English translation of a paper intially publisdhed in French in Dialogue under the title 'Une solution pour le paradoxe de Goodman'. In the classical version of Goodman's paradox, the universe where the problem takes place is ambiguous. The conditions of induction being accurately described, I define then a framework of n-universes, allowing the distinction, among the criteria of a given n-universe, between constants and variables. Within this framework, I distinguish between two versions of the problem, respectively taking place: (...) (i) in an n-universe the variables of which are colour and time; (ii) in an n-universe the variables of which are colour, time and space. Finally, I show that each of these versions admits a specific resolution. (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: [email protected]. (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)

The talk is mainly defensive. I won’t offer positive accounts of the “paradoxical” cases I will discuss (but, see “Extras”). I’ll begin with Harman’s defense of classical deductive logic against certain (epistemological) “relevantist” arguments.

Historically, Nelson Goodman’s paradox involving the predicates ‘grue’ and ‘bleen’ has been taken to furnish a serious blow to Carl Hempel’s theory of confirmation in particular and to purely formal theories of confirmation in general. In this paper, I argue that Goodman’s paradox is no more serious of a threat to Hempel’s theory of confirmation than is Hempel’s own paradox of the ravens. I proceed by developing a suggestion from R. D. Rosenkrantz into an argument for (...) the conclusion that these paradoxes are, in fact, equivalent. My argument, if successful, is of both historical and philosophical interest. Goodman himself maintained that Hempel’s theory of confirmation was capable of handling the paradox of the ravens. And Hempel eventually conceded that Goodman’s paradox showed that there could be no adequate, purely syntactical theory of confirmation. The conclusion of my argument entails, by contrast, that Hempel’s theory of confirmation is incapable of handling Goodman’s paradox if and only if it is incapable of handling the paradox of the ravens. It also entails that for any adequate solution to one of these paradoxes, there is a corresponding and equally adequate solution to the other. (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)

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

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 argue that metaphysical realism is insufficient to solve Goodman's grue paradox.

Hempel‘s paradox of the ravens, and his take on it, are meant to be understood as being restricted to situations where we have no additional background information. According to him, in the absence of any such information, observations of FGs confirm the hypothesis that all Fs are G. In this paper I argue against this principle by way of considering two other paradoxes of confirmation, Goodman‘s 'grue‘ paradox and the 'tacking‘ (or 'irrelevant conjunct‘) paradox. What these (...) paradoxes reveal, I argue, is that a presumption of causal realism is required to ground any confirmation; but once we grant causal realism, we have no reason to accept the central principles giving rise to the paradoxes. (shrink)

In a recent paper on Goodman's paradox, I have argued that ‘grue’ is unprojectible because the grue-evidence is doxastically dependent on the evidence that the samples are examined before t. Christopher Dorst replies that doxastic dependence is unable to yield a language-independent asymmetry with respect to ‘green’ and ‘grue’ and hence cannot resolve Goodman's paradox. In this response I hope to show that Dorst's considerations are flawed: his argument for the language-relativity of doxastic (...) dependence is inconclusive at best—even if his construal of doxastic dependence were correct. It is incorrect, however: Dorst mistakes counterfactual dependence of beliefs for belief in counterfactual dependence. I will also argue that doxastic dependence properly understood is not threatened by any of his objections. (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)

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)

Article presenting basic methodological tenets in Goodman's philosophical development with their mutual connections, like the new riddle of indutcion, counterfactual conditionals and his use of reflective equilibrium as a methodological basis.

An admirable introduction to inductive logic, this book is both informative and lucidly written. After an excellent introductory chapter comparing deductive with inductive logic, the author presents Hume's problem of induction and several proposed methods for solving or dissolving it, none of which are adequate. Chapter III is devoted to Goodman's paradox about "grue" and the problems it poses for induction. No attempt, however, is made to develop a calculus of projectibility, which is needed to solve this (...) new riddle of induction. The systematic part of inductive logic is presented in the fourth and longest chapter. This chapter begins with a brief account of elementary truth functions which the author then uses to present an updated and rather elegant version of Mill's methods. The rest of the chapter is devoted to the development of the probability calculus in a systematic manner, without, however, any method of assigning initial probabilities. An account of statistics is appended, which is too brief to be of much value. The fifth chapter is devoted to interpretations of the probability calculus. The frequency interpretation of probability is described as an adequate account of descriptive probability. Two interpretations of inductive probability are presented: Carnap's "logic" interpretation and the frequency interpretation of Reichenbach. Both, however, are found lacking in ultimate justification. Though not flawless, this book is of very high quality.—F. S. M. (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)

The purpose of this note is to examine the claim made by Howard Smokler that “Goodman's paradox should be considered as an independent argument against a conception of inductive logic which makes use of rules of acceptance”.Smokler's claim arises from his treatment of Goodman's paradox in the form given it by Israel Scheffler. Schefflerhas discussed this paradox primarily in the context of a methodology of induction which views inductive rules as rules of acceptance permitting one (...) to assert detached conclusions. The inductive rule considered by Scheffler is described as follows: What leads us to make one particular prediction rather than its opposite is not its deducibility froIII evidence but rather its congruence with a generalization thoroughly in accord with all such evidence, and the correlative disconfirmation of the contrary generalization by the same evidence.. (shrink)

The paper develops an inductive extension of AGM-style belief base revision theory with the aim of formally implementing Freitag’s :254–267, 2015, Dialectica 70:185–200, 2016) solution to Goodman’s paradox. It shows that the paradox dissolves once belief revision takes place on inductively closed belief bases, rather than on belief sets.

