Tuesday, February 22, 2011

An argument for the material conditional account of indicatives

The material conditional account of indicatives is that "If s, then u" is true if and only if s is false or u is true or both.

  1. (Premise) If the indicative conditional has the same truth values as the material conditional in the standard cases which are alleged to be counterexamples to the material conditional account, then the material conditional account is correct.
  2. (Premise) The indicative conditional has mind-independent truth value.
  3. (Premise) If the indicative conditional has mind-independent truth value, then it has the same truth values as the material conditional in the standard cases which are alleged to be counterexamples to the material conditional account.
  4. Therefore, the material conditional account is correct.
In this argument, I am convinced of premises (1) and (3), but not sure of premise (2). Consequently, what the argument convinces me of is that either (2) is false or (4) is true. Premise (1) is not that controversial, I think. The material conditional account is simple and elegant, verifies modus ponens and contraposition, is well-defined and mind-independent. The only problem is that it appears to give the wrong answers for certain standard cases. If this appearance were undercut, the material conditional account would be the winner.

The hard work is going to be justify (3). Let us start by giving three representative alleged counterexamples, classified by the truth values of the antecedent and consequent:

  1. "If I will have dinner with the queen tonight, I will eat dinner tonight in my pajamas." (Antecedent and consequent are both false.)
  2. "If I will have dinner with the queen tonight, everyone that I will have dinner with tonight will be a family member." (Antecedent is false and consequent is true.)
  3. "If it is snowing in the United States, it is snowing in Central Texas." (Suppose this was uttered a couple of days ago when it was snowing in Central Texas. Antecedent and consequent were both true.)
The material conditional account says that all three conditionals are true. But all three conditionals sound wrong (assuming I am not a member of the royal family and that I wouldn't wish to insult the queen).

I will argue that:

  1. If the indicative conditional has mind-independent truth value, then (5)-(7) are all true.
The method of argument generalizes to all the standard counterexamples, and thus yields (3).

Here's the way I will argue for (8). Let "a" be the antecedent in the alleged counterexample. Let "c" be the consequent. Suppose I have the belief, justified or not, that at least one of "not-a" and "c" is true, and I have no further, more specific beliefs about the matters in a and in c. Since I believe that at least one of "not-a" and "c" is true, I should be able to sincerely say to someone:

  1. I may not know much about the queen, dinners, pajamas, snow, etc., but I do believe that at least one of "not-a" and "c" is true. Hence, if a, then c.
This seems very reasonable.

Suppose now that I learn all the relevant facts about the queen, dinners, pajamas, snow, etc. In particular, I learn such facts as that people tend not to wear pajamas for dinner with the queen, that central Texas is one of the somewhat less likely places in the US to have snow, etc. I also learn the truth values of "a" and "c". None of the things I learn gives me reason to retract the claim that at least one of "not-a" and "c" is true. And neither have I any reason to retract the conclusion I drew, that if a, then c.

Therefore, when I said (9), I said something true. If it wasn't true, I would have reason to withdraw it. But the difference between the circumstances in my story in which I said the conditional in (9) and standard circumstances was in my beliefs—when I said (9), I lacked various beliefs that normal people in our culture have. Thus, if the indicative conditional has mind-independent true value, I have to conclude that actually the conditional "if a, then c" is also true. And so we have an argument for (8).

5 comments:

Heath White said...

I have no settled views on this question, though I lean away from the material-conditional account. But I think you've overlooked an important possibility that would deny either 2 or 3. That is that, properly speaking, indicative conditionals have no truth values.

The argument, first put forward by David Lewis, turns on questions of probability. The claim is that conditionals can be more or less probable, and if they are, we should measure that probability as P(c|a). However, there is no proposition q such that P(q) = P(c|a). (This was the surprising result.) Hence the indicative conditional a->c does not express any proposition q.

I don't know how you'd want to slot that in to your argument but its an important result to consider.

P.S. I think you have an error in 7.

Susan said...

You meant both "true" in (7).

Alexander R Pruss said...

Susan:

Yup. Fixed it moments before reading your comment. Thanks.

Heath:

I am arguing that if the indicative conditional has mind-independent truth value, then it has the truth conditions of the material conditional. There are two ways of lacking mind-independent truth value: by lacking truth value and by having mind-dependent truth value.

I am open to the idea that the right view of indicatives is contextual. In some contexts they have truth value and are material. In others, indicative conditional claims are expressions of conditional probability.

I wonder if one can't just marry the two by distinguishing what the conditional expresses from what says. it expresses conditional probability. It says not-s or u. That's a variant of Grice's implicature idea.

enigMan said...

(9) is true, I think, because if at least one of not-A and C is true, then it's true that if A then C, because if A is true then it's not not-A that's true, and so it's C.

I also agree with your variant of Grice's idea; e.g. (7) seems to express a subjunctive conditional, but could means lots of things in different contexts. But therefore it may be that the indicative conditional only expresses the material conditional, in such contexts as the one you gave to justify (9).

I tend to think that the indicative conditional does not have mind-independent truth value. We use such conditionals when we reason, so why should they be mind-independent? Indeed, why should disjunction be mind-independent?

Alexander R Pruss said...

I'm glad you brought up disjunction. It's a puzzling thing that philosophers are very puzzled by "if...then..." but by and large take "...or..." to be unproblematic. At least some of the "paradoxes of material implication" are pretty close to as paradoxical in the case of the corresponding disjunctions.

1. The queen won't invite me for dinner tonight.
2. So: The queen won't invite me for dinner tonight or I will eat dinner in my pajamas.
3. So: If the queen invites me for dinner tonight, I will eat dinner in my pajamas.

I think the ordinary person is at least just as puzzled by the move from 1 to 2 as by the move from 2 to 3.