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)

The spectrum of a first-order sentence is the set of natural numbers occurring as the cardinalities of finite models of the sentence. In a recent survey, Durand et al. introduce a new class of real numbers, the spectral reals, induced by spectra and pose two open problems associated to this class. In the present note, we answer these open problems as well as other open problems from an earlier, unpublished version of the survey. Specifically, we prove that every algebraic real (...) is spectral, every automatic real is spectral, the subword density of a spectral real is either 0 or 1, and both may occur, and every right-computable real number between 0 and 1 occurs as the subword entropy of a spectral real. In addition, Durand et al. note that the set of spectral reals is not closed under addition or multiplication. We extend this result by showing that the class of spectral reals is not closed under any computable operation satisfying some mild conditions. (shrink)

I argue that Goodman's puzzle of grue at least poses no real challenge about inductive inference. By drawing on Stove's characterisation of Hume's characterisation of inductive inference, we see that the premises in an inductive inference report experienced impressions; and Goodman can be interpreted as posing a real challenge about inductive inference only if we treat an epistemic subject's observations more as logical contents and less as experienced impressions. So, even though the grue puzzle was effective against its (...) stated logicist targets, it is not thereby an enduring difficulty regarding experience's ability to impart epistemic justification via inductive evidence. (shrink)

The paper presents a comprehensive solution to the new riddle of induction. Gruesome induction is blocked because “grue” is not independent of our sampling and observation methods. Before presenting my theory, I critically survey previous versions of what I call the “independence strategy”, tracing the strategy to three different papers from the 1970s by (respectively) Wilkerson, Moreland, and Jackson. Next I critically examine recent approaches by Okasha, Godfrey-Smith, Schramm, and Freitag. All of these approaches have their virtues, but none (...) of them rules out every problem case. Nor do any of them alone explain exactly what goes wrong in all types of gruesome reasoning. My account aims to do both. Learning lessons from my criticisms of previous theories, I argue that there are several crucial types of independence. All of them are needed to rule out every problem case. I close by suggesting that the independence solution can also be adopted by proponents of other approaches—Bayesians, fans of natural kinds, and pragmatists. (shrink)

A logical empiricist “baseline statement” can formalize some propositions established by a body of evidence or set of observations. However, it may not necessarily capture, of two propositions it entails, whether all the subsets of the evidence that establish one proposition also establish the other, vice versa, or neither. Yet, according to this paper, which obtains should sometimes matter for confirmation. It illustrates by showing how this “evidential dependence” can be used to address problems with generalizations of grue-like predicates, (...) and do so still within a very simple broadly Hempelian framework. (shrink)

The paper explores the disjunctive riddle for induction: If we know the sample Ks to be P, we also know that they are P or F. Assuming that we also know that the future Ks are non-P, we can conclude that they are F, if only we can inductively infer the evidentially supported P-or-F hypothesis. Yet this is absurd. We cannot predict that future Ks are F based on the knowledge that the samples, and only they, are P. The ensuing (...) challenge is to account for the unprojectibility of the disjunctive hypothesis. I provide an explanation in terms of epistemic dependence. The P-or-F hypothesis is unprojectible because the evidence supporting it depends epistemically on the evidence for the defeated P-hypothesis. The paper also shows that the disjunctive riddle covers the essence of Goodman's infamous grue-problem, which, therefore, can be resolved by the same means: In contrast to the green-hypothesis, the grue-hypothesis is unprojectible because the grue-evidence depends on the evidence for a defeated hypothesis. (shrink)

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)

In 1955 the fi rst Danish chair in education was set up at the University of Copenhagen and Knud Grue-Sørensen – Doctor of Philosophy – became appointed as holder of the chair. In 1965 the chair had an institute,Institute of Educational Th eory, connected to it.The following deals with the nineteen years in which Grue-Sørensen worked as a professor of educationat the university. The assumption upon which the essay rests is that his main ambition during theseyears was to (...) lay the scientific foundations of educational theory as a an autonomous discipline in its own rightnext to neighbouring disciplines like, say, psychology and sociology. Although well acquainted with those disciplineshe nevertheless consequently subjected their research results to critical examination of their relevanceto the solution of educational problems. Infl uenced in general by a strong interest in language matters andby English philosophers in particular he practiced a method of ordinarylanguage analysis and applied it to bring to light important language nuances often overlooked in empiricalresearch. Convincingly, he demonstrated this method in his analysis of the concept of learning. (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)

