Why a green apple "proves" all ravens are black
In the 1940s, logician Carl Gustav Hempel showed a strange quirk in how we confirm hypotheses. The statement "all ravens are black" is logically equivalent to "all non-black things are non-ravens." Therefore, observing a green apple—which is non-black and not a raven—technically provides inductive evidence that all ravens are black. This logical puzzle forces philosophers to rethink how evidence actually works.
The Common Sense of Confirmation
Scientific inquiry and daily reasoning rely heavily on induction—the process of drawing general conclusions from specific observations. When someone claims that all swans are white or that all metals expand when heated, the natural way to test that claim is to examine swans or heat pieces of metal. Each time an observation aligns with the rule, our confidence in the general statement grows stronger.
In the early twentieth century, French philosopher Jean Nicod formalized this intuitive rule into what logicians call Nicod's criterion. Nicod proposed that observing an object that possesses both the subject property and the predicate property confirms a universal conditional statement. In simpler terms, seeing a raven that is black provides positive evidence for the hypothesis that all ravens are black. Conversely, seeing a raven that is not black completely refutes the claim. Objects that are not ravens, according to this intuitive baseline, should have no bearing whatsoever on the hypothesis.
The Logic of Contrapositives
In the 1940s, the German logician Carl Gustav Hempel identified a striking contradiction emerging from these basic assumptions. Hempel applied a fundamental rule of classical deductive logic known as contraposition. In formal logic, any conditional statement of the form 'All A are B' is strictly equivalent to the statement 'All non-B are non-A.' The two statements necessarily share the exact same truth value under all circumstances.
Applied to ornithology, the hypothesis 'All ravens are black' is logically identical to 'All non-black things are non-ravens.' If the universe contains no counterexamples to the second statement, it contains no counterexamples to the first. Logic also dictates the equivalence condition: any piece of evidence that confirms a given hypothesis must equally confirm any logically equivalent formulation of that hypothesis. If evidence supports one sentence, it must support any sentence that means the exact same thing.