Carl Hempel famously crystallised an obstruction to the formalisation of inductive reasoning as the “Raven paradox”: Suppose I am an ornithologist, concerned to prove my world-shaking hypothesis, “All ravens are black”. I could go out into the field with binoculars and observe ravens. Suppose that over the course of the week I see 198 black ravens, 0 white ravens, 0 green ravens, and so on. These are strong data in favour of my hypothesis, and my publication in the Journal of Chromo-ornithology is assured. (And if they turn it down, I’ve heard there are numerous black studies journals…) But it gets cold out in the field, and sometimes damp, so I could reason as follows: “‘All ravens are black’ is equivalent to ‘all non-black objects are not ravens’.” And in my warm and dry study there may be no ravens, but there are many non-black objects. So I catalogue all the pink erasers and yellow textbooks and white mugs, and list them all as evidence for my hypothesis.
The status of this charming story as a paradox depends on the belief that no one would actually make such an inference. Behold, the president of the United States: Last week the special prosecutor for matters related to Russian interference with the 2016 US election released an indictment of 13 Russians. None of them had worked with the Trump campaign. Trump’s response:
In other words, while it is proving too difficult to collect proof of the contention “No anti-American voter fraud was performed by Trump,” he is collecting evidence that “There were actions not performed by Trump that were anti-American voter fraud.”
Common Infirmities 