Indicative and counterfactual ‘only if’ conditionals
Introduction
People often imagine counterfactual alternatives about what might have been different in the past, particularly after bad outcomes, e.g., ‘if John had felt well he would have passed the examination’ (Kahneman & Tversky, 1982; Mandel et al., 2005, Markman et al., 2009; Roese & Olson, 1995). People understand the counterfactual conditional to mean something different from an indicative one, e.g., ‘if John felt well he passed the examination’ (Byrne, 2002, Byrne, 2005, Byrne, 2007). Moreover, they understand an indicative conditional based on ‘if’ to mean something different from one based on ‘only if’, e.g., ‘John felt well only if he passed the examination’ (Johnson-Laird & Byrne, 1989). How do people understand counterfactual conditionals based on ‘only if’, such as ‘John would have felt well only if he had passed the examination’? The answer is not known and our aim is to test a new account of what people think about when they understand ‘only if’ conditionals, both indicative and counterfactual.
We provide a novel account of how people understand and reason from indicative and counterfactual ‘only if’ conditionals. First we sketch the view that people envisage possibilities to understand indicative ‘if’ conditionals (Johnson-Laird & Byrne, 2002), and we consider evidence that they think about more possibilities to understand counterfactual ‘if’ compared to indicative ‘if’. We outline our new account in Sections 2 and 3, we report three experiments that test predictions derived from this account by comparing indicative and counterfactual ‘if’ and ‘only if’ conditionals.
Section snippets
Indicative and counterfactual ‘if’
People may understand a conditional such as ‘if Mary went to the meeting then she received the documentation’ (if A then B) by thinking about possibilities, such as ‘Mary went to the meeting and she received the documentation’ (A and B) (Johnson-Laird & Byrne, 2002). The possibilities they think about may be constrained by principles. For example, people think about true possibilities but not false possibilities, such as ‘Mary went to the meeting and she did not receive the documentation’ (A
Indicative and counterfactual ‘only if’
A conditional of the form ‘if Mary goes to the meeting then she receives the documentation’ (if A then B) is of course logically equivalent to one of the forms ‘Mary goes to the meeting only if she receives the documentation’ (A only if B) (Jeffrey, 1981). But their equivalence is not immediately obvious to most people. Nonetheless, people can appreciate that both conditionals are false in the same situation, that is, Mary goes to the meeting and she does not receive the documentation (A and
Experiment 1
The aim of the first experiment was to examine the possibilities that reasoners judge to be consistent with indicative and counterfactual ‘only if’, and to compare them to indicative and counterfactual ‘if’. We gave participants problems that consisted of a conditional premise, e.g., ‘Joe would have been in Meath only if Ann had been in Dublin’. They were given four possibilities: ‘Joe was in Meath and Ann was in Dublin’, ‘Joe was not in Meath and Ann was not in Dublin’, ‘Joe was not in Meath
Experiment 2
The aim of the second experiment was once again to examine the possibilities that reasoners judge to be consistent with indicative and counterfactual ‘A only if B’, and to compare them to indicative and counterfactual ‘if A then B’, this time for four possibilities in the B to A order: B and A, not-B and not-A, not-B and A, and B and not-A. We made the same predictions as in the previous experiment. We aimed to test the prediction that people would judge ‘not-B and not-A’ to be consistent with
Experiment 3
The aim of the experiment was to examine the inferences that reasoners make from indicative and counterfactual ‘if’ and ‘only if’. Participants were given a conditional such as, ‘Joe would have been in Meath only if Ann had been in Dublin’. They were given a second premise such as ‘Ann was in Dublin’. They were asked to say what if anything follows from the premises, and they chose their conclusion from a set, ‘therefore, (a) Joe was in Meath, (b) Joe was not in Meath, (c) Joe may or may not
General discussion
We have provided a new account of the mental representations and cognitive processes underlying ‘A only if B’. An indicative conditional, ‘if A then B’ is understood by keeping in mind initially the possibility ‘A and B’ (Johnson-Laird & Byrne, 2002). In contrast, ‘A only if B’ is understood by thinking about two possibilities from the outset, in the B to A direction: ‘B and A’ and ‘not-B and not-A’. We have also provided the first account of the mental representations and cognitive processes
Acknowledgements
The research was supported by a Research Grant from Enterprise Ireland’s basic Research Grants Scheme to Ruth Byrne and by a Government of Ireland Postgraduate Scholarship from the Irish Research Council for the Humanities and Social Sciences to Suzanne Egan. Some of the results were presented at the International Meeting on Cognitive Processes and Context in Counterfactual Thinking, Lisbon, 2002; at the Second International Conference on Reasoning and Decision-making, Padua, 2003 and at the
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