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Truth and falsity of indicative conditional statements

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Loosefish Scapegrace
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Truth and falsity of indicative conditional statements

Post by Loosefish Scapegrace » 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?

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Mosesquine
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Re: Truth and falsity of indicative conditional statements

Post by Mosesquine » July 24th, 2018, 5:16 am

Indicative conditionals are dealt with, not only in philosophy of language textbooks, but also in formal logic ones. The standard truth table for indicative conditionals, though controversial, is usually offered as follows:

p q p → q
T T T
T F F
F T T
F F T

This means that indicative conditionals are always true when their antecedent is false. (where "T" is a schematic letter for "The True", and "F" for "The False") Additionally, the indicative conditional 'p → q' is logically equivalent to '~p ∨ q'. The truth table for '~p ∨ q' goes as:

p q ~p ∨ q
T T T
T F F
F T T
F F T

You can see that the truth table for 'p → q' above is the same result as the truth table for '~p ∨ q' above.

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Re: Truth and falsity of indicative conditional statements

Post by ThomasHobbes » July 24th, 2018, 5:28 am

Loosefish Scapegrace wrote:
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."
Maybe this is nothing more than the particular case, not the general.
Since you cannot "BE" and have died. In other words, being is the opposite of death, the statement 'you are dead now' is an absurdity.
However since the conditional does not actually involve you in having taken arsenic then you can be around to hear receive the statement. The indicative entails you not being able to receive the statement?

The Oswald case it true, assuming that Kennedy was killed by someone, rather than dying of some accident, or other cause. There is no contradiction.

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Loosefish Scapegrace
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Re: Truth and falsity of indicative conditional statements

Post by Loosefish Scapegrace » July 24th, 2018, 9:14 am

Thanks for the replies.

The indicative conditional truth table is interesting, though I can see why it's controversial. The third and fourth lines appear counter-intuitive (especially the fourth), which, having just done a quick online search on this topic, seems to be generally acknowledged as the cause of a good deal of confusion. It certainly appears to be the sort of thing for which concrete examples are needed to make it comprehensible.

Having thought about your replies and mulled over the arsenic example a bit more, the key point appears to be what Papineau describes as "what we should believe on learning the antecedent p".

In the Kennedy example, if you learn that p is actually the case, i.e. that Oswald didn't kill Kennedy, should you still believe that q - someone else did - is true? Yes, that clearly does still follow. But in the second example, if you learn that p is the case, i.e that you really have eaten arsenic, does it still follow that you should believe that q is true, i.e should you now believe that you are dead now? No, that does not still follow, since you know you are not dead. This, I assume, is why this indicative conditional is false. Of course, in such a situation you might very well believe that you are going to die, but that is not the same thing as believing that you are dead now, which is what the indicative conditional specifies.

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