Sunday, March 16, 2008

bernoulli and I on necessity

Necessary and Contingent.

I share these concepts with Bernoulli it turns out. “A proposition is called necessary, relative to our knowledge, when its contrary is incompatible with what we know.” Is how Hacking 19975 explains Bernoulli's use of necessary and contingent propositions. Suppose we are wondering whether H is certain given evidence E. There are 4 possibilities:

1. E is known, H given E is uncertain. Argument contingent, H contingent
2. E is uncertain, H given E is uncertain. Argument contingent, H contingent
3. E is known, H given E is certain Argument necessary, H necessary
4. E is uncertain, H given E is certain. Argument necessary, H contingent

Whether or not E is known would be to an empiricist and empirical matter. This is as much as to say that there are no foundational singular statements of fact. There could be some doubt to this, but this need not worry us here.

What is confusing and equivocal is what is means for H given E to be certain. A straight forward interpretation is that p (H given E) = 1. Now we must wonder what kind of interpretation of probability is at play here. To a rationalist, we might think that H given E is certain if it is a priori. This would be as much as to say that only logical and mathematical inferences are certain and therefore only mathematical and logical truths are necessary. But why can’t we be certain of H given E on the basis of experience? Well, because of the problem of induction. But that is circular, since the problem of induction is only a problem if we accept that we can only be certain of conditionals through pure reason.
Here are some certain conditionals that would count as being learned through experience:
If it is a Blue Whale then it is a Mammal.
If an act is motivated purely by cruelty, then it is wrong.
If a piece of Music is written by Mozart, then it is Classical.
If Jones intentionally fired the gunshot that killed Smith, then Jones killed Smith.
If Smith fell into a meat mincing machine and was turned into mince meat, then Smith is dead.
If x thinks, then x exists.
I guess that many contemporary post graduate students of philosophy would say that the above conditionals are contingent. Would you? I for one am certain of all of them, though I could imagine a different conceptual scheme where they weren’t certain. If Mozart had written some Baroque music, for example, or if “intentionally” included cases of hypnosis, or if Smith was some kind of super being who could regenerate himself, or if “Blue Whales” referred to something ostensibly similar to Blue Whales, but for hidden “scientific” reasons to do with molecules weren’t actually Mammals. I could imagine a society of sadists and masochists where only cruel acts were just. I can imagine a character who thinks, but yet does not exist. Hamlet, for example. But what do all these flights of fantasy have to do with necessity and contingency? Nothing useful, I say. A distinction monger might want to talk of what is necessary in the actual world and what is necessary in every possible world. So Blue Whales are only necessarily mammals here, whereas other worlds they are only contingently mammals. But then we have lost possible world modal semantics. To focus on the one example. Suppose we are certain of proposition E x is a Blue Whale where the reference of x is fixed by clear spatio temporal co ordinates. Now I count it as common knowledge that in general if x is a Blue whale then x is a mammal. Let H be the hypothesis that x is a mammal. Is H necessary or contingent?


Anonymous Lee W said...

You are using 'uncertain' as the dual of 'knowledge'. But why think we cannot know things we are uncertain of? I suspect that is a whole other post.

Similarly, you say in your 1-4 that if H is not necessary (and I presume its negation not necessary) then it is contingent. But it is truths/facts that are contingent and H maybe be false in these cases, so presumably it is that H is possible in these cases - possibility, not contingency, is the dual of necessity.

As for your conditionals, I think the only one that is clearly contingent is the Mozart one. It could have been that Mozart only wrote folk music. But plausibly blue whales are necessarily mammals, pure cruelty is necessarily wrong etc.

In any case, this just shows that Bernoulli is using 'necessary' to pick out an epistemic modality and not an alethic one. Perhaps he and you are sceptical of the latter. Fair enough, but that is a different matter.


Are you really certain about the Mozart conditional - would you bet your life on it for no reward?

11:48 AM  
Blogger bloggin the Question said...

Thanks Lee,
Yes, I am using uncertain as the dual of knowledge. The lottery case I take to demonstrate that no degree of uncertainty is compatible with knowledge. Lewis's contextualism deals with intuitively plausible cases of uncertain knowledge. There are such things a probabilisitic inferences where the conclusions are contingent but where the inference is well established. In these cases what are we to say? We don't want to say the inference is unknown, we might not want to say that it is uncertain, but if we take uncertain just to mean p(H|E) < 1, then we can be as confident of the inference as we like and yet the inference itself still be uncertain. (If its noon in June in England then the weather will be warm).
I'm not sure if I follow your second point. Surely necessity is the dual of contingency and possibility is the dual of impossibility. I'm not sure that there is any good distinction to be made here, and I'm not clear on how "dual" is being used. In 3, if E is certain and P(H|E) = 1 then it is just not true that H maybe false. There is no situation where the utterance "H maybe false" would be anything but misleading.

