Robert Stalnaker

A Theory of Conditionals

A conditional sentence expresses a proposition which is a function of two other propositions, yet not one which is a truth function of those propositions. I may know the truth values of “Willie Mays played in the American League” and “Willie Mays hit four hundred” without knowing whether or not Mays, would have hit four hundred if he had played in the American League. This fact has tended to puzzle, displease, or delight philosophers, and many have felt that it is a fact that calls for some comment or explanation. It has given rise to a number of philosophical problems; I shall discuss three of these.

Conceptual analysis, dualism, and the explanatory gap

The explanatory gap. Consciousness is a mystery. No one has ever given an account, even a highly speculative, hypothetical, and incomplete account of how a physical thing could have phenomenal states (Nagel 1974, Levine 1983). Suppose that consciousness is identical to a property of the brain-say, activity in the pyramidal cells of layer 5 of the cortex involving reverberatory circuits from cortical layer 6 to the thalamus and back to layers 4 and 6-as Crick and Koch have suggested for visual consciousness (Crick 1994). Still, that identity itself calls out for explanation! Proponents of an explanatory gap disagree about whether the gap is permanent. Some (e.g., Nagel 1974) say that we are like the scientifically naive person who is told that matter = energy, but does not have the concepts required to make sense of the idea. If we can acquire these concepts, the gap is closable. Others say the gap is unclosable because of our cognitive limitations (McGinn 1991). Still others say that the gap is a consequence of the fundamental nature of consciousness.

On the Representation of Context

This paper revisits some foundational questions concerning the abstract representation of a discourse context. The context of a conversation is represented by a body of information that is presumed to be shared by the participants in the conversation – the information that the speaker presupposes a point at which a speech act is interpreted. This notion is designed to represent both the information on which context-dependent speech acts depend, and the situation that speech acts are designed to affect, and so to be a representation of context that is appropriate for explaining the interaction of context and the contents expressed in them. After reviewing the motivating ideas and the outlines of the apparatus, the paper responds to a criticism of the framework, and considers the way it can help to clarify some phenomena concerning pronouns with indefinite antecedents.

Knowledge, Belief and Counterfactual Reasoning in Games

Deliberation about what to do in any context requires reasoning about what will or would happen in various alternative situations, including situations that the agent knows will never in fact be realized. In contexts that involve two or more agents who have to take account of each others’ deliberation, the counterfactual reasoning may become quite complex. When I deliberate, I have to consider not only what the causal effects would be of alternative choices that I might make, but also what other agents might believe about the potential effects of my choices, and how their alternative possible actions might affect my beliefs. Counter factual possibilities are implicit in the models that game theorists and decision theorists have developed – in the alternative branches in the trees that model extensive form games and the different cells of the matrices of strategic form representations – but much of the reasoning about those possibilities remains in the informal commentary on and motivation for the models developed. Puzzlement is sometimes expressed by game theorists about the relevance of what happens in a game ‘off the equilibrium path’: of what would happen if what is (according to the theory) both true and known by the players to be true were instead false. My aim in this paper is to make some suggestions for clarifying some of the concepts involved in counterfactual reasoning in strategic contexts, both the reasoning of the rational agents being modeled, and the reasoning of the theorist who is doing the modeling, and to bring together some ideas and technical tools developed by philosophers and logicians that I think might be relevant to the analysis of strategic reasoning, and more generally to the conceptual foundations of game theory.

Belief revision in games: forward and backward induction1

Abstract The rationality of choices in a game depend not only on what players believe, but also on their policies for revising their beliefs in response to surprising information. A general descriptive framework for representing belief revision policies in game situations is sketched, and the consequences of some assumptions about such policies are explored. Assumptions about epistemic independence and a rationalization principle are considered. It is argued that while such assumptions may be appropriate in some contexts, no substantive constraints on belief revision policies can be justified on the basis of the assumption of common knowledge of rationality.

