Empiricism versus Pragmatism in Epistemology: the Appeal to
Public Reason
Loránd Ambrus-Lakatos
17 January 2000
1. Introduction
 Starting point is a controversy among philosophers of science.
Empiricism as a scientific method is concerned with the issue of how
beliefs should be formed and how new evidence should be
accommodated. This is intimately connected to techniques of Bayesian
statistics. In his papers on issues connected to belief formation, van
Fraassen (1984, 1995) points to an important consequence of adopting
this technique. Demonstrating that the internal coherence of Bayesian
information processing can be enforced by the use of the well-known
Dutch Book Argument, the formal coherence won through these means
comes together with an instance of conceptual incoherence. Namely,
the agent has to adopt a full belief in his infallibility as an information
processor to avoid the wrath of the Dutch Bookie. This he interprets as
a requirement to commit to epistemic stances. The pertinent question
then becomes: on what ground can the Empiricist make practical
decisions concerning what to believe in?
 I would like to use his argument in order to discuss not only the
Bayesian framework, but contemporary formal decision theory as well.
 Then I will go on to argue that the formal rules an agent faces in a
Bayesian decision problem can be viewed as a contractual framework
for belief formation. This amounts to the contention that the
Empiricists strives to adopt a set of rules in confines of which evidence
can be processed in a ruly manner. Then the rest of his epistemology
can be characterized with the wish to create circumstances under which
epistemic statements can be legitimately judged.
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 First, this reconstruction has important consequences for the
interpretation of contemporary moral contractualism, the prevailing
approach in that area.
 Second, this picture of what the Empiricist is up to relaxes the
significance of finding a satisfactory treatment of how he could make
practical decisions without too much comprise to his hard-core
attitudes toward evidence. Positing agreement as a main value could
justify prescriptions without invoking instrumental reasoning.
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2. Dynamic Coherence of Beliefs
 We start from a concern with the truth of some statement, labeled as H.
This could be a proposition, a hypothesis, a claim, or a theory.
 Consider the possible position concerning this statement: “I am quite
convinced about the truth of H, but it is also possible that in a year
from now I will still be convinced even though it is in fact false.” Van
Fraassen: this is a sensible and not unlikely state of one’s mind.
 But it should not be had by someone who is to be regarded as rational.
 Let us first note, for the sake of fixing associations, some examples for
H:
a. as far as I can see, rose R is red
b. horse H will win at the race tomorrow
c. the Darwinian theory of evolution T is by and large true
 Suppose now that you are asked about the truth of H now; and also you
consider what you will think about it at some later time. The main
didactic example of van Fraassen: the hypothesis is that horse H will
win at the race tomorrow.
 Consider also the proposition (labeled as E) that you will think that H
is true tomorrow morning before the race.
 Suppose next that your beliefs are characterized like this:
P(E)=0.4
P(not H and E)=0.2
 This is not unlikely, sensible, and still censored by rationality.
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3. The Dutch Bookie as the Censor
 The formal framework of Bayesian statistics and decision theory
necessitates the adoption of peculiar constraints on how beliefs should
be formed. Usually, the enforcement of the mental compliance with
these constraints is accomplished through the so-called Dutch Book
Arguments.
 In general, they identify a series of bets that
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given the beliefs and the preferences of the agent
will be all accepted
and if the beliefs and the preferences do not meet certain criteria
there is a sure loss for the agent
 Note: I propose here not to subsume preferences under beliefs.
 An immediate reaction to the paradox just demonstrated is to recall that
these Dutch Book Arguments can do much more than enforcing
diachronic coherence. It can enforce the compliance with all the
aspects of formal decision theory.
 Take the example of intransitive preferences. An agent has three
objects to choose from A, B, and C. He has intransitive preferences
over them: A is preferred to B, B is preferred to C, C is preferred to A.
Having one of these objects, the switch to an other one costs him , 
being very small. Assume further that if this agent prefers an object to
the other, than he also prefers the object to the bundle of retaining the
old one and not paying . Then if a Dutch Bookie presents him
persistently with the choice of retaining the old object or getting the
one preferred to it then the agent will never stop switching and is
drained of all his resources by the accumulation of the -s.
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 Similar examples can be constructed for the enforcement of correct
deductions or the compliance with the basic rules of probability
calculus, or the Independence Axiom in the theory of decisions under
uncertainty. What this overwhelming power of the Dutch Book
Argument hints at is that there might be something in the formal nature
of the situations in which it is successfully employed.
