Editing New riddle of induction (section)

===Projectible predicates===
[[File:US government example for Goodman's new riddle of induction_svg.svg|thumb|500px|US government example for time-dependent predicates: [[List of Presidents of the United States#List of presidents|Before March 1797]], arbitrarily many observations would support both versions of the prediction ''"The [[United States Armed Forces|US forces]] were always [[commander-in-chief#United States|commanded]] by { {{su|p=[[George Washington]]|b=[[President of the United States|the &nbsp; US &nbsp; President]]}} }, hence they will be commanded by him in the future"'', which today is known as { {{su|p=false|b=true}} }, similar to ''"Emeralds were always { {{su|p=grue|b=green}} }, hence they will be so in the future"''.]]
The new riddle of induction, for Goodman, rests on our ability to distinguish ''lawlike'' from ''non-lawlike'' generalizations.  ''Lawlike'' generalizations are capable of confirmation while ''non-lawlike'' generalizations are not.  ''Lawlike'' generalizations are required for making predictions.  Using examples from Goodman, the generalization that all copper conducts electricity is capable of confirmation by a particular piece of copper whereas the generalization that all men in a given room are third sons is not ''lawlike'' but accidental.  The generalization that all copper conducts electricity is a basis for predicting that this piece of copper will conduct electricity.  The generalization that all men in a given room are third sons, however, is not a basis for predicting that a given man in that room is a third son.

The question, therefore, is what makes some generalizations ''lawlike'' and others accidental.  This, for Goodman, becomes a problem of determining which predicates are projectible (i.e., can be used in ''lawlike'' generalizations that serve as predictions) and which are not. Goodman argues that this is where the fundamental problem lies. This problem is known as '''Goodman's paradox''': from the apparently strong evidence that all [[emerald]]s examined thus far have been green, one may inductively conclude that all future emeralds will be green. However, whether this prediction is ''lawlike'' or not depends on the predicates used in this prediction.  Goodman observed that (assuming ''t'' has yet to pass) it is equally true that every emerald that has been observed is ''grue''.  Thus, by the same evidence we can conclude that all future emeralds will be ''grue''.  The new problem of induction becomes one of distinguishing projectible predicates such as ''green'' and ''blue'' from non-projectible predicates such as ''grue'' and ''bleen''.

Hume, Goodman argues, missed this problem.  We do not, by habit, form generalizations from all associations of events we have observed but only some of them. All past observed emeralds were green, and we formed a habit of thinking the next emerald will be green, but they were equally grue, and we do not form habits concerning grueness. ''Lawlike'' predictions (or projections) ultimately are distinguishable by the predicates we use. Goodman's solution is to argue that ''lawlike'' predictions are based on projectible predicates such as ''green'' and ''blue'' and not on non-projectible predicates such as ''grue'' and ''bleen'' and what makes predicates projectible is their ''entrenchment'', which depends on their successful past projections.  Thus, ''grue'' and ''bleen'' function in Goodman's arguments to both illustrate the new riddle of induction and to illustrate the distinction between projectible and non-projectible predicates via their relative entrenchment.