Many believe that Goodman’s new riddle of induction proves the impossibility of a purely syntactical theory of confirmation. After discussing and rejecting Jackson’s solution to Goodman’s paradox, I formulate the “new riddle of deduction,” in analogy to the new riddle of induction. Since it is generally agreed that deductive validity can be defined syntactically, the new riddle of induction equally does not show that inductive validity cannot be defined syntactically. I further rely on (...) the analogy between induction and deduction in order to explain why some predicates, such as “grue,” are unprojectible. (shrink)

The paper deals with the New Riddle of Induction set forth by N. Goodman in his Fact, Fiction, and Forecast. The problem is introduced through the definition of grue-predicate. The relation between the grue-hypothesis and empirical evidence is examined. Goodman’s underlying thesis about the neutrality of empirical evidence is undermined. The intelligibility of the idea that disjunctive properties such as Grue can be observed and seen is questioned. A solution of Goodman’s riddle is outlined by means of (...) the definition of the identity of empirical properties and further deve- loped through postulating of the necessary condition of induction executability which prohibits the inference from “Some a, b, c, d emeralds are green” to the hypothesis “All emeralds are grue”. (shrink)

I explain the New Riddle of Induction (Goodman 1946, 1955) in very brief words.

In a recent paper in this journal, Schramm presents what he takes to be an answer to Goodman’s New Riddle of Induction. His solution relies on the technical notion of evidential significance, which is meant to distinguish two ways that evidence may bear on a hypothesis: either via support or confirmation. As he puts his view in slogan form: “confirmation is support by significant evidence”. Once we make this distinction, Schramm claims, we see that Goodman’s famous riddle (...) is dissolved, and we are no longer forced into the “intolerable result” that anything confirms anything. Schramm makes a number of incisive observations in his paper, but I do not think he has solved the New Riddle. There are two reasons for this. First, Schramm has an overly narrow conception of what the Riddle amounts to; I would venture to guess that it is narrower than that of most contemporary philosophers. Thus his proposal does not address the primary concern. Second, Schramm’s notion of significant evidence relies on a counterfactual condition that bears more than a passing resemblance to that made famous by Jackson in his paper on the topic. However, Jackson’s proposal faces several well-known counterexamples, some of which can be adapted into Schramm’s framework. Schramm’s solution thus inherits a number of outstanding problems from Jackson’s proposal, which he has not shown us how to handle. (shrink)

Drawing on past work, we introduce a new approach to the New Riddle of Induction, showing that the inductive projection of gruesome properties is unreliable under particular ideal conditions that are sufficient for the reliable inductive projection of non-gruesome properties. As an auxiliary to our account, we introduce rules for resolving conflicts between background information and the conclusions of otherwise reliable inductive inferences. Our approach to the New Riddle of Induction is quite permissive in the range (...) of properties it recognizes as suitable for inductive projection, allowing for the inductive projection of highly gerrymandered non-natural properties. However, as an addendum to our discussion of the New Riddle, we show that natural properties do form a more reliable basis for inductive projection in cases where one’s sample is small. (shrink)

That past patterns may continue in many different ways has long been identified as a problem for accounts of induction. The novelty of Goodman’s ”new riddle of induction” lies in a meta-argument that purports to show that no account of induction can discriminate between incompatible continuations. That meta-argument depends on the perfect symmetry of the definitions of grue/bleen and green/blue, so that any evidence that favors the ordinary continuation must equally favor the grue-ified continuation. I argue (...) that this very dependence on the perfect symmetry defeats the novelty of the new riddle. The symmetry can be obtained in contrived circumstances, such as when we grue-ify our total science. However, in all such cases, we cannot preclude the possibility that the original and grue-ified descriptions are merely notationally variant descriptions of the same physical facts; or if there are facts that separate them, these facts are ineffable, so that no account of induction should be expected to pick between them. In ordinary circumstances, there are facts that distinguish the regular and grue-ified descriptions. Since accounts of induction can and do call upon these facts, Goodman’s meta-argument cannot provide principled grounds for the failure of all accounts of induction. It assures us only of the failure of accounts of induction, such as unaugmented enumerative induction, that cannot exploit these symmetry breaking facts. (shrink)