 Back to our case of horse race betting:
The three bets used by the Bookie:
(i) pays 1 if I come to believe H, but H is really false – this costs 0.2
(ii) pays 0.5 if I do not come to believe H – this costs 0.3
(iii) pays 0.5 if I do come to believe H – this costs 0.2
Note that all these prices are fair given my beliefs, and that I have to pay
0.7 for the three bets together.
Then there are two relevant scenarios:
: I do not come to believe H. I win the second bet and get 0.5. So I lose
0.2.
: I do indeed come to believe H: I lose the second bet, but win the third
one, so get paid 0.5. However, in order to be able to win the third bet, I
reveal that I believe H to the Bookie. So he buys back the first one “for a
pittance”. So I get altogether a little bit more than 0.5 and lose again.
All this is despite the fact that the Bookie has no clue about whether H is
or is not true.
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 So the Dutch Bookie forces out that my beliefs are diachronically
coherent in the following sense:
(Principle of Reflection) Pt (H| p t+x(A) = r) = r
This has to be true for each rational agent.
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4. On Evidence and Bayesian Updating
 Thus this principle forces the cognitive agent, due to the danger of
losing to the Dutch Bookie, to be overly confident in his capability of
recognizing when a signal pertaining to his knowledge about the true
state of nature arrived. This latter statement shows that then it requires
that the agent would have a possibility correspondence with a
partitional structure, in the above terminology. Thus he is required to
know the whole underlying model of how he processes information.
The framework first of all recognizes a set of possible and conceivable
states of nature, S. A generic element of this set is denoted by s. In one
distinguished interpretation, S stands for all the possible configuration
of truth values of N propositions, all the possible ways they can be
either true or false.
 Next, an agent engaged in cognition is considered. This agent is
assumed to have a prior probability distribution over the states he
considers as possible. Next, the agent is confronted with a signal,
which describes the new information he acquires. The views of the
agent about the true state of nature are fully characterized by a
possibility correspondence P, that assigns to a given s a subset of S.
This means that given a true state, the possibility correspondence
describes the states he thinks as possible to be the true one. This
correspondence may have certain properties.
(i) non-deludedness For all s  S, s  P(s);
(ii) “knowing that you know”: If s'  P(s), then P(s')  P(s);
(iii) “nestedness”: If s' in S, then P(s')  P(s).
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 If these properties all hold, the possibility correspondence has a
partitional structure, that is
for all s and s' in S: P(s) = (s'| P(s') = P(s)).
Here the possible states of nature are regimented into equivalence classes,
within these classes they are indistinguishable. Coorespondingly, P is
regarded to have a non-partitional structure if the above condition (1) does
not hold. A non-partitional structure could have several specific
properties. Here I would like to mention three of them:
 In this distinguished model, the information arrival is conceived of as a
successive refinement of previous partitions, the agent can exclude
successively more and more possible states, until the process enables
him to narrow down the possibilities to one state.
 Thus assuming a non-partitional structure amounts to assuming that
the agent either does not know the whole framework or forgot it. This
is because knowing the prior and the whole model, one can always
deduce more than what the possibility structure allows to know.
 The possibility correspondence P can be indexed by agents and by
time. Clearly, different agents can have different information about the
true state of nature at a given moment, and the views of one particular
agent can change across time. But then the need for a further
specification in this model arises, what do agents know about what the
others know, and also, what do agents know about what they knew or
they will know. One aspect of this question will be discussed in the
next section, but I will only treat the knowledge of one agent about
what he knows in other times.
 An example of how all this matters for making correct decisions.
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 The major conclusion: the requirement of Reflection presupposes
infallibility in recognizing what kind of evidence will be able to settle a
truth claim; and also recognizing the arrival of that evidence. But then
the conclusion has to be that it was a crucial feature of the requirement
of Reflection that it used a distinguished point in time. This very point
was the one when the Dutch Bookie approached the cognitive agent.
All what was required from the agent was that he knew all the
ramifications of his knowledge and would not forget them until the bet
lasts. Here I would like to the propose that this is indeed the very
nature of every formal decision problem, therefore also that of the
decision problem of taking the Dutch Bookie bets or not.
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5. The Bayesian Model and the Harsanyi Doctrine
 A more general description of Bayesian decision problems.
 The signal structure: each agent receives a signal first about possible
states, and then proceeds by first updating them by Bayes’ Rule.
 A note: this allows he treatment of interactive situations. The example
of the Battle of the Sexes.
 In fact, every formal decision problem has to take the following form.
The agent is presented with the problem. Possible actions to be taken,
payoffs, moves of chance are all given. if there is any residual
uncertainty than these are compressed into the description of the
uncertainty the agent faces as it seen at the time the problem is tackled.
