play. My
aim is only to analyse a limited number of norms which happen to be
similar to those that scientists seem to employ. So, I plainly admit that
other authors may discover that different norms are more consistent with
actual scientific practice and more satisfactory for each researcher than
the norms studied here; but if this happens, I think such a discovery should
count as a success of the contractarian approach.

In the third place, this approach does not attempt to assess the effi-
ciency of scientific research through the comparison of scientists’ actual
performance with some absolute epistemic standard engendered in the
philosopher’s cabinet, one trying to reflect a God’s eye point of view (to
use an expression suggested by an anonymous referee); neither does it try
to provide a mathematical procedure for ‘aggregating’ scientists’ prefer-
ences, or for ‘weighting’ their cognitive and their private interests in order
to find an ‘objective’, ‘supra-individual’ criterion of theory evaluation. As
Hands (1997) has pointed out, behind most economic analysis of scientific
research there is the ambition of offering an ‘invisible hand’ argument
showing that researchers’ ‘selfish’ behaviour tends to produce cognitive
results which are sound from an ‘objective’ point of view (by the way, this
ambition explains the use of general equilibrium tools). The main problem,


       307

3. This may be due to the fact that those epistemic preferences are learned during the
process of becoming a member of the discipline. To honour the evolutionary approach,
this entails that history (or ‘path-dependency’) might matter a lot in explaining the
prevalence of some scientific norms, but I will not pursue this line of thought further
at this point.

as Hands rightly indicates, is that current techniques of economic analysis
do not guarentee that one can coherently use this ‘objective point of view’,
understood as an aggregation of individual perspectives. On the other
hand, the constitutional approach is radically committed to methodolog-
ical individualism; the ‘public’ state of scientific knowledge about a certain
issue is simply identified with the specification of what proposition (if any)
each member of the scientific community has accepted concerning that
issue. For the constitutional approach, therefore, unanimity is the only
acceptable ‘aggregation mechanism’, though it works just in those cases
where no aggregation mechanism is needed; in the remaining cases, this
approach does not look for any ‘collective point of view’.

In the fourth place, as long as methodological norms are subjected to
negotiation by the members of a scientific community, and as long as the
norms have wide applicability and are adopted as unanimously as possi-
ble, they will tend to be neutral. One reason is that it will be difficult for
scientists to accurately predict the effect of each possible norm on their
expectations of getting a high level of recognition; hence, researchers will
have to use some additional criteria in order to decide what norms to
accept, such as their epistemic preferences or their estimations of the prob-
ability of getting a solution if certain norms are established. Another rea-
son is that, although the pursuit of recognition can be understood as a
‘zero-sum game’ (with some space open to cooperation, nevertheless), this
will not be so in the negotiation about the norms of that game, partly
because it is unlikely that there are dramatic differences in scientists’ es-
timation of the general probabilities of success or in the cognitive interests
of the members of a scientific community.3

3. The Persuasion Game. According to many sociologists, scientists’ main
motivation is not ‘the pursuit of truth’ but ‘the pursuit of recognition’. I
will operationalise this concept as the number of colleagues who explicitly
accept as correct, the models, hypotheses, or theories presented by you. As
a referee of a former version of this paper pointed out, this definition is
very close to David Hull’s (1988, 306), who says that “scientists must seek
first and foremost to have their work accepted by their peers, not by gov-
ernment officials, science reporters, or the general public” (italics mine).
Besides the obvious similarity between both definitions, some differences
are worth mentioning: firstly, it seems that, for Hull, the pursuit of peer


Ú .  308

recognition is not a basic desire of scientists, but a kind of behaviour which
is somehow ‘imposed’ on them by the scientific community (hence the
‘must’). Secondly, and more importantly, according to Hull “the most
important recognition that scientists can receive for their work is its use
by those scientists working in the same area, including of course their
closest competitors” (pp. 309–10; italics mine). Though admitting that this
can be a correct description of the way recognition is actually gained, I
think that, in order to justify the conclusion that competition among
recognition-seeking scientists can be an epistemically efficient mechanism,
it would be necessary to explain why scientists would prefer to use those
statements they think are true, if they also assume that their colleagues
are not ‘truth-seekers’. In particular, we can point to three missing expla-
nations in Hull’s account: the first refers to the question with which I
started: how to decide when a hypothesis is so well confirmed that it is
worth using? If no common rule is established about this, then each sci-
entist will be free to assert that any rival theory (or any data contradicting
his own theory) is not still ‘confirmed enough’, and he will tend to use
only those data which support his own theory. The second problem is that
Hull seems to presuppose that it will always be clear when a result supports
a theory; my aim is, instead, to show how scientists can agree on certain
rules which define that relation of support. Lastly, and more importantly,
even if a colleague ‘internally’ accepted that your theory is right and us-
able, he might refrain from expressing publicly his belief, just in order not
to increase your recognition level; it is necessary to explain, therefore, how
the strategy of ‘giving recognition’ can become a rational decision in spite
of this possibility.

