Stand-offs

The Ramesy Test ties the truth of an indicative conditional for any given subject, S, with S's probability of C conditional on A. The Ramsey Test, therefore ties the indicative to subjective probability. But, this result is complex an inelegant. A number of philosophers, notably, Wayne Davis, have made attempts to objectivize the Ramesy Test (see Davis, "Indicative and Subjunctive Conditionals"). Davis's approach centers on the following strategy: when assessing the truth value of an indicative conditional, instead of adding A to your present belief system, you should add A to the whole truth about the actual world (making adjustments as conservative as possible). This will generate results base on objective probabilities.

A counterexample presented by Alan Gibbard demonstrates that attempts to objectivize the Ramsey Test are doomed to failure. In, "Two Recent Theories of Conditionals," (Harper et al. eds. 1981) Alan Gibbard presented the following case:

During a hand of poker, everyone has folded except Pete and one other player. Two spectators, Winifred and Lora, leave the room at this point. A few minutes later, Winifred sees Pete not scowling in the way that he does after calling and losing. She thinks, "If Pete called, he won." Lora sees Pete's opponent holding more money than he had when she left the room and thinks, "If Pete called, he lost."

This is a Gibbardian stand-off: a case in which one person is fully licensed to accept A→C and another is fully licensed to accept A→¬C.

What are we to make of this? Here are some possibilities: 1) both conditionals are true, 2) one conditional is true and the other is false, 3) both conditionals are false, 4) both conditionals are neither true nor false.

Potential Responses

Accepting option 1, both conditionals are true, violates the Principle of Conditional Non-Contradiction, ¬((A→C) ∨ (A→¬C)). This is unproblematic for philosophers who accept the Equivalence Thesis, A→C=A⊃C, since the Principle of Conditional Non-Contradiction already fails on that account. But, nearly all philosophers who reject the material account accept the principle, and must look elsewhere to resolve the Gibbardian Stand-off.

Option 2, one conditional is true and the other is false, is fruitless. Gibbard suggests (and this suggestion seems plausible) that one accepts something false only if one is mistaken about some relevant matter of fact; neither Winifred nor Lora has made any such mistake. Further, if we assert that one conditional is true and one conditional is false we have to be able to identify the faulty claim; by what lights could we make such a determination? What fact could make one conditional true and the other false?

Option 3, both conditionals are false, is made equally implausible by Gibbard's remarks about falsity. Neither speaker is mistaken about relevant facts.

Conclusions

Bennett, and Edgington, and Lycan all develop responses in line with the fourth suggestion, neither conditional is objectively true or false. On this view, indicative conditionals have no objective truth-values. Edgington's view stands apart in that Edgington holds that indicative have not truth value until/unless the antecedent is true (See Edgington "On Conditionals").

William Lycan makes an attempt at another approach. Lycan holds that indicatives have no objective truth-values. For Lycan, however, they have subjective truth-values.

Consider the proposition, "I grew up in New York City." The truth of the proposition depends not only on the sentence, but also on who is speaking. On Lycan's view, the truth of the conditional A→C depends not only on A, C, and the meaning of →, but on some further fact about the speaker or accepter of the conditionals. (See Lycan. Real Conditionals, 2001)

How can we flesh out this suggestion further? On this view, we have to hypothesize that → operates over A, C, and the speaker's belief state (on Lycan's view, which possibilities seem real to the speaker given A).

Here is a problem Bennett points out for this view: Imagine that someone asserts, "If water is cooled to 0° C, it will freeze." Intuitively, we think that she is asserting that the probability of the consequent on the antecedent is high. But, if we accept the notion that → is a ternary operator, the speaker is asserting something quite different, that is, the probability that she assigns to the consequent given the antecedent is high. This doesn't seem like what we mean when we assert conditionals. This problem, and other difficulties with assigning a speaker-relative proposition a truth-value, leads Bennett to conclude that indicatives have neither objective nor subjective truth-values. (See Bennett, A Philosophical Guide to Conditionals, 2003)

Further Thoughts

It is interesting to note that subjunctive conditionals cannot enter into stand-offs. Let's consider why this is the case. In the Top Gate examples, A→C (If Top Gate opened, water would flow East) and A→¬C (If Top Gate opened, water would not flow East) were both acceptable for different agents precisely because the antecedent is false. But consider the antecedent in the counterfactual case, "If it were the case that Top Gate opened,..." It is unclear what the worlds at which it is true will be like. Either all of the relevantly similar worlds will be ones at which C obtains, in which case A>C is true. Or all of the relevantly similar worlds will be ones at which ¬C obtains, in which case A>¬C will be true. A third option is that C will be true at some, but not all of the relevant worlds, in which case neither conditional is true. There is no case that makes both subjunctives acceptable.