Maher made Good's argument more precise by using Carnap's theory of induction to formalize the notion that if there is one raven, then it is likely that there are many. Maher's argument considers a universe of exactly two objects, each of which is very unlikely to be a raven (a one in a thousand chance) and reasonably unlikely to be black (a one in ten chance). Using Carnap's formula for induction, he finds that the probability that all ravens are black decreases from 0.9985 to 0.8995 when it is discovered that one of the two objects is a black raven. Maher concludes that not only is the paradoxical conclusion true, but that Nicod's criterion is false in the absence of background knowledge (except for the knowledge that the number of objects in the universe is two and that ravens are less likely than black things). Distinguished predicates Quine argued that the solution to the paradox lies in the recognition that certain predicates, which he called natural kinds, have a distinguished status with respect to induction. This can be illustrated with Nelson Goodman's example of the predicate grue. An object is grue if it is blue before (say) and green afterwards. Clearly, we expect objects that were blue before to remain blue afterwards, but we do not expect the objects that were found to be grue before to be blue after , since after they would be green. Quine's explanation is that "blue" is a natural kind; a privileged predicate we can use for induction, while "grue" is not a natural kind and using induction with it leads to error. This suggests a resolution to the paradox – Nicod's criterion is true for natural kinds, such as "blue" and "black", but is false for artificially contrived predicates, such as "grue" or "non-raven". The paradox arises, according to this resolution, because we implicitly interpret Nicod's criterion as applying to all predicates when in fact it only applies to natural kinds. Another approach, which favours specific predicates over others, was taken by Hintikka. Hintikka was motivated to find a Bayesian approach to the paradox that did not make use of knowledge about the relative frequencies of ravens and black things. Arguments concerning relative frequencies, he contends, cannot always account for the perceived irrelevance of evidence consisting of observations of objects of type A for the purposes of learning about objects of type not-A.