Allan Gibbard

Two Recent Theories of Conditionals

In recent years, two new and fundamentally different accounts of conditionals and their logic have been put forth, one based on nearness of possible worlds (Stalnaker, ‘A Theory of Conditionals’, 1968, this volume, pp. 41–55; Lewis, Counterfactuals, 1973) and the other based on subjective conditional probabilities (Adams, The Logic of Conditionals, 1975). The two accounts, I shall claim, have almost nothing in common, They do have a common logic within the domain on which they both pronounce, but that, as far as I can discover, is little more than a coincidence. Each of these disparate accounts, though, has an important application to natural language, or so I shall argue. Roughly, Adams’ probabilistic account is true of indicative conditionals, and a nearness of possible worlds account is true of subjunctive conditionals. If that is so, the apparent similarity of these two ‘if constructions hides a profound semantical difference.

Meaning and normativity

1. Introduction 2. Normativity and Community 3. Kripkes Wittgenstein on Meaning 4. Correct Belief 5. Horwich on Meaning 6. The Normative Meaning Role 7. Reference, Truth, and Context 8. Meaning and Plans 9. Interpreting Interpretation 10. Expressivism, Non-Naturalism, and Us Appendix 1: The Objects of Belief Appendix 2: Schroeder on Expressivism References Index

Social Choice And The Arrow Conditions

Arrow’s impossibility result stems chiefly from a combination of two requirements: independence and fixity. Independence says that the social choice is independent of individual preferences involving unavailable alternatives. Fixity says that the social choice is fixed by a social preference relation that is independent of what is available. Arrow found that requiring, further, that this relation be transitive yields impossibility. Here it is shown that allowing intransitive social indifference still permits only a vastly unsatisfactory system, a liberum veto oligarchy. Arrow’s argument for independence, though, undermines any rationale for fixity.

Arrow's Theorem with a Fixed Feasible Alternative*

Arrows Theorem, in its social choice function formulation, assumes that all nonempty finite subsets of the universal set of alternatives is potentially a feasible set. We demonstrate that the axioms in Arrows Theorem, with weak Pareto strengthened to strong Pareto, are consistent if it is assumed that there is a prespecified alternative which is in every feasible set. We further show that if the collection of feasible sets consists of all subsets of alternatives containing a prespecified list of alternatives and if there are at least three additional alternatives not on this list, replacing nondictatorship by anonymity results in an impossibility theorem.

Utilitarianism and Human Rights

INTRODUCTION We look to rights for protection. The hope of advocates of “human rights” has been that certain protections might be accorded to allof humanity. Even in a world only a minority of whose inhabitants live under liberal democratic regimes, the hope is, certain standards accepted in the liberal democracies will gain universal recognition and respect. These include liberty of persons as opposed to enslavement, freedom from cruelty, freedom from arbitrary execution, from arbitrary imprisonment, and from arbitrary deprivation of property or livelihood, freedom of religion, and freedom of inquiry and expression. Philosophers, of course, concern themselves with the theory of rights, and that is partly because of the ways questions of rights bear on fundamental normative theory. By far the most highly developed general normative theory has been utilitarianism. Now many opponents of utilitarianism argue that considerations of rights discredit utilitarianism, that utilitarianism yields conclusions about rights that we would normally regard as faulty, and that moreover, the reasons for regarding those conclusions as faulty turn out, upon examination, to be stronger than the reasons forregarding utilitarianism as valid. A valid theory cannot have faulty conclusions, and so thinkingabout rights shows utilitarianism not to be a valid normative theory. Jeremy Bentham, the founder of the utilitarian movement in nineteenth century England, accepted the incompatibility of utilitarianism and “the rights of man, ” and rejected talkof the latter as “anarchical fallacies”. His great successor John Stuart Mill, however, argued that a perceptive and far–sighted utilitarianism supports strong rights both of democratic participation and of individual freedom of action.

Rights and the Theory of Social Choice

Publisher Summary This chapter discusses the rights and the theory of social choice. The first libertarian claim is that for each person, there are features of the world that are his business alone, and if two histories differ only in one of those features, that person is morally decisive between them. This first libertarian claim expresses a part of what all liberals believe. The second libertarian claim is inconsistent with the weak Pareto principle: that if everyone prefers one history to another, then that history is socially better. The chapter explains that liberalism seems more directly, though, to be a theory of the legitimacy of social and governmental institutions. The norms of liberalism are the norms of who should be free to control what and the tools of social choice theory-functions of arrays of preferences have proved to be poor at representing control.

Causal Decision Theory

Many will find the answer easy—though they may disagree with each other on which the answer is. A standard line on the prisoner’s dilemma rests on dominance: What you do won’t affect what Twin does. Twin may rat or keep mum, but in either case, you yourself will do better to rat. Whichever Twin is doing, you would spend less time in jail if you were to rat than if you were to keep mum. Therefore the rational way to minimize your own time in jail is to rat.

Indicative Conditionals and Conditional Probability: Reply to Pollock

In ‘Indicative Conditionals and Conditional Probability’ (this volume, pp. 249–252), Pollock constructs an intriguing situation to serve as a counterexample to the ‘Ramsey test’ thesis. Here by the Ramsey test thesis, I mean the thesis that, in whatever ways the acceptability, assertability, and the like of a proposition depend on its subjective probability, the acceptability, assertability, and the like of an indicative conditional A→B depend on the corresponding subjective conditional probability ρ(B/A). (I shall use ‘→’ as a symbol for the indicative conditional connective, and otherwise follow Pollock’s notation. The systematic development of the Ramsey test thesis was the work of Ernest Adams, 1975). I think that I can give an argument to show that in Pollock’s example, contrary to what he judges, if B → D is acceptable before one learns R, it is acceptable after one learns R.

Act-Utilitarian Agreements

Would rational act-utilitarians keep their agreements? Suppose two highly rational act-utilitarians agree to meet for a walk in the park. The best outcome they can achieve is to meet as agreed, and the next best is for both to stay home and read. Because each would find it distressing to come and not find the other, the worst outcome they can achieve is for one to come to the park and the other to stay at home. Suppose everything above is common knowledge between them, in the sense that each knows it, each knows the other knows it, each knows the other knows that he knows it, and so on ad infinitem. Under these circumstances, either person would keep the agreement if he knew the other would, for he could then conclude that his coming as agreed would yield the best outcome, that they meet, whereas his staying at home would yield the worst outcome, that one comes and the other stays home. On the other hand, either would break the agreement if he knew that the other would break it, for in that case he could reason that if he came as agreed, he would achieve the worst outcome, that one comes and the other stays at home, whereas if he stayed home, he would achieve the intermediate outcome that both stay home. All this will be common knowledge between the two. Does any of it, though, give either of them grounds for keeping the agreement?

SOCIAL DECISION, STRATEGIC BEHAVIOR, AND BEST OUTCOMES

What ought to happen depends at least in part on what the people involved prefer. I shall take that as a truism, though it may need qualifications: perhaps what ought to happen depends not on what people actually prefer, but on what they would prefer if they were fully informed and clearheaded, and perhaps it depends not on what people prefer on the whole, but on what each person prefers as regards himself. Accepting these qualifications, though, would only make the problem I raise in this paper more difficult. I shall assume here that what ought to happen depends at least partly on the preferences the people involved actually have. If the reader thinks that only informed preferences matter, he can think of the paper as addressing the special case where actual preferences are fully informed, and if he thinks that only self-regarding preferences matter, he can think of the paper as tackling the special case where everyone’s preferences are self-regarding.