Although the relevance and importance of his work has been recognized only belatedly, Charles Sanders Peirce was, throughout his life, a careful student and significant contributor to the development of logic, scientific theory, and philosophy generally. Occasionally, complete appreciation of Peirce's efforts has been hampered because his work is often unique and, at times, highly idiosyncratic. Yet, we hope to show in this paper that for one aspect of his work in logic Peirce did not abandon the ordinary without purpose. (...) Only relatively recently have philosophers of science become interested in the logic of discovery - that is, in the logic of the selection of hypotheses to be tested rather than simply in the ways of testing hypotheses which have already been selected. (shrink)

The most innovative and important parts of Bertrand Russell's Human Knowledge were the result of his first attempt in three decades to come to grips with the problem of induction, or, more generally, ‘non-demonstrative inference’. My purpose here is to argue that that work constituted giant progress on the problem; if I succeed, something will have been done to restore this work to its proper place in the history of philosophy and, correlatively, to rearrange that history.

Although the relevance and importance of his work has been recognized only belatedly, Charles Sanders Peirce was, throughout his life, a careful student and significant contributor to the development of logic, scientific theory, and philosophy generally. Occasionally, complete appreciation of Peirce's efforts has been hampered because his work is often unique and, at times, highly idiosyncratic. Yet, we hope to show in this paper that for one aspect of his work in logic Peirce did not abandon the ordinary without purpose. (...) Only relatively recently have philosophers of science become interested in the logic of discovery - that is, in the logic of the selection of hypotheses to be tested rather than simply in the ways of testing hypotheses which have already been selected. (shrink)

The hidden strength of Goodman's ingenious "new riddle of induction" lies in the perfect symmetry of grue/bleen and green/blue. The very same sentence forms used to define grue/bleen in terms of green/blue can be used to define green/blue in terms of grue/bleen by permutation of terms. Therein lies its undoing. In the artificially restricted case in which there are no additional facts that can break the symmetry, grue/bleen and green/blue are merely notational variants of the same facts; or, (...) if they represent different facts, the differences are ineffable, and no account of induction should be expected to pick between them. This still obtains in the more interesting case in which we embed grue/bleen in a grue-ified total science; the grue-ified and regular total sciences are merely equivalent descriptions of the same facts. In the most realistic case, we allow additional facts that break the symmetry and then we can also evade Goodman's new riddle by employing an account of induction rich enough to exploit these facts. Unaugmented enumerative induction is not such an account and it is the primary casualty of Goodman's new riddle. (shrink)

I propose a novel solution to Goodman's new riddle of induction, one on which aspects of scientific methodology preclude significant confirmation of the Grue Hypothesis. The solution appeals to intuitive constraints on the confirmation of explanatory hypotheses, and can be construed as a fragment of a theory of Inference to the Best Explanation. I give it an objective Bayesian formalisation, and contrast it with Goodman's and Sober's solutions, which make appeal to both methodological and non-methodological considerations, and those (...) of Jackson, Godfrey-Smith, and White, on which explanatory considerations play a very different role. (shrink)

In this paper, I consider Goodman’s new riddle of induction and how we should best respond to it. Noticing that all the emeralds so far observed are green, we infer that all emeralds are green. However, all emeralds so far observed are also grue, so we could also infer that they are grue. Only one of these inductive inferences or projections could, however, be valid. For the hypothesis that all emeralds are green predicts that the next observed emerald (...) will be green; whereas the hypothesis that they are grue predicts that it will blue. Goodman’s new riddle is the problem of saying why the inductive inference involving “green” is the valid one. Goodman’s own solution appeals to the idea of entrenchment. His idea is that “green” is a more entrenched predicate than “grue” in the sense that it has figured many more times in our past projections than has “grue”. In his view, this explains why “green” is projectible whereas “grue” isn’t. I argue that this response doesn’t go far enough and that we additionally need an explanation of why “green” is more entrenched than “grue”—that we are otherwise left with the unsatisfactory view that its superior entrenchment is a mere linguistic accident. I try to supplement Goodman’s solution with an explanation of this kind. I argue that “grue” is not entrenched be- cause past successful inductions involving “green” show that past projections that could have been made using what I call “grue-like” predicates—predicates which are like “grue” except that the times featuring in their definitions are past—would have been unsuccessful. (shrink)

