Nomic dependencies & Contrary-to-fact Conditionals

Consider Dretske's measles example (from page 74 in his Knowldege and the Flow of Information (MIT/Bradford: 1981) ): since the question of whether Alice's being one of Herman's children carries the information that she has the measles is a question about conditional probabilities, we must be careful about our specification of the condition, the antecedent. Although we are to suppose that it is a true generalization that all of Herman's children have the measles, since that is a coincidence, we can just as well suppose that Alice is an only child with the measles. It is of course true that the conditional probability of Alice's having measles given that she has the measles is 1; but that is not relevant to the question Dretske raises. In Dretske's example, the question is whether Alice's being Herman's child carries the information that she has measles. And so the relevant condition in this example is simply Alice's being Herman's child. While it is in fact true that Alice has the measles, that isn't part of the condition: for the question is, "how probable is the one state of affairs given some other state of affairs," not "how probable is the one state of affairs given that same state of affairs." Thus, given that Alice is Herman's child, she nevertheless might have been measle-free. Since it is possible for Alice not to have had the measles despite being Herman's child, there is not the right kind of connection between her being his child and her having measles to underwrite an informational relationship. In Dretske's original example, the fact of all Herman's children having the measles was no more relevant than Alice's happening to have measles.
Now consider a variant of Dretske's example: suppose that both Herman and his wife, Betsy, have the genetic carrier for hemophelia; as a result, all of their (natural) children have hemophelia. What is the probability of Alice's having hemophilia given that she is one of the (natural) children of Herman and Betsy? Here, unlike the former example, we can answer "one." Notice that in this second example, it is true that
If Alice were not hemophilic, she wouldn't be one of Herman's and Betsy's natural children;
actually, I imagine that we would typically phrase this somewhat differently, saying
If Alice were not hemophilic, she could not be one of Herman's and Betsy's natural children.
In other words, to suppose that Alice isn't hemophilic is to suppose that she is not a (natural) child of Herman and Betsy. But returning to the earlier example, to suppose in those circumstances that Alice does not have the measles is not to suppose that she is not Herman's child; in that earlier example,
It is not true that were Alice not to have the measles, she would not be one Herman's children.
Thus,
Even if Alice were not to have the measles, she would still be one of Herman's children.
Notice that what makes it true that all of Herman's and Betsy's (natural) children must have hemophilia is logically independent of Alice's having hemophilia; the genetic condition existed prior to, and might have been discovered before, Alice's conception . Dretske says that the second sort of correlation or generality (here, based upon genetic laws) is special because it involves a nomic dependency between two states of affairs.
Consider two conditional ("if-then") sentences which, in the decade in which Ayer's Foundations of Empirical Knowledge was written, logicians used automatically to classify as being of the material implication persuasion:

1. If Boardman is a (bufonid) toad, he has warty bumps all over his non-moist skin. [According to the "Q &A" column in the New York Times' Science Times section (11-15-94, p. B8), I must add "bufonid" to be safe in this example.]
Compare that conditional sentence to this second one:
2. If Boardman is a (bufonid) toad, he has feathers.
If we were to understand these sentences as expressing material implication, we would have to say that both are true--since their antecedents are false. But, of course, we should normally understand the sentences as contrary-to-fact conditionals, and we should standardly and properly express them this way:
1'. If Boardman were a (bufonid) toad, he would have warty bumps all over his non-moist skin.
2'. If Boardman were a (bufonid) toad, he would have feathers.
If we consider these subjunctive conditionals (notice the plural verb used with the singular subject in the antecedent, and notice the use of "would" in the consequent--tell-tale marks of a subjunctive conditional), then we should realize that while the first is true, the second is false--notwithstanding the fact that it is false that Boardman is a toad (bufonid or otherwise). These sentences are not correctly understood in accordance with the material implication of symbolic logic, since their having false antecedents does not automatically make them true. What makes the first sentence true is not that Boardman is not a toad, but that (bufonid) toads must have warty bumps over their non-moist skin; so
If Boardman has no warty bumps all over his non-moist skin, he cannot be a (bufonid) toad.
Now suppose that Marie is the only woman in the course this term, and that one day, being ill, she does not come to class. On that day the following is a true generalization about the members of our class:
Everyone attending the class today is male.
We can, of course, use the generalization as a premise in logical inference:
Everyone in class today is male.
Marie is not male.
Therefore, Marie is not in class today.
No one, least of all Dretske, is challenging the matter of logic which has just been illustrated. But in the last decades, philosophers have come to recognize that some general assertions are special, and that one mark of their special nature is that they "support" or imply contrary-to-fact conditionals while mere statements of true correlation do not. Consider the true generalization about the class members of that fateful day; surely we could not infer this:
Had Marie been in class that day, she would have been male.
Notice that our true generalization has an equivalent rephrasing, which is called "contraposition":
No one who is not male was in class today.
From the fact that Boardman was not absent from class, we could conclude that he is not non-male. But could we also conclude that
Had Boardman been female, he (she?) would not have been in class ?
Surely the fact that only males were in class that day was a complete coincidence: there was not some law-like principle operating which would have made it true that had X been in class, X would have been male, or had X not been male, X would not have been in class. In our example, although it was coincidentally true that all the people in class were male, there was no sort of law-like mechanism which made one's membership in the class dependent upon one's sex. So the generalization, although true, will not support contrary-to-fact conditionals. But also notice that we can imagine a state of affairs surrounding the class in Main Hall on that fateful day in which such contrary-to-fact conditional would be supported: suppose some Limbaugh-like radical-anti-feminists invade Main Hall in the early morning prior to the class and install fail-proof machines at all the doors and windows which vaporize any females who try to enter. As a result of the installation of this machinery, it would then have been true that, on that fateful day,
Had Boardman been female, he (she?) would not have been in class.
So some general statements will support contrary-to-fact conditionals: for example, the general statement about toads' having warty bumps all over their non-moist skins. When philosophers have wondered why some general statements will support counterfactuals, they have answered that there must be something special about those general statements, that they were expressing something which in some sense must be true, rather than something that merely happens to be true. And therefore, the general assertions which do support them have been called nomic--i.e., statements of lawful relationships.
Incidentally, municipal laws (as well as natural laws of science) seem to support contrary-to-fact claims. Suppose that a speed trap is set up on highway 41 just south of Appleton, and Boardman gets caught for speeding. Then one can say about Boardman,
Had he not been driving over the speed limit, he would not have been arrested.
But suppose on the day on which Boardman is arrested, it is true by sheer coincidence that everyone who is arrested has the letter "a" in his last name. So it is true that on that fateful day, no one is arrested who lacks an "a" in his last name. But could it be plausibly claimed that
Had Boardman's last name not been spelled with an "a," he wouldn't have been arrested?
Surely not: the general claim, while true, did not express a lawful relationship; spelling wasn't a criterion used in Boardman' arrest; and so despite the true alphabetic generalization we can truly say
Even if Boardman's last name had lacked an "a" he would still have been arrested.
A's having some unique set of characteristics does not automatically make the set carry information about A.