Other economic explanations of the process of scientific research are
also elaborated on the basis of assumptions similar to those of Hull’s. I
refer in particular to the theories developed by Goldman and Shaked, and
Kitcher. For example, according to the model of Goldman and Shaked
(1991), it is possible that recognition-seeking scientists perform relatively
well in epistemic terms, if they receive recognition proportionally to the
change in their colleagues’ subjective probabilities produced by the reve-
lation of the results of the experiments made by the former. This model
takes for granted that those colleagues will have a reason to believe the
revealed results (and to change their subjective probabilities accordingly),
that they will also have a reason to manifest their true subjective proba-
bilities, and that the experiments’ outcomes have been sincerely revealed.
On the other hand, the models in Kitcher (1993 ch. 8) also take it for
granted that scientists will be sincere in revealing both the results of their
experiments or observations and their opinions about the correctness of
each hypothesis; this allows him to use rather uncritically such concepts
as ‘wrong result’, ‘right result’, ‘correct finding’, ‘getting solution’, ‘suc-


       309

4. Kitcher (1993), p. 304, note 2: “As will become apparent, I shall be concerned more
with assessing competence than evaluating honesty, but this should not be taken to
imply that issues about sincerity are unimportant.”

cess’, and so on. Kitcher explicitly recognises the existence of this problem,
though he decides to concentrate on a different set of questions.4 The aim
of my own approach is, on the contrary, to study which norms defining
what must be counted as ‘honest’ behaviour can be established by scien-
tists themselves, if they take into account their own real interests (which
may certainly include epistemic criteria, but also include ‘recognition’).
Stated in other terms, the model presented in this paper tries to offer an
idealised and simplified economic explanation of the process of deciding
what constitutes a piece of knowledge whose acceptance is compulsory; as
far as I know, this process remains unexamined in the economics-of-
science literature, and I think that it deserves attention quite independently
of whether or not one accepts the simplified model I will present here.

The discussion of the preceeding paragraphs points towards the neces-
sity of explaining why a scientific discipline has the fundamental meth-
odological norms it has, instead of others. According to the contractarian
approach, the ‘constitution’ of a scientific discipline should be understood
as an exchange of constraints on the acceptance of scientific statements:
every member accepts the submission of his own choices of statements
(data, hypotheses, models, laws, theories, and so on) to certain patterns
of scrutiny, in exchange for his colleagues’ acceptance of the same pat-
terns. What the members of a scientific community have to negotiate is,
which specific constraints they are going to accept. The rules which seem
to be necessary in order to constitute such a game can be classified as
follows:

a) Norms of inference: These norms state that if you have accepted
certain propositions, and if a different proposition is in some spe-
cific relation to them, then you must accept this second proposi-
tion. A reasonable assumption is that, if these norms are chosen
‘under a veil of ignorance’, they will normally be consistent with
the elementary rules of logic and mathematics, in order to be truth
preserving.

b) Norms about comparison of statements: These rules, which I will
also call ‘norms of theory assessment’, are similar to those of type
a, but, instead of forcing the participants to accept the conclusion
that a certain proposition must be accepted, they only force them
to accept that one statement is better than another. So, these norms
allow the establishment of an ordering of statements by their ‘qual-
ity’ (though this ordering is probably not complete). These order-
ing rules may be used to defend the preference for a particular


Ú .  310

5. For a dicussion of what these cognitive preferences could be, and what norms for
theory comparison would derive from them, see the papers quoted in note 2.