This essay demonstrates a previously unnoticed connection between formal and statistical learning theory with regard to Nelson Goodman’s new riddle of induction. Discussions of Goodman’s riddle in formal learning theory explain how conjecturing “all green” before “all grue” can enhance efficient convergence to the truth, where efficiency is understood in terms of minimizing the maximum number of retractions or “mind changes.” Vapnik-Chervonenkis (VC) dimension is a central concept in statistical learning theory and is similar to Popper’s notion (...) of degrees of testability. I show that for a class inductive problems of which Goodman’s riddle is one example, a reliable inductive method minimizes the maximum number of mind changes exactly if it always conjectures the hypothesis from the set with lowest VC dimension consistent with the data. I also discuss the relevance of these results to language invariance and curve fitting. (shrink)

There are three riddles of induction. The New Riddle is this: How do we give a definition of 'projectible hypothesis' which is noncircular, and which yet divides all universal hypotheses unerringly into two disjoint classes--the projectible and the unprojectible? This is a purely analytical problem: build a machine which sorts hypotheses in the intuitively correct way, it making no difference why the machine works, so long as it works : Why should we rely on inductions to acquire beliefs (...) about the unobserved, rather than on any other method of inference to acquire alternative beliefs about the unobserved? ;Here, we solve all three riddles. Chapter One is devoted to the New Riddle. Chapter Two serves to introduce some important matters concerning counterfactuals and causation, necessary for the hard labor of Chapter Three, which addresses the Old Riddle. The true pattern of inference from experience is discussed and two kinds of counterfactuals are distinguished, suggesting an answer to Hume. (shrink)

Nelson Goodman's new riddle of induction forcefully illustrates a challenge that must be confronted by any adequate theory of inductive inference: provide some basis for choosing among alternative hypotheses that fit past data but make divergent predictions. One response to this challenge is to distinguish among alternatives by means of some epistemically significant characteristic beyond fit with the data. Statistical learning theory takes this approach by showing how a concept similar to Popper's notion of degrees of testability is (...) linked to minimizing expected predictive error. In contrast, formal learning theory appeals to Ockham's razor, which it justifies by reference to the goal of enhancing efficient convergence to the truth. In this essay, I show that, despite their differences, statistical and formal learning theory yield precisely the same result for a class of inductive problems that I call strongly VC ordered, of which Goodman's riddle is just one example. (shrink)

Goodman'snew riddle of induction can be characterized by the following questions: What is the difference between grue and green?; Why is the hypothesis that all emeralds are grue not lawlike?; Why is this hypothesis not confirmed by its positive instances?; and, Why is the predicate grue not projectible? I argue in favor of epistemological answers to Goodman's questions. The notions of lawlikeness, confirmation, and projectibility have to be relativized to (actual and counterfactual) epistemic situations that are determined by (...) the available background information. In order to defend this thesis, I discuss an example that is less strange than the grue example. From the general conclusions of this discussion, it follows that grue is not projectible in the actual epistemic situation, but it is projectible in certain counterfactual epistemic situations. (shrink)

A challenger of traditions and boundaries A pivotal figure in 20th-century philosophy, Nelson Goodman has made seminal contributions to metaphysics, epistemology, aesthetics, and the philosophy of language, with surprising connections that cut across traditional boundaries. In the early 1950s, Goodman, Quine, and White published a series of papers that threatened to torpedo fundamental assumptions of traditional philosophy. They advocated repudiating analyticity, necessity, and prior assumptions. Some philosophers, realizing the seismic effects repudiation would cause, argued that philosophy should retain the familiar (...) framework. Others considered the arguments compelling, but despaired of doing philosophy without the framework. Goodman disagreed with both factions. Rather than regretting the loss of structure, he capitalized on the opportunities that arise when the strictures of tradition are loosened. (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.

Logic for Dewey is a normative inquiry into the nature of inquiry itself. Goodman’s grue example is assessed in light of Dewey's vocabulary for logic as presented in his 1938 Logic.

