The logic of induction is what most science today utilizes in order to draw conclusions. Inductive logic is that which draws a conclusion that is probably (not necessarily) valid, given that the premises from which the conclusion is drawn are true. With the use of inductive logic, however come select problems. Carl Hempel was a philosopher of the twentieth century, who pointed out one of these problems, or paradoxes; namely, “The Raven Paradox”.
The Raven Paradox concerns with the problem of inductive generalizations and immediate inferences. Hempel uses the example of a raven. Basic facts we know about ravens are that they are black birds. If we observe many instances in which this is true, and none that oppose it, then we usually use this knowledge as inductive support. Thus, all ravens are black birds.
By the rules of contraposition we can therefore also say all non-black birds are non-ravens. To elucidate, contraposition is a kind of immediate inference in which you have a conditional statement “All S are P”, switch the subject and the Predicate, “All P are S”, and apply their complimentary, “All non-P are non-S”. Thus we have two claims:
(1) All ravens are black birds.
(2) All non-black birds are non-ravens.
At first glance, nothing seems wrong with this. In fact, many people use this logic in their daily life, that of immediate inference. To be clear, an immediate inference is an assumption that can be made by only one statement, just as (2) was derived from (1). The two statements are logically equivalent, so there should be nothing wrong with statement (2). So, each time I observe a raven that is black, it supports my first claim. Also, each time I observe something that is a non-black bird, it supports my second claim.
However, when studied closer the paradox arises. The paradox of this inductive logic is that if (1) and (2) are equivalent, then any evidence to support (1) should also support (2), and vice versa. That is to say, anything that is a non-black bird is evidence to the first statement, that all ravens are black birds. Does this seem right? Is the fact that a cardinal is red, thus a non-black bird, support that all ravens are black birds? To go even further, does the fact that my computer is silver support the statement? The laws of immediate inference claim that these statements do, in fact, support the claim that all ravens are black birds.
Hempel is merely demonstrating the potential problems of how we usually think. We make these sort of immediate inferences all of the time and see no problem with it, but when we think about the aforementioned paradox, this circular logic seems redundant. There is not a solution to the Raven paradox, or else it would not be a paradox, but it stands instead to exhibit that there is something “deeply puzzling about the nature of reasoning” (DeWitt 63).
Hempel certainly points out a “flaw” of inductive reasoning (“flaw” is in quotes as it is not a true flaw). Logicians such as Hume and Sextus Empiricus have noted such problems in their work too. Hume agrees with Hempel in that there seems to be a certain disturbing circularity to induction. Hume’s main argument is the human justification for the future (namely that we believe the future will be same/similar to the past due to our experience in the past of this being true). He believes this to be a bit upsetting, as most of us do. The fact of the matter is, this is what inductive reasoning does for us. Not always, but in many cases circularity in inductive reasoning is very apparent.
Empiricus points out another flaw in this problem of immediate inference, not in response to the Raven Paradox, of course, but to the reasoning as a whole. Nonetheless, to compare it to the Raven Paradox, Empiricus points out that inductive reasoning draws universals from particulars, which simply cannot be with absolute certainty. If we do not observe all of the particulars, then we do not know all of them to be confirming evidence, but conversely, it would be impossible, or near it, to observe all the ravens in the world.
Another problem of this paradox seems to be the nature of kind. Surely non-raven-ness and raven-ness are not projectable properties onto any object other than ravens. This distinction does not solve the paradox, however, as the same problem can be applied to other situations with out this problem.
For me, this paradox does exactly what it should; it puzzles me. It makes me feel uneasy that we make such inferences even when they seem ludicrous when we look at them closer. I think it is a rather silly paradox, but I suppose that is the point. I find it disconcerting that this reasoning is valid, and I wish it were not a natural way to infer, but alas, it is. I think that Hempel makes a very good point in his paradox. People seem to unknowingly make these immediate inferences all of the time, and though it is logically sound, it certainly puzzles me when I think about the underlying meaning of saying that all non-black birds are non-ravens.
I do not believe that the paradox is of extreme importance in science. I trust Hempel did not take this as a true threat to the essential logic of science either. Merely because this Raven Paradox holds strong with out a true solution does not mean that contraposition does not work, or that we should abandon use of it.