Kripke's lectures, published as Wittgenstein on Rules and Private Language , posed a sceptical problem about following a rule, which he cautiously attributed to Wittgenstein. He briefly noticed an analogy between his new kind of scepticism and Goodman's riddle of induction. ‘Grue’, he said, could be used to formulate a question not about induction but about meaning: 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 did not mean grue by “green”, so that now I should call the sky, not the grass, “green”?’. (shrink)

Begins by explaining then proving a generalized language dependence result similar to Goodman's "grue" problem. I then use this result to cast doubt on the existence of an objective evidential favoring relation (such as "the evidence confirms one hypothesis over another," "the evidence provides more reason to believe one hypothesis over the other," "the evidence justifies one hypothesis over the other," etc.). Once we understand what language dependence tells us about evidential favoring, our options are an implausibly strong (...) conception of the a priori, a hard externalism on which agents are unable to determine what their evidence favors, or a subjectivist view that makes evidential favoring relative to features of the agent. (shrink)

Recent solutions to the curve-fitting problem, described in Forster and Sober ([1995]), trade off the simplicity and fit of hypotheses by defining simplicity as the paucity of adjustable parameters. Scott De Vito ([1997]) charges that these solutions are 'conventional' because he thinks that the number of adjustable parameters may change when the hypotheses are described differently. This he believes is exactly what is illustrated in Goodman's new riddle of induction, otherwise known as the grue problem. However, the (...) 'number of adjustable parameters' is actually a loose way of referring to a quantity that is not language dependent. The quantity arises out of Akaike's theorem in a way that ensures its language invariance. (shrink)

It is notoriously difficult to spell out the norms of inductive reasoning in a neat set of rules. I explore the idea that explanatory considerations are the key to sorting out the good inductive inferences from the bad. After defending the crucial explanatory virtue of stability, I apply this approach to a range of inductive inferences, puzzles, and principles such as the Raven and Grue problems, and the significance of varied data and random sampling.

I present a solution to the epistemological or characterisation problem of induction. In part I, Bayesian Confirmation Theory (BCT) is discussed as a good contender for such a solution but with a fundamental explanatory gap (along with other well discussed problems); useful assigned probabilities like priors require substantive degrees of belief about the world. I assert that one does not have such substantive information about the world. Consequently, an explanation is needed for how one can be licensed to act (...) as if one has substantive information about the world when one does not. I sketch the outlines of a solution in part I, showing how it differs from others, with full details to follow in subsequent parts. The solution is pragmatic in sentiment (though differs in specifics to arguments from, for example, William James); the conceptions we use to guide our actions are and should be at least partly determined by preferences. This is cashed out in a reformulation of decision theory motivated by a non-reductive formulation of hypotheses and logic. A distinction emerges between initial assumptions--that can be non-dogmatic--and effective assumptions that can simultaneously be substantive. An explanation is provided for the plausibility arguments used to explain assigned probabilities in BCT. -/- In subsequent parts, logic is constructed from principles independent of language and mind. In particular, propositions are defined to not have form. Probabilities are logical and uniquely determined by assumptions. The problems considered fatal to logical probabilities--Goodman's `grue' problem and the uniqueness of priors problem are dissolved due to the particular formulation of logic used. Other problems such as the zero-prior problem are also solved. -/- A universal theory of (non-linguistic) meaning is developed. Problems with counterfactual conditionals are solved by developing concepts of abstractions and corresponding pictures that make up hypotheses. Spaces of hypotheses and the version of Bayes' theorem that utilises them emerge from first principles. -/- Theoretical virtues for hypotheses emerge from the theory. Explanatory force is explicated. The significance of effective assumptions is partly determined by combinatoric factors relating to the structure of hypotheses. I conjecture that this is the origin of simplicity. (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)

