Tuesday, August 07, 2007

Actual Possibilities, by Jonny Blamey

When people try to explain to me what is meant by metaphysical possibility, and possible world semantics, they tell me that possible worlds are “ways the world could be”. I feel like I understand. But when I say what I understand by “the ways the world could be” I am usually accused of mixing up metaphysical modality with epistemic modality. My intuitive understanding of “the ways the world could be” is actually a misunderstanding, since intuitively (to me) the ways the world could be is an epistemic notion. What is more “the world” in “the ways the world could be” is the actual world. I have no interest, certainly no practical interest, in the ways some possible world could be. I am a fan of science fiction, my interest is excited because the scenarios presented could happen here, in this world, albeit in the future. I equally enjoy fiction set in historical times. If the book is well researched then the events portrayed could have happened, they are ways this world, my world, could have been. The probability, according to my evidence, that Rob Roy cut an Englishman in half, like in the film, is zero and I am quite aware of this. But he could have done. The probability that Rob Roy became King of England is likewise zero, but this could not have happened, this is not a way the world could have been. If someone were to tell me that Rob Roy could have become king of England, I should respond by asking how. I would then sit back and enjoy listening to what facts would need to be unpicked, what chance happenings would have had to have occurred for Rob Roy to capture the throne. This pathway, to be of any interest to me, would have to be picked and unpicked out of the fabric of this world, my world, the only world there is.

Enough preamble. Here are two arguments that I take to be both modal and valid, but that seem to be about about the actual world and notabout possible worlds at all but . Neither are they about epistemic modals given the wonderful principle laid out by Moritz Schulz in this blog: (MIGHT c(might x) = 1 if c(X) > 0.)

POSITIVE MODAL ARGUMENT:

Premise: If John had set his alarm for eight o’clock he would have got here on time.
Premise: John could have set his alarm for eight o’clock.
­­­­­­­­­­­­­­­­­­­­­­­Conclusion: John could have got here on time.

The conclusion is modal. We are to assume that in fact John did not get here on time. It is not consistent with our evidence that John got here on time, so this is not epistemic possibility. The probability that John got here on time is 0. So according to MIGHT it is not true that John might have got here on time. However, there is surely a possible world where John got here on time whether he set his alarm clock or not. But the conclusion of this argument is not trivially true. The second premise is necessary for the conclusion to follow.

NEGATIVE MODAL ARGUMENT.

Premise: The only way that John could have got here on time would have been by car.
Premise: John does not have a car.
Conclusion: John could not have got here on time.

This time the conclusion is not counterfactual, since it is assumed that John did not get here on time. So the probability that John did not get here on time is 1. We again are not using epistemic modals here since according to MIGHT John must have got here on time and the conclusion is redundant. In this second argument, the second premise must be true in the actual world for the argument to go through. Are there possible worlds in which John has a car? In these worlds he could have got here on time. But we know that in this world he doesn’t have a car, so in this world he couldn’t have got here on time.

These modal arguments are important, especially in assessing culpability, but also in improving design and assessing scientific evidence. But they don’t seem to fit either metaphysical modality nor epistemic modality.

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4 Comments:

Blogger Richard said...

I think what you've pointed to is just a case of restricted quantification. Like saying "there's no beer" (restricting the domain to the fridge only), we might say "John could not have got here on time," restricting our attention only to contextually salient possible worlds, i.e. those where the premises are satisfied, and John doesn't have a car (or superhuman speed, etc.). Does that help?

2:00 AM  
Anonymous Jonny said...

Yes, it helps. The contextually salient worlds though seem to be restricted by what we know ("we" being the interlocuters) plus or minus a few facts that we are deliberately adding or deleting. This seems to be much closer to epistemic modality than metaphysical modality.
Let Ktn = what we know at tn.
Let H = He gets here on time.
"He might be here on time" can be formalised according to MIGHT as:
P(H|Ktn) > 0. Where tn = now.
"He might have been here on time" becomes P(H | Ktn) > 0. Where tn = some previous time.
"He might have been here on time if he had set his alarm" becomes
P (H | Ktn + he set his alarm at tn) > 0. Where tn is the time at which he could have set his alarm but didn't.
We can deal with negative conditions as well so
"He might have been here on time had he not been hit by a car becomes
P (H | Ktn - he got hit by a car) > 0. Where tn is just before he got hit by a car.
Deleting and adding propositions from K can be seen as a way of restricting the set of possible worlds under considerations, but it need not be, and we can see that it renders possible worlds redundant. Why not just take "possible" to mean "consistent with what we know plus or minus a few specified assumptions" and dispense with possible worlds altogether? This way there is just one modality, epistemic modality. Logical, metaphysical, natural modality are just ways of specifying what is not to be deleted from K.

11:09 AM  
Blogger Richard said...

"Why not just take "possible" to mean "consistent with what we know plus or minus a few specified assumptions" and dispense with possible worlds altogether?"

Well, the notions are interdefinable: P and Q are consistent iff there's some logically possible world where both are true. So they basically come along for free. And possible worlds talk seems very useful for various philosophical purposes (explicating supervenience and other modal relations, for example). So it's a freebie worth accepting ;-)

"This way there is just one modality, epistemic modality."

One objection, discussed here, is that this doesn't seem to do justice to the modal force of natural necessities. But I'm sympathetic to the view that what philosophers typically call "metaphysical possibility" is ultimately grounded in the more 'epistemic' realm of conceptual possibility. (See also David Chalmers' papers on meaning and modality - e.g. 'epistemic space'.)

10:34 AM  
Anonymous Jonny said...

You say "P and Q are consistent iff there is some logically possible world where both are true"
I agree that this is the dogma, but it is also what I am trying to get away from. The reason is Hume's problem of induction. The notion of epistemic possibility I am playing with is that P is consistent with K if P|K > 0. I want to argue that inductive certainty exists, so that it can be the case that P|K = 1 even though there is a logically possible world where both K and ~P are the case. Since practically all our knowledge is inductively based, then this is no small technical matter, it means that logically possibility doesn't capture our practical understanding of possibility at all.
Some examples: I know that AIDS is caused by HIV, but there could well be a logically possible world where my experience was just as it is and HIV does not cause AIDS.
Given what I know the probability that the sun rose this morning is 1, but there could be a logically possible world where I had just the same brain states and yet the sun did not rise.
There is a sense in which it is possible that I am wrong about these things (that HIV causes AIDS, and the sun rose this morning) I could delete a load of assumptions from my knowledge and add a load more to make these things possible. But if we are talking about logical possibility, I need not touch anything, since these things are logically consistent with what I know already.

12:27 PM  

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