bernoulli and I on necessity
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?