Uncertainty is a pervasive feature of human life and almost all our decisions must be made without certainty about what the consequences of our actions will be for ourselves or others. Human attitudes such as hope, fear and even regret depend on it. Despite this, philosophy has given little attention to uncertainty, largely treating it as just lack of certainty (apparently the real interest). In both the mathematical and empirical sciences, on the other hand, the emphasis has been on the development of techniques to manage it. So central has the concept of probability been to this enterprise that it has come to seem as if uncertainty was nothing other than the flipside of probability.

The concept of probability emerged surprisingly late in human history, in the seventeenth-century work of Blaise Pascal and Pierre de Fermat.1 In this work, and much that followed, probability was conceived both in terms of the stochastic properties of chance processes, such as dice rolls and card deals, and the properties of beliefs about events regarding which full knowledge was lacking. In time this hardened into a distinction between two different forms of uncertainty: objective or aleatory uncertainty, which derives from features of the world (indeterminacy, randomness), and subjective or epistemic uncertainty, which derives from lack of information about it. In modern decision theory, there is a dominant theory of how each form of uncertainty should be quantified (in both cases, by a probability measure) and of how, so quantified, it should weigh in the evaluation of actions. For situations of objective uncertainty (or risk, as it typically called) decision theorists look to the version of expected utility theory originally due to von Neumann & Morgenstern (2007/1944), while for those characterised by epistemic uncertainty they look to subjective expected utility theory, whose classic statement is to be found in the work of Leonard Savage (1974/1954).

This distinction between risk and epistemic uncertainty, important and useful though it may be, does not remotely do justice to the variety of forms and degrees of uncertainty relevant to decision making.

We not only take attitudes to prospects, we also take conditional attitudes to them: attitudes on the hypothesis, supposition or assumption that something is true. On the assumption that I will not be tired tonight, I would rather go out than stay in. On the supposition that interest rates will rise, I believe that housing prices will fall. And so on. Conditional attitudes, like their unconditional counterparts, come in grades, a feature that is crucial to the role they play in decision making. I might find the prospect of going to the beach desirable, conditional on it being a sunny day, but not at all so, conditional on it being rainy. Whether I should go to the beach depends not only on the relative probability of sun and rain but also on the relative strengths of these conditional desires. One aim of this chapter is to identify the different kinds of suppositions involved in forming graded conditional attitudes, to propose rationality conditions that are characteristic of them and then to examine the implications of these conditions. A second is to explore the role that conditional attitudes play in hypothetical reasoning. Throughout I will assume the conceptual framework developed in the previous chapter.

First, two points should be made about what conditional attitudes are not. A common view is that conditional beliefs and desires given some β are dispositions to believe and desire conditional on β being true or on coming to believe that β. But this view is not quite right. While we should expect there to be a close relation between our conditional attitudes and the attitudes we take when we learn that the condition in question holds, sometimes this relation is disturbed by the conditions under which the learning occurs. I would prefer, were I confronted by a bully, that I would act bravely rather than run away. If I were confronted by a bully, however, I would (I predict) prefer to run. I believe that, were I to drink a lot, my driving ability would be impaired. Were I to drink too much, however, I would believe my driving to be better than ever.

PROSPECTS AND POSSIBLE WORLDS

Agency requires a number of abilities: to recognise and represent salient contingencies or prospects, to form consistent attitudes to them and to act in the light of these attitudes. In the second part of the book I gave an account of the requirements that rationality imposes on the beliefs and desires that an agent forms in negotiating her way around her environment. In doing so I refrained from saying anything specific about the contents of these attitudes, simply bundling them under the category of ‘prospects’. This has certain advantages, not least that it allows this account of rationality to be paired with more than one conception of what the objects of belief and desire are. But on the downside it left open the question of whether the proposed rationality constraints are consistent with any account of prospects, a question whose importance is highlighted by the triviality results previously alluded to. So before tackling how decisions should be guided by beliefs and desires we need to address the question of what prospects are.

The philosophical importance of this question lies in the central role that an account of prospects must play in any general theory of thought, reasoning and action. Prospects serve not only as the objects of attitudes such as belief and desire but also as the contents of sentences that agents use to express such beliefs and desires and to reason about the world and their place in it. An agent who says ‘It will rain on Thursday’ is able to express her belief that it will rain on Thursday by uttering this sentence in virtue of the fact that it has as its content or meaning just the prospect that she believes true. When she reasons from this to the thought ‘I will get wet if I don't take an umbrella’ the inference she makes is assisted by the semantic relationships between these sentences and others.

