This is an essay drafted in response to a question in a Philosophy of Science Course at the local university. The reading in the list is the relevant section of Nelson Goodman’s book Fact, Fiction and Forecast in the 1950s. W V O Quine wrote that it was one of the books published in the year that you really had to read!
The question. Grue and bleen. What are they, why are they a problem, and what do you think we should do about them?
Goodman discovered a “new problem of induction” as he explored a problem of projection of predicates that emerged after the dissolution of the original problem of induction.
The argument of this essay proceeds by placing Goodman’s new problem of induction in the larger context of confirmation theory. The suggestion is that the problem of confirmation may be insoluble and some other approach might be attempted – a program of epistemological pluralism rather like Cartwright’s causal pluralism (another essay topic is Cartwright on causal pluralism).
The green grue problem occurs in Nelson Goodman’s book Fact Fiction and Forecast (1955) under the heading The New Problem of Induction. He started by describing how the original problem of induction is dissolved as follows: In the same way that deductive inferences can be justified by their conformity to general rules, so inductive inferences can be justified by conformity to general rules and “predictions are justified if they conform to valid canons of induction ; and the canons are valid if they accurately codify accepted inductive practices” .
He then found that some problems arise in regard to certain types of prediction or projection as exemplified by his invention of grue emeralds that are green up to some future time t and grue afterwards. My simple-minded thought was to wait until time t and see what happens.
However he finds that his use of these unfamiliar predicates demonstrates a deeper problem. He is not content to put this anomalous situation aside merely for the simpleminded or commonsense reason that we are unlikely to encounter the problem in the normal course of events.
“If our definition works for such hypotheses as are normally employed, isn’t that all we need? In a sense, yes; but only in the sense that we need no definition, no theory of induction, and no philosophy of knowledge at all. We get along well enough without them in daily life and in scientific research. But if we seek a theory at all, we cannot excuse gross anomalies resulting from a proposed theory by pleading that we can avoid them in practice”  my italics
He concludes that this displays “the symptoms of a widespread and destructive malady” namely the unsatisfactory state of the theory of confirmation [80-81].
The original problem of induction was a manifestation of the more general problem of confirmation or justification, it arose in the empirical branch of the epistemology concerning the confirmation of general statements based on particulars. The problem persisted through various iterations of probability theory with Bayesian subjectivism being favoured approach at present.
The theory of inductive confirmation is one of the forms justification of beliefs that has been the major concern of epistemology for ever. The other major form of justification is rationalism or intellectualism (as described in a previous essay on empiricism and rationalism).
Karl Popper challenged the inductive mode of confirmation in Logik Der Forschung 1935 to show that scientists could get along with deductive testing and a theory of conjectural knowledge instead of a theory of justified belief. Popper’s theory is widely rejected and seldom mentioned in books classified as epistemology on the Fisher shelves. In those circles it is not regarded as a theory of knowledge at all.
William W Bartley took up Popper’s response and wrote a great deal about justification and justificationism to take the argument with the inductivists to a deeper level but it never caught on outside the Popper school. The gravitational attraction of the imperative to seek justification has been too strong.
Popper’s concession was to talk about the justification of a critical preference for one theory rather than another on the basis of pluralistic criteria – explanatory power, internal consistency, consistency with other well-tested theories, with the presupposition of a metaphysical research program. This makes a connection with Nancy Cartwright’s theoretical pluralism.
The last part of Goodman’s discussion turns to the problem of projecting from any set of cases to others, like projecting that green emeralds will be green in future. He makes the point against Hume that predictions based on some regularities are valid while some others are not . On the specific matter of green and grue, he notes that “To say that valid predictions are those based on past regularities, without being able to say which regularities, is thus quite pointless.” 
Taking up this issue about which regularities are indeed regular, consider the colour of emeralds. They have the crystal structure of the mineral beryl (Be3Al2(SiO3)6) colored green by trace amounts of chromium and sometimes vanadium [Wiki]. This is an intrinsic property of emeralds, an essential property rather than an incidental like a coat of green paint. So if the emeralds changes from green to blue at some stage we have an interesting scientific question to ask about the process that occurred to produce the effect. In the absence of such a process the green colour of emeralds would appear to be a paradigm case of the regularity that permits valid predictions.
We may be excited to find the change in colour if it happens because the violation of expectations is one of the great triggers for scientific advances. Hence the importance of Popper’s critical approach based on efforts to falsify hypotheses. It is not that we want falsified hypotheses, indeed he suggested we need some hypotheses to stand up to indicate that we are making progress. Nor does this mean that a falsified hypothesis or theory is instantly cast into outer darkness, there may be no better available. Besides there are two other considerations (1) the effect has to be repeatable if it really matters (see the claim to cold fusion) and (2) pace Cartwright some competing theories may perform better than others on some criteria or in some domains of application but not in all.
To conclude, there is a program of critical preference available as well as the program of confirmation/justification. This derives from Popper’s critical approach and conjectural knowledge, extended by Bartley’s work on the logic of justification in relation to various problems of rationality, including the rationality of science. Among the consequences of this program are the dissolution of inductive confirmation pace Hume and Goodman, also the problem of Hempel’s ravens and the Gettier problem.