Many attempts have been made to solve Hume's problem. However, the assumptions leading to the problem have remained largely unnoticed. Moreover, since Goodman introduced the predicate "grue", philosophers without relevant mathematical education have been confused. In addition, various delusive arguments from convergence have been presented. In this book, it is maintained that knowledge has to be feasible and relevant and that several solutions fail to meet that demand. It is argued that the crucial presupposition of the (...) class='Hi'>problem of induction is that clairvoyance is impossible and that this presupposition is unproven. Generalized Goodman predicates are introduced. To criticize arguments from convergence, the notion of "undecided game" is introduced. A relationship between Zeno's paradox and the problem of induction is revealed. A distinction between "do not know" and "cannot know" is consistently held. It is concluded that, as yet, we do not know the future and that it is impossible to prove that it is impossible to know the future. This book should be useful to professionals in epistemology and philosophy of science, and might be of interest to logicians and mathematicians. (shrink)

This paper consists of an investigation of three debates concerning propositional identity: the tension between structured propositions and higher-order logic, the principle Only Logical Circles, and Kaplan’s Paradox. The literature at large has mistaken the consequences of each of these debates. Structuralists are not committed to the claim that identical properties have different extensions; rather, they are committed to existence monism. Only Logical Circles does not preclude the identification of green in terms of grue; some further (and, as of (...) yet, undisclosed) principle is required for that result. And Kaplan’s Paradox does not count against the possible-worlds conception of propositions; it applies to every account of propositions whatsoever. (shrink)

This chapter examines gruesome predicates, the most notorious of which is 'grue'. It proceeds by extending the analysis of Theo A. F. Kuipers' From Instrumentalism to Constructive Realism in three directions. It proposes an amplified typology of grue problems, first of all, and argues that one such problem is the root of the rest. Second, it suggests a solution to this root problem influenced by Kuipers' Bayesian solution to a related problem. Finally, it expands the (...) class of gruesome predicates by incorporating Quine's 'undetached rabbit part', 'rabbit stage', and the like, and shows how they can be managed along the same Bayesian lines. (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)

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.

State of the art paper on the problem of induction: how to justify the conclusion that ‘all Fs are Gs’ from the premise that ‘all observed Fs are Gs’. The most prominent theories of contemporary philosophical literature are discussed and analysed, such as: inductivism, reliabilism, perspective of laws of nature, rationalism, falsificationism, the material theory of induction and probabilistic approaches, according to Carnap, Reichenbach and Bayesianism. In the end, we discuss the new problem of induction of Goodman, raised (...) by the grue predicate. (shrink)

Confirmation and falsification are different strategies for testing theories and characterizing the outcomes of those tests. Roughly speaking, confirmation is the act of using evidence or reason to verify or certify that a statement is true, definite, or approximately true, whereas falsification is the act of classifying a statement as false in the light of observation reports. After expounding the intellectual history behind confirmation and falsificationism, reaching back to Plato and Aristotle, I survey some of the main controversial issues and (...) arguments that pertain to the choice between these strategies: the Raven Paradox, the Duhem/Quine problem and the Grue Paradox. Finally, I outline an evolutionary criticism of inductive Bayesian approaches based on my assumption of doxastic involuntarism. (shrink)

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)

What makes a prediction arbitrary? This article explores the possibility that one source of arbitrariness is asserting “P iff Q” when the justifications of P and Q are, in the relevant sense, independent. It uses this idea to draw a formal distinction between non-arbitrary and arbitrary predictions, even if they are also correct. It initially illustrates with Goodman’s New Riddle. There are, by now, so many different literature-prominent variants of grue, emerose or other odd-looking predicates that, surprisingly, the criterion (...) handles them relatively straightforwardly. As the proposal is markedly distinct from existing resolution strategies centred on predicate projectability or counterfactual analysis, it sidesteps their well-known problems. The article makes the case that testing entailments for arbitrariness enjoys advantages over the currently dominant approach of directly putting conditions on when an F that is G should support “All F are G.” The article then surveys possible broader objections and offers two formal tools for identifying when and especially why a hypothesis makes good – that is, correct and non-arbitrary – predictions or not. (shrink)

