Two Recent Theories of Conditionals

Abstract

In recent years, two new and fundamentally different accounts of condi-tionals 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, Counter/actuals, 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 dis-parate 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. 1. THE TWO ACCOUNTS I begin with a rough and simplified sketch of the two accounts and relationships between them. First, some terminology: I shall use 'proposition' as a theory-laden word, the theory being a representation of subjective probability , or credence. On this representation, we start with a set t of all epistemically possibk worlds (or worlds). Any proposition is identified with a set of worlds, the worlds in which the proposition is true. Not every subset of t need be a 'proposition'; rather the 'propositions' comprise a fixed set Y of subsets of t. Y is required to be a 'field of sets' whose 'universal set' is t. Y is a field of sets iff Y is a set of sets and, where t = U Y, t E Y and Y is closed under the operations of union and t-complemen-tation. t is called the universal set of Y. Members of Y are called propositions of Y, and members of t are called worlds of Y. A person's credences, or degrees of belief, are represented by real numbers from zero to one, and the function p which gives them is a probability measure on Y: a non-negative real-valued function whose domain is Y, such that p(t) = 1 and where propositions a and b are disjoint, p(a U b) = p(a) + p(b). (See Kyburg, 1980, pp. 14-18). When p(a) =/:-0, p(b/a) is defined as the quotient 211 W. L. Harper, R. Stalnaker, and G. Pearce (eds.), Ifs, 211-247.