New Riddle Of Induction Research Articles

Induction With and Without Natural Properties: a New Approach to the New Riddle of Induction

Induction With and Without Natural Properties: a New Approach to the New Riddle of Induction

Conceptual Spaces: A Solution to Goodman’s New Riddle of Induction?

AbstractNelson Goodman observed that we use only certain ‘good’ (viz. projectible) predicates during reasoning, with no obvious demarcation criterion in sight to distinguish them from the bad and gruesome ones. This apparent arbitrariness undermines the justifiability of our reasoning practices. Inspired by Quine’s 1969 paper on Natural Kinds, Peter Gärdenfors proposes a cognitive criterion based on his theory of Conceptual Spaces (CS). He argues the good predicates are those referring to natural concepts, and that we can capture naturalness in terms of similarity. In contrast to Quine, he does not primarily rely on logic, but geometry. He frames his account as a descriptive project, however, and it is not obvious how it addresses the normative dimension of Goodman’s Riddle. This paper develops a charitable reconstruction of his argument, based on the idea that the instrumental success of our projectible concepts is grounded in their cognitive-pragmatic naturalness. It then explores three lines of reasoning against the argument: Evolutionarily motivated skepticism, the miracles argument, and the relation between instrumental and pragmatic success. I conclude that in its current form, the CS account fails to provide any justification of reasoning beyond appealing to its instrumental success, and that a metaphysically robust notion of naturalness helps to achieve the desired goal.

The role of scenarios in paradoxes

This paper fills a gap in the existing metaphilosophical research on paradoxes by focusing on the role of scenarios. Typical philosophical paradoxes contain a scenario description whose contribution to paradoxes remains unexplored. I argue that scenarios are examples or instantiations of the abstract schema of paradoxes. As such, scenarios contribute to paradoxes on two levels. First, they make the argument more concrete, thus enhancing the dialectical force of paradoxes and facilitating their understanding, especially for non-experts. This function is external to the paradox itself, but has important practical implications for the use of paradoxes and their effect on philosophical debates, and it contributes to explaining why philosophical paradoxes are usually introduced by a scenario. Second, and more crucially, scenarios are essential to the epistemic dimension of paradoxes. By definition, paradoxes have two necessary components: the argumentative structure and the plausibility/implausibility of the premises/conclusion. By providing examples of the abstract schema, scenarios contribute to making the premises plausible. In particular, scenarios are the source of plausibility and justification for those premises that contain an empirically grounded assertion of existence. Examples of such paradoxes are the Sorites paradox, the Lottery paradox, and the Grue paradox. Contrary to the dialectical role, the epistemic function of scenarios is indispensable, as it connects paradoxes to the real world and underscores their significance in specific debates.

The independence solution to grue

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 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. Correct characterizations of all of them are needed to rule out every problem case. I close by suggesting that the independence solution can be adopted by other approaches—Bayesians, fans of natural kinds, and pragmatists.

The Putnam-Goodman-Kripke Paradox

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.

The Statistical Riddle of Induction

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

Fifty shades of grue: Indeterminate categories and induction in and out of the language sciences

Abstract It is hard to define structural categories of language (e.g. noun, verb, adjective) in a way which accounts for linguistic variation. This leads Haspelmath to make the following claims: i) unlike in biology and chemistry, there are no natural kinds in language; ii) there is a fundamental distinction between descriptive and comparative linguistic categories, and; iii) generalisations based on comparisons between languages can in principle tell us nothing about specific languages. The implication is that cross-linguistic categories cannot support scientific induction. I disagree: generalisations on the basis of linguistic comparison should inform the language sciences. Haspelmath is not alone in identifying a connection between the nature of the categories we use and the kind of inferences we can make (e.g. Goodman’s ‘new riddle of induction’), but he is both overly pessimistic about categories in language and overly optimistic about categories in other sciences: biology and even chemistry work with categories which are indeterminate to some degree. Linguistic categories are clusters of co-occurring properties with variable instantiations, but this does not mean that we should dispense with them: if linguistic generalisations reliably lead to predictions about individual languages, and if we can integrate them into more sophisticated causal explanations, then there is no a priori requirement for a fundamental descriptive/comparative distinction. Instead, we should appreciate linguistic variation as a key component of our explanations rather than a problem to be dealt with.

Philosophy through Machine Learning

In a previous article (2019), I motivated and defended the idea of teaching philosophy through computer science. In this article, I will further develop this idea and discuss how machine learning can be used for pedagogical purposes because of its tight affinity with philosophical issues surrounding induction. To this end, I will discuss three areas of significant overlap: (i) good / bad data and David Hume’s so-called Problem of Induction, (ii) validation and accommodation vs. prediction in scientific theory selection and (iii) feature engineering and Nelson Goodman’s so-called New Riddle of Induction.

Goodman e o projeto de uma definição construtiva de “indução válida”

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

Philosophy of Science for Scientists: The Probabilistic Interpretation of Science

Recently we proposed “quantum language” (or, “the linguistic Copenhagen interpretation of quantum mechanics”, “measurement theory”) as the language of science. This theory asserts the probabilistic interpretation of science (=the linguistic quantum mechanical worldview), which is a kind of mathematical generalization of Born’s probabilistic interpretation of quantum mechanics. In this paper, we consider the most fundamental problems in philosophy of science such as Hempel’s raven paradox, Hume’s problem of induction, Goodman’s grue paradox, Peirce’s abduction, flagpole problem, which are closely related to measurement. We believe that these problems can never be solved without the basic theory of science with axioms. Since our worldview (=quantum language) has the axiom concerning measurement, these problems can be solved easily. Thus we believe that quantum language is the central theory in philosophy of science. Hence there is a reason to assert that quantum language gives the mathematical foundations to science.

