"Grue" and "Third Child" Are Sometimes Projectible

The observation that some batch of emeralds is green is evidence for the hypothesis (K) that all emeralds are green, and is not evidence for the hypothesis (H) that all emeralds are grue. But this need not be the case. Suppose we lived in a world in which the spectral reflectance curve of everything that comes into existence, after a certain length of time n, shifts some specified amount. In particular, the shift is such that, after a duration of n, everything that comes into existence as a green object becomes blue. Suppose, further, that no emeralds naturally form in this world. Then, at time t – n, Jack synthesizes the first batch of emeralds ever to come into being in this world. Jack observes that the emeralds are green.

Isn’t it the case, here, that Jack’s observation is evidence for H, but not for K? Isn’t it the case, here, that “grue” is projectible over objects created at t – n?

A similar and perhaps slightly less ridiculous imaginary case would be a nearby possible world in which birth order strongly impacted the way we form friendships, so that people with the same number of older siblings were much more likely to be friends. Then if friends are more likely to be amongst one another than with others, then the observation that five people in a room of thirty are third children is evidence for the hypothesis that (at least most of) the other twenty five are also third children.

What are the consequences of this? Well, if “grue” and “third child” are projectible when we have certain background information or given certain background conditions* and unprojectible when our information or conditions are otherwise, then we sometimes need certain information about our own information or the condition of the world in order to determine whether a hypothesis or predicate is projectible. If we want to maintain that claims about the projectibility of a hypothesis or predicate are a priori, then we will have to relativize “projectible” to a specification of the condition of the world or our own information (and even that might not work). Otherwise, we will have to say that claims about the projectibility of a hypothesis or predicate are a posteriori, and that the information about our own background information or about the condition of the world is somehow evidence for the projectibility claim. Either way, the most important consequence is that the best theories of projectibility cannot distinguish the projectible from the unprojectible solely on the basis of necessary or irreducibly monadic features of given hypotheses or predicates.

Note also that, in Jack’s world, in populations of objects existing for a duration of n or longer, then we can only project normal color predicates (e.g. “green”/“blue” – not “grue”/“bleen”) from samples. So, in this case, even within a given world, sometimes “green” will be projectible and sometimes “grue” will be projectible. This seems to have nothing to do with how entrenched “green” and “grue” are in the world.
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* - I say “background information or given certain background conditions” because it is not clear what is making “grue” and “third child” projectible in these scenarios – that they have certain weird features or that we know they have the weird features.