Dear Kevin,
I truly liked your essay (don't look for my mark, I'll rate all essays at the end, I just say this not to be confounded with some other voter).
In particular, I liked the distinction between contingent and determined laws, a matter to which I also dedicated quite some thought, only to arrive at the same impression as you: that the division between them is not truly sharp. One could claim that determined laws are fixed by the requirement of consistency. Yet, consistency implies that no two realities, one the opposite of the other, can be derived from the theory. Yet, the notion of 'opposite' is not always clear. We are used to thinking that any statement has its opposite, that is the case in the formal logical systems we usually employ in mathematics. But what is the opposite of a physical reality? What should be the two things that cannot simultaneously happen in the universe? If we could answer this question, we might be able to deduce which should be the determined laws. In fact, the more we know about the world (going up to truly high speeds, or to really tiny or huge scales) the more it seems that weird things can happen, things that in earlier times would have been though of impossible, almost, of inconsistent. We now know that the notion of simultaneity is observer-dependent, in earlier times that would have been considered illogical, perhaps even inconsistent. We also know that in the quantum realm, what happens or does not happen depends on the observer, and that unobserved variables have no defined values. Again, a fact that in earlier times would have seemed inconsistent.
In my essay, I propose a parallelism between mathematical and physical theories, a parallelism that tries to separate contingent from determined laws. I claim that only when the separation is evident we have a conceptual theory. Yet, I agree with you that there is no guarantee that the distinction can be made on sharp theoretical grounds. Nothing ensures we can make the distinction in the universe we know, and nothing guarantees that it can be done in any other possible universe. If the separation between the two types of laws cannot be done, the universe in question will still exist, but we will not be able to say we have a conceptual theory about it. The whole point is, of course, is to define what a possible universe is. But that is a tricky question. We only live once, and we only gather evidence once. But no theory can be constructed gathering data in a single trial. So we must parse our evidence into 'similar trials', and from our single experience, construct ensambles that can be used to construct and test theories. Such a construction is only legitimate if we have some prior knowledge of what is similar and what is not. That notion will allow us to group our experience into multiple trials of one single situation. So it would seem that the distinction between what is determined and contingent depends on our priors...
Ok, this message got long. Sorry if the message is not too clear, I'm thinking as I write. Not a very clever stategy, but hey, I'll send it anyway, just to say I liked your thoughts a lot, and that they triggered quite a bit of thinking from my side. But I'm still circling in them, I fear...
Thanks for that!
Inés.