Westphal, Jonathan - The Indicative Conditional: An Amendment to Stalnaker

11/06/2009

Unpublished

This paper explores the indicative conditional and the material conditional. Author starts with this 'old familiar question' and thinks that Stalnaker's answer is nearly correct: the conditional "if p then q" is true if 'the consequent is true, not necessarily in the world as it is, but in the world as it would be if the antecedent were true'.

Author gives the case of Seabiscuit, and the conditional: if Seabiscuit runs, he will win. "If r then w". First author distinguishes between regular cases where the race is fair, and the conditional is picking out the salient features of the situation. The trouble here is that the truth table could have a weird outcome in the case of the antecedent being false and the consequent being true. How could Seabiscuit win and not have run? So there is a kind-of dependence between the 'guide propositions'. Author concludes that for the truth tables to apply, there must be genuine independence between them.

Author then considers what happens when there is genuine independence but the antecedent is false. In these cases, it seems that the conditional is true when the consequent is true, but it isn't the 'if p then q' setup that 'force[s] it true'. When the consequent is true, this 'allow[s]' the conditional to be true-- but the distinction between 'forcing' and 'allowing' is lost in the analysis.

Author revisits the Seabiscuit conditional, "If Seabiscuit runs, he will win":

If R then W

If the antecedent is true and the consequent is false, then the conditional is false no matter what Seabiscuit does-- whether he does run or not. Even in the weird case where the antecedent is false and the consequent is true (he doesn't run, but wins), the conditional is... false! This is a 'line-dependent' outcome that the author points out. If both the antecedent and the consequent is true, then the conditional is true no matter what Seabiscuit does. So the final two lines of the truth table (where the antecedent is false) depend on the the first two lines, where the truth of the consequent varies.

Author considers finally 'silly conditionals', like: 'if the moon is cheese, then 17 is prime'. He concludes that the material conditional is the correct analysis here.

Author concludes that in cases of the indicative conditional, when the antecedent is false the conditional is undetermined-- or at least dependent on the outcome of the consequent when the antecedent is true. This makes it an open question whether the 'if... then...' rule is equivalent to 'not p, or q' (~p v q).