Subjective Bayesianism is the current orthodoxy in confirmation theory. In broad outline, this view claims a) that confirmation is a relation of positive relevance, viz., that a piece of evidence confirms a theory if it increases its probability; b) that this relation of confirmation is captured by Bayes’s theorem; c) that, hence, the only factors relevant to confirmation of a theory are its prior probability, the likelihood of the evidence given the theory and the probability of the evidence; d) that (...) the specification of the prior probability of a theory is a purely subjective matter; e) that the only constraint on an assignment of prior probabilities to several theories should be that they obey the axioms of the probability calculus; f) that, hence, the reasonableness of a belief does not depend on its content; nor, ultimately, on whether the belief is made reasonable by the evidence; and g) that degrees of belief are probabilities and that belief is always a matter of degree. This theory has had many successes. Old tangles, like the ravens paradox or the grue problem, are resolved. New tangles, like the problem of old evidence, have been, to some extent, resolved. But there is still a pervasive dissatisfaction with subjective Bayesianism. This dissatisfaction concerns all of the theses to above, but it is centred mostly around the point that subjective Bayesianism is too subjective to offer an adequate theory of confirmation and of rational belief. Yet, up until recently this dissatisfaction had not borne fruits in a fully developed alternative theory of confirmation. Perhaps, only Deborah Mayo’s error-statistical approach was a fully developed alternative, but this too faced considerable problems, one central among them being that she takes all probabilities to be relative frequencies. One thing is sure. Probability theory should place a central role in a theory of confirmation. But how are we to interpret probabilities if we want to avoid the subjective element of Bayesianism and the objective element of the error-statistical approach? (shrink)

In this slim but excessively priced volume, Paul Horwich attempts "to exhibit a unified approach to philosophy of science, based on the concept of subjective probability... by offering new treatments of several problems... and... by providing a more complete probabilistic account of scientific methods and assumptions than has been given before". Starting with the view that beliefs are not all-or-nothing matters but rather are susceptible to varying degrees of intensity, and interpreting this via a modified Bayesian use of subjective probability, (...) Horwich treats well-known puzzles in philosophy of science by considering the following topics: accommodation of data, statistical evidence, severe tests, surprising predictions, paradox of confirmation, the "grue" problem, simplicity, ad hoc hypotheses, diverse evidence, prediction vs. accommodation, desirability of further evidence, and realism vs. instrumentalism. Preceding treatment of these topics is an acceptance of the Bayesian principle that "the degrees of belief of an ideally rational person conform to the mathematical principles of probability theory" and a treatment of probability theory and its various standard interpretations which comprises a quarter of the text. (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)

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)

I have no problem with Millikan's saying that Mama, milk, and mouse are substances, but I do not see why this list cannot be extended with white, red cows, things, vovetas, lhenxa, GRUE, and so on. In the right circumstances, given the right training, the characteristics of substances that Millikan provides work equally well for each of them.

Nelson Goodman's acceptance and critique of certain methods and tenets of positivism, his defence of nominalism and phenomenalism, his formulation of a new riddle of induction, his work on notational systems, and his analysis of the arts place him at the forefront of the history and development of American philosophy in the twentieth-century. However, outside of America, Goodman has been a rather neglected figure. In this first book-length introduction to his work Cohnitz and Rossberg assess Goodman's lasting contribution to philosophy (...) and show that although some of his views may be now considered unfashionable or unorthodox, there is much in Goodman's work that is of significance today. The book begins with the "grue"-paradox, which exemplifies Goodman's way of dealing with philosophical problems. After this, the unifying features of Goodman's philosophy are presented - his constructivism, conventionalism and relativism - followed by an discussion of his central work, The Structure of Appearance and its significance in the analytic tradition. The following chapters present the technical apparatus that underlies his philosophy, his mereology and semiotics, which provides the background for discussion of Goodman's aesthetics. (shrink)