Barker and Achinstein misread Goodman's definitions of 'grue' and 'bleen'. If we stick to Goodman's definition of 'grue' as applying "to all things examined before t just in case they are green but to other things just in case they are blue" (my italics), and his parallel definition of 'bleen', then Barker and Achinstein's arguments are seen to be irrelevant. The result is to by-pass the question whether Mr. Grue sees things as grue rather than as green while showing that (...) it is possible for human conceptual schemes to employ different sensory terms. These two issues are separate. (shrink)

With his new riddle of induction, Goodman raised a problem for enumerative induction which many have taken to show that only some ‘natural’ properties can be used for making inductive inferences. Arguably, however, (i) enumerative induction is not a method that scientists use for making inductive inferences in the first place. Moreover, it seems at first sight that (ii) Goodman’s problem does not affect the method that scientists actually use for making such inferences—namely, classical statistics. Taken (...) together, this would indicate that (iii) ‘naturalness’ is not such a relevant concept for the problem of induction, after all. I have no objections against (i) and (iii). But, contrary to (ii), I argue that classical statistics does face a version of Goodman’s problem, which I call the statistical riddle of induction. Given that his problem merely is an instance of the more general problem of underdetermination, this is hardly surprising. Perhaps more importantly, I also show how my riddle can be used for exposing a common fallacy in probabilistic reasoning, without relying on Bayesian assumptions. (shrink)

The limited aim here is to explain what John Dewey might say about the formulation of the grue example. Nelson Goodman’s problem of distinguishing good and bad inductive inferences is an important one, but the grue example misconstrues this complex problem for certain technical reasons, due to ambiguities that contemporary logical theory has not yet come to terms with. Goodman’s problem is a problem for the theory of induction and thus for logical theory in general. Behind the whole discussion (...) of these issues over the last several decades is a certain view of logic hammered out by Russell, Carnap, Tarski, Quine, and many others. Goodman’s nominalism hinges in essential ways on a certain view of formal logic with an extensional quantification theory at its core. This raises many issues, but the one issue most germane here is the conception of predicates ensconced in this view of logic. (shrink)

Yehezkel presents an interesting argument to resolve Goodman’s New Riddle of Induction, and in effect to claim that a purely syntactical theory of confirmation is possible. In this paper I suggest that Yehezkel’s argument relies on two premises not proven in his paper. The first premise is that if “a New Riddle of Deduction” can be formulated then there is no New Riddle of Induction. This premise seems to be wrong as I claim in part (...) 2 of this paper. The second premise is that a New Riddle of Deduction can be formulated. Despite Yehezkel’s efforts to prove this claim, it seems to me false, or at least, unproven. I therefore conclude that there is no New Riddle of Deduction, and therefore, no actual resolution to the New Riddle of Induction. (shrink)

This paper presents parts of a theory of radical translation with applications to the problem of construing reference. First, in sections 1 to 4 the general standpoint, inspired by Goodman's approach to induction, is set forth. Codification of sound translational practice replaces the aim of behavioral reduction of semantic notions. The need for a theory of translational projection (manual construction on the basis of a finite empirical correlation of sentences) is established by showing the anomalies otherwise resulting (e.g. from (...) Quine's position). Then in section 5 a partial characterization of what constitutes an "admissible translation manual" is developed in the form of rules of translational projection governing correspondence of sentence-parts of a language-pair. Finally, in section 6, we give applications of the theory to the problem of construing reference. The general rules of section 5 suffice to rule out deviant referential schemes which have been held inscrutable alternatives to standard schemes. (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)

The problem of induction is perennially important in epistemology and the philosophy of science. In response to Goodman's 'New Riddle of Induction', Frank Jackson made a compelling case for there being no new riddle, by arguing that there are no nonprojectible properties. Although Jackson's denial of nonprojectible properties is correct, I argue here that he is mistaken in thinking that he thereby shows that there is no new riddle of induction, and demonstrate that his (...) solution to the grue paradox fails to rule out the possibility of equally justified contradictory inductions. More importantly, in illuminating where Jackson's argument fails, the paper casts a new light on the problem of induction, locating the problem not in the nature of the next (unexamined) x, but in the counterfactual robustness of properties of already examined x's. (shrink)

