New riddle of induction

The new riddle of induction was presented by Nelson Goodman in Fact, Fiction, and Forecast as a successor to Hume's original problem.

For Goodman they illustrate the problem of projectible predicates and ultimately, which empirical generalizations are law-like and which are not.

[1][2] Goodman's construction and use of grue and bleen illustrates how philosophers use simple examples in conceptual analysis.

On January 2, 2035, however, emeralds and well-watered grass are bleen, and bluebirds or blue flowers are grue.

In this section, Goodman's new riddle of induction is outlined in order to set the context for his introduction of the predicates grue and bleen and thereby illustrate their philosophical importance.

The new riddle of induction, for Goodman, rests on our ability to distinguish lawlike from non-lawlike generalizations.

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 also addresses and rejects this proposed solution as question begging because blue can be defined in terms of grue and bleen, which explicitly refer to time.

[5] Richard Swinburne gets past the objection that green may be redefined in terms of grue and bleen by making a distinction based on how we test for the applicability of a predicate in a particular case.

Qualitative predicates, like green, can be assessed without knowing the spatial or temporal relation of x to a particular time, place or event.

Locational predicates, like grue, cannot be assessed without knowing the spatial or temporal relation of x to a particular time, place or event, in this case whether x is being observed before or after time t. Although green can be given a definition in terms of the locational predicates grue and bleen, this is irrelevant to the fact that green meets the criterion for being a qualitative predicate whereas grue is merely locational.

Carnap's approach to inductive logic is based on the notion of degree of confirmation c(h,e) of a given hypothesis h by a given evidence e.[b] Both h and e are logical formulas expressed in a simple language L which allows for The universe of discourse consists of denumerably many individuals, each of which is designated by its own constant symbol; such individuals are meant to be regarded as positions ("like space-time points in our actual world") rather than extended physical bodies.

[16] Willard Van Orman Quine discusses an approach to consider only "natural kinds" as projectible predicates.

Quine investigates "the dubious scientific standing of a general notion of similarity, or of kind".

Already Heraclitus' famous saying "No man ever steps in the same river twice" highlighted the distinction between similar and identical circumstances.

Ostensive learning[30] is a case of induction, and a curiously comfortable one, since each man's spacing of qualities and kind is enough like his neighbor's.

[31] In contrast, the "brute irrationality of our sense of similarity" offers little reason to expect it being somehow in tune with the unanimated nature, which we never made.

[33] However, this cannot account for the human ability to dynamically refine one's spacing of qualities in the course of getting acquainted with a new area.

[o] In his book Wittgenstein on Rules and Private Language, Saul Kripke proposed a related argument that leads to skepticism about meaning rather than skepticism about induction, as part of his personal interpretation (nicknamed "Kripkenstein" by some[34]) of the private language argument.

He proposed a new form of addition, which he called quus, which is identical with "+" in all cases except those in which either of the numbers added are equal to or greater than 57; in which case the answer would be 5, i.e.: He then asks how, given certain obvious circumstances, anyone could know that previously when I thought I had meant "+", I had not actually meant quus.

Kripke then argues for an interpretation of Wittgenstein as holding that the meanings of words are not individually contained mental entities.