6. A brief description of a norm of this kind is offered in Zamora Bonilla (forthcoming b).

theory in those cases where norms of type a do not uniquely de-
termine the choice of one theory among a set of alternatives. These
norms will also be used to define a certain ‘quality level’ such that
only those theories which happen to surpass it can be accepted. It
is not necessary to determine this level quantitatively (although I
will do so in the following sections in order to simplify my argu-
ments), for it can also be determined by means of examples (i.e.,
if a tentative solution to a problem is as supported by the evidence
as this solution to this other problem was, then the former must
be accepted). Under the veil of ignorance, norms consistent with
the epistemic preferences of scientists will tend to be chosen, for it
is unlikely that one will be able to forecast the influence of a norm
of this kind on the probability of ‘winning’ in a scientific contest.5

Nevertheless, each researcher may have a preference for a rule
which favours those theories which have a virtue she is particularly
apt to produce (for example, if one is very able in expressing the-
ories axiomatically, she would tend to ‘vote’ for a rule which fa-
vours axiomatic theories over informal ones).

c) Norms related to actions: Rules of type a only allow you to per-
suade a colleague to accept your theory if he happens to have pre-
viously accepted some pertinent statements; so you would need to
persuade him to accept these statements. This can be done by show-
ing that their acceptance follows from other rules of type a and the
fact that he has accepted still other (more basic) statements, and
so forth. But this process can not proceed infinitely, so, if the game
of persuasion is to be possible at all, there must exist some different
procedure for forcing a scientist to accept some statements. For
positivists, this procedure was the ‘direct’ observation of empirical
facts, but our approach gives scientists the freedom to decide what
kinds of actions, performed under what circumstances, are to pro-
duce results whose acceptance is compulsory. These norms would
regulate, for example, the procedures for performing experiments
or observations, including not only their ‘technical’ aspects, but
also their ‘institutional’ ones (who must be taken as a qualified
experimenter, how the results must be published, and so on). It is
reasonable to think that, under the veil of ignorance, scientists
would prefer action related norms with the property of encourag-
ing the performance of experiments which yield unbiased results,
as well as the sincere revelation of these results.6


       311

7. Norms of enforcement are, therefore, ‘metanorms’ in Axelrod’s sense (see Axelrod
(1997), ch. 3). This author shows that introducing this kind of norm in computer ‘pris-
oner’s dilemma’ tournaments drastically reduces the frequency of ‘defections’. On the
other hand, ‘metanorms’ are even more difficult to justify than ‘norms’ from the bare
assumption of instrumental rationality (see Elster (1989), ch. 3).

8. For the dynamics of theory choice, as opposed to the choice of rules for theory choice,
see Brock and Durlauf (1999) and Zamora Bonilla (1999).

d) Norms of enforcement: These establish the penalty that has to be
imposed on a scientist who has disobeyed some rule. They are not
only addressed to the ‘infractors’ of the other kinds of rules, but
to all the members of the scientific community, who, according to
these norms, have the obligation to ‘punish’ the ‘infractors’. As a
consequence, there will be some norms establishing a penalty for
those scientists who have failed to apply a sanction when they were
required to do so.7

Once the rules of a scientific discipline are more or less explicitly defined
and accepted, research processes can take place within it. My aim in this
paper is not to study the dynamics of those processes, but simply to illu-
minate some mechanisms which may serve to select the rules under which
the game of persuasion is played.8 In particular, I will only try to study
the negotiation of a norm of type a: one indicating when a theory has
reached an epistemic value so high that it deserves to be accepted. It should
be noted that usually no system of norms is able, by itself, to warrant a
universal agreement on every topic within a scientific community. As I
said in the last section, norms are used to justify decisions, but this does
not entail that, in each case, only one possible decision is justifiable. What
is important is that norms preclude the justification of some decisions in
some cases.

4. The Success Function. The norms of inference I will study in the next
section refer to the choice of a level of epistemic value a hypothesis has to
surpass in order to become acceptable as ‘the’ correct solution to a given
problem. A preliminary assumption is, hence, that a certain ordering of
the possible levels of epistemic value must have been agreed upon by the
members of a discipline or subdiscipline, and this will have been done on
the basis of the ‘norms for theory comparison’ referred to in the last sec-
tion. Just for concreteness, we can understand this level as a weighted sum
of the number of conceptual and empirical tests that the hypothesis has
passed and the number of tests it has failed to pass, but other interpreta-
tions can reasonably be defended (my interpretation is obviously close to
Laudan’s notion of ‘problem solving capability’, cf. Laudan 1977). How-
ever, the difficulty exists that both the definition of the epistemic values


Ú .  312

Epistemic
value

Probability
of i’s theory
being of
value x at
most 1

x1

1 – Fi(x1)

Fi(x1)

Fi(x)

Figure 1.

and the determination of the value of a concrete hypothesis can be matters
of disagreement: not every researcher will necessarily attach the same
strength or relevance to each kind of test, and it can even be an open
question whether a given theory has passed a given test or not (this prob-
lem demands the application of ‘norms related to action’). If such dis-
agreements persist at a fundamental level within a scientific discipline, it
will be difficult for its members to reach a ‘social contract’ on inference
norms; nevertheless, in many disciplines it seems that such disputations
are more or less easily resolved, which can be taken as an indication that
norms of theory comparison and norms related to action work reasonably
well in those areas.