AGENTS

To make decisions, agents must have a range of capabilities. Firstly, they must have an ability to represent, and discriminate between, different possible features or states of their environment. Secondly, they must be able to perceive or infer the presence or absence of these features, i.e. to form beliefs about the world. Thirdly, they must be able to compare these possible features or states according to some standard of value – i.e. be able to judge whether they are more or less desirable. And, finally, if they are to be capable of not just thinking about the world but also acting on it, agents need to be able to determine what options they have, to evaluate them and to exercise them. In summary, they must be able to identify both the possible states of the world and their options for changing them and to form cognitive and evaluative attitudes towards both.

This list of conditions may seem quite demanding, but it should be borne in mind that there is no requirement that these judgements be at all refined or detailed, or even that they be conscious. So even cognitively quite primitive entities may well have most or all of the required capabilities. Consider a thermostat, for instance. It inarguably represents features of the world – the temperature – and judges which of these states in the actual one. It also has a crude value system that can be summarised as: cold is bad, warm is good. The actions available to it – switching the heating on or off or doing nothing – are chosen in the light of information it receives about the state of the world and implicitly in view of the consequences of selecting the action.

On the other hand, the way the thermostat makes decisions, if one is happy to speak in such terms, lacks a number of the essential characteristics of human decision making. Although we might say that the reason why the thermostat switches the heating on is that the room is cold and that by doing so it will warm up, the reason we refer to is not the cause of the thermostat's switching on. The thermostat does not itself make the judgements about what would happen if it performed one or other of the actions available to it.

INTRODUCTION

In the first part of the book we developed a theory of rational prospective agency based around a set of claims about what rationality requires of the judgements of agents: consistency between her beliefs, desires and preferences; between her conditional and unconditional attitudes; and between her attitudes and her choices. This theory can reasonably be criticised both for being too demanding and for being insufficiently so. Too demanding because real agents face resource constraints which make it impossible to form opinions about all possible contingencies and unwise that they attempt to do so. Insufficiently demanding, on the other hand, because it requires of agents only that their beliefs and desires be consistent, and not that they be responsive to what is true or valuable in any way. In the next part of the book we will take up the first challenge. Our task in this chapter will be to respond to the second.

There are two directions in which one might seek to constrain the sorts of attitudes that a rational agent can permissibly hold. First, one might put forward conditions that go beyond consistency but which fall short of simply demanding that the agent believe only truths and desire only what is good (which would be to demand what cannot generally be achieved). Second, one might require that the agent improves her opinions over time by responding appropriately to information acquired through interaction with the environment or through deliberation. Many conditions of both kinds are to be found in the epistemological literature, for different conceptions of belief, but I will focus on those deriving from the widely shared thought that an agent's beliefs should be constrained by the evidence she holds about the state of the world and, more generally, that her attitudes should reflect what she has learnt from experience.

Let us restrict attention to belief for the moment and return to the other attitudes later. Evidence-based constraints on belief can take both a synchronic form – that an agent's beliefs at a particular time should appropriately reflect the evidence that she holds at that time – and a diachronic one – that she should revise her beliefs appropriately in response to the acquisition of new evidence.

What reasons do we have for accepting or rejecting Bayesian decision theory? Empirical theories stand or fall on the basis of their ability to handle the facts; above all, by the quality of their explanations and the accuracy of their predictions. As an empirical theory of judgement and decision making, subjective expected utility theory has endured a good deal of criticism in the last 30 years or so, with a range of experimental results suggesting that it is a poor predictor of people's behaviour. On the other hand, none of the main rival empirical theories seem to do much better when confronted with data other than that used to generate them; according to some studies they do worse.1 So, while there is every reason to be cautious about the theory's predictive abilities in a wide range of cases, there is as yet no good reason to abandon it entirely.

It is as a normative theory, however, that we are interested in the problem of justifying acceptance of Bayesian decision theory. Although normative theories cannot be refuted by direct appeal to the facts, the general principles of a normative theory can be assessed in a similar way to an empirical one. A scientific theory will have its laws assessed by deriving predictions about concrete cases and then testing to see whether the predictions turn out to be true or not. A normative theory doesn't make predictions, but it will have implications for concrete situations which can be compared with our judgements about what is correct in those cases. A theory of valid inference, for instance, can be tested against concrete instances of inferences that we are inclined (or otherwise) to make: a theory of grammar against sentences that competent speakers find acceptable; and so on.

The fundamental lesson of the Quine–Duhem problem – that the falsity of a scientific hypothesis can rarely be deduced from a set of observations – applies equally to normative theories. When general normative principles clash with our judgements regarding a concrete case, all that follows is that we cannot coherently hold onto both.