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)

I will now describe several applications of the theory of n-universes across different probabilistic scenarios. First, I will explain how n-universes can extend the probability spaces used in traditional probability theory. These extended probability spaces enable more refined modelling of complex probabilistic situations and align more intuitively with our perceptions of the physical universe. Next, I will demonstrate the use of n-universes as a methodological tool through two thought experiments described by John Leslie. Finally, I will model Goodman's (...) class='Hi'>paradox within the framework of n-universes, showing how they closely resemble Goodmanian worlds. (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 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)

Essential for the concept of the law of nature is not only spatio-temporal universality, but also functionality in the sense of the dependency on physical conditions of natural entities. In the following it is explained in detail that just the neglect of this functional property is to be understood as the real reason for the occurrence of the Goodman paradox – with the consequence, that the behavior of things seems to be completely at the mercy of change of unique (...) unrepeatable temporal points. It is exactly this (mis-)understanding that also generated the induction problem. From the intrinsic connection between universality and functionality, however, – that is my claim – the ontological consequence of a nature results, for which lawfulness is coupled to essentially functionally defined time sequences, thereby implying a potentiality dimension of nature, too. (shrink)

The structure of Reichenbach's pragmatic vindication of induction is analysed in detail. The argument is seen to proceed in two stages, the first being a pragmatic justification of the frequency interpretation of probability which is taken as a license for considering the aim of induction to be the discovery of limiting relative frequencies, and the second being the pragmatic justification of induction itself. Both justifications are found to contain flaws, and the arguments used to support Reichenbach's definition of the aim (...) of induction presuppose the availability of a type of predicate which generates paradoxes closely related to Goodman's "grue-bleen" paradox. Next, Salmon's "Criterion of Linguistic Invariance" is evaluated as a canon of inductive logic, which singles out the "straight rule" from an infinite class of convergent inductive rules. Upon close examination, its credentials are seen to be unimpressive. In connection with Salmon's work on linguistic invariance, we take a closer look at the impact of the Goodman paradox on probability estimator rules like Reichenbach's "straight rule." We find that its undesirable consequences for such systems of inductive logic cannot be escaped by Salmon's solution, or indeed by any solution whose motivating idea is to rule "queer" predicates out of court. Finally, the discussion of the Goodman paradox leads us to a modest methodological proposal for systems of inductive logic which incorperate probability estimator rules of the type at issue. (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)

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)

1. Confirmation Theory One, which we shall construct, when applied to the Raven Hypothesis yields the following results: Any black raven confirms the Raven Hypothesis.Any black non-raven confirms the Raven Hypothesis.Any non-black raven disconfirms the Raven Hypothesis.Any non-black non-raven is neutral to the Raven Hypothesis.Theory One consists of two parts: six basic concepts from confirmation theory proper, and the underlying logic.

The Kripke/Wittgenstein paradox and Goodman’s riddle of induction can be construed as problems of multiple redescription, where the relevant sceptical challenge is to provide factual grounds justifying the description we favour. A choice of description or predicate, in turn, is tantamount to the choice of a curve over a set of data, a choice apparently governed by implicitly operating constraints on the relevant space of possibilities. Armed with this analysis of the two paradoxes, several realist solutions of Kripke’s (...) class='Hi'>paradox are examined that appeal to dispositions or other non-occurrent properties. It is found that all neglect crucial epistemological issues: the entities typically appealed to are not observational and must be inferred on the basis of observed entities or events; yet, the relevant sceptical challenge concerns precisely the factual basis on which this inference is made and the constraints operating on it. All disposition ascriptions, the thesis goes on to argue, contain elements of idealization. To ward off the danger of vacuity resulting from the fact that any disposition ascription is true under just the right ideal conditions, dispositional theories need to specify limits on legitimate forms of idealization. This is best done by construing disposition ascriptions as forms of (implicit) curve-fitting, I argue, where the “data” is not necessarily numeric, and the “curve” fitted not necessarily graphic. This brings us full circle: Goodman’s and Kripke’s problems are problems concerning curve-fitting, and the solutions for it appeal to entities the postulation of which is the result of curve-fitting. The way to break the circle must come from a methodology governing the idealizations, or inferences to the best idealization, that are a part of curve-fitting. The thesis closes with an argument for why natural science cannot be expected to be of much help in this domain, given the ubiquity of idealization. (shrink)

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)

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)

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)

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)

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.