Professor Goodman first presented his "new riddle of induction" in 1946 but it was mainly the more elaborated version published in his Fact, Fiction and Forecast in 1955 that has captured the attention of philosophers. Since then, numerous attempts to solve his "paradox of grue" appeared in press; none of them, however, proved to be wholly satisfactory. In this paper I want to present a solution to this 30-years old puzzle. In the first section I shall try to (...) show that my solution, which is based on a Gedankenexperiment, is immune to the objections leveled against previous attempts. In light of this solution I shall re-examine the status of the paradox and show that in order to preserve the meaningfulness of the paradox some type of Platonic framework for the theory of meaning should have to be assumed. In the last section I shall discuss a proposed solution to the paradox using counterfactual claims. I will show that despite the similarity between counterfactuals and thought-experiments, the counterfactual approach does not lead to a satisfactory solution. (shrink)

As scientists start to adopt machine learning (ML) as one research tool, the security of ML and the knowledge generated become a concern. In this paper, I explain how supervised ML can be improved with better data ontology, or the way we make categories and turn information into data. More specifically, we should design data ontology in such a way that is consistent with the knowledge that we have about the target phenomenon so that such ontology can help us make (...) the inductive leap. I do so by thinking through a thought experiment, Goodman’s New Riddle of Induction (Fact, fiction, and forecast, Harvard University Press, 1955). Goodman’s riddle helps flesh out three problems of induction: (1) the problem of equal goodies, that there are often too many equally good inductive results given the same data; (2) the problem of diverging performance, that these equally good results can give opposite predictions in the future; and (3) the problem of mediocrity, that when averaged across all equally possible datasets and tasks, no inductive algorithm outperforms any other. I show that all these three problems are manifested as real obstacles in ML practice, namely, the Rashomon effect (Breiman in Stat Sci 16(3):199–231, 2001), the problem of underspecification (D’Amour et al. in J Mach Learn Res, 2020, https://doi.org/10.48550/arXiv.2011.03395 ), and the No Free Lunch theorem (Wolpert in Neural Comput 8(7):1341–90, 1996, https://doi.org/10.1162/neco.1996.8.7.1341 ). Lastly, I argue that proper data ontology can help mitigate these problems and I demonstrate how using concrete examples from climate science. This research highlights the links between philosophers’ discussions of induction and implications in ML practice. (shrink)

The idea that reason can justify induction was famously criticized by David Hume. Hume concluded that there is no rational justification for inductive inferences and hence, no rational justification for most of our daily beliefs. Many philosophers attempted to solve Hume's problem with no success. Bertrand Russell commented regarding Hume's problem: "[if we cannot justify induction] we have no reason to expect the sun to rise tomorrow, to expect bread to be more nourishing than a stone, or to (...) expect that if we throw ourselves off the roof we shall fall." The New Riddle of Induction was introduced by Nelson Goodman in his book Fact, Fiction and Forecast, published in 1954. Goodman's problem raised some serious doubts about our ability even to describe inductive principles. In this Book Rami Israel is attempting to solve Both Hume's and Goodman's philosophical problems by introducing a new approach to the subject and by drawing a new picture of our inductive practices. (shrink)

First, a brief historical trace of the developments in confirmation theory leading up to Goodman's infamous "grue" paradox is presented. Then, Goodman's argument is analyzed from both Hempelian and Bayesian perspectives. A guiding analogy is drawn between certain arguments against classical deductive logic, and Goodman's "grue" argument against classical inductive logic. The upshot of this analogy is that the "New Riddle" is not as vexing as many commentators have claimed. Specifically, the analogy reveals an intimate connection between Goodman's problem, (...) and the "problem of old evidence". Several other novel aspects of Goodman's argument are also discussed. (shrink)

Collin Howson (2000) challenges van Cleve’s reliabilist defense of induction (1984) based on an adaptation of Goodman Paradox (or new riddle of induction). I will try to show that Howson’s argument does not succeed once it is self-defeating. Nevertheless, I point out another way which Howson could have employed the new riddle to undermine the reliabilist defense.

