The extensions of Goodman’s ‘grue’ predicate and Kripke’s ‘quus’ are constructed from the extensions of more familiar terms via a reinterpretation that permutes assignments of reference. Since this manoeuvre is at the heart of Putnam’s model-theoretic and permutation arguments against metaphysical realism (‘Putnam’s Paradox’), both Goodman’s New Riddle of Induction and the paradox about meaning that Kripke attributes to Wittgenstein are instances of Putnam’s. Evidence cannot selectively confirm the green-hypothesis and disconfirm the grue-hypothesis, because the theory of which the green-hypothesis (...) is a part has an unintended model in which the grue-hypothesis is equally confirmed; and there are no meaning-facts that determine reference, because the objects referred to by the referring terms of any language or set of intentional mental states are permutable in a way that is consistent with the truth-values of all other sentences in that language or beliefs in that set. The upshot is that the three paradoxes need to be solved in a unified way. (shrink)

This paper deals with the problem of vindicating a particular type of inductive rule, a rule to govern inferences from observed frequencies to limits of relative frequencies. Reichenbach's rule of induction is defended. By application of two conditions, normalizing conditions and a criterion of linguistic invariance, it is argued that alternative rules lead to contradiction. It is then argued that the rule of induction does not lead to contradiction when suitable restrictions are placed upon the predicates admitted. Goodman's grue-bleen paradox (...) is considered, and an attempt to resolve it is offered. Finally, Reichenbach's pragmatic argument, hinging on convergence properties, is applied. (shrink)

This paper examines problems of order and periodicity which arise when the attempt is made to define a confirmation function for a language containing elementary number theory as applied to a universe in which the individuals are considered to be arranged in some fixed order. Certain plausible conditions of adequacy are stated for such a confirmation function. By the construction of certain types of predicates, it is proved, however, that these conditions of adequacy are violated by any confirmation function defined (...) for the type of language in question. Various possible solutions to these difficulties are explored and found to be inadequate. In particular, a proposal which stems from the suggestion to restrict a fundamental principle of confirmation to hypotheses containing only non-positional predicates is cited. This proposal, however, is shown to prevent confirmation functions from taking periodicities into account, and so is deemed unsatisfactory. A general theorem is proved to the effect that if non-positional predicates are taken to satisfy the conditions of adequacy which have been formulated, then no periodicity predicates whatsoever (i.e., predicates used in formulating hypotheses which foretell periodicities) can be subject to these conditions, on pain of contradiction. Yet it seems that periodicity predicates must be subject to these conditions of adequacy if a confirmation function is to recognize periodic occurrences. Thus, an impasse seems to be reached. In the final sections we consider the beginnings of one possible solution to these difficulties. Our proposal involves treating sets of individuals, rather than individuals themselves, as instances of an hypothesis which predicts a periodicity. On this basis we formulate new conditions of adequacy which are free from the previous difficulties and which will permit a confirmation function that satisfies them to take periodicities into account. (shrink)

One of the fundamental problems in the fields of inductive logic and the philosophy of science is the one concerning inferences or projections containing so-called “grue-like” or “pathological” predicates. This problem was first put into sharp focus by Nelson Goodman, who called it the “new riddle of induction.”Goodman has shown that the few attempts by others to solve this problem are not adequate. However, very little has been written concerning Goodman's own attempt to solve the problem, namely his theory of (...) entrenchment. The purpose of this article is to show that Goodman's entrenchment theory also is inadequate as a solution to the new riddle of induction. I shall try to do this by presenting two kinds of counterexamples to the entrenchment theory: one kind illustrating a general objection to the theory as a whole ; the other kind, specific objections to particular parts of the theory. (shrink)