Now the problem resulting from these two claims, known as the "raven paradox," can be seen when we consider that the universal statementClearly the HD theorist has the burden of explicating what sort of
evidence is alleged to "confirm" a hypothesis. For empiricists the
evidence must of course be empirical, something that can be
observed. However, all that is observed, as reported in
observation statements, are particular instances.
Hempel's basic idea was the obvious one that a hypothetical law, which is of course universal (and so, because of the problem of induction, cannot be proved by inductive inference from observation), is "confirmed" by each "positive instance," i.e., each instance in which what the hypothesis says is universally so, is found by observation to be so. [This is sometimes known as the "Nicod Criterion" after the name of the logician who first proposed this formulation.] Thus, the stock example of a lawlike universal statement, "All ravens are black." is confirmed by each instance of a black raven which is observed. In other words, our rational justification for accepting as a law the universal claim that all ravens are black, is based on the evidence of particular observed black ravens.
However, the HD advocate also wants to be able to claim that if he
is justified in accepting a law as confirmed, then everything that
can be validly deduced from that law is equally justified. In
other words, any evidence that confirms a hypothesis confirms any
other hypothesis which can be validly deduced from that original one.
The HD theorist must accept this assumption because he wants to be able to make the relationship between evidence and laws a logical relationship of deductive entailment or implication. Of course this goes with the DN model of explanation, according to which "higher level" laws explain "lower level empirical laws" (and particualr observed instances of the regularities expressed by such empirical laws) precisely because the lower level laws can be validly deduced from the higher. Thus if we are to have any rational grounds for accepting such explanations, evidence in favor of any given general law must also be accepted as evidence for any other statement which can be validly deduced from that statement.
is logically equivalent to the hypothesis that "All ravens are black." in the formal sense that each can be validly deduced from the other. [This is so because of the logical principle known as "contraposition" in traditional logic or as "transposition" in symbolic logic.] Now a positive instance of the hypothesis that "All non-black things are non-ravens," would be anything that is neither black nor a raven, for example a white piece of chalk. One may very well agree that a white piece of chalk is evidence which confirms that hypothesis that "All non-black things are non-ravens." But since that hypothesis is logically equivalent to the hypothesis that "All ravens are black," whatever confirms the one, confirms the other.
Thus on this analysis of the relationship between evidence and the laws that are confirmed by the evidence we are inevitably led to conclude that that same white piece of chalk also is evidence which confirms the hypothesis that "All ravens are black." While it would surelybe rational to regard the ornithologist's particular observations of black ravens as evidence for claiming that all ravens are black, it seems preposterous to regard observation of a white piece of chalk as evidence for a hypothesis about birds! Yet the HDist seems to be in the bind of having to agree that the justificatory work of such "indoor ornithologists" is on a logical par with the evidence presented by the observation of birds in the bush.