There is No New Riddle of Deduction: a Reply to Yehezkel

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

Routes for Roots: A Mapping Shorthand Symbolism with Reference to Nelson Goodman’s Hidden Ars Combinatoria

A shorthand symbolism for the relational mapping of categories (MSS) is introduced and developed on the basis of Nelson Goodman's structural methodology. Through a reconstruction of extensional isomorphism that Goodman introduces as a criterion for definitional accuracy, and a brief reminder of the argument structure behind his ‘new riddle of induction’, Goodman's radical ontological relativism is turned into a protological principle of what I call ‘domain constituting philosophy’. MSS is demonstrated with reference to Goodman's symbol theory, particularly his notion of exemplification, as well as in a final structured comparison of Frege's ‘sense’ with Goodman's straightforward construction of ‘secondary extension’.

The New Riddle of Induction and the New Riddle of Deduction

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.

Indução, confiabilidade e predicados do tipo verdul

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.

Evidence, Significance, and Counterfactuals: Schramm on the New Riddle of Induction

In a recent paper in this journal, Schramm (Erkenntnis 79:571–591, 2014) presents what he takes to be an answer to Goodman’s New Riddle of Induction. His solution relies on the technical notion of evidential significance, which is meant to distinguish two ways that evidence may bear on a hypothesis: either via support or confirmation. As he puts his view in slogan form: “confirmation is support by significant evidence” (p. 571). Once we make this distinction, Schramm claims, we see that Goodman’s famous riddle is dissolved, and we are no longer forced into the “intolerable result” that anything confirms anything. Schramm makes a number of incisive observations in his paper, but I do not think he has solved the New Riddle. There are two reasons for this. First, Schramm has an overly narrow conception of what the Riddle amounts to; I would venture to guess that it is narrower than that of most contemporary philosophers. Thus his proposal does not address the primary concern. Second, Schramm’s notion of significant evidence relies on a counterfactual condition that bears more than a passing resemblance to that made famous by Jackson in his (J Philos 72:113–131, 1975) paper on the topic. However, Jackson’s proposal faces several well-known counterexamples (and even charges of petitio principii), some of which can be adapted into Schramm’s framework. Schramm’s solution thus inherits a number of outstanding problems from Jackson’s proposal, which he has not shown us how to handle.

I BET YOU'LL SOLVE GOODMAN'S RIDDLE

The paper develops a defeasibility approach to Goodman's paradox according to which the unprojectibility of ‘grue’ is an extrinsic feature of the predicate, a product of epistemic context. I first introduce a general puzzle concerning disjunctive weakenings of discriminating predicates, i.e., predicates whose projections enjoy full support by positive instances but are defeated by undermining background information. The resulting challenge is to identify the precise conditions under which such disjunctive projections are defeated as well. I then argue that the grue-paradox is an instance of this general puzzle and that ‘grue’ fails to be projectible because it is evidentially dependent on a discriminating predicate.

On Learning New Primitives in the Language of Thought: Reply to Rey

AbstractA theory of conceptual development must provide an account of the innate representational repertoire, must characterize how these initial representations differ from the adult state, and must provide an account of the processes that transform the initial into mature representations. In Carey, 2009 (The Origin of Concepts), I defend three theses: 1) the initial state includes rich conceptual representations, 2) nonetheless, there are radical discontinuities between early and later developing conceptual systems, 3) Quinean bootstrapping is one learning mechanism that underlies the creation of new representational resources, enabling such discontinuity. I also claim that the theory of conceptual development developed inThe Origin of Conceptsaddresses two of Fodor's challenges to cognitive science; namely, to show how learning could possibly lead to an increase in expressive power and to defeat Mad Dog Nativism, the thesis that all concepts lexicalized as mono‐morphemic words are innate. A recent article by Georges Rey (Mind & Language, 29.2, 2014) argues that my responses to Fodor's challenges fail, because, he says, I fail to distinguish concept possession from manifestation and I do not confront Goodman's new riddle of induction. My response is to show that, and how, new primitives in a language of thought can be learned, that there are easy routes and hard ones to doing so, and that characterizing the learning mechanisms involved is the key to understanding both concept possession and constraints on induction.

Evidence, Hypothesis, and Grue

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

Revamping Hypothetico-Deductivism: A Dialectic Account of Confirmation

We use recently developed approaches in argumentation theory in order to revamp the hypothetico-deductive model of confirmation, thus alleviating the well-known paradoxes the H-D account faces. More specifically, we introduce the concept of dialectic confirmation on the background of the so-called theory of dialectical structures (Betz 2010, 2012b). Dialectic confirmation generalises hypothetico-deductive confirmation and mitigates the raven paradox, the grue paradox, the tacking paradox, the paradox from conceptual difference, and the problem of surprising evidence.

Explanation and the New Riddle of Induction

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