"The Day the Ravens Left the Tower"

Several years ago, I had the opportunity to speak at a one of the Risky Business conferences, which were a series of conferences whose sole purpose was to share experiences and ideas from different high-risk industries, all with the goal of improving safety and outcomes in the health care industry.  The conferences were started by two pediatric critical care specialists named Allan Goldman and Peter Laussen and a British Airways pilot named Guy Hirst.  Many of these conferences were held in London, England.  Unfortunately, I don't think that they've had a conference since the COVID-19 pandemic.  Regardless, I would have to say that attending this conference was truly one of the highlights of my career, at least up to that point.  I've posted a couple of times about the conference (see "Risky Business" and "Fallor, ergo sum"), which obviously made a big impression on me.  

As one of the invited speakers (actually I was an invited speaker at a joint pediatric patient safety conference held at the same time), I was invited to attend the Ceremony of the Keys at the Tower of London.  Every night for the past several centuries, the Chief Yeoman Warder of the Queen's Royal Guard by soldiers as he locks up the fortress.  It was simply amazing!  The members of the Queen's Royal Guard (the legendary Beefeaters) also gave us a tour, and we were introduced to the famous Tower ravens.  Legend has it that "if the Tower of London ravens are lost or fly away, the Crown will fall and Britain with it" (the legend is the subject of an awesome song from the 1980's "The Day The Ravens Left The Tower" by The Alarm).  As you can imagine, the ravens are very well-cared for!

I don't know about the legend, but there is also a famous paradox that involves ravens, called simply the "raven paradox".  The German philosopher Carl Hempel first discussed this paradox in a 1965 essay entitled "Studies in the Logic of Confirmation".  The paradox has to do with inductive reasoning (see my post on induction versus deduction, "Elementary, my dear Watson" for more).  Remember, induction moves from the specific to the general, while deduction moves from the general to the specific (syllogisms, introduced in my last post, are examples of deduction).  

Suppose you see a raven (maybe at the Tower of London) and note that it is black.  You then see another raven, maybe in a different location or perhaps in the same location on a different day.  Again, you note that these ravens are black too.  After seeing several ravens and noting that all of them are black, you make the inductive argument, "All ravens are black."  Essentially, you have followed the scientific method by (1) make an observation, (2) form a hypothesis, (3) test the hypothesis, and (4) generate a conclusion.  

Here is where things get interesting (at least to me).  There is another side to this argument.  If you accept the statement that "all ravens are black", then you can logically accept the statement (by induction) that "if an object is a raven, then it is black."  Similarly, you can also logically accept the statement (this is called a contrapositive statement), "If an object isn't black, it's not a raven."  You are essentially following the logic, "If A, then B" is an equivalent statement to "If not B, then not A."

Here's the problem (and the reason why this is called the "raven paradox").  Suppose you now go outside and pick a green apple off the tree in your backyard.  The object in your hand is not black, so it's not a raven.  Well, of course that makes sense, right?  But hold on, I said above that the two statements "If A, then B" and "If not B, then not A" are equivalent.  So, by saying that "the green apple is not black, so it's not a raven" is functionally equivalent to saying that "all ravens are black".  Moreover, it doesn't have to be a green apple (apparently experts in logic like green apples) - it could be a red sports car, the blue sky, the green grass.  Whatever object you see that is not black and therefore not a raven is strengthening your original statement that "all ravens are black."  And therein lies the paradox.  We have actually strengthened our original hypothesis by finding a green apple!

The myriad ways that individuals over the years have attempted to resolve this paradox is even more complicated and confusing, so I think I will just stop here.  My point in all of this is to foster some interest in exploring further the very fascinating (at least in my opinion) discipline of formal logic, which is a topic that I hope to return to in future posts.