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.
  • 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.

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:
  1. as far as I can see, rose R is red
  2. horse H will win at the race tomorrow
  3. 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.

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

-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.
  • 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.

  • 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.

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).

  • 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.
  • 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.

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.

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.

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?

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.
  • 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.
  • 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.
  • 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?
  • 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.
  • 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 non-personified 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.

9. Public Commitment to Rules