Extant literature on Goodman’s ‘New Riddle of Induction’ deals mainly with two versions. I consider both of them, starting from the (‘epistemic’) version of Goodman’s classic of 1954. It turns out that it belongs to the realm of applications of inductive logic, and that it can be resolved by admitting only significant evidence (as I call it) for confirmations of hypotheses. Sect. 1 prepares some ground for the argument. As much of it depends on the notion of evidential significance, this (...) concept is defined and its introduction motivated. Further, I introduce and explain the distinction between support and confirmation: put in a slogan, ‘confirmation is support by significant evidence’. The second section deals with the Riddle itself. I demonstrate that, given the provisions of the first section, not ‘anything confirms anything’: significant green-evidence confirms only green-hypotheses (and no grue-hypotheses), and significant grue-evidence confirms only grue-hypotheses (and no green-hypotheses), whichever terms we use for expressing these evidences or hypotheses. The third section rounds off my treatment. First I show that Frank Jackson’s use of his counterfactual condition is unsuccessful. Further, I argue that no unwanted consequences result, if one starts from the other, ‘objective’, definition of ‘grue’, as it constitutes no more than a mere fact of logic that cannot do any harm. Finally, I present a grue-case involving both kinds of definition, where the exclusive confirmation of either the green- or the grue-hypothesis is shown. (shrink)

Israel 2004 claims that numerous philosophers have misinterpreted Goodman’s original ‘New Riddle of Induction’, and weakened it in the process, because they do not define ‘grue’ as referring to past observations. Both claims are false: Goodman clearly took the riddle to concern the maximally general problem of “projecting” any type of characteristic from a given realm of objects into another, and since this problem subsumes Israel’s, Goodman formulated a stronger philosophical challenge than the latter surmises.

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 article argues that a successful answer to Hume's problem of induction can be developed from a sub-genre of philosophy of science known as formal learning theory. One of the central concepts of formal learning theory is logical reliability: roughly, a method is logically reliable when it is assured of eventually settling on the truth for every sequence of data that is possible given what we know. I show that the principle of induction (PI) is necessary and sufficient for logical (...) reliability in what I call simple enumerative induction. This answer to Hume's problem rests on interpreting PI as a normative claim justified by a non-empirical epistemic means-ends argument. In such an argument, a rule of inference is shown by mathematical or logical proof to promote a specified epistemic end. Since the proof concerning PI and logical reliability is not based on inductive reasoning, this argument avoids the circularity that Hume argued was inherent in any attempt to justify PI. (shrink)

In this paper I raise a difficulty for Joseph LaPorte's account of chemical kind terms. LaPorte has argued against Putnam that H₂O content is neither necessary nor sufficient to fix the reference of the kind term 'water' and that we did not discover that water is H₂O. To this purpose, he revisits Putnam's Twin Earth story with the fictional scenario of Deuterium Earth, whose ocean consists of 'dwater', to conclude that we did not discover that deuterium oxide is (a kind (...) of) water (usually called 'heavy water'). Instead, according to LaPorte, by including deuterium oxide in the extension of the term 'water', we simply refined our vague use of the term 'water'. But we could have decided to exclude deuterium oxide from the extension of the term 'water'. Let us call this the thesis of semantic stipulation. I raise two problems for LaPorte's Deuterium Earth story. First, I show that 'dwater' (i.e. deuterium oxide not as a kind of water) does not have the same scientific credibility of 'heavy water' (i.e. deuterium oxide as a kind of water). Second, I argue that for the thesis of semantic stipulation to go through one would need to show that 'dwater' is semantically on a par with 'heavy water'. Namely, one would need to show that 'dwater' is a projectible kind term, capable of supporting inductive inferences. But, in fact, it is not, because the term is vulnerable to an unwelcome Goodmanian scenario, unless one surreptitiously reintroduces some Putnamian assumptions about D₂O content being necessary and sufficient to fix the reference of the term. (shrink)

Goodman published his "riddle" in the middle of the 20th century and many philosophers have attempted to solve it. These attempts almost all shared an assumption that, I shall argue, might be wrong, namely, the assumption that when we project from cases we have examined to cases we have not, what we project are predicates. I shall argue that this assumption, shared by almost all attempts at a solution, looks wrong, because, in the first place, what we project are generalizations (...) and not predicates, and a generalization is projectible relative to a given context. In this paper I develop the idea of explainable-projectible generalizations versus unexplainable-unprojectible generalizations, relative to a specific context. My main claim is that we rationally project a generalization if and only if we rationally believe that there is something that explains the general phenomenon that the generalized statement in question asserts to obtain, and that a generalization is projectible, if and only if its putative truth can be explained, whether we know that it can be or not. (shrink)