A Defense of Conditional Excluded Middle

This paper is a polemic about a detail in the semantics for conditionals. It takes for granted what is common to semantic theories proposed by David Lewis,1 John Pollock,2 Brian Chellas,3 and myself and Richmond Thomason4 in order to focus on some small points of difference between the theory I favor and the others. I will sketch quickly and roughly the general ideas which lie behind all of these theories, and the common semantical framework in which these ideas are developed. Then I will describe the divergences between my theory and the others — I will focus on the difference between my theory and the one favored by Lewis — and argue that my theory gives a better account of the way conditionals work in natural language.

On the Evaluation of Solution Concepts

It is proposed that solution concepts for games should be evaluated in a way that is analogous to the way a logic is evaluated by a model theory for the language. A solution concept defines a set of strategy profiles, as a logic defines a set of theorems. A model theoretic analysis for a game defines a class of models, which are abstract representations of particular plays of the game. Given an appropriate definition of a model, one can show that various solution concepts are characterized by intuitively natural classes of models in the same sense that the set of theorems of a logic is characterized by a class of models of the language. Sketches of characterization results of this kind are given for rationalizability, Nash equilibrium, and for a refinement of rationalizability —strong rationalizability — that has some features of an equilibrium concept. It is shown that strong rationalizability is equivalent to Nash equilibrium in perfect information games. Extensions of the model theoretic framework that represent belief revision and that permit the characterization of other solution concepts are explored informally.

Assertion Revisited: On the Interpretation of Two-Dimensional Modal Semantics

This paper concerns the applications of two-dimensional modal semantics to the explanation of the contents of speech and thought. Different interpretations and applications of the apparatus are contrasted. First, it is argued that David Kaplans two-dimensional semantics for indexical expressions is different from the use that I made of a formally similar framework to represent the role of contingent information in the determination of what is said. But the two applications are complementary rather than conflicting. Second, my interpretation of the apparatus is contrasted with that of David Chalmers, Frank Jackson, and David Lewis. It is argued that this difference reflects a contrast between internalist and externa list approaches to the problem of intentionality.

Saying and Meaning, Cheap Talk and Credibility

In May 2003, the US Treasury Secretary, John Snow, in response to a question, made some remarks that caused the dollar to drop precipitously in value. The Wall Street Journal sharply criticized him for ‘playing with fire,’ and characterized his remarks as ‘dumping on his own currency’, ‘bashing the dollar,’ and ‘talking the dollar down’. What he in fact said was this: ‘When the dollar is at a lower level it helps exports, and I think exports are getting stronger as a result.’ This was an uncontroversial factual claim that everyone, whatever his or her views about what US government currency policy is or should be, would agree with. Why did it have such an impact? ‘What he has done,’ Alan Blinder said, ‘is stated one of those obvious truths that the secretary of the Treasury isn’t supposed to say. When the secretary of the Treasury says something like that, it gets imbued with deep meaning whether he wants it to or not.’ Some thought the secretary knew what he was doing, and intended his remarks to have the effect that they had. (‘I think he chose his words carefully,’ said one currency strategist.) Others thought that he was ‘straying from the script,’ and ‘isn’t yet fluent in the delicate language of dollar policy.’ The Secretary, and other officials, followed up his initial remarks by reiterating that the government’s policy was to support a strong dollar, but some still saw his initial remark as a signal that ‘the Bush administration secretly welcomes the dollar’s decline.’1 The explicit policy statements apparently lacked credibility. Perhaps their meaning was not as deep as the meaning of the “secret” signal that currency traders and other observers had read into the initial remarks.

Possible worlds and situations

In the days before situation semantics1, some of us who wished to take a little of the metaphysical wind out of the sails of possible worlds semantics took to referring to possible worlds as “possible situations.” Now that the term “situation” has been pre-empted — tied to a certain theory and a certain ideology — I suppose those who still like possible worlds ought to find a new label. On the other hand, maybe it wouldn’t be so bad to use terminology which helps to blur the line between situations, in the new technical sense of Jon Barwise and John Perry, and possible worlds. I think the contrasts and conflicts between these notions, and between the respective theories or frameworks which take their names from them, have been exaggerated. There may be important substantive differences, technical and philosophical, between situation semantics and one or another formulation of possible worlds semantics, but they need to be characterized more sharply than they have been before the notions and theories can be compared.