Truth and falsity of indicative conditional statements
Posted: July 23rd, 2018, 8:33 pm
Having not read much philosophy since my university days, I'm currently making my way through David Papineau's Philosophical Devices. It covers a lot of ground I know little or nothing about, much of it more mathematically inclined, so it's not easy reading, but I'm making steady progress. However, the section on indicative and subjunctive conditional statements is a bit puzzling - or rather, one of the exercise questions at the end of the chapter is. In the main text of this chapter Papineau gives an example of an indicative conditional statement which is true:
"If Oswald didn't kill Kennedy, then someone else did."
One of the exercise questions is to say whether the following indicative conditional statement is true or false:
"If you have eaten arsenic, then you are dead now."
The next question concerns the subjunctive conditional statement:
"If you had eaten arsenic, then you would be dead now."
The subjunctive conditional is true, as you would expect. However, the indicative conditional is, apparently, false. I found this surprising because it looks an awful lot like the Kennedy/Oswald example.
As Papineau notes, the antecedent "Oswald didn't kill Kennedy" is false, but the indicative conditional statement "If Oswald didn't kill Kennedy, then someone else did" is still true. Similarly, while the antecedent "you have eaten arsenic" is false, the indicative conditional statement "If you have eaten arsenic, then you are dead now" certainly looks, on the face of it, as though it should be true. But Papineau says it's false.
Why is this? What is the difference between the two examples? Both are indicative conditional statements, both have false antecedents, and it would seem that both have a consequent which follows from its antecedent. Unfortunately Papineau doesn't include any examples of a false indicative conditional in the main text of his chapter, which doesn't exactly help in trying to grasp his reasoning.
His explanation of how indicative conditionals work is that they are concerned "with rational changes of belief. They tell us what we should believe on learning the antecedent p". So if you're told by someone you trust that Oswald didn't kill Kennedy, it's logical to change your belief by concluding that there was a different killer. But similarly, it seems that if you find that you have eaten arsenic, you should expect to be dead.
I assume the explanation must have something to do with the fact that in the second example, the consequent "you are dead now" is false, and this renders the antecedent "you have eaten arsenic" false. But the precise explanation is not clear.
Any thoughts?
"If Oswald didn't kill Kennedy, then someone else did."
One of the exercise questions is to say whether the following indicative conditional statement is true or false:
"If you have eaten arsenic, then you are dead now."
The next question concerns the subjunctive conditional statement:
"If you had eaten arsenic, then you would be dead now."
The subjunctive conditional is true, as you would expect. However, the indicative conditional is, apparently, false. I found this surprising because it looks an awful lot like the Kennedy/Oswald example.
As Papineau notes, the antecedent "Oswald didn't kill Kennedy" is false, but the indicative conditional statement "If Oswald didn't kill Kennedy, then someone else did" is still true. Similarly, while the antecedent "you have eaten arsenic" is false, the indicative conditional statement "If you have eaten arsenic, then you are dead now" certainly looks, on the face of it, as though it should be true. But Papineau says it's false.
Why is this? What is the difference between the two examples? Both are indicative conditional statements, both have false antecedents, and it would seem that both have a consequent which follows from its antecedent. Unfortunately Papineau doesn't include any examples of a false indicative conditional in the main text of his chapter, which doesn't exactly help in trying to grasp his reasoning.
His explanation of how indicative conditionals work is that they are concerned "with rational changes of belief. They tell us what we should believe on learning the antecedent p". So if you're told by someone you trust that Oswald didn't kill Kennedy, it's logical to change your belief by concluding that there was a different killer. But similarly, it seems that if you find that you have eaten arsenic, you should expect to be dead.
I assume the explanation must have something to do with the fact that in the second example, the consequent "you are dead now" is false, and this renders the antecedent "you have eaten arsenic" false. But the precise explanation is not clear.
Any thoughts?