If there is any difficulty with these frames then there is always a
gamemaster in the background, who could have created the rules but is
certainly a rule-enforcer. If there is a difficulty for the agent in figuring
out what signal arrived, the gamemaster will tell him. The lack of
ambiguity concerning the payoffs endows the optimal formal rule with
a normative force. (Compare here the role of the experimental
psychologist, decision or game theorist.) The agent has to rely on this
Master in order to make sense of the normative question of what he
should under the circumstances described by the situation. It is possible
to ask the question what agents should do or what beliefs they should
have in a general as opposed to a preset situation, but first the situation
has to be described in a unambiguous to make the question amenable
for a regimented answer.
 So, if one takes it that a formal decision problem needs to have the
ramifications of every possible knowledge, action, and payoffs as
given, from the point of view of a distinguished time: then one
subscribes to the Harsanyi Doctrine.
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6. Attempts at Defending the Requirement of Reflection
 Reasonable doubts about what I will take as evidence tomorrow. But:
this completely undermine the Bayesian picture.
 Report of my mental state in forecast. But: but forecast requires
reliability or sincerity.
 Harman: probabilities are not functions. So storage is an issue:
priorities.
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7. van Frassen’s Defense: Intention and Commitment
 Intention makes a statement true. Moore’s Paradox and the Paradox of
the Preface.
 Therefore, it could also be seen as a commitment. But to what?
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8. An Other View: Challenging the Dutch Book Story
 So : is it admissible for me to fully believe in a proposition without
subjecting it to Bayesian requirements of information processing? A
negative answer is equated here with the position of a naive Empiricist.
And this position is, in turn, scrutinized by a demonstration of a
paradox for this naive Empiricist: if he believes his method is the only
one justifiable, then he has to agree that this belief can be rationalized
by the same means he requires from the rationalization of other beliefs.
The construction of the paradox uses the Dutch Book argument
discussed in the previous section, in the following manner: if someone
would believe in a proposition and would not subject it to Bayesian
rigor then he would lose in bets against the Dutch Bookie.
 Since what is at stake here is beyond the formal coherence of a theory,
it is the foundation of epistemic contentions, one is inclined to ask why
the Dutch Book story could have a force in this latter realm. Why does
one have to bend his or her head in front of the Dutch Bookie? In order
to answer this question, I propose to give content to the Argument with
the elaboration of situations in which an agent engaged in cognition
could really fear a situation i which the Dutch Bookie is at present.
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 So what is this Dutch Book story? Proceeding slowly, we should
imagine the Bookie somehow coming to the person contemplating the
truth of some propositions. Recall that in this wide epistemic context,
the propositions can be of several kind. (The three examples:)
(E1) rose R is red
(E2) horse X will win tomorrow on the horse track
(E3) theory T is correct
On the other hand: who this Bookie be? I find three plausible identity for
her:
(I1) she is a real person
(I2) she represents society (the epistemic and moral community the agent
belongs to)
(I3) she represents evolution (of some sort)
 Now, again, this identity figures crucially in the plausibility of the
Dutch Book arguments. My strategy is the following: first, I take the
first and the third identities in turn, and discuss the assumptions
involved in the use of their identity. Second, I will conclude that an
identity closest to a version of the second possibility is the most
convincing in these stories, and continue with the claim that a
reconstruction of the position of the Empiricist ought to consider this
variant. But then the presuppositions coming with this interpretation
should be embraced, and their implications elucidated. This will, I
contend, lead to the view that the epistemic stance of the Empiricist is
interwoven with a contractualist ethics.
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 So the work starts with fleshing out the feasible assumptions behind
the first and the third identities, respectively. Concerning the first, then,
just imagine a real Bookie approaching you with some bets focusing
the truth values of some propositions. She announces the rules
connected to the these bets. I do understand what she says. Under these
circumstances two salient features of the arguments around the
Principle of Reflection receive a new look. The first one concerns
propositions of type E2. It is no longer necessary for me to worry
whether a certain signal arrived or not (whether the rose Y is really red
or not), it is part of the game that I will know for sure that it did, the
rules circumscribing the bet involve the announcement of them by the
gamemaster. This is just a manifestation of the formal nature of
decision problems, visited above. The bet is embedded in a contractual
situation, the bet is security. It is not a primary question whether the
Bookie or I could cheat, or does not perform according to the
agreement. There is a Third Party behind our transaction who enforces
the rules and these rules include the announcement of the true state of
nature - as this state is defined by the bet. Proposition of the E1-type
are natural candidates for these bets, and we can bet on the color of a
particular rose, too. But then, it seems to me, we have to agree on who
would decide what color it has if we would still disagree after a
serious examination of the color. This line of argument thus generates a
temptation to assert that it is not irrational to fully believe in our future
capability of recognizing signals in a 'real' betting situation, this
capability is built in the bet, being an example of a social situation.