Mathematical investigation, when done well, can confer understanding. This bare observation shouldn’t be controversial; where obstacles appear is rather in the effort to engage this observation with epistemology. The complexity of the issue of course precludes addressing it tout court in one paper, and I’ll just be laying some early foundations here. To this end I’ll narrow the field in two ways. First, I’ll address a specific account of explanation and understanding that applies naturally to mathematical reasoning: the view proposed (...) by Philip Kitcher and Michael Friedman of explanation or understanding as involving the unification of theories that had antecedently appeared heterogeneous. For the second narrowing, I’ll take up one specific feature (among many) of theories and their basic concepts that is sometimes taken to make the theories and concepts preferred: in some fields, for some problems, what is counted as understanding a problem may involve finding a way to represent the problem so that it (or some aspect of it) can be visualized. The final section develops a case study which exemplifies the way that this consideration – the potential for visualizability – can rationally inform decisions as to what the proper framework and axioms should be. The discussion of unification (in sections 3 and 4) leads to a mathematical analogue of Goodman’s problem of identifying a principled basis for distinguishing grue and green. Just as there is a philosophical issue about how we arrive at the predicates we should use when making empirical predictions, so too there is an issue about what properties best support many kinds of mathematical reasoning that are especially valuable to us. The issue becomes pressing via an examination of some physical and mathematical cases that make it seem unlikely that treatments of unification can be as straightforward as the philosophical literature has hoped. Though unification accounts have a grain of truth (since a phenomenon (or cluster of phenomena) called “unification” is in fact important in many cases) we are far from an analysis of what “unification” is.. (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)

Nelson Goodman's acceptance and critique of certain methods and tenets of positivism, his defence of nominalism and phenomenalism, his formulation of a new riddle of induction, his work on notational systems, and his analysis of the arts place him at the forefront of the history and development of American philosophy in the twentieth-century. However, outside of America, Goodman has been a rather neglected figure. In this first book-length introduction to his work Cohnitz and Rossberg assess Goodman's lasting contribution to philosophy (...) and show that although some of his views may be now considered unfashionable or unorthodox, there is much in Goodman's work that is of significance today. The book begins with the "grue"-paradox, which exemplifies Goodman's way of dealing with philosophical problems. After this, the unifying features of Goodman's philosophy are presented - his constructivism, conventionalism and relativism - followed by an discussion of his central work, The Structure of Appearance and its significance in the analytic tradition. The following chapters present the technical apparatus that underlies his philosophy, his mereology and semiotics, which provides the background for discussion of Goodman's aesthetics. The final chapter examines in greater depth the presuppositions underlying his philosophy. (shrink)

In her recent (2009) book, The Origins of Concepts, Susan Carey argues that what she calls ‘Quinean Bootstrapping’ and processes of analogy in children show that the expressive power of a mind can be increased in ways that refute Jerry Fodor's (1975, 2008) ‘Mad Dog’ view that all concepts are innate. I argue that it is doubtful any evidence about the manifestation of concepts in children will bear upon the logico-semantic issues of expressive power. Analogy and bootstrapping may be ways (...) to bring about the former, but only by presupposing the very expressive powers Carey is claiming they explain. Analogies must be understood, and bootstrapping involves confirmation of hypotheses already expressible; otherwise they can't select among an infinitude of hypotheses compatible with the finite data the child has encountered, a fact rendered vivid by Goodman's ‘grue’ paradox and Chomsky's poverty of stimulus argument. The problems have special application to minds, since there is no reason to expect a child's concepts to be ‘projectible’ or to correspond to mind-independent natural kinds. I conclude with an ecumenical view that concepts are reasonably regarded as both innate and often learned, and that what is learned can in fact increase what really concerns Carey, the functioning psychological expressive power of the child, even if it leaves untouched what concerns Fodor, the semantic expressive power. Less ecumenically: maybe Fodor (2008) miscast the debate, and the real issue that bothers people concerns not nativism, but an issue on which Carey and Fodor surprisingly agree, his conceptual Atomism, or the view that all mono-morphemic concepts are primitive and unanalyzable. The issue deserves further discussion independently of Mad-doggery. (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 (...) class='Hi'>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)