Let us assume, then, that an ordering of epistemic levels has already
been collectively defined. A priori, each researcher who is trying to solve
a certain problem can produce a solution to it of any possible value (after
an appropriate amount of testing), but not all the values will be equally
likely. Let Fi(x) be the probability that the solution proposed by the i-th
researcher has an epistemic value of at most x . So, 1 � Fi(x) will be the
probability that his theory surpasses the level x (see Figure 1). The basic
property of this function is that it is increasing in x: the higher is the
epistemic value, the more probable it is for a researcher to reach a theory
of that value at most, and the less probable it is for him to reach a theory
better than that level. It is neither essential that F(0) � 0, as in the figure
(this would mean that there is a non-negative probability of devising a
theory of null value), nor that F(x) equals 1 at some point (this would


       313

mean that it is impossible for the scientists to devise a theory better than
the quality level associated with that point). We might assume that F also
depends on the size of the scientific community, since co-operation and
the accumulation of knowledge can make the discovery of better theories
more probable, but I will ignore this complication in the rest of the paper.
In the next section I will make the additional simplification that F is the
same for all community members, an assumption which will be removed
in Section 6. Note also that high levels of epistemic value can only be
reached after a long process of testing, since they entail that the theory
will have surpassed many strong tests. So, the choice of a certain quality
level will implicitly determine the amount of the time after which there is
no need to keep on testing the hypothesis in order to determine its ac-
ceptability.

F (or better, 1 � F ) is what I will call the ‘success function’ of a re-
searcher. The basic question of this paper refers to the collective choice of
a level of success such that theories surpassing that threshold may become
(or must be) accepted by the members of a research community. If all the
members of the scientific community had the same basic preferences, they
would simply agree on choosing the threshold which maximises each re-
searcher’s expected utility, and there would be no ‘competition’, since the
optimal choice would be the same for all (real competition comes after the
rule of inference has been chosen and each researcher tries to invent a
theory which surpasses the chosen threshold, and also tries to show that
this is the case). But if researchers’ preferences are not the same, or if they
have different estimations of their probability of success, then it is possible
that different scientists may prefer different inference thresholds; in this
case, a real ‘negotiation’ to collectively choose a unique norm will be
needed. I will study this possibility in Section 6.

5. Some Possible Rules of Inference. According to the fundamental as-
sumption of the contractarian approach, the people who are going to be
subjected to a norm could devise an indefinite number of alternative
norms, and could negotiate which one to institute; it is even possible that
the chosen norm does not coincide with anybody’s optimal rule, because
the former can be a ‘compromise’ between people’s different preferences.
Taking this into account, my goal will simply be to study the properties
of some plausible rules of inference (‘plausible’ in the sense that they are
intuitively similar to some patterns of theory choice actually used in sci-
ence) in order to understand why they might have been chosen by recog-
nition seeking researchers. The three alternative norms I am going to ex-
amine have a common feature: they establish a minimum level of epistemic
value such that if a tentative solution to a scientific problem has surpassed


Ú .  314

that level (or ‘inference threshold’), then this would justify its acceptance
as a valid solution. These three competing rules are the following:

(R-I) A level of epistemic value is established such that the theory
with the highest value must be accepted by every member of the dis-
cipline, provided that it has surpassed that threshold. If no theory
passes the threshold, the rule commands the suspension of judgement.

(R-II) A level of epistemic value is established such that the theory
with highest epistemic value must be accepted by every member of the
discipline, provided that it is the only one which has surpassed that
threshold. If none or more than one theory has surpassed the thresh-
old, the rule commands the suspension of judgement.

(R-III) A level of epistemic value is established such that the theories
which have not surpassed that threshold can not be accepted. If only
one theory passes the threshold, it must be accepted. If more than one
pass it, then each researcher can either choose one of them, or suspend
judgement.

