Conditionals, supposition, and euthyphro

ABSTRACT

Williamson proposes that a ‘suppositional procedure’ is a central heuristic we use to evaluate the truth of conditionals, though he also argues that this method often leads us astray. An alternative approach to the link between supposition and conditionals is to claim that we are guided by our antecedent conditional judgements in our supposing, and in particular in our determining which things follow from an initial supposition. This alternative explanation of the close link between conditionals and supposition is developed and compared to Williamson's proposal.

KEYWORDS:

• Conditionals
• supposition
• indicative conditionals

Acknowledgements

Thanks to Sara Bernstein, Franz Berto and Robbie Wiliams for discussion.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Material-conditional accounts the truth-conditions of indicative conditionals are experiencing a resurgence: for another recent defence, see van Inwagen 2022.

2 Williamson also extends the suppositional rule to conditionals on the assumption of other premises/assumptions in chapter 3, especially 3.4. It is this suppositional rule, on the basis of assumptions BB, which he puts together with a suppositional rule for "would" to yield his account of supposition and counterfactuals.

3 There is a family of other suppositional approaches to conditionals, including at least Barker 1995 and Barnett 2006, 2010. Many of them, including Edgington, draw comfort from Mackie 1972, 92–93, who says that the key to understanding conditionals is to see them as asserting the consequent under the supposition of the antecedent. For a recent approach identifying as belonging to this tradition, see Carter 2021.

4 The most promising approach might be a non-monotonic logic of supposition, analogous to the non-monotonic logic Badura and Berto 2019 presents as a logic of fiction, to deal with the fact that standard logical principles may fail in fictions where suitably logically impossible things happen. Berto 2022 chapter 5 offers a treatment of supposition with a more restricted range of worlds, but extended in the direction of Badura and Berto 2019 it would capture a lot of what we want.

5 Divers and Elstein 2012; 122 and Williams 2012, 648–649 both appeal to Oswald and Kennedy cases to suggest there are (at least) two kinds of supposition. What I lose in originality I make up for in good company.

6 I choose the example over ones that are more easily conceivable, given the sorry state of the world, so as to not comment on any of the world's more likely flashpoints. Of course I think there is basically no realistic chance of French nuclear weapons being used in this way.

7 Since I think the evidence that counterfactuals are context dependent is overwhelming, if the analogues of Williamson's arguments were to lead to the conclusion that counterfactuals were not context dependent, that would strongly suggest that the arguments are flawed. So this suggests that Williamson's arguments against the context-dependence of indicative conditionals are flawed as well.

8 Of course, indicative conditionals with expressions like "I" or "here" or other context-dependent expressions will have context-dependent truth-conditions, even on Williamson's theory. Williamson rejects any additional context-dependence from indicative conditional constructions.