In the 1940s, the logical empiricist philosopher and epistemologist Carl Gustav Hempel proposed the raven paradox. Hempel sought to illustrate a problem where inductive logic runs counter to intuition, and to show how, as we observe facts that fit our theories, these theories become more powerful. The paradox raises some interesting questions, such as the fact that observing a red apple reinforces our confidence in the belief that all ravens are black. Intrigued? Keep reading!
Carl Gustav Hempel was born in Oranienburg, Germany, in 1905 and became a US citizen in 1937. A philosopher, logical empiricist, and epistemologist, he taught at various universities. He wrote several books that were key to 20th-century epistemology and was the founder of the Deductive-Nomological Model of science.
Throughout his life he developed various enlightening concepts about the nature of scientific explanation, while also mounting a fervent critique of all kinds of “metaphysical” ideas. One of his most interesting (and accessible to the general public) works is the so-called “raven paradox,” also known as the negation paradox or Hempel's paradox.
The black raven paradox
Hempel explained that when people spend time observing facts that fit well within the framework of their theories, they tend to believe that such theory has a greater chance of being true. This makes their confidence in it increase with each new observation that fits the mental framework we have built. This type of reasoning can be summarized in the principle of induction:
If a particular case X consistent with theory T is observed, then the probability that T is true increases.
Remember that induction is a procedure by which we reach, by generalization, a universal law from a certain number, not exhaustive, of particular cases. Hempel himself provides an example of this principle when he proposes as a theory “All ravens are black.”
If we take the trouble to conscientiously examine a large number of ravens (a couple of million or so) and they all turn out to be black, our confidence in the theory “all ravens are black” will increase a little with each observation. So far, the principle of induction seems to go hand in hand with intuition. But Hempel will quickly set out to show us how wrong we are.
From the point of view of cold logic, our statement “all ravens are black” is equivalent to the statement “all non-black things are non-ravens.” This means that if we saw something other than a raven that is not black, our confidence in the belief that all ravens are black should increase. This means, no more no less, that seeing a red apple should make our faith in the color of ravens strengthen. The principle of induction, all of a sudden, no longer seems so aligned with intuition.
Induction seems a reasonable procedure, but sometimes it presents difficulties in its application. The most evident is that we can almost never have absolute certainty of its results, because to achieve it, we would need to examine all the objects referred to in the general statement. In the case of ravens, we would need to have access to (and review) all ravens that exist, have existed, and will exist. Of course, philosophers have attacked the paradox tooth and nail looking for a way for logic to once again coincide with what intuition suggests.
Nelson Goodman, another American philosopher, proposes that the existence of the red apple should only increase our belief in the theory “all non-black things are non-ravens,” but not modify in any way our confidence in the original theory (“all ravens are black”). To complicate things further, Goodman's suggestion has been questioned with the argument that it is not valid to reaffirm two beliefs if you know that both are either true or false at the same time.
Others cling to logic and postulate -perhaps rightly- that it is our intuition that fails. It can also help us solve the paradox the relevance theory proposed by Sperber and Wilson in 1986. According to these authors, we consider information relevant when, by joining with previous assumptions, it provokes cognitive effects or, what is the same, allows us to make inferences that help create new theories or reject previous ones. Obtaining cognitive effects implies a certain mental effort (or cognitive effort) and it seems that the greater this effort, the less relevant the information obtained seems to us. If this is correct and the human mind is really adapted to maximize relevance, Hempel's paradox is resolved, since less cognitive effort is invested in checking ravens than in checking objects of a color other than black and, furthermore, it provides greater cognitive effects.
In any case, what is clear is that this paradox is very important in the development of cognitive research such as that which attempts to create artificial intelligences following the human cognitive model. If we fail to understand the way our brain works, especially at the cognitive level, we will hardly be able to reproduce its functioning.