Wolfgang Freitag claims to have developed a proposal that solves Goodman's famous New Riddle of Induction. His proposal makes use of the notion of ‘derivative defeat’; the claim is that in certain circumstances, the projection of some predicates is derivatively defeated, i.e., it is inductively invalid. Freitag develops the proposal using some compelling examples, and then shows that it likewise applies to the argument at the basis of the New Riddle. There, he alleges, the projection of ‘grue’ (...) is derivatively defeated, whereas the projection of ‘green’ is not. We thus have a justification for preferring the green induction over the grue induction. I do not think Freitag has solved the New Riddle. The problem is that his proposal tacitly assumes certain counterfactual claims that a grue-speaker would dispute. I thus argue that Freitag's claims beg the question against the grue-speaker, and I show why the grue-speaker would reject them. (shrink)

When Goodman put forward his “New Riddle of Induction”, he distinguished if from the old problem of justifying the so-called “Principle of Uniformity of Nature”: proving that the future will resemble the past, and that still standing lawful regularities will continue to hold. He intended to break with these ancient questions, while asking about lawlike generalizations and projectible predicates instead: how are we to separate those generalizations which are rightfully confirmed by their observed instances (i.e. nomological) and those (...) accidental ones which are nonetheless empirically equivalent? One shall not seek a ground for induction anymore, but a criterion for nomological hypothesis. Therefore Goodman’s claim seems twofold: (A) one has to face a second problem of induction, which is distinct from the old one while genuinely being a problem about induction, and (B) this new problem is solvable by a criterion of empirical confirmability, which discriminates nomological from accidental generalizations. We claim that one cannot genuinely (A) face this new problem of induction while (B) looking for such a criterion. Indeed, we argue, when one compares several hypothesis or generalizations on the same observational basis, then they must appear as equally nomological. Conversely, if one is considering hypothesis or generalizations which are not equally nomological, then one is actually unable to compare them on the same observational basis, hence to formulate the “New Riddle”. Therefore the issue raised in (A) cannot be adequately solved in (B). Yet we do accept the claim (A) that a new and distinct problem of induction is to be confronted. Thus we deny that (B) offer an adequate type of solutions to this problem, which we shall finally formulate in a more suitable manner. (shrink)

It is a common intuition in scientific practice that positive instances confirm. This confirmation, at least based purely on syntactic considerations, is what Nelson Goodman’s ‘Grue Problem’, and more generally the ‘New Riddle’ of Induction, attempt to defeat. One treatment of the Grue Problem has been made along Bayesian lines, wherein the riddle reduces to a question of probability assignments. In this paper, I consider this so-called Bayesian Grue Problem and evaluate how one might proffer a solution (...) to this problem utilizing what I call a phenomenological approach. I argue that this approach to the problem can be successful on the Bayesian framework. (shrink)

In Fact, Fiction and Forecast, Nelson Goodman claims that the problem of justifying induction is not something over and above the problem of describing valid induction. Such claim, besides suggesting his commitment to the collapse of the distinction between the context of description and the context of justification, seems to open the possibility that the new riddle of induction could be addressed empirically. Discoveries about psychological preferences for projecting certain classes of objects could function as a (...) criterion for determining which predicates are after all projectible. In this paper, I argue that Goodman's claim must be construed within his project for constructional definitions, which is methodologically oriented by reflective equilibrium. The description of inductive practice is committed to the articulation of the extension of the class selected by the predicate ‘valid induction’. The mutual adjustment between theoretical considerations and inductive practice involved in the proposal of a definition of ‘valid induction’ must preserve that practice as much as possible, there is no way to get rid of entrenchment. Empirical discoveries about the psychological mechanism that underlies projections may help that adjustment but they cannot substitute the role played by the entrenchment of predicates. (shrink)

The paper aims to stress the structural similarities between Nelson Goodman’s ‘new riddle of induction’ and Edmund Gettier’s counterexamples to the standard analysis of knowledge.

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)

'Practices without foundations' is, in genesis and in effect, a discussion of the following quotation , which serves therefore as an epigraph to it: ;Nelson Goodman's discussion of the 'new riddle of induction' ... deserves comparison with Wittgenstein's work. Indeed ... the basic strategy of Goodman's treatment of the 'new riddle' is strikingly close to Wittgenstein's sceptical arguments .... Although our paradigm of Wittgenstein's problem was formulated for a mathematical problem it ... is completely general and can (...) be applied to any rule or word. In particular, if it were formulated for the language of color impressions, as Wittgenstein himself suggests, Goodman's 'grue', or something similar, would play the role of 'quus'. But the problem would not be Goodman's about induction--"Why not predict that grass, which has been grue in the past will be grue in the future?"--but Wittgenstein's about meaning: "Who is to say that in the past I didn't mean grue by 'green', so that now I should call the sky, not the grass, 'green'?" vskip9pt ;This fascinating remark of Kripke's suggests a project, that of charting out both the interpretive and philosophic points of connection and disconnection between Wittgenstein, Goodman and Kripke. That project is this dissertation. ;My work severely tests Kripke's remark. For I argue that Kripke not only misreads Wittgenstein, but also mistakes the extremity of the 'scepticism' of his version of Wittgenstein for the priority of the philosophical puzzle that Goodman has bequeathed to us. ;To reach this conclusion, I show that Kripke's Wittgenstein's 'meaning-scepticism' is unanswerable if statable, but actually unstatable; and that, under certain interpretations, the same is true of putative scepticisms derivable from Goodman's text. The upshot is that the sceptical reading of most twentieth century philosophy must be displaced in favour of 'post-scepticism' and 'philosophical ethnography'. The latter concepts, sketched toward the end of the dissertation, are perhaps its telos. (shrink)

