John Cantwell

This paper explores the possibility that causal decision theory can be formulated in terms of probabilities of conditionals. It is argued that a generalized Stalnaker semantics in combination with an underlying branching time structure not only provides the basis for a plausible account of the semantics of indicative conditionals, but also that the resulting conditionals have properties that make them well-suited as a basis for formulating causal decision theory. Decision theory (at least if we omit the frills) is not an esoteric science, however unfamiliar it may seem to an outsider. Rather it is a systematic exposition of the consequences of certain well-chosen platitudes about belief, desire, preference and choice. It is the very core of our common-sense theory of persons, dissected out and elegantly systematized. (David Lewis, Synthese 23:331–344, 1974, p. 337). A small distortion in the analysis of the conditional may create spurious problems with the analysis of other concepts. So if the facts about usage favor one among a number of subtly different theories, it may be important to determine which one it is. (Robert Stalnaker, A Defense of Conditional Excluded Middle, pp. 87–104, 1980, p. 87)

It is argued that expressivists can solve their problems in accounting for the unity and autonomy of logic – logic is topic independent and does not derive from a general ‘logic’ of mental states – by adopting an analysis of the logical connectives that takes logically complex sentences to express complex combinations of simple attitudes like belief and disapproval and dispositions to form such simple attitudes upon performing suppositional acts, and taking acceptance and rejection of sentences to be the common mental denominator in descriptive and evaluative discourse, and structural requirements governing these to be the basis for logic. Such an account requires that attitudes like belief, intention and disapproval can come in hypothetical mode – plausibly linked to the capacity to mentally simulate or emulate one's own attitudes – and, if correct, suggests that these form the basic building blocks for our capacity to understand logically complex sentences.

An alleged counterexample to causal decision theory, put forward by Andy Egan, is studied in some detail. It is argued that Egan rejects the evaluation of causal decision theory on the basis of a description of the decision situation that is different from—indeed inconsistent with—the description on which causal decision theory makes its evaluation. So the example is not a counterexample to causal decision theory. Nevertheless, the example shows that causal decision theory can recommend unratifiable acts which presents a problem in the dynamics of intentions. It is argued that we can defuse this problem if we hold that decision theory is a theory of rational decision making rather than a theory of rational acts. It is shown how decisions can have epistemic side-effects that are not mediated by the act and that there are cases where one can only bring oneself to perform the best act by updating by imaging rather than by conditioning. This provides a pragmatic argument for updating by imaging rather than by conditioning in these cases.

The connectives of classical propositional logic are given an analysis in terms of necessary and sufficient conditions of acceptance and rejection, i.e. the connectives are analyzed within an expressivist bilateral meaning-is-use framework. It is explained how such a framework differs from standard inferentialist frameworks and it is argued that it is better suited to address the particular issues raised by the expressivist thesis that the meaning of a sentence is determined by the mental state that it is conventionally used to express. Furthermore, it is shown that the classical requirements governing the connectives completely characterize classical logic, are conservative and separable, are in bilateral harmony, are structurally preservative with respect to the classical coordination requirements and resolve the categoricity problem. These results are taken to show that one can give an expressivist bilateral meaning-is-use analysis of the connectives that confer on them a determinate coherent classical interpretation.

When a belief set is contracted only some beliefs are eligible for removal. By introducing eligibility for removal as a new semantic primitive for contraction and combining it with epistemic entrenchment we get a contraction operator with a number of interesting properties. By placing some minimal constraint upon eligibility we get an explicit contraction recipe that exactly characterises the so called interpolation thesis, a thesis that states upper and lower bounds for the amount of information to be given up in contraction. As a result we drop the controversial property of recovery. By placing additional constraints on eligibility we get representation theorems for a number of contraction operators of varying strength. In addition it is shown that recovery contraction is a special case that we get if eligibility is explicitly constructed in terms of logical relevance.

A semantics is presented for belief revision in the face of common announcements to a group of agents that have beliefs about each other’s beliefs. The semantics is based on the idea that possible worlds can be viewed as having an internal-structure, representing the belief independent features of the world, and the respective belief states of the agents in a modular fashion. Modularity guarantees that changing one aspect of the world (a belief independent feature or a belief state) has no effect on any other aspect of the world. This allows us to employ an AGM-style selection function to represent revision. The semantics is given a complete axiomatisation (identical to the axiomatisation found by Gerbrandy and Groeneveld for a semantics based on non-wellfounded set theory) for the special case of expansion.

The problems that surround iterated contractions and expansions of beliefs are approached by studying hypertheories, a generalisation of Adam Grove's notion of systems of spheres. By using a language with dynamic and doxastic operators different ideas about the basic nature of belief change are axiomatised. It is shown that by imposing quite natural constraints on how hypertheories may change, the basic logics for belief change can be strengthened considerably to bring one closer to a theory of iterated belief change. It is then argued that the logic of expansion, in particular, cannot without loss of generality be strengthened any further to allow for a full logic of iterated belief change. To remedy this situation a notion of directed expansion is introduced that allows for a full logic of iterated belief change. The new operation is given an axiomatisation that is complete for linear hypertheories.

This paper provides finitary jointly necessary and sufficient acceptance and rejection conditions for the logical constants of a first order quantificational language. By introducing the notion of making an assignment as a distinct object level practice—something you do with a sentence—(as opposed to a meta-level semantic notion) and combining this with the practice of (hypothetical and categorical) acceptance and rejection and the practice of making suppositions one gains a structure that is sufficiently rich to fully characterize the class of classical first order theories. The analysis thus provides a way of characterizing classical first order quantification by expressivist means.