Tuesday, January 23, 2007

Jonny on Lee Walters on counterfactuals

Lee Walters gave a talk today at (The legendary) William Bynoe’s Metaphysics Group on my favourite topic: counterfactuals. Unfortunately I had to go just when it was getting interesting so this is a counterfactual post about what I would have said if I had been there.
I’ll jump straight to the controversy. I bet five pounds on tails. The coin comes up heads. Now we have the counterfactual.
1) If I had bet on heads I would have won.
First up: does this sentence express a true proposition? Intuitions please. (Yes it does)
A quick word on why this is important. It seems that a good theory of counterfactuals should make 1) come out true given that the coin actually came up heads. However, the problem lies in trying to give an account of counterfactuals where you hold the past fixed up to the point where the counterfact antecedent happens and then forward from there following the expected causal consequences of the counterfact. (I’ve just made up the word “counterfact” meaning the antecedent of a counterfactual, in this case that I bet on heads). But if I had bet heads, at the time of betting given that coin tosses are indeterministic, then the chance of me winning would have only been ½. So the counterfactual should come out as
2) If I had bet on heads I might have won and I might have lost.
Lee bites the bullet and says that 1) is in fact false. But this is only on the assumption that the consequent was indeterministic. I don’t understand objective probability, nor what indeterministic means in any non epistemic sense. I believe that all probability is relative to an epistemic frame of reference. If we specify the frame of reference the problem goes away.
So as far as I knew at the time, I might have lost with a bet on heads; but I now know that had I bet on heads I would have won. Here 1) and 2) are compatible.
My analysis of counterfactuals is that a counterfactual is relative to an epistemic frame of reference. The epistemic frame of reference includes any facts that are known to the relevant subject minus any counterfacts and their causal consequences specified or tacitly assumed. The relevant subject would normally be the speaker, but could be the subject of a counterfact action.
An example to show the plausibility of this view.
Person 1. If you’d bet on heads you’d have won.
Person 2. Yes, but there is no way I could have known that. As far as I knew at the time, if I had have bet on heads, I could have lost.

The agreement between person 1 and 2 shows that the epistemic frame of reference changes the truth conditions of the counterfactual, since otherwise person 1 and person 2 are asserting inconsistent counterfactuals.

Suppose Person 1 said before the toss but after Person 2 has bet on tails:
“If you had have bet on heads you would be going to win”

I think the most natural interpretation of this counterfactual is that it is true if the coin comes up heads. It is a bit difficult to parse because Person 1 would not be in a position to know that the coin was to come up heads so the knowledge norm of assertion forbids him from asserting it. But if we take a rigged horse race or a non gambling situation it becomes more plausible.
If you’d have caught the train, you would be going to arrive on time.
If you’d only have bet on Black Beauty, you’d be buying us all a drink tonight.

The point is that 1) is true if the fact that the coin is heads is fixed in our epistemic frame of reference. It is false otherwise.
One last example. Persons 1 and 2 enter into a gambling den and are offered a bet of £2000 on either heads or tails for the next toss of a coin. Being puritans they walk out in disgust without waiting to see whether the coin came up heads or tails.
Person 1 says; 1) “If you had bet on heads, you would have won.”
I think that Person 1 is in no position to assert this, but if he did it would have been true if and only if the coin had landed heads. Because in his epistemic frame of reference the coin landed heads has a probability of 50%, person 2 could rebuke him by saying. “No, you are wrong, I could just as easily have lost.” This is because from their epistemic frame of reference, it is true that if they had bet on heads they would have had a 50% chance of winning and it is therefore false that if they had bet on heads they would have won.

Thursday, January 11, 2007

Jonny Blamey V Timothy Pritchard on the Truthlessness of Sentences

Tim's talk last night was very inspiring. However I completely disagree with his conclusion.
I understood the talks main point to be this:
When one puts a sentence in inverted commas, as in "elbows bend" then one is referring to the bit of language, let us say the sentence. When one uses a that clause, eg. "that elbows bend", however, one is referring to the propositional content of the sentence. Interestingly from my perspective, "if" does the work of "that". So for example
1 "Elbows bend" has a kind of alliteration.
2 It is a good job that elbows bend.
3 If elbows bend then this is not an elbow.
Depending on what you are trying to say, one of these forms will be incorrect. They are never interchangeable. So the following are wrong:
1 That elbows bend has a kind of alliteration.
2 It is a good job that "elbows bend"
3 If "elbows bend" then this is not an elbow.
Never? Well what about truth? We might want to say, with a host of semanticists, that "elbows bend" is true if and only if elbows bend. Tim thinks this is wrong because
4 "Elbows bend" is true.
Doesn't make sense, since the appropriate form is
5 That elbows bend is true. Or more naturally: It is true that elbows bend.

I find this very informative, but I do so because I think Tim is wrong and that 4 and 5 are both correct, but Tim is right in that it is a coincidence if both 4 and 5 are true. By revealing this to me Tim has open my eyes to the informativeness of complex sentences like:
6 "elbows bend" is true if and only if elbows bend.
By realising the contingent nature of 6, I come to appreciate its informativeness. In probabilistic terms, Tim’s talk made me see how unlikely it is that "elbows bend" is true if and only if elbows bend. The increase in unlikliness increases the informativeness. But Tim thinks that it is not merely unlikely but actually false, and truth cannot be predicated of sentences at all, only of the content of sentences. Against Tim then I will offer cases where it must be the case that we are talking about the sentence and not the propositional content when we predicate truth. I'll just give the examples without saying what my own intuitions are.

1 If the sentence "I love you" is true, then the sentence "Ich liebe dich" is true.
Contrast with:
2 If it is true that I love you then it is true that Ich leibe dich.

3 If Bonn were called "Berlin", and Bonn was on fire, then the sentence "Berlin on fire" would be true.
Contrast with:
4 If Bonn were called "Berlin", and Bonn was on fire then it would be true that Berlin was on fire.

5 There is a prophet among us who speaks in tongues. We believe that whenever he speaks in tongues he is the mouth piece of God but speaks a language we do not understand. Yesterday he uttered the sentence: "Dithrock pertuns bladly." We are sure that the sentence "Dithrock pertuns bladly" is true, but we have no idea what it means.