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 identity predicate can be defined using second-order quantification: a=b =df ∀F(Fa↔Fb). Less familiarly, a dyadic sentential operator analogous to the identity predicate can be defined using third-order quantification: ϕ≡ψ =df ∀X(Xϕ↔Xψ), where X is a variable of the same syntactic type as a monadic sentential operator. With this notion in view, it is natural to ask after general principles governing its application. More grandiosely, how fine-grained is reality? -/- I will argue that reality is not structured in anything like (...) the way that the sentences we use to talk about it are structured. I do so by formulating a higher-order analogue of Russell’s paradox of structured propositions. I then relate this argument to the Frege-Russell correspondence. When confronted with the alleged paradox, Frege agreed that reality was not structured, but maintained that propositions (i.e. thoughts) were structured all the same. Russell replied that his paradox showed Frege’s theory of structured thoughts to be inconsistent, to which Frege replied that Russell’s argument failed to heed the distinction between sense and reference. Most recent commentators have sided with Russell. In defense of Frege, I establish the consistency of one version of his rejoinder. I then consider and reject some ways of resisting the argument against a structured conception of reality. I conclude that, if propositions are structured, this is because they correspond not to distinctions in reality, but rather to ways in which those distinctions can be represented. (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)

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

This paper begins with a rigorous critique of David Stove''s recent bookThe Rationality of Induction. In it, Stove produced four different proofs to refute Hume''s sceptical thesis about induction. I show that Stove''s attempts to vindicate induction are unsuccessful. Three of his proofs refute theses that are not the sceptical thesis about induction at all. Stove''s fourth proof, which uses the sampling principle to justify one particular inductive inference, makes crucial use of an unstated assumption regarding randomness. Once this assumption (...) is made explicit, Hume''s thesis once more survives.The refutation of Stove''s fourth proof leads to some observations which relate Goodman''s grue paradox with randomness of a sample. I formulate a generalized version of Goodman''s grue paradox, and argue that whenever a sample, no matter how large, is drawn from a predetermined smaller interval of a population that is distributed over a larger interval, any conclusion drawn about the characteristics of the population based on the observed characteristics of the sample is fatally vulnerable to the generalized grue paradox. (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 general, the eleven, previously unpublished papers are not as strong as those in the first series. Bromberger attempts to detail the necessary and sufficient conditions for something's being an explanation; Anscombe offers some provocative but inconclusive remarks on the intentionality of sensation; Malpas examines some criteriological puzzles which arise in considering the location of sound as a bit of unlearned perceptual behavior. The rest of the papers are second order assessments and attacks upon positions maintained by other analytical philosophers. (...) Of these Putnam's attack on Malcolm's brand of behaviorism and Butler's attempted dissolution of Goodman's "grue" paradox make their points most effectively. Moravcsik contends, against Strawson, that events are at least as primitive in our conceptual scheme as physical bodies. Wiggins questions some Fregean analyses of the logic of identity-statements; taking off from Strawson, Woods distinguishes a principle of individuation from a criterion of identity and attempts to clarify their separate but related roles by an analysis of the sorts of questions that require their use in giving answers. Rundle is concerned to modify certain Quinean answers to paradoxes of tense requirements that arise in the quantification of modal statements; Savan questions Vlastos' ascription of fallacies to the Socratic argument on the unity of Wisdom and Temperance in the Protagoras. Finally, Shorter points out the general inconclusiveness of "transformational analysis" by exhibiting specific shortcomings of Vendler's analysis of causality in the first volume of this series.—E. A. R. (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)

The work on prototypes in ontologies pioneered by Rosch [10] and elaborated by Lakoff [8] and Freund [3] is related to vagueness in the sense that the more remote an instance is from a prototype the fewer people agree that it is an example of that prototype. An intuitive example is the prototypical “mother”, and it is observed that more specific instances like ”single mother”, “adoptive mother”, “surrogate mother”, etc., are less and less likely to be classified as “mothers” by (...) experimental subjects. From a different direction Gärdenfors [4] provided a persuasive account of natural predicates to resolve paradoxes of induction like Goodman’s “Grue” predicate [5]. Gärdenfors proposed that “quality dimensions” arising from human cognition and perception impose topologies on concepts such that the ones that appear “natural” to us are convex in these topologies. We show that these two cognitive principles — prototypes and predicate convexity — are equivalent to unimodal (convex) fuzzy characteristic functions for sets. Then we examine the case when the fuzzy set characteristic function is not convex, in particular when it is multi-modal. We argue that this is an indication that the fuzzy concept should really be regarded as a super concept in which the decomposed components are subconcepts in an ontological taxonomy. (shrink)