Paradox Of The Ravens (Confirmation Paradox)

[michaellevenson]

Statement R " All ravens are black" is logically equivalent to;
Statement R2 " Nothing which is not black is a raven."
A white pen confirms R2 but surely does not confirm R, although R says the same as R2.
To say R is logically equivalent to R2 is to say that in every possible situation in which one is true so is the other. R2 which is the "contrapositive" of R has the same content.
A generalisation like R - all ravens are black- is supported by finding confirming instances of black ravens. And accordingly it would seem that R2- nothing which is not black is a raven- is supported by confirming instances of things which are neither black nor ravens, like white pens. But a white pen does not seem to support - all ravens are black. Most of the things we see are neither black nor ravens. Does each of these really add to our support of this generalisation?

 

[michaellevenson]

Spoiler

One response, that of Carl Hempel who devised the paradox in the publication "Mind" in 1945, is to insist that a white pen does confirm R in that it gives it some support, or confirmation as the term is used in confirmation theory.
The trouble is it seems , that a white pen should confirm R to the same extent as it confirms R2, and at first sight it does not.
But how is the best way to confirm R2? Looking at things that are not black will not get you very far, since they are so numerous and varied. Compare " nothing which doesn't have two legs is a man." You could look at thousands of things without two legs without coming across a one- legged man.
The best way to confirm R2 would be to look for ravens and see what colour they were, since there are far fewer ravens than non- ravens.
So the assumption that the best way to confirm generalisations of the form ," all As are B "is always to find confirming instances, instances of As which are B is untenable.
This is particularly obvious in a case like," all ravens live outside Rutland." Far from confirming this statement, the sighting of ravens outside Rutland particularly in adjoining counties with similar climate and environs would tend to disconfirm it.
Unless we have some special reason for excluding them from Rutland, the more pervasive their presence in surrounding areas the less likely they are to be absent from the tiny county of Rutland.
The unreliability of mere accumulation of confirming instances was dramatically illustrated by Bertrand Russell with his example of the chicken whose neck is wrung. We can imagine the chicken fed day after day by the farmer. As the days go by the chicken's expectation that it will be fed every day grows firmer , until one day the farmer comes and wrings its neck.
In short confirmation is not accumulation of confirming instances. In particular we need to take into account other background knowledge, in the case of ravens, colour, this background knowledge will include the fact that birds plumage serves to protect their species by camouflaging them, otherwise they would have been killed off. So it is important to look for ravens in different environments- temperate, tropical, snowy, than to accumulate more evidence of ravens in our own environment. For all we know polar ones might be white. And once relevant background knowledge is taken into account, any apparent difference in confirmation between R and R2 will tend to disappear.

 

[michaellevenson]

From the book