The members of a scientific discipline have to decide in the first place
which type of inference norm to establish, and secondly which inference
threshold to choose (actually, this threshold may be defined by means of
‘paradigmatic examples’, instead of through a quantitative measure). The
constitutional perspective suggests that these choices are prior to knowing
which specific theory or solution is going to be invented by each member
of the discipline, or, at least, prior to knowing whether these theories will
pass enough tests. These choices can even be prior to knowing which spe-
cific problems will have to be solved in the future. Under these circum-
stances, the expected utility associated with choosing one of these norms
plus a definite threshold will depend on three factors: the probability the
scientist has of devising an acceptable solution, the probability of there
being more than one acceptable solution (these two factors will depend on
the success function), and the utility of getting one’s theory accepted by
all or some colleagues. We can add a fourth factor, which is that stronger
thresholds will be preferred to weaker ones, ceteris paribus, indicating, at
least, that the recognition for having won a strong competition is higher
than for winning a weaker one. Nevertheless, I will also present the com-
parison of the three rules without assuming this fourth factor, because it
is interesting to analyse the possibility of a constitutional agreement about
a norm of inference even when scientists are motivated exclusively by the
pursuit of fame and are given ‘exogenously’ the scale on which their the-
ories are to be judged.

Assuming that every member of the community has the same basic
preferences, it can be shown that R-I dominates R-II, since there can be


       315

situations in which one has proposed a theory which is acceptable under
R-I but not under R-II (i.e., if one’s theory is the best one, but there is at
least one more theory surpassing the inference threshold), but not vice
versa. R-II is also dominated by R-III, for the same reason (if one has
proposed a theory which is not the only one surpassing the threshold, one
can get some utility under R-III, but not under R-II, while, if one’s theory
is the only acceptable one, the utility received is the same under both rules).
On the other hand, no comparison is possible a priori between R-I and
R-III: which rule provides a higher expected utility will depend on the
particular forms of the utility function and the success function. All this
entails that, facing a choice between R-I, R-II and R-III, a scientific com-
munity would discard the second, and would establish one of the other
two. It is possible that those disciplines where a wider agreement on the-
ories exists have opted for a rule close to R-I, while disciplines where
disagreement is more frequent are regulated by R-III or some similar
norm. Nevertheless, it is also possible that this disagreement about the
right solutions to scientific problems is due, not to the character of the
rules of inference, but to the inherent difficulty of applying any rule to
specific cases.

Table 1 summarises the results on the optimum inference threshold for
each rule, both assuming that scientists have only a preference for recog-
nition (column a), and assuming that they also have a preference for
knowledge (column b); the calculations are given in the appendix. The
variable used to describe the optimum threshold t is 1 � F(t), i.e., the
probability a researcher has, a priori, of finding an acceptable solution to
the problem, if the level which determines acceptability is t. So, a high
level of 1 � F(t) will correspond to a low threshold, and vice versa. The
variable n represents the number of members of the research community
who are trying to solve a given problem.

The interpretation of these results is the following: in the first place, for
scientists merely worried about recognition, the optimum choice if R-I
were established would be the absence of a threshold (1 � F(t) � 1): the
best proposed theory should be accepted by every member independently
of the epistemic value of that theory. It does not seem that scientists behave
in such a way. For some problems, all the proposed solutions are taken
to be too bad to be acceptable, and hence, either real scientists do have a
preference for knowledge, or they have chosen some type of inference rule
other than R-I. In the first case, it is shown in the table that when R-I is
instituted, and scientists prefer a higher inference threshold to a lower one,
ceteris paribus, the probability of devising an acceptable solution will be
less than one, though the exact value of this probability can not be deter-
mined a priori; since, as we will see below, it is also impossible determine
a priori the threshold associated with R-III assuming epistemic prefer-


Ú .  316

TABLE 1. OPTIMUM INFERENCE THRESHOLDS.

KIND OF PREFERENCES

RULE

a
Only with a preference for

recognition

b
With a preference for

recognition and for
knowledge

R-I
(the best theory must be
chosen, if it passes t; in
other case, suspend
judgement)

1�F(t) � 1 0 � 1�F(t) � 1

R-II
(the best theory must be
chosen, if it is the only
passing t; in other case,
suspend judgement)

1�F(t) � 1/n 0 � 1�F(t) � 1/n

R-III
(the best theory must be
chosen, if it is the only one
passing t; if more theories
pass t, choose any of them
or suspend judgement; in
other case, suspend
judgement)

1/n � 1�F(t) � 1 0 � 1�F(t) � 1

(Note: n � number of scientists who try to solve a certain problem; 1 � F(t) � probability
of devising a theory better than threshold t).

9. Kitcher (1993) argues, on the basis of historical cases, that eliminative induction is
one of the most widely used methodological rules in scientific research.

ences, so the only possible way to establish empirically that R-III (or a
similar rule) has been chosen instead of R-I would be to find some sci-
entists who have decided to accept a hypothesis which they recognise to
be inferior (for the time being) to another one, and their colleagues find
that decision to be legitimate (which indicates that they do not think some
rule has been violated).

