General Discussion

The four experiments reported above offer insight into how our beliefs change when we learn a testimonial conditional. Experiments 2.1 and 2.2 showed that assertion increases the conditional probability, though with a diminishing return: ratings were not higher in the multiple-assertion condition than in the single-

antecedent or the probability of the consequent. Experiments 2.3 and 2.4 showed that source expertise likewise increases the conditional probability, but here there was no diminishing return: ratings were reliably higher for expert than inexpert sources. Again, though, the effect was limited to the conditional probability: expertise did not reliably influence the probability of the antecedent and the probability of the

consequent. These data can be taken to generalize the findings of Stevenson and Over (2001) to testimonial contexts and to a different manipulation, the Assertion manipulation.

The data are also consistent with a large body of work in the psychology of reasoning which argues that the meaning of the conditional is closely associated with the conditional probability. As we saw in the Introduction, one way to interpret this association is the suppositional theory of meaning. On this account, when we hear a conditional If A, B, ‘[we] suppose (assume, hypothesize) that A, and make a

hypothetical judgment about B, under the supposition that A, in light of your other beliefs’ (Edgington, 2014). This judgment amounts to the conditional probability (for extended discussion, see, e.g., Evans & Over, 2004). Here is how a

suppositional theorist could account for the present data. Participants supposed that the antecedent was true, and judged the conditional probability. In making their judgments, participants in the assertion task simply drew on the fact of assertion; participants in the source-expertise task drew also on the information about the source. But why should participants increase29 the conditional probability? Here, the suppositional theorist can invoke the pragmatic assumption: that asserting a

29 _{Or, more strictly, why should participants in the assertion conditions give higher}

ratings than the control condition? I am assuming, here, that the between-subjects design approximates learning a conditional.

conditional implies high conditional probability. In this experiment, then,

participants moved from a non-committal probability to a higher one. Participants did not, however, reliably modify their belief in the antecedent. Coherently, then, they also did not reliably modify their belief in the consequent. This picture is also consistent with an account in linguistics which takes conditionals to be defined by remoteness: that is, in uttering an indicative conditional, a speaker is not committing to the truth (or falsity) of the antecedent (Elder & Jaszczolt, 2016).

The data sit less well with two other prominent accounts. The first takes the indicative conditional to be the material conditional. Although this account has had prominent supporters (Grice, 1975; Jackson, 1979), it is not widely supported in contemporary philosophy (Bennett, 2003; Hartmann & Rafiee Rad, 2017). The material conditional does, however, seem to underpin the approach to the conditional of Mental Models Theory30 (Johnson-Laird & Byrne, 2002). The material

conditional has limited appeal in part because its account of learning a conditional has counterintuitive consequences (for discussion, see Hartmann & Rafiee Rad, 2017; Popper & Miller, 1983). Assuming the material conditional, recall, means assuming that the probability of the conditional ‘If P, Q’ is equivalent to the disjunction P(~P v Q). Accordingly, learning a conditional can be construed as conditioning on the disjunction. This conditioning is compatible with an increase in the conditional probability, P(Q|P). To illustrate, take the simple case in which conditioning means assigning P = 1 to the disjunction. The disjunction (~P v Q)

30_{The Mental Models account is not clearly expressed. Although Johnson-Laird and}

Byrne (2002) try to distinguish their account from the material conditional, referring to possibilities rather than truth, it still seems to reduce to the material conditional, plus highly flexible semantic and pragmatic modulation (for discussion, see Krzyżanowska, Collins, & Hahn, 2017).

corresponds to four conjunctions. Cases (1) to (3) make the disjunction true; case (4) makes it false: (1) ~P & Q (2) ~P & ~Q (3) P & Q (4) P & ~Q

Conditioning on (~P v Q) means eliminating case (4): there are no P cases which are not also Q cases. The conditional probability P(Q|P), therefore, increases to 1. But, less happily, as long as two constraints hold – 0 < P < 1 and 0 < Q < 1 – when we learn a conditional we should decrease the probability P and increase the probability of Q (for the proofs, see Popper & Miller, 1983). These latter predictions are not only counterintuitive; they are not supported by the data above.

The second prominent account takes learning a conditional to be governed by an attempt to minimize the difference between the prior and posterior distributions, defined formally as the Kullback-Leibler divergence (Hartmann & Rafiee Rad, 2017). This account has the same consequences for the probability of the antecedent as the material conditional as long as we assume a model for the conditional such as Figure 2.13, where ‘H’ represents the antecedent and ‘E’ the consequent:

H

E

Figure 2.13. Simple Bayesian belief network for a conditional

of the relevant situation. Doing so, as Hartmann and Rafiee Rad (2017) show, leads to other, more intuitively appealing revisions of belief. This strategy does not seem plausible for the present materials, however, as they are deliberately light on causal information. An alternative but related strategy, which models information about the sources, will be described in Chapter 4.

Although the present data cohere well with the dominant theory of the conditional within psychology and philosophy, there is reason to doubt how well the data will generalize. Consider the following intuitions.

Intuition 1: It is a sunny day, without a cloud in the sky, but you have not seen the weather forecast. Someone says to you, ‘If it rains this afternoon, they’ll have to postpone the tennis match’.

In this context, it seems likely that the hearer would increase their judgment of the probability of rain.

Intuition 2: You have been promised a job, and you believe that you are certain to get it. A trusted and knowledgeable colleague says to you, ‘If you get the job, we can collaborate more’.

In this context, it seems likely that the hearer would decrease their judgment of the probability of getting the job. This intuition may be clearer with the intonation ‘IF you get the job, we can collaborate more’. The relevant factor seems to be the hearer’s prior beliefs. Similar intuitions underlie the examples in Douven’s (2012) influential paper and the following passage from Evans and Over (2004, pp. 144-5):

‘”If p then q” is not assertable – or at least has low relevance – in most contexts if P(p) is too or if P(q|p) is too low. As conditionals only apply to p- states, such states must normally be reasonably probable (at least in the near future for a conditional statement to have relevance.’

Presumably, then, the hearer of a conditional will assume that the antecedent is reasonably probable. Chapter 4 will explore these intuitions further.

Finally, in this chapter, there is an important limitation in the present design: namely, that participants responded with point estimates. While such responses are simple and intuitive, they may conceal subtle belief change. For instance,

participants’ beliefs might be better captured by a distribution, the central tendency corresponding to the point estimate. The point estimates may not pick up changes to the underlying distributions. This possibility will be explored in the next chapter.