This paper uses famous problems from philosophy of science and philosophical psychology—underdetermination of theory by evidence, Nelson Goodman’s new riddle of induction, theory-ladenness of observation, and “Kripkenstein’s” rule-following paradox—to show that it is empirically impossible to reliably interpret which functions a large language model (LLM) AI has learned, and thus, that reliably aligning LLM behavior with human values is provably impossible. Sections 2 and 3 show that because of how complex LLMs are, researchers must interpret their learned functions (...) largely in terms of empirical observations of their outputs and network behavior. Sections 4–7 then show that for every “aligned” function that might appear to be confirmed by empirical observation, there is always an infinitely larger number of “misaligned”, arbitrarily time-limited functions equally consistent with the same data. Section 8 shows that, from an empirical perspective, we can thus never reliably infer that an LLM or subcomponent of one has learned any particular function at all before any of an uncountably large number of unpredictable future conditions obtain. Finally, Section 9 concludes that the probability of LLM “misalignment” is—at every point in time, given any arbitrarily large body of empirical evidence—always vastly greater than the probability of “alignment.”. (shrink)

I here aim to show that a particular approach to the problem of induction, which I will call “induction by direct inference”, comfortably handles Goodman’s problem of induction. I begin the article by describing induction by direct inference. After introducing induction by direct inference, I briefly introduce the Goodman problem, and explain why it is, prima facie, an obstacle to the proposed approach. I then show how one may address the Goodman problem, assuming one adopts (...) induction by direct inference as an approach to the problem of induction. In particular, I show that a relatively standard treatment of what some have called the “Reference Class problem” addresses the Goodman Problem. Indeed, plausible and relatively standard principles of direct inference yield the conclusion that the Goodman inference (involving the grue predicate) is defeated, so it is unnecessary to invoke considerations of ‘projectibility’ in order to address the Goodman problem. I conclude the article by discussing the generality of the proposed approach, in dealing with variants of Goodman’s example. (shrink)

The paper argues that relations of probabilistic independence between evidence statements must be preserved in enumerative induction. It further shows that, given such a preservation principle, there is a straightforward Bayesian solution to Goodman's new riddle of induction.

This paper does not purport to offer yet another ‘solution’ to the much discussed ‘new riddle’ of induction. The focus, instead, is on the genesis of Goodman's paradox and its relation to the classic problem of induction. In the arguments which led Goodman from the dissolution of Hume's problem to the discovery of the new riddle, I reveal a fundamentally flawed assumption about the nature of inductive inference which undermines Goodman's contention that the genuine problem of (...) induction consists in distinguishing between projectible and non‐projectible regularities. I further show that if the same set of observations may indeed support an indefinitely large number of inductive predictions, then the rationale for dismissing the classic problem of induction disappears. Stripped of its erroneous assumptions, the new riddle becomes nothing more than a special case of Hume's problem. (shrink)

The paper investigates the prospects of Spohn’s ranking theory with respect to Goodman’s New Riddle of Induction. Based on a novel analysis of the riddle (Freitag [manuscript]), we show it to be an inductive extension of Hansson’s puzzle (Hansson 1992, 1999). As a consequence, a solution needs to take into account the dependence relations between evidential beliefs: “grue” is unprojectible because it depends on evidence whose projection is defeated. It will be suggested that this solution can be (...) implemented into Spohn’s ranking theory, but that ranking theory is unable to provide a proper explanation of the required conditional ranks. (shrink)