The resemblance is plain to see between Kripke’s Wittgenstein introducing bizarre rules such as quaddition (in illustrating the sceptical paradox against theories of meaning) and Goodman’s introducing the equally bizarre grue (in generating the new riddle of induction). But the two sorts of bizarre cases also differ in interesting respects. For those familiar with Goodman’s case, this similarity sparks a strong temptation to enlist to the meaning sceptic’s cause key elements of Goodman’s new riddle, which are missing from Kripke’s (...) case. In this essay, I characterize a natural way of doing just this, which targets dispositionalist solutions to the sceptical paradox. I also show that, despite initial appearances, this new objection to dispositionalism (the symmetry problem) is not nearly as worrisome as originally thought. The solution offered on behalf of semantic dispositionalists does require a trade-off, though, from the severe form of indeterminacy advanced by the meaning sceptic to a much milder thesis. (shrink)

In the framework of set theory we cannot distinguish between natural and non-natural predicates. To avoid this shortcoming one can use mathematical structures as conceptual spaces such that natural predicates are characterized as structurally nice subsets. In this paper topological and related structures are used for this purpose. We shall discuss several examples taken from conceptual spaces of quantum mechanics (orthoframes), and the geometric logic of refutative and affirmable assertions. In particular we deal with the problem of structurally distinguishing (...) between natural colour predicates and Goodmanian predicates like grue and bleen. Moreover the problem of characterizing natural predicates is reformulated in such a way that its connection with the classical problem of geometric conventionalism becomes manifest. This can be used to shed some new light on Goodman's remarks on the relative entrenchment of predicates as a criterion of projectibility. (shrink)

The aim of this paper is to show that (elementary) topology may be useful for dealing with problems of epistemology and metaphysics. More precisely, I want to show that the introduction of topological structures may elucidate the role of the spatial structures (in a broad sense) that underly logic and cognition. In some detail I’ll deal with “Cassirer’s problem” that may be characterized as an early forrunner of Goodman’s “grue-bleen” problem. On a larger scale, topology turns out (...) to be useful in elaborating the approach of conceptual spaces that in the last twenty years or so has found quite a few applications in cognitive science, psychology, and linguistics. In particular, topology may help distinguish “natural” from “not-so-natural” concepts. This classical problem that up to now has withstood all efforts to solve (or dissolve) it by purely logical methods. Finally, in order to show that a topological perspective may also offer a fresh look on classical metaphysical problems, it is shown that Leibniz’s famous principle of the identity of indiscernibles is closely related to some well-known topological separation axioms. More precisely, the topological perspective gives rise in a natural way to some novel variations of Leibniz’s principle. (shrink)

Invoking metaphysical naturalness is “perhaps the most popular proposed solution” to the problem of grue (Hedden in Can J Philos 45:716–743, 2016). Accordingly, Bradley (Mind 129:179–203, 2020) develops a “Lewisian” method for constraining priors based on the syntactic simplicity of descriptions of possible worlds in a language whose predicates correspond to natural properties. The Lewisian method therefore requires a solution to the arguably unsolved problem of measuring syntactic simplicity. But this paper argues that _given_ a solution to (...) this problem, there is a better alternative to the Lewisian method: a novel “Neo-Carnapian” method for constraining priors based on the indistinguishability of experiences. (shrink)