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 This assertion could be challenged on the gorund that in the specific
Dutch Book Argument presented in van Fraassen (1984) it did not
matter what the nature of the evidence was from the point of view of
the agent. The agent was required to tell what his state of mind was,
and the Bookie was extracting money from him: no matter what he
said. This counterargument activates the second salient feature of the
argument for the Principle of Reflection. This amounts to the
observation that nothing explains the honesty of our agent in a betting
situation. The agent is seriously concerned about the correctness of the
doctrines of evolutionary biology. He might currently believe those
doctrines and simultaneously can imagine that he will abandon them at
some point. But why should he not suspend this state of mind for the
sake of not losing the bets?
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 The third interpretation can circumvent these features. According to
this one, an outside force, whose deeds are beyond the control of the
epistemic agent, make this agent face a series of decision problems (the
bets of the Dutch Bookie) and the he will be provided with some
payoffs depending on his actual decisions. The agent is not necessarily
able to comprehend the whole situation, but we think of him as
perceiving that there is a decision to be made. And of course, he will
have some impression of what and how much the payoffs happened to
be. The gist of this interpretation is that unless the agent adopts the
Principle, he will be punished by these evolutionary forces and might
even wiped out from existence (or he will not have offsprings). Here
there is no contractual framework which would set the rules explicitly,
the agent is presented with the bets/securities and then reacts. The
weakness of this is, of course, that one needs to fabricate specific
reasons for the assumption that evolution constructs strategies, and
very clever strategies indeed, and also that it is through securities with
unshakable characteristics that evolution operates. Nor can we think of
the prizes being able to give an overarching reason to comply with the
requirement of diachronic coherence, since the stakes might not even
be perceived. Once they are comprehended, they give reasons for
adopting these distinguished rules for belief formation, the value being
survival or viability in this world. It is manifestly not the task of this
paper to state anything about the nature of evolution, so the following
compromise is proposed. The evolutionary interpretation could be seen
as a metaphor. It highlights situations in which the explicit contractual
framework is missing and the prizes are only vaguely perceived, but
still somehow all these are present. Then it projects a vision: if
someone would not conform to certain formal rules of belief formation
then that will be harmful to him. The nature of the harm remains to be
specified.
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 But then it is some version of the second interpretation that is best able
to support the Dutch Book story. But initially the concession has to be
made that the story has to be thought of as a metaphor. The lesson from
the first interpretation was exactly that in a real, clear-cut betting
situation there is no compelling reason why the cognitive agent should
not suspend what he really believes. But which feature of the
discussion of the previous two interpretations can this metaphor
usefully employ? The first one pointed at the importance of the
perception of explicit rules, and the trust in their enforceability, and the
significance of the perception of a valuable prize to be attained. The
third pointed to the possibility that the betting partner is nonpersonified entity, a faceless agency. Now, according to the second
interpretation it is society, the moral and epistemic environment of the
cognitive agent which is the betting party. This community could lay
down a set of explicit rules which will be binding for the agent, given
that this very same community provides means with which these rules
are enforced. Also, it is conceivable that this community possesses
some mechanism which generates prizes for those who do the best
under these circumstances.
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9. Public Commitment to Rules
 Preliminary observation: a distinguished technique for commitment is
via a contract. The example of Schelling.
 A more general proposal: the most suitable way one can think of
common rules facilitating commitment is to project the existence of a
contract for all the cognitive and moral agents in this community which
prescribes what the ramifications of decision problems could be in this
community. It is crucial that these rules would be embedded in an
environment in which both the rules and the possible knowledge of the
agents are decidable for those who are responsible for the enforcement
of the social compact. Thus the contract has to specify beforehand the
possible states the agents can be in, as well as the actions they can take
in those states. This presumes that those states have to be identifiable in
a way which is foreseen by the contract. Further if there are disputes
about the true states, it should be decidable for the parties what to do.
 All this could also be supported by reference to “ethics” of those who
are committed to empiricism in science. Van Fraassen (1995: 33): call
for participation in a common venture.
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10. Further: Public Reason and Moral Contractualism
 Rawls, Theory of Justice, section 10: a moral theory has to
presuppose rules the ramifications and interpretations of which are
transparent to everyone. This is later formulated by him in terms of
the requirement to rely on public reason in settling moral arguments.
Note that this claim is not about a concrete formal decision problem,
but rather about how to formulate one.
 One can illustrate the impact of this stance by reference to a simple
distributional problem.
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