I see a green apple and yet all Ravens are not black

Early in the morning, we often offer green apples together with coffee before the game drive. I see them all piled up on their plate. We also have pied crows around the reserve, we can often see them perching on trees or poles, and as their name suggests, their colour is black and white. How is that relevant to the green apples? Well, we’ll see that now.
Not long ago I was on a game drive, the weather was nice, and the bush was rather quiet, it was a very relaxing early winter drive. We were getting closer to a small knob-thorn thicket and as a crow came flying in our direction, a forked-tailed drongo sprang from the intertwined branches to the crow, harassing it until it flew away. We followed them circling around in the sky, eventually, the unimpressed crow came back to perch on the tree next to our car. A typical mobbing behaviour from the drongo, not unknown to the crow either, as they also do it to bigger birds!
So, we had that crow perching a few meters away from us, exposing its white belly, and one of my guests asked me: “Is that a magpie?”
As the crow started cawing, she got suddenly a bit confused: “It looks like a magpie, but it sounds like a crow”.
I just replied: “Yes, it is a crow, a pied crow”. But I had this kind of reaction before. Somehow for most people, crows can only be black, just like the grass is green, and if it is not fully black, it must be something else. Crows are easily overlooked because they are just crows, but I find them always interesting to watch, sometimes very useful as they can lead us to a carcass, and also, being black and white, they remind me and prove the point, of Raven’s paradox.
Now, what is Raven’s paradox? More than a mathematical paradox, Raven’s paradox is a philosophical observation imagined by the German philosopher Carl Gustav Hempel in his essay “Studies in the Logic of Confirmation”, published in the 1940s. It questions the scientific method and especially inductive reasoning, which means making broad generalisations over specific observations. It goes like this:
Observing a green apple increases the likelihood of all ravens being black.
What does it mean? It starts with a simple observation: a black raven. Let’s say you live in a place where all the ravens (and crows) that you see are black. You can conclude that this is more than a coincidence and form a hypothesis: All ravens are black. This is now a hypothesis based on your observation. The next step is to either confirm or refute the hypothesis with experimentation. Here, it is very straightforward: observing as many ravens as possible and confirming that they are all black.
This is of course impossible. To absolutely confirm the hypothesis, it would require counting all ravens in the world, including all the ones that are already dead, and also the ones that are still yet to be born. This is the first impassable limit of the experiment. However, it is easy to consider that each new observation of a black raven tends to confirm the hypothesis. And if no raven of a different colour suddenly appears, it feels right to give our hypothesis the status of natural law.
Another question is raised, and it is whether this is logical or not.
In the field of logic, the statement “All ravens are black“ has the form of a conditional, that is: if A then B. If a given object is a raven, then that object is black.
According to the laws of logic, a conditional is equivalent to its contrapositive: if not B, then not A.
The statement “if I work at Thanda, then I work in KZN” is logically equivalent to the statement “if I do not work in KZN, then I do not work at Thanda”.
Thus “All ravens are black” has the equivalent “All non-black things are non-ravens”, or “if an object isn’t black, then it is not a raven.
Now it gets a bit tricky because it means that if every sighting of a black raven confirms our hypothesis, it is also equally confirmed by every sighting of any object that is not black and not a raven. I wear a khaki uniform, and it is not a raven: confirmation. A rock is an ochre, my game viewer is green, and the sky is blue… all these statements confirm the hypothesis that all ravens are black.
Intuitively, it seems silly. There is a countless number of objects that are not black and not ravens. And how is any object that is not black, like the aforementioned green apple, relevant to a raven? Besides, we know that at some point, one egg will produce a leucistic or an albino raven. They are of course extremely difficult to observe, but just one white raven, even if it is never found, would disprove the hypothesis. Worse, we could also imagine that a biologist somewhere in the world only sees one raven in his/her life, and that is a leucistic one. He/She could then deduce that ravens are, first, very rare, and then, all white. And, following the laws of logic, every non-white, non-raven thing in the universe would strengthen that hypothesis too! So, the same reasoning can confirm two radically opposed hypotheses. And here you have your paradox.
Why is the paradox interesting? You will find many different ways to solve it, but as I said earlier, I never took it as a mathematical paradox that needed to be solved. And I would even say that if you try to mathematically solve it, you are missing the point. It was originally written as an amusing, absurd thought experiment to remind scientists that they must constantly probe and test the steps of the established scientific processes and stay away from broad generalisations. No theory, however, established, should be immune to challenge or debate, and science must adapt to change as new evidence is uncovered.
And what does it say for us, non-scientists? To keep our minds open, accept change, and not dwell on our certainties. Sure, all ravens can be black, until you come to South Africa and you see White-necked ravens and Pied crows!
Personally, I can see Raven’s paradox as some painting of Magritte hung somewhere on a wall in my brain, as a reminder to keep looking at the world with fresh eyes and be ready to always be surprised!
Story by: Vincent Hindson