In his commentary on my paper, “Means-Ends Epistemology”, David Chart constructs a Riddle of Induction with the following feature: Means-ends analysis, as I formulated it in the paper, selects “all emeralds are grue” as the optimal conjecture after observing a sample of all green emeralds. Chart’s construction is rigorous and correct. If we disagree, it is in the philosophical morals to be drawn from his example. Such morals are best discussed by elucidating some of the larger epistemological issues involved. (...) “Means-ends Epistemology” sought a normative theory of hypothesis selection. I defined what it means for an inductive method to reliably and efficiently find a correct hypothesis from a set of alternative hypotheses. (In fact, I investigated a number of standards of empirical success for inductive methods.) Call such methods optimal. We may take optimal inferences to be those made by optimal methods. This defines a relation Optimal-Inference(h,e,H): “given the set of alternative hypotheses H, and evidence e, hypothesis h is an optimal inference”. One fundamental difference between the means-ends approach and traditional confirmation theory is that the latter has sought a two-place relation between theory and evidence alone, something like “hypothesis h is highly confirmed given evidence e”. From my point of view, posing the problem of induction as discerning the right relation between theory and evidence is elliptical because it leaves unspecified the set of alternative hypotheses under investigation (as well as other relevant factors, such as the scientist’s background knowledge, observational means, cognitive capacities and epistemic values). Chart’s Riddle highlights the fact that depending on the space of alternative hypotheses, means-ends analysis may select a different hypothesis on the same evidence: “all emeralds are green” in my Goodmanian Riddle, and “all emeralds are grue” in his. To my mind, his example.. (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)

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)

Goodman’s account of the ‘grue’ paradox stands at a crossroads in the history of twentieth century epistemology. Published in 1954, Fact, Fiction, and Forecast is a reaction to the logical empiricist views that held sway in the first half of the last century and anticipates many of the conventionalist and/or relativist moves popular throughout the second half. Through his evaluation of Hume’s problem of induction, as well as his own novel reformulation of it, Goodman comes to reject a (...) number of the fundamental parts of logical empiricism. In particular, Goodman argues that the formal epistemic methods the logical empiricists wanted to rely upon are insufficient. This leads him to turn towards conventionalism, which is the basis of his rejection of the objective view of knowledge. In his conventionalism he is a precursor of writers such as Hanson, Kuhn and Feyerabend, who, seeing the inadequacy of formalism, sought to fill the gaps it left in epistemic methodology with scientific values, tacit knowledge and linguistic practices. Making use of Susan Haack’s distinction between three different kinds of foundationalism, we analyse Goodman’s position and its relation to the views of the logical empiricists. The two are reflections of each other in that, where the logical empiricists are foundationalists in their views on empirical evidence, methods used and objective criteria of justification, Goodman consistently opts for the corresponding coherentist options. As it turns out, this choice of options makes it impossible for Goodman to deal with the very objections he raises against the logical empiricists. In adding the new problem of induction to the old one, Goodman adds a problem which clearly can not be resolved by a purely syntactic solution. The charge Goodman raises is that logical empiricists cannot determine which predictions are sound and which are not. We argue that his method of identifying acceptable predictions based on the use of entrenchment is, in the end, arbitrary and only postpones the underlying problem. (shrink)

Since Hume, philosophers of induction have debated the question of whether we have any reason for assuming that nature is uniform. This debate has always presumed that the uniformity hypothesis is itself coherent. In Part 1 of the following I argue that a proper appreciation of Nelson Goodman's so-called grue-green problem1 should lead us to the conclusion that the uniformity hypothesis, under its usual interpretation as a strictly ontological thesis, is incoherent. In Part 2 I argue that further consideration (...) of the grue-green problem leads to the conclusion that certain popular versions of the thesis of physical supervenience/the primacy of physics, under their usual interpretation as strictly ontological theses, are false. In Part 3 I argue that the notions of natural kinds and nature's joints should not be taken as ontologically objective notions but as interest relative. Together Parts 1, 2, and 3 provide support for the Nietzsche-Goodman thesis that philosophers are prone to mistakenly identify as absolute, mind and language independent, features of the world which are in fact only features of a particular discourse, or of the world relative to a particular discourse. (shrink)

