IN THE 1940s a philosopher called Carl Hempel showed that by manipulating the logical statement “all ravens are black”, you could derive the equivalent “all non-black objects are non-ravens”. Such topsy-turvy transformations might seem reason enough to keep philosophers locked up safely on university campuses, where they cannot do too much damage.Now, I'm slightly baffled as to how this is a suprising statement. It certainly seems obvious to me. To illustrate why, let's consider a basic syllogism.
If A then BIn this case, the premise (the if-then statement) is, "All ravens are black," or more formally, "If a bird is a raven, then the bird is black." Therefore any time anyone tells me they're seeing a raven, I can safely assume it is black (neglecting albinos and poor ravens which have been painted blue, or just bumped against Tobias Funke).
A, therefore B
The converse is not necessarily true.
If A then BIf a bird is not a raven, that does not necessarily mean that it is not black. It may be a crow, a vulture, a blackbird, or any of a number of other black birds.
Not A, therefore perhaps B, perhaps not B.
The "topsy-turvy transformation" listed above is to turn that around, and suggest the following syllogism:
If A then B.This just follows logically. Imagine the following exchange.
Not B, therefore not A
"Hey, I see a bird. Is it a raven?"It's just neither topsy nor turvy.
"Dunno is it black?"
"Nope, it's blue"
"Then it ain't a raven (again neglecting the Blue Man Group's pet raven, Gerald)."
Now, Carl Hempel wasn't just noodling about solving trivial non-problems like the one above. He was attempting to improve the logical rules associated with observational science. So his Raven Paradox is not just assuming that we know that all ravens are black, but looking at the case when we are trying to observe whether all ravens are black, and seeing what implications that has for our logical constructions.
Suppose we are trying to figure out whether all ravens are black. One natural consequence would be that all non-black things are not ravens. However, finding 100 ravens and observing that each is black is helpful. Finding 100 things that aren't black, and observing that none are ravens is useless. When finding non-black non-ravens, you are making observations that are consistent with your theory. After all, if your theory is correct, then non-black objects must not be ravens, as proven above. But these observations of non-black non-ravens do little to confirm the main theory regarding black ravens.
It is unsuprising to find things that aren't black that aren't ravens, because it is unsuprising to find things that aren't ravens. Look out your window. In my case, I see trees and cars and leaves and buildings and clouds and the sky. Of the millions of things I see out there, only a very few, some tires, a few bits of roof racks on trucks, and one Jeep Cherokee, are black. None of the things I see are ravens. So I have seen many non-black non-ravens, and a few black non-ravens, but I saw no black ravens, nor non-black ravens. Fully half of the possible states of combined ravenness and blackness are left with no observations from my experiment. I just can't say much about the correlation of ravenness and blackness.
As a scientist, I see that the problem of observing non-black objects to test the black-raven theory is that it fails to exclude competing theories. I may have a competing theory that Blue Man Group has painted all the world's ravens blue as a performance art piece. Observing many blue things and finding that none of them is a raven woulds still do very little to distinguish between the blue-raven theory and the black raven theory.
The point of the Raven Paradox, then, is to show that observations that fit a theory are only useful if they don't fit other theories just as well. Could be of some use to the current debate on String Theory.
Note, my title in no way implies that all illogical things are useless. It does however, imply that logic is useful.