If-Clauses and Probability Operators

Abstract

International audienceAdams' thesis is generally agreed to be linguistically compelling for simple conditionals with factual antecedent and consequent. We propose a derivation of Adams' thesis from the Lewis-Kratzer analysis of if-clauses as domain restrictors, applied to probability operators. We argue that Lewis's triviality result may be seen as a result of inexpressibility of the kind familiar in generalized quantifier theory. Some implications of the Lewis-Kratzer analysis are presented concerning the assignment of probabilities to compounds of conditionals

Triviality For Restrictor Conditionals

“…For a broadly similar claim, see Égré and Cozic (). (But see Rothschild, ) for a suggestion that a good theory of the conditional should indeed make room for such probabilities.)…”

“…According to Kratzer, there is, for instance, no “semantic value of the conditional” whose surface form is , when or C is embedded under an operator whose domain A functions to restrict (cf. Égré and Cozic, , 23), as in: Probably, if my keys aren't in my coat, they are on the table If my keys aren't in my coat, they are probably on the table …”

“…Égré and Cozic (, 25) mention a subtler version of this position, according to which an expression like may be undefined on the Kratzer analysis, because (i) it is equivalent to ; (ii) the probability of a Boolean compound is hard to make sense of for Kratzer: “If the role of the if‐clause A is to restrict the domain of an operator, then here it appears that A cannot restrict the domain of the probability operator… since the conditional clause in this case is syntactically dominated by the conjunction.” But this can be sidestepped by understanding to estimate the probability of the conjunction of the proposition that is (according to Kratzer) expressed by the bare conditional in some standard context of utterance with the proposition expressed by C . If the conditional expresses a proposition, we may (indeed, should) flatly insist that the probability of that proposition must, e.g., obey the Law of Total Probability.…”

Capturing the relationship between conditionals and conditional probability with a trivalent semantics

“…But I will leave further discussion of these points to another occasion, so that this discussion may be considered as presenting an alternative to Kratzer's account of (1-a) and (1-b). See von Fintel (2007), Égré and Cozic (2010), and Rothschild (2011, in press) for further discussion.…”

The Probabilities of Conditionals Revisited

“… Although see Égré and Cozic () for a recent discussion of the Lewis–Kratzer view from a philosophical perspective. …”