Abstract
There is strong disagreement about whether indicative conditionals have truth values. In this paper, I present a new argument for the conclusion that indicative conditionals have truth values based on the claim that some true statements entail indicative conditionals. I then address four arguments that conclude that indicative conditionals lack truth values, showing them to be inadequate. Finally, I present further benefits to having a worldly view of conditionals, which supports the assignment of truth values to indicative conditionals. I conclude that certain types of account of indicative conditionals, which have been ignored in the literature partly on the basis of assigning truth values to indicative conditionals, deserve consideration.
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Notes
I confine my discussion to indicative conditionals, as distinguished grammatically from subjunctive conditionals. For my purposes here, subjunctive conditionals contain the helping words ‘have’, ‘has’, ‘had’, ‘were’ + infinitive, or ‘would’. Though some argue that this grammatical distinction fits ill with certain data [see, for example, Dudman (1983), Bennett (1988) and Edgington (1995)], many continue to employ the distinction along grammatical lines. For readability, I will sometimes omit ‘indicative’.
For simplicity, I assume throughout that true and false are the only truth values, but nothing in this paper depends on this assumption. The conclusion that some indicative conditionals are true and some are false does not rule out the possibility that some are neither.
Thanks to a reviewer at Philosophical Studies for suggesting examples similar to the following.
Thanks to a reviewer at Philosophical Studies for making this point.
To avoid the logical possibility that miracles could be ordinary—perhaps God cannot stand the thought of a high-pressure bottle—we would need to specify what is actually ordinary.
Thanks to a reviewer at Philosophical Studies for the suggestion.
See the probabilistic soundness criterion in Adams (1975), chapter one.
According to the Material Implication Account, ‘If A, then B’ is false when A is true and B is false, and true otherwise.
Stalnaker (1970).
Lewis actually presents two arguments, but since the first contains unnecessarily stronger assumptions than the second, and the two have the same conclusion, I will present only the second of the two arguments.
For discussions of the more formal aspects of Lewis’s argument, see, e.g., Hajek and Hall (1994).
Douven (2008) presents examples of this kind. See p. 21.
This fact is met with acceptance by some. For example, Edgington (1986) defines the indicative conditional as the conditional whose antecedent is an epistemic possibility, thus excluding the possibility of an indicative conditional with a zero-probability antecedent at the outset. McDermott (1996) likewise embraces the result. McDermott draws inspiration from bets, and since a conditional bet is called off if the event in the antecedent does not obtain, he is content to treat a conditional with a zero-probability antecedent as having an undefined truth value. Others are less enthusiastic about the result and make stipulations to avoid it. For example, Stalnaker (1970) stipulates that conditionals with zero-probability antecedents are trivially true.
Note the difference between the indicative (19) and the counterfactual, ‘If God were to exist, there would be some morally sufficient explanation for the evil that actually occurs’. One can accept (19) and reject this counterfactual based on the belief that, if God were to exist, then there would be no evil. This belief is compatible with the belief that, if God does exist, there is some morally sufficient explanation for the evil that actually occurs.
Edgington also presents her criterion in other terms, which she sees as equivalent to this version, with the caveat that this version assumes that a precise numerical value can be attached to credences. Edgington seems to want to remain neutral on that assumption, but it is useful to consider this version because of its relation to Lewis’s Assumption, discussed above. The main difference between Lewis’s Assumption and Edgington’s criterion is that her version has to do with whether or not a person accepts a conditional (finds it fit for rational endorsement) rather than an assignment of probability of truth to the conditional. Thus, Edgington’s criterion is similar to Adams’s (1975) treatment of conditional probabilities.
To call in poker is to request that the round be over with the revealing of everyone’s hands and subsequent judgment of the winner.
One might want to restrict the principle to cases in which the antecedent is not a contradiction. Thanks to Graeme Forbes for pointing out this possibility.
Pendlebury (1989) agrees that Zack was wrong, and his assessment was a relief to encounter.
Lycan (2001) points out that (Z) has a similar flavor to what Lycan calls backtracking conditionals. See pp. 178ff. Lycan’s assessment differs from mine, because he thinks that (Z) itself should be considered to be a backtracker, whereas I contend that Zack mistakenly accepts (Z) as a consequence of (29).
Assuming limited readership.
The Material Implication Account is a worldly account, as are versions of the Possible Worlds Account that do not treat the conditional as radically indexical [which rules out Stalnaker (2005) and Nolan (2003)]. [Nolan (2003) holds a version of Possible Worlds Account that treats conditionals as radically indexical, but which maintains some worldliness by holding that it is our knowledge (rather than mere belief or firm belief) that determines which possible worlds are closest to ours. Krzyzanowska et al. (2014) do something similar within their Suppositional/Probabilistic Account by requiring that the relevant epistemic states be knowledge states.] Suppositional/Probabilistic Accounts such as those of Adams (1975), Edgington (1995), Gibbard (1981), and Barnett (2006), which eliminate truth values, do not closely tie conditionals to the extra-mental world.
Some conditionals are explicitly about people’s beliefs, such as the conditional ‘If S believes A, then S probably believes B’, but the relevant difference here concerns whether or not an account treats the acceptability or truth of all conditionals as dependent just on a person’s beliefs.
A truth-maker is the state of affairs, event, individual, etc., that makes a true sentence or true proposition true. For example, my laptop, or the fact that my laptop exists, is one of the truth-makers for the sentence ‘At least one laptop exists’.
I changed the year such that it is in the future relative to the time at which this paper is written.
This complaint is related to Edgington’s (1995) rain dance case. Edgington points out that conditionals such as ‘If we perform this rain dance, then it will rain’ are justifiably acceptable for people who believe that rain dances bring rain, according to non-worldly accounts, whereas in reality they are false/unacceptable.
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Acknowledgements
Many thanks to anonymous reviewers at Philosophical Studies for helpful and formative comments. Thanks to David Barnett and Graeme Forbes for extensive comments on previous versions of Sects. 2 and 3 and to Scott Weirich for helpful feedback.
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Weirich, K. Defending truth values for indicative conditionals. Philos Stud 177, 1635–1657 (2020). https://doi.org/10.1007/s11098-019-01278-0
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DOI: https://doi.org/10.1007/s11098-019-01278-0