I have argued that a probabilistic account of conditionals (specifically Stalnaker’s account or alternate probabilistic account with the essential features of Stalnaker's account) is able to describe the aggregate of competent uses of the conditional in natural language better than any other logical account. I conclude that Stalnaker’s account of conditionals is the most descriptively accurate logical account. In chapter one I outlined expert intuitions that conflict with the standard truth functional account of conditionals in the form of the paradoxes of the material conditional. Some of the counter-intuitive results of the truth table for the material conditional are that every conditional with a false antecedent is true and every conditional with a true consequent is true. I showed that C. I. Lewis’s attempt to resolve the paradoxes of the material conditional by developing an account of strict implication fails as this account simply results in strengthened paradoxes that arise from contradictions or logical truths. For example, in Lewis’s account every conditional with an antecedent that is a contradiction is true and every conditional with a consequent that is a tautology is true. I also argued that connection accounts fail to satisfy expert intuitions about conditional use as they reject some inferences that are intuitively valid and accept some inferences that are intuitively invalid.
In chapter two I outlined an attempt to save the standard truth functional account of conditionals by explaining the paradoxes of the material conditional in terms of
assertibility, i.e., the claim that the conditionals outlined in the paradoxes of the material conditional are true but not assertible. I argued that Quine’s account of assertibility fails as it cannot accommodate the use of counterfactuals in natural language. I then
described Jacksons’s account of conditionals whereby conditionals have both truth conditions and conditions of assertibility. Indicative conditionals in this account are able to retain the truth table for the material conditional and the counter-intuitive aspects of this truth table are explained away in terms of assertibility. Jackson’s account based on assertibility is much more successful than Quine’s but ultimately also fails to capture natural language use of conditionals as the intuitions that conflict with the material conditional for naive reasoners are far more widespread than Jackson claims. Jackson attempts to argue that these intuitions must be mistaken since David Lewis’s triviality proof showed that probabilistic conditionals result in triviality or contradiction. I showed that the triviality proof does not lead to such a strong conclusion and that Jackson’s account of conditionals fails to adequately describe natural language use of
conditionals.
In chapter three I outlined the probabilistic, possible worlds account of
conditionals that Stalnaker developed in 1968. Stalnaker’s account is loosely based on Kripke’s modal logic and relies upon possible world semantics. An absurd world that allows for contradictions, and a selection function that determines the ordering of possible worlds, are added to Kripke’s modal logic. The selection function restricts the ordering of possible worlds in the following ways: the antecedent must be true in the selected world; if the antecedent is true in the actual world, then the actual world must be selected (the world selected must differ as minimally as possible from the actual world); the absurd world must only be selected if it is required in order to make the antecedent true; and ordering of possible worlds must remain consistent. Jackson argues that the unified account offered by Stalnaker is flawed as only subjunctive
conditionals should be analyzed probabilistically. This argument fails to successfully challenge Stalnaker’s account as we don’t typically consider differences in grammatical tense to require different logical analyses and Jackson provides no non ad hoc reason why conditionals should be different. David Lewis argues that Stalnaker’s selection function leads to semantic indeterminacy. I defend Stalnaker’s account against
criticisms from David Lewis by arguing that the small degree of semantic indeterminacy in Stalnaker’s account is worth the greater degree of descriptive accuracy.
In chapter four I outline some empirical support for a probabilistic psychological account of conditionals by arguing that the use of conditionals by naive reasoners is primarily probabilistic. My purpose in this chapter is to get a better picture of the phenomena— natural language use of conditionals— by including assessments of conditional reasoning by naive reasoners. The first part of this chapter is an examination of how a probabilistic psychological account is able to explain the systematic responses on reasoning tasks with conditionals. A probabilistic psychological account can explain variation among subject responses and the reason for performance errors in the suppression effect experiments. Specifically, I argued that the theory of conditionals provided by Schroyens and Schaeken is the most descriptively accurate psychological account. I then argued that Stalnaker’s account of conditionals is the logical theory most compatible with these probabilistic theories of conditional use from psychologists (for example, SSCEPPTRE). Stalnaker’s account shares essential characteristics with the psychological account of conditionals presented by Schroyens and Schaeken. The ability of the alternative mental models account to reliably predict responses on the conditional reasoning task and define what were previously considered performance
errors as rational belief testing mechanisms, supports the descriptive accuracy claims of a logical account of conditionals that shares a basic structure with this psychological account.
In chapter five I outline some experimental challenges to a probabilistic account. I argue that Brain and O’Brien’s challenge to Stalnaker’s account fails as it merely shows that Stalnaker’s logical account would make an incomplete psychological account of conditionals, not that Stalnaker’s hypothesis is descriptively inaccurate. I outline an experiment that Johnson-Laird and Byrne take as evidence against Adams’s thesis and Stalnaker’s hypothesis but conclude that, due to the formulation of the question in this task, the experiment does not in fact test assessments of conditional probability. Finally, I examined experiments that Douven and Verbrugge present against Adams’s thesis. These arguments present a moderate challenge to the claim that Adams’s thesis is descriptively accurate but do not present any challenge to the claim that Stalnaker’s hypothesis is descriptively accurate.
I have presented evidence from both expert reasoners in the form of
philosophical arguments and naive reasoners in the form of psychological experiments in human reasoning that support a probabilistic interpretation of conditionals. The experimental evidence that naive subjects are operating with a probabilistic conditional in mind is overwhelming and there is almost no evidence to be found that counters this view. A probabilistic account of conditionals (such as that provided by Stalnaker in 1968) is able to model the vast majority of competent uses of the conditional. Therefore, such an account is the most descriptively accurate logical account of conditionals, i.e., is the
account that most aptly models conditional use in natural language and provides the best representational model of the data of conditional use in natural language.