This paper follows the paper of Gaifman (1979), published in Erkenntnis. Two aspects of Gaifman's solution of the raven paradox are unsatisfactory: Firstly, the use of a subjective probability is unsatisfactory because its choice is arbitrary. Secondly, Gaifman's solution is not symmetric concerning an implication and its contraposition.
We shall therefore try to solve the raven paradox in the system of Carnap (1958) in particular with Carnap's c*-function. The fundamental idea we use is Gaifman's idea that the premise of the calculated probabilities must contain the proposition that the proportion of ravens to non-black things is small in our universe. This proposition we symbolize as follows: e~(6) := (R/-1S <-6). a Factually, Gaifman first considers the premise that the proportion of ravens to non-black non-ravens is small in our universe. This premise we symbolize as follows: e;(6) := (R/(-nS ^ -qR) = 8). 2 Gaifman calculates the following probabilities: P (all ravens are black, eg(~) ^ the first n observed ravens are black) P (all ravens are black, e~(8)^ the first n observed nonblacks are non-ravens)
The first of these probabilities calculated by Gaifman does not depend on 8. His solution is that the second probability is always less or equal than the first and for small 6 is considerably less than the first.
This may be quite correct but it shows that the premise eD(g) does not give a solution of the paradox. To get a solution we must have a premise e(6), so that if 6 is low the first probability is higher than the second and vice versa if 6 is high.