Conditionals and inferential connections: toward a new semantics^*

Abstract

In previous published research (“Conditionals and Inferential Connections: A Hypothetical Inferential Theory,” Cognitive Psychology, 2018), we investigated experimentally what role the presence and strength of an inferential connection between a conditional’s antecedent and consequent plays in how people process that conditional. Our analysis showed the strength of that connection to be strongly predictive of whether participants evaluated the conditional as true, false, or neither true nor false. In this article, we re-analyse the data from our previous research, now focussing on the semantics of conditionals rather than on how they are processed. Specifically, we use those data to compare the main extant semantics with each other and with inferentialism, a semantics according to which the truth of a conditional requires the presence of an inferential connection between the conditional’s component parts.

Keywords:

• Conditionals
• inference
• semantics
• logic
• indeterminacy

Acknowledgments

We are greatly indebted to David Over for many useful discussions on the subject matter of this article. Thanks also to two anonymous referees and Christopher von Bülow for valuable comments on previous versions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Vidal and Baratgin, (2017), and to some extent also Markovits et al. (2019), present experimental results in support of an inferentialist semantics; see also Skovgaard-Olsen et al. (in press). For some apparently countervailing results, see Skovgaard-Olsen et al. (2016).

2 Given that our data consist only of truth evaluations, it is not possible to include in the comparison Jeffrey and Edgington’s (1991) semantics, according to which “If φ, ψ” evaluates to $\mathrm{Pr}(\psi | \phi )$ in case φ is false. This omission is unfortunate, given that Jeffrey’s semantics has been much in the limelight lately; see Over and Baratgin (2017) and references given there.

3 This is not to say that it is entirely uncontroversial nor that all semantics other than Stalnaker’s do validate it. Most notably, it is invalid in Jeffrey’s semantics referenced in note 2; see Gilio and Sanfilippo (2014).

4 We are assuming classical probability theory here. By extending that theory with a primitive notion of conditional event, Gilio, Over, Pfeifer, and Sanfilipp (2017) obtain an account of conditionals in which $\mathrm{Pr}(\text{If} \psi ,\chi | \phi )$ is defined, in spite of the fact that the conditional is still not a proposition in the classical sense (see also Gilio & Sanfilippo, 2013, 2014). How much this is going to help non-propositionalists depends on the extent to which Gilio and coauthors, or others, will be able to clarify the metaphysical status of conditional events, which so far they have not given us much guidance on.

5 Weirich (in press) presents a number of other a priori reasons for rejecting non-propositionalism.

6 See Baratgin and Politzer (2016) for an argument to the effect that, for de Finetti, non-propositionalism and the three-value are not separate semantics but rather constitute different levels of epistemic analysis of one and the same semantic phenomenon.

7 To avoid spurious debate, it is to be noted that linguists and philosophers have long recognized that there are special classes of conditionals—sometimes called “nonconditional conditionals” (Lycan, 2001) or “unconditionals” (Merin, 2007; Spohn, 2013)—which do not require the existence of a connection between their antecedent and consequent. These include Dutchman conditionals (Jackson, 1979, 1987), non-interference conditionals (Bennett, 2003; Burgess, 2004), and relevance conditionals (Bennett, 2003). Krzyżanowska and coauthors explicitly propose their brand of inferentialism as a semantics for standard conditionals, not for unconditionals.

8 Note that, as a result, the conditionals’ component parts also had the same term specificity, in the sense of Gazzo Castañeda and Knauff (2019), which these authors showed to matter to how conditionals are evaluated.

9 For data on group sizes, see Table 6.1 in Douven et al., (2018, p. 57).

10 It might be thought that the former world preserves the fact that the two patches are of the same color. But that fact supervenes on the facts concerning the colors of the patches, and is therefore not to be considered in determining closeness between worlds. This relies on Lewis’ aforementioned proposal, and—as an anonymous referee pointed out—there is no clear consensus on how to define closeness, and different proposals lead to different predictions. However, Lewis’ proposal does have many advocates in philosophy and we ourselves deem it plausible enough to assume it here.

11 The R scripts are available at: https://osf.io/eskw5/.

12 We are grateful to David Kellen for his advice regarding this analysis.

13 Needless to say, given Inferentialism, one expects to find many responses in accordance with Centering. For example, it is reasonable to suppose that anyone with normal vision will judge patches 13 and 14 to be green. And Inferentialism also makes it reasonable to expect anyone to judge as true the conditional “If patch number 13 is green, so is patch number 14.”

14 We thank an anonymous reviewer for suggesting to investigate this question.