As for your last point if you accept the others as necessary then I'm happy. You're right about the Mozart one, I'm not really certain of it. But not for the reasons you give. The inference is false if Mozart wrote one piece of music that is not Classical, and for all I know he did. However if Mozart only wrote classical music, then the inference is necessary, even though counterfactually he could have written something else. I think, as we discussed this before, this can be analysed in terms of deleting facts from our knowledge base. eg. If we didn't know that M only wrote C, then it would be possible, given what else we know about M, that he wrote F. The ways the world could be is not coextensive with the ways the world could have been.
I guess with the pre Laplacians and Einstein and Frege I think alethic modality is bunk. My main argument is non epistemically P (A\A) = 1 for all propositions. God does not play dice.

1:43 PM  
Anonymous Anonymous said...

Don't confuse the notions of necessary (contingent) with certain (uncertain) or a priori (a posteriori) or analytic (synthetic) or rational (empirical).

If Bernoulli uses such terminology interchangeably, this is apt to confuse and is good reason to stay away from him.

Also, open sentences don't have modal status; they don't even have truth-values.

5:25 PM  
Blogger bloggin the Question said...

I am making no such confusion:
the objects of certainty and uncertainty are beliefs
A belief is certain when there is no doubt.
The objects of necessity and contingency are propositions, or inferences.
A proposition is necessary if it is true in all cases, or, to put it another way, if it couldn't have been otherwise.
A priori is a way of coming to know something. This is perhaps the hardest to characterise, perhaps because it is dodgy, as Williamson says. Ordinarily a priori reasoning is when you add to your stock of knowledge without further observation. eg. if you know that two internal angels of a triangle are 60 degrees a piece, you can deduce a priori that the third is 60 degrees, meaning simply that you do not have to measure it to find out. Of course you would have to assume an axiom of Euclidian geometry than is demonstrably false so it should be clear that a priori reasoning is fallible and should not be confused with necessity or certainty.
I don't want to go into rational/empirical or analytic/synthetic since I don't see how these distinctions are supposed to work, which is a reasonable avowal of ignorance on my part since many people think these distinctions can't be made. For example, I think it perfectly rational to believe that a wine glass will break if dropped from a great height onto a diamond slab. I am happy to say that this is an empirical fact, though I have never experienced a single instance and probably never will. I am happy also to say that it follows from my concepts of diamond and wine glass and great height. It is certainly a claim I can make from my armchair. But it is neither necessary nor certain. Once "great height" was specified and the type of glass specified and a diamond slab created, then I would not be certain that every glass would break. I could still accept that in fact it was necessary, though I myself am not certain. This would be a matter of how many glasses I would get through before I gave up hope that one wouldn't break. Of course, I'm still in my armchair, and there is no diamond slab and never will be.

Necessity and certainty and a priori reasoning are relative to a body of beliefs or propositions. In the seminar Papineau said that "beliefs" was too subjective and wanted to amend it to "truths". He was defining necessity in terms of counterfactuals. Was it necessary that I was born of my parents? Necessity means "it couldn't have been otherwise". So the argument for the necessity of my parents is that counterfactually if I had had different parents I wouldn't have been me. Since this seems to be a contradiction: I wouldn't have been me, then it is necessary that I had my parents since it couldn't have been otherwise. But now we can wonder what the argument for this counterfactual is:
If I had had different parents, I wouldn't have been me?
For the whole edifice to work, we can't appeal to necessity to answer this question. The answer to this question has deep moral and political implications. I'm with Hume: when I look into myself I don't find anything that corresponds to my self. So how can it be that I have any idea whether my self is necessarily attached to the accident of my birth, or my genes or my family name? The whole propostion is a dangerous myth that leads to egoism, aristocracy, racism and crime. Kripke when confronted with Jesus's advice to love thy neighbour as thy self would respond by his own logic that what Jesus was asking him to do was inconsistent since it is a necessary truth that his neighbour is not himself. Any empathy requires counterfactuals like this:
If I were her, I would want someone to come to my aid.
Is this counterfactual necessarily true since the antecedent is necessarily false? We must take a stance against any over enthusiastic logicians who try and rule out empathy and love as illogical.
Conclusion: the counterfactual "If I had different parents I wouldn't have been me" is contingent.

2:03 PM  

Post a Comment

<< Home