In the second place, the value 1 � F(t) � 1/n corresponds to the case
where the expected number of ‘acceptable’ solutions to each problem is
exactly 1, if n researchers are trying to find one solution. The choice of
such a threshold would institute a rule of acceptance which has some
‘family resemblance’ to eliminative induction,9 since both have as their
main function the leaving of only one theory or hypothesis acceptable.
However, three important differences exist between the two rules. Firstly,
eliminative induction is assumed to ‘prove’ (at least under the assumption
of ‘background knowledge’) that all non-acceptable theories are false,
whereas the rule we are discussing institutes a conventional definition of
what it is to be not-acceptable. Secondly, the application of eliminative


       317

induction (especially when it is not fully conclusive) requires us to take
into account the probability each theory has of being true, whereas the
other rule simply requires us to take into account the probability that
researchers have of finding an ‘acceptable’ theory. Lastly, eliminative in-
duction demands that we keep on testing until only one theory remains,
while the other rule establishes a priori a level of epistemic value such that,
on the average, there will be one acceptable solution per problem, but it
is possible that, ex post facto, some problems will have more than one
solution and others have none (R-I and R-II differ in allowing and not
allowing, respectively, the acceptance of rival solutions if there are more
than one). The hypothesis I would like to advance is that something similar
to the rule derivable from R-II or R-III (with epistemic preferences) is
what has been tacitly agreed upon in many scientific disciplines, and that
philosophers of science have usually misinterpreted this agreement as an
indication that another similar rule (eliminative induction) is actually used
by scientists.

In the third place, Table 1 shows that, starting from R-II under the
assumption that researchers have no epistemic motivations, introducing
this type of preference will lead to an increase in the chosen threshold,
whereas allowing the acceptance of any theory which has passed the
threshold (i.e., accepting R-III instead of R-II) will lead to a reduction in
the threshold. The consequence of this is that, if both changes are made,
it will not be possible to tell, a priori, whether the chosen threshold will
be higher or lower than that for which 1 � F(t) � 1/n. Nevertheless,
since the utility associated with being the only ‘winner’ is probably much
higher than the utility associated with being one among several ‘winners’,
the displacement of the optimum threshold upwards due to the presence
of epistemic preferences will probably be more intense than its displace-
ment downwards due to the possibility of accepting more than one solu-
tion (cf. the appendix). As a result, if scientists agree to establish a rule
like R-III and they have epistemic preferences, then their optimum thresh-
old will very likely be one for which 1 � F(t) � 1/n; i.e., there will be at
most one acceptable solution per problem.

6. The Choice of A Rule When Preferences Are Not Identical. In the pre-
vious section it was assumed that all the members of a research community
had exactly the same basic preferences and the same success function, and
hence, the same expected utility associated with each possible choice of
norms. The aim of this section is to show that agreement on a rule is
possible even if scientists do not agree about which norm would be the
optimum one, provided that their preferences are not too different. The
possibility of such an agreement should also serve to recall that the con-
tractarian approach to scientific norms does not attempt to prove a priori


Ú .  318

Expected
utility

Epistemic
value

r L r
S

EU
L

EU
S

a b

RUL

RUS

Figure 2.

10. That such inconsistent (or, more precisely, inefficient) choices are possible is shown,
in a different context, in Zamora Bonilla (1999), where it is proved that it may be the
case that all researchers believe that theory T is better than theory T �, but that T� is
accepted by more scientists than T.

that a certain system of rules is optimum in an objective sense, since,
according to this approach, scientists possess the freedom to establish the
rules they want. No rule resulting from such an agreement should be taken
as ‘worse’ than another in the epistemic sense, save when it is possible to
prove that the choice goes against scientists’ actual preferences.10

Suppose, for simplicity, that there are only two researchers working on
a problem. One of them, whom I will call ‘Strict’, has either a stronger
preference for knowledge, a higher estimation of his success function, or
both, which makes him prefer a higher inference threshold. The second
scientist, ‘Lenient’, prefers instead a lower threshold. Given the expected
utility functions of both researchers, Strict would prefer to establish rS as
the minimum acceptable level of success, while the Lenient would prefer
rL. RU1 represents their reservation utility; the utility which would be re-
ceived if no agreement were reached and each scientist joined another
community or found a different job (it is not necessary to suppose that
both scientists have the same reservation utility, but this assumption sim-
plifies the figure). More specifically (see Figure 2), Strict would neither
accept a threshold lower than a (since it would yield less than his reser-
vation utility), nor one lower than rL (since rL is better for both than any


       319

other point to the left), and Lenient would not accept any point to the
right of rS or b, for analogous reasons. So, any rule between a and rS would
be a Nash equilibrium, and hence, a possible ‘point of contract’ between
Lenient and Strict. If, on the other hand, the reservation utility of these
scientists were RU2, then no point of contract would exist, since any
threshold giving an expected utility to Lenient higher than RU2 would not
be acceptable for Strict, and vice versa (this explains why the preferences
of scientists must not be too different if they are to agree on an specific
norm).