Oddity One : Kripke claims that Wittgenstein has invented "a new form of scepticism", one which inclines Kripke "to regard it as the most radical and original sceptical problem that philosophy has seen to date, one that only a highly unusual cast of mind could have produced" (K, p. 60). However, Kripke also claims that there are analogies (and sometimes the analogies look very much like identities) between Wittgenstein's sceptical argument and the work of at least three and maybe (...) four other philosophers, viz., Quine, Goodman, Hume and Berkeley. Strange stuff indeed. The originality of Wittgenstein's work is especially difficult to see after Kripke claims that Wittgenstein presents a problem concerning the nexus between past . . . 'meanings' and present practice" (K, p. 62), and says that Hume is said to have questioned "the causal nexus whereby a past event necessitates a future one, and the inductive inferential nexus from the past to the future." (K, p. 62). Whither the originality? And the connection with Goodman's work with 'grue' is even closer than that between Kripke's Wittgenstein and Hume. Given that Kripke had read Goodman before "discovering" the rule-following paradox in Wittgenstein, one ought to be sceptical of Kripke's claim that Wittgenstein has invented a new form of scepticism. It would be much more accurate to say that Kripke has strapped Wittgenstein with a hybrid scepticism drawn from Hume and Goodman. (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)

Goodman’s paradox gives rise to a cluster of problems, problems that are in need of different answers. I will discuss some variants of the grue hypothesis applied to the technological context. One conclusion in this paper is that there is room for rational decisions, and that solutions to the paradoxes in technology can be found in the practical choice situation. *Received April 2008. †To contact the author, please write to: Department of Medical and Health Sciences, Linköping University, SE‐581 83 (...) Linköping, Sweden; e‐mail: ingemar.nordin@liu.se. (shrink)

Broadly taken, the term “induction” denotes our whole nondeductive procedure of acquiring, maintaining, and discarding beliefs about what is so far unobserved or undetected or unknown. In this chapter, I examine induction from the perspective of my account of warrant. I first take up what is now referred to as “the old riddle of induction,” rejecting David Hume's claim that inductive reasoning is not rationally justified and defending the view that beliefs formed on the basis of inductive reasoning can have (...) warrant. I then turn to Nelson Goodman's ruminations on grue and the “new riddle of induction,” which is the question: what makes a property projectible? I reject Goodman's own solution to this problem, examine other inadequate solutions, and then suggest that an answer can be found by making reference to the proper function of the human intellect; projectible properties are just those properties that a properly functioning adult human being in our circumstances will in fact project. (shrink)

I I set out my view that all inference is essentially deductive and pinpoint what I take to be the major shortcomings of the induction rule.II The import of data depends on the probability model of the experiment, a dependence ignored by the induction rule. Inductivists admit background knowledge must be taken into account but never spell out how this is to be done. As I see it, that is the problem of induction.III The induction rule, far from providing (...) a method of discovery, does not even serve to detect pattern. Knowing that there is uniformity in the universe is no help to discovering laws. A critique of Reichenbach's justification of the straight rule is constructed along these lines.IV The induction rule, by itself, cannot account for the varying rates at which confidence in an hypothesis mounts with data. The mathematical analysis of this salient feature of inductive reasoning requires prior probabilities. We also argue, against orthodox statisticians, that prior probabilities make a substantive contribution to the objectivity of inductive methods, viz. to the design of experiments and the selection of decision rules.V Carnap's general criticisms of various estimation rules, like the straight rule and the ‘impervious rule’, are seen to be misguided when the prior densities to which they correspond are taken into account.VI Analysis of Hempel's definition of confirmation qua formalization of the enumerative (naive) conception of instancehood. We show that from the standpoint of the quantitative measure P(H/E):P(H) for the degree to which E confirms H, Hempel's classificatory concept yields correct results only for sampling at large from a finite population with a two-way classification all of whose compositions are equally probable. We extend the analysis to Goodman's paradox, finding cases in which grue-like hypotheses do receive as much confirmation as their opposite numbers. We argue, moreover, the irrelevancy of entrenchment, and maintain that Goodman's paradox is no more than a straightforward counter-example to the enumerative conception of instancehood embodied in Hempel's definition.VII We rebutt the objection that prior probabilities, qua inputs of Bayesian analysis, can only be obtained by enumerative induction (insofar as they are objective). The divergence in the prior densities of two rational agents is less a function of subjectivity, we maintain, than of vagueness.VIII Our concluding remarks stress that, for Bayesians, there is no problem of induction in the usual sense. (shrink)