INTRODUCTION

Agents must make decisions in situations characterised by uncertainty that differs both in kind and in severity. Differs in kind because they face not only factual uncertainty about the state of the world but also option uncertainty about what the consequences would be of performing one or other of the actions available to them, evaluative uncertainty about the desirability of these possible consequences and modal uncertainty about the space of relevant contingencies. Differs in severity because the quality, amount and coherence of the information that the agent has about relevant prospects can vary to a considerable degree. Mainstream Bayesian decision theory recognises some distinctions in severity (between risk and uncertainty, for instance) but measures all the different kinds of uncertainty in the same way, namely by means of a probability function defined on the set of possible states of the world.

In the first two parts of the book, I argued that such reduction of all uncertainty to factual uncertainty is not always possible or useful, and offered an alternative theory that was applicable even when it was not. Firstly, the probability measure of factual uncertainty was complemented with a desirability measure of evaluative uncertainty that explicitly incorporated dependence on both beliefs about the facts and belief-independent judgements of value, and which could be revised as these beliefs and evaluations changed. Secondly, option uncertainty was captured by a suppositional probability on prospects conditional on an intervention of some kind. These fed into a decision rule prescribing choice, from the set of available options, of the ones that maximise expected desirability gain, relative to the status quo, on the supposition of its performance. When options can be formulated as Savage-style acts this decision rule coincides with that of maximising subjective expected utility.

This broadly Bayesian decision theory shares with its mainstream cousins the assumption that agents come to decision problems equipped with a complete set of probability and desirability judgements. It is, in other words, a decision theory suitable for a maximally opinionated agent. This implies that, if decision makers want to use such a Bayesian decision theory as a guide to their choices, then they need to reach precise judgements on at least all contingencies relevant to the decision problem they face.

THE RAMSEY TEST FOR BELIEF

This remark of Frank Ramsey appears only as a footnote to his paper ‘General Propositions and Causality’, but it has sufficed to lend his name to a hypothesis that has figured prominently in contemporary debate in both the semantics and pragmatics of conditionals. This interest in the Ramsey Test hypothesis, as it is usually called, is fuelled by widespread dissatisfaction with the material conditional as a rendition of the semantic content of ordinary language conditionals. Discontent is focused on two points: the fact that the material conditional interpretation appears to support fallacious reasoning and the fact that reasonable belief in conditionals appears to diverge from that demanded by the material conditional interpretation of them.

On the material conditional construal of conditionals, α → β is logically equivalent to ￢α ∨αβ. Hence, for example, ￢(α→β) implies that α. But the inference from ‘It is not the case that if it snows tomorrow then the government will fall’ to ‘It will snow tomorrow’ is clearly not valid, because denying that the weather will have an impact on the government's fortunes does not commit one to any particular meteorological prognosis. Likewise, disbelieving that the government will fall if it snows does not mean believing that it will snow (and, in summer, should not).

Nor does the material conditional do any better as an interpretation of counterfactuals – indeed, if anything, it does worse. On a material conditional interpretation, the claim expressed by the sentence ‘If George Bush had been concerned to protect the environment, then he would have lowered the tax on fuel’ should be highly credible, because of the improbability of its antecedent (this follows from the fact that this view implies that P(α → β) = P(￢α) + P(αβ)). But intuitively the claim is implausible because environmentalists typically believe that fuel taxes should be raised.

DECISION PRINCIPLE

Decision theory addresses two questions. What states of mind or sets of judgements are rationally permissible? And what choices should we make, given our state of mind or judgement? The previous chapters have proposed an answer to the first question and enough is now in place for us to turn to the second.

There is broad agreement amongst decision theorists that, under the conditions characterised by subjective uncertainty about the state of the world and in which the agent has determinate degrees of belief in, and preference for, all relevant prospects, actions should be chosen in accordance with the expected subjective benefit of so doing. In contrast, there is a good deal of variety in the way that this idea is cashed out. Much of this is driven by differences in the way that decision problems, and especially the objects of choice, are conceived and formally represented. But some of it emanates from more substantial differences both in the interpretation of the principle of maximising expected benefit and in the formal assumptions made for the purposes of deriving it. One aim of this chapter will be to explore the relationship between these theories. Another will be to defend a particular one. As the theory of rationality presented in the previous chapter is essentially an extension of Richard Jeffrey's decision theory, it is natural to start by reminding ourselves about what he says about choice of action. In Jeffrey's theory, an action is simply a prospect that can be made true at will (i.e. which is a genuine option for an agent to exercise) and its choice-worthiness is identified with its desirability as defined earlier – i.e. as the conditional expectation of utility given the performance of the action. We can therefore express his theory of choice thus:

Jeffrey Of all the prospects that constitute options for you, pick one with greatest desirability.

Although Jeffrey's theory has been very influential in philosophy, it has few contemporary supporters, with the majority of philosophical decision theorists accepting the objections to it lodged by causal decision theory.