On Nicod's Condition, Rules of Induction and the Raven Paradox
  Philosophers writing about the ravens paradox often note that Nicod's
Condition (NC) holds given some set of background information, and fails to
hold against others, but rarely go any further. That is, it is usually not
explored which background information makes NC true or false. The present paper
aims to fill this gap. For us, "(objective) background knowledge" is restricted
to information that can be expressed as probability events. Any other
configuration is regarded as being subjective and a property of the a priori
probability distribution. We study NC in two specific settings. In the first
case, a complete description of some individuals is known, e.g. one knows of
each of a group of individuals whether they are black and whether they are
ravens. In the second case, the number of individuals having a particular
property is given, e.g. one knows how many ravens or how many black things
there are (in the relevant population). While some of the most famous answers
to the paradox are measure-dependent, our discussion is not restricted to any
particular probability measure. Our most interesting result is that in the
second setting, NC violates a simple kind of inductive inference (namely
projectability). Since relative to NC, this latter rule is more closely related
to, and more directly justified by our intuitive notion of inductive reasoning,
this tension makes a case against the plausibility of NC. In the end, we
suggest that the informal representation of NC may seem to be intuitively
plausible because it can easily be mistaken for reasoning by analogy.
