Fact, Fiction, and Forecast

n his book Fact, Fiction, and Forecast, Goodman introduced the "new riddle of induction", so-called by analogy with Hume's classical problem of induction. He accepted Hume's observation that inductive reasoning (i.e. inferring from past experience about events in the future) was based solely on human habit and regularities to which our day to day existence has accustomed us. Goodman argued, however, that Hume overlooked the fact that some regularities establish habits (a given piece of copper conducting electricity increases the credibility of statements asserting that other pieces of copper conduct electricity) while some do not (the fact that a given man in a room is a third son does not increase the credibility of statements asserting that other men in this room are third sons). How then can we differentiate between regularities or hypotheses which construe lawlike statements from those which are contingent or based upon accidental generality?

Hempel's confirmation theory argued that the solution is to differentiate between hypotheses, which apply to all things of a certain class, and evidence statements, which apply to only one thing. Goodman's famous counterargument was to introduce the color grue, which applies to all things examined before a certain time t just in case they are green, but also to other things just in case they are blue and not examined before time t. If we examine emeralds before time t and find that emerald a is green, emerald b is green, and so forth, each will confirm the hypothesis that all emeralds are green. However, emeralds a, b, c,..etc. also confirm the hypothesis that all emeralds are grue. In this case emeralds a,b,c, examined after time t should be grue, and therefore blue!

Goodman's example showed that the difficulty in determining what constitutes lawlike hypotheses is far greater than previously thought, and that once again we find ourselves facing the initial dilemma that "anything can confirm anything".

From the wikipedia article Nelson Goodman