When the collective choice of a rule and an inference threshold is made
by a group of more than two scientists agreement is more difficult, since
it is more probable that there is not any level of epistemic value such that
the expected utility associated with that level is higher than the reservation
utility of every researcher. The problem for the scientific community be-
comes, therefore, that of choosing a threshold such that ‘enough’ members
accept it, even if it does not coincide with their optima. It can be proved
that, if the distribution of optimum thresholds is symmetric around an
average point, the level of epistemic value associated with that point will
be the threshold which maximises the number of researchers deciding to
accept it; so, if the members of a discipline attempted to attract as many
colleagues as possible to their research area, they will tend to choose their
average optimum threshold. But other, more complicated possibilities are
open, for example, it might be the case that some researchers decide to
employ the choice of an inference threshold strategically, reasoning that,
if they choose a level higher than their own optima, this will deter other
researchers from entering the competition; this strategy will be rational as
long as a decrease in the number of competitors may increase the proba-
bility of being the only one to find a solution. From the epistemic point
of view, this ‘collusive’ behaviour would have the virtue of rising the av-
erage epistemic value of the accepted solutions. In any case, these nego-
tiation mechanisms are mentioned here just as open lines of research, the
most important point was simply to show that it is possible for the mem-
bers of a scientific discipline to reach an agreement about a norm of in-
ference, even when their preferences on such a norm are not identical.

7. Conclusion. In this paper I have tried to justify the view according to
which the methodological rules of a scientific discipline can be understood
as the result of an agreement between the members of that discipline. Seen
from this perspective, methodological rules can be divided into those
which are about theory evaluation and those which are about theory
choice. It may be expected that, the thicker is the ‘veil of ignorance’ under
which the ‘methodological contract’ is negotiated, the stronger will be the
influence of epistemic preferences on the choice of theory evaluation rules


Ú .  320

(these norms, nevertheless, have not been the topic of this paper). On the
other hand, rules about theory choice, or inference rules, will mainly be
influenced by the interest of researchers in having their own theories ac-
cepted by their colleagues/rivals, and hence, these norms will depend more
on ‘social factors’, although the presence of cognitive interests will tend
to make the preferred inference rules still more demanding. As a conclu-
sion, we can assert that the ‘pursuit of fame’ determines how good scientific
theories can be expected to be (and, with enough talented researchers en-
gaged in competition, they will usually be quite good!), though it is the
‘pursuit of knowledge’ which, basically, determines in what sense ‘good’
scientific theories are good.

Another interesting conclusion is that an inference rule more or less
similar to ‘eliminative induction’ may be a likely outcome of the negoti-
ation of a methodological contract. Besides the work of devising and an-
alysing other rules of inference, other lines of research derive naturally
from the contractarian approach offered in this paper. To indicate just a
few, the constitutional-choice model can be applied to the selection of the
other kinds of rules mentioned in Section 3; it would also be interesting
to explore whether the ‘negotiations’ studied by historians, sociologists
and ethno-methodologists of science may be reinterpreted as the bargain-
ing about the constitutional constraints which should be observed during
subsequent research. This reinterpretation would be a reasonable one if it
were regularly observed that methodological choices are seen by scientists
as compromises, i.e., if a researcher’s acceptance of a methodological rule
when it helps to support her own theory is taken by her colleagues as a
promise to follow the same rule in the future. Such a detailed survey of
case studies falls, however, outside the scope of this more analytical paper.

I think that the main virtue of the contractarian approach presented
here is that it offers a new point of view from which to consider the old
problem of the normative character of methodological rules. According to
this approach, what makes a scientific norm a norm is neither the fact that
it is regularly followed by scientists (as many historians and sociologists
might have assumed), nor the fact that it follows from logical or empirical
arguments about wise strategies for achieving epistemic goals (as it is usu-
ally defended by rationalist or naturalist philosophers of science). Rather,
what gives scientific norms their normative character is that they are taken
as compromises, both by the scientists who submit their decisions to them,
and by their colleagues, who expect that those compromises are going to
be respected. The more freedom researchers have to decide what norms
to abide by, and the more disconnected this decision is from short-term
rewards, the more impartial this compromise will be, and hence, the
stronger it will be from the normative point of view.


