Raven Paradox
This is so wrong that even if I explain it in extreme detail and follow the logic step by step, you still want to reject the truth, because it defies common sense so much.
Black Raven
So you saw a lot of black ravens and set up a hypothesis: “All ravens are black.” So if you see another black raven again, your hypothesis is strengthened. If you see a white raven, your hypothesis is falsified.
The mind-bending fact is that
A green apple (Anything non-black non-raven) strengthens the hypothesis too.
(while normally you think that a green apple has nothing to do with black ravens.)
Although many still dispute over this, with some arguing whether a black raven really strengthens the hypothesis (which equally defies our common sense), and whether there are different types of strengthening of a hypothesis, the following argument is quite valid.
This is a highly philosophical question that fundamentally questions the method of science. Here we will talk about why such a paradoxical conclusion can be deductively obtained. These are based on three premises:
(1) Anything that strengthens a hypothesis also strengthens the equivalent of it.
This is easy to accept because if you have an equivalent hypothesis, basically everything that supports or falsifies the hypothesis should also do the same for its equivalent.
(2) The hypothesis “All ravens are black” is equivalent to “All non-black objects are not ravens”.
This needs some time to take in. Let’s draw a Venn diagram:
What the first hypothesis shows is something like this: the raven circle lies completely inside the black things circle.
What the second hypothesis shows is that the raven circle completely does not lie outside the black things circle (which is basically what the first hypothesis says anyway).
(3) A green apple strenghtens the hypothesis “All non-black objects are not ravens.”
Yes! A green apple is (1) not black and (2) not a raven.
Therefore the three premises:
(1) Anything that strengthens a hypothesis also strengthens the equivalent of it.
(2) The hypothesis “All ravens are black” is equivalent to “All non-black objects are not ravens”.
(3) A green apple strengthens the hypothesis “All non-black objects are not ravens.”
lead naturally to the conclusion that
A green apple (Anything non-black non-raven) strengthens the hypothesis too.
It really defies our common sense, but this is really true. Try to rethink whether or not you can trust your common sense!
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