This focuses on the logical-empiricism work of analyzing the confirmation-and-logic of generalizations by observations of their instances. The problem = how is it that repeated observations of black ravens can confirm the generalizations that all ravens are black?
A simple solution would be that if we observe a large number of black ravens and no nonblack ones then at least we are cutting down the number of ways in which the hypothesis that all ravens are black might be wrong. As we see each raven, that is one less raven that might fail to fit the theory. The problem with this solution is the case of generalizations that cover an infinite number of instances. For each raven we see would not decrease the number of ravens that might fail to fit the theory. Another problem is with cases of projection as while each raven might decrease the number of ways a generalization might be false, it does not tell us anything about what to expect with the next raven we see.
Hempel’s solution
The Raven’s problem is based on the following points of logic =
- any observation of F that is also G supports the generalization All F’s are G’s
- any evidence that confirms a hypothesis H also confirms any hypothesis that is logically equivalent to H
- Logical equivalence = if H is logically equivalent to H* then it is impossible for H to be true but H* to be false, and vice versa
The hypothesis H “all ravens are black” is logically equivalent to H* “all nonblack things are non-ravens.”
If you reformulate the hypothesis to its logical equivalence (H*), then anything not black that is not a raven counts as evidence in favor for the hypothesis H. Therefore, a white shoe confirms the hypothesis H. This is paradoxical because while it may be “logically correct”, it seems intuitively wrong.
For Hempel, this conclusion (any non-black non-raven thing confirms the hypothesis that all ravens are black) is acceptable and it is our intuition that is wrong. Every sighting of a non-black non-raven does support, even a little bit, the hypothesis that all ravens are black. In fact, Hempel believes that “All Fs are Gs” is not a statement about Fs but a statement about everything in the universe.
I.J Good’s solution
Another way to look at the Raven’s problem is that observing a non-black non-raven or a black raven may or may not confirm the hypothesis “all ravens are black”, and that what counts as evidence in favor of the hypothesis depends on other factors.
This response is based on the issue of holism about testing, and demonstrates that logical equivalence is not sufficient as evidence for a hypothesis.
Good also points out that logical-empiricism examples are artificially simplified; no biologist would consider whether seeing a thousand black ravens makes it likely for all ravens to be black, as we know from genetics and ornithology that there can be variation (albino ravens) if we have seen no other colored ravens.
Context about the world is also an important factor. Consider the two hypothesis =
- all ravens are black, and extremely rare
- all ravens are black, few are white, and ravens are common To see a black raven would support hypothesis (2) rather than (1), for if all ravens are black, we would not see any because they are rare. Similarly, a white shoe may or may not confirm a hypothesis, depending on what else we know.
Whether a black raven or a white shoe confirms the hypothesis “all ravens are black” also depend on the order in which you learn the properties of the object. For example, knowing that object is not a raven, it would be irrelevant to the hypothesis what color it is. But, knowing that there is a white object, it becomes relevant to the hypothesis whether the object is a raven.
Hempel’s response to Good’s solution - does context matter?
Hempel’s response to Good’s argument that other factors are needed is that Hempel wanted to analyze the relation of confirmation that exists just between a hypothesis and the observation itself, regardless of the extra information we might have, or the order in which observations are made.
It could be said that there is no such relation; that we cannot know whether an observation of a black raven confirms the generalization unless we have context of the observation or other underlying assumptions.