       321

Appendix: The Calculation of Optimum Thresholds

For simplicity, I will assume that the utility of not getting one’s own
theory accepted is 0, that the utility of getting it accepted is U � 0 for
scientists without a preference for knowledge, and that this is U(t) � 0
for scientists with a preference for knowledge if the chosen threshold is t.
I will assume that U(x) is positive and increasing, and U�(x) decreasing.
The optimum thresholds do not change for utility functions which are a
linear transformation of these. In addition, n is the number of scientists
trying to solve a problem.

R-I without a preference for knowledge: The expected utility of choosing
threshold x is U times the probability of one’s theory being the only one
passing x; i.e.:

� n�1 n �EU(x) � � f(y)F(y) Udy � (U/n)[F(y) ]x x
n n n� (U/n)(F(�) � F(x) ) � (U/n)(1 � F(x) ) (1)

From the last expression it follows that expected utility is maximised when
x � 0.

R-I with a preference for knowledge: The expected utility is now:

� n�1 nEU(x) � � f(y)F(y) U(x)dy � (U(x)/n)(F(�)x
n n� F(x) ) � (U(x)/n)(1 � F(x) ) (2)

The first order condition for maximisation is

n�1 nU�(x)/U(x) � nF(x) ((1 � F(x) ).

For x � 0, the right hand side is 0, and increases as x does; our assump-
tions about U(x) entail that U�(0)/U(0) is positive and decreasing, and
hence, the optimum threshold will be greater than 0.

R-II without a preference for knowledge: Now, the expected utility as-
sociated with threshold x is:

n�1 n�1 nEU(x) � (1 � F(x))F(x) U � (F(x) � F(x) )U (3)

The first order condition for maximisation is:

n�2 n�1dEU(x)/dx � U[(n � 1)F(x) f(x) � nF(x) f(x)] � 0, (4)

which entails (for f(x) � 0) that in the optimum threshold, F(x) �
(n � 1)/n, and hence, that 1 � F(x) � 1/n.

R-II with a preference for knowledge: Now equations (3) and (4) are
transformed into:

n�1 nEU(x) � (F(x) � F(x) )U(x) (5)

and


Ú .  322

n�2 n�1[(n � 1)F(x) f(x) � nF(x) f(x)]U(x)
n�1 n� (F(x) � F(x) )(U�(x)) � 0. (6)

Since the last three arguments (U(x), (F(x)n�1 � F(x)n) and U�(x))
are positive, the first one ((n � 1)F(x)n�2f(x) � nF(x)n�1f(x)) must be
negative, and this entails that F(x) � (n � 1)/n, i.e., 1 � F(x) � 1/n.

R-III without a preference for knowledge: Let V be the expected utility
associated with having one’s theory among a group of ‘acceptable’ theo-
ries. Obviously, V � U, since you get U when your theory is unanimously
accepted. In this case, the expected utility associated to threshold x is:

n�1 n�1EU(x) � (1 � F(x))F(x) U � (1 � F(x))(1 � F(x) )V, (7)

and the condition for optimisation is:

n�2 n�1dEU(x)/dx � Uf(x)[(n � 1)F(x) � nF(x) ]
n�1 n�2� Vf(x)[nF(x) � (n � 1)F(x) � 1] � (8)

n�2 n�1(n � 1)F(x) f(x)(U � V) � nF(x) f(x)(U � V)
� Vf(x) � 0

This entails (assuming again that f(x) � 0) that (n � 1)F(x)n�2 �
nF(x)n�1 � V/(U � V) � 0, and hence, that 1 � F(x) � 0.

R-III with a preference for knowledge: In this last case, the expected
utility associated with threshold x is:

n�1EU(x) � (1 � F(x))F(x) U(x)
n�1� (1 � F(x))(1 � F(x) )V(x), (9)

where U(x) is as before, and V(x) is the expected utility associated with
having one’s theory amongst a group of ‘acceptable’ theories, when the
scientist also has a preference for knowledge. As was said above, it can
not be known a priori whether the chosen threshold will be higher or lower
than that of R-I without a preference for knowledge; nevertheless, the
smaller V(x) is as compared to U(x), and the bigger U�(x) is, the higher
the chosen threshold will be, and vice versa.

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