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This chapter challenges the predominant “top-down” view of early inductive inference. According to this view, induction and categorization by infants as young as 9 to 11 months of age is based on abstract knowledge about the properties of things that is acquired through specialized mechanisms, modules, or innate principles. This perspective is contested both on theoretical and empirical grounds. First, it is proposed that infants' concepts for objects and entities are generated via general rather than specific mechanisms. As a corollary of this view, it is argued that early knowledge about the properties of things in the world involves associative links between specific surface features and those properties, and that such representations are not in place until the middle or end of the second year of life. Second, it is argued that care must be taken in interpreting infants' behavior within the inductive generalization procedure. In particular, (1) infants' behavior in the task is not always driven by knowledge acquired prior to arriving at the laboratory; and (2) the basis for induction for any property must be studied before conclusions can be drawn about the nature and content of infants' concepts. In support of these views, data is provided from inductive generalization studies with 14- to 26-month-olds, which show that infants are influenced by the model exemplar used by the experimenter, and that perceptual features—such as legs and wheels— act as the basis for early induction for motion properties.

This chapter describes the logic of inductive inference as seen through the eyes of the modern theory of personal probability, including a number of its recent refinements and extensions. The structure of the chapter is as follows. After a brief discussion of mathematical probability, to establish notation and terminology, it recounts the gradual evolution of the probabilistic explication of induction from Bayes to the present. The focus is not in this history per se (fascinating as it is), but in its use to highlight the key assumptions, criticisms, refinements, and achievements of that theory. Along the way, the structure of the modern theory is presented, and its relation to the problem of induction discussed.

Argues that the same principles of complexity reduction that he used to explain principles of perceptual entitlement in the preceding chapter can be used to explain the principles of inductive inference. When we have a sound, non‐conclusive inductive inference from a variety of Fs being G to the conclusion that all Fs are G, this holds because the easiest way for the evidence to hold is one that also makes it the case that all Fs are G. Clarifies and elaborates this thesis and traces out its consequences.

In 1865 and 1866, Peirce appealed to Aristotle’s proposal that an inductive inference be understood as a transformation of a categorical syllogism by permuting the major premise and the conclusion supported by a conversion of the minor premise to develop his own formal account of induction. He completed his theory by taking hypothetic inference to be the product of permuting the minor premise and the conclusion of the categorical syllogism. Peirce sought to extend the proposal beyond transformations of categorical syllogisms to cover reasoning where the major premise of the categorical syllogism is no longer a categorical proposition but is statistical. This chapter traces the adjustments Peirce made in his theory by the time he published “A Theory of Probable Inference” in 1883. “A Theory of Probable Inference” is rightly understood to contain an anticipation of the suggestion to replace inductive inference by inductive behavior found in the method of significance testing and confidence interval estimation proposed by Neyman and Pearson a half-century later. In 1883, Peirce continued, however, to classify hypothetic inference as a permutation of the premises of statistical syllogisms. In 1902, Peirce acknowledged that the account of hypothetic inference he had been proposing was confused. During this period, he replaced the term “hypothetic inference” by “abduction” and explicitly took the position that abduction has as its conclusion the introduction of a conjecture for testing rather than an inference to the best explanation.

Why, given the ancient pedigree of scepticism, did we have to wait until Hume for the problem of induction? This chapter begins by considering whether the problem in fact antedates Hume: there is earlier discussion of non-demonstrative reasoning, e.g., in Sextus and in Bacon, and there is, in various forms, sceptical concern about induction, but Hume's negative proof that there is no possible justification of induction, either demonstrative or non-demonstrative, is something new. After canvassing various unsatisfactory answers, the chapter offers its own, showing that Hume's philosophical orientation provided him with both the motive and the opportunity to generate his great sceptical argument: his naturalism provided the motive to construct a ‘method of doubt’ that would wean us from the picture of ourselves as creatures of reason and replace it with the picture of creatures governed by natural instincts, and his radical empiricism and atheism provided him with a way of revealing the pervasiveness of inductive inference, from which his argument naturally follows.

A theory of induction, based on the formalism of algorithmic complexity theory, is introduced in this chapter. This is then used to underpin a theory of learning and a computable basis for inductive inference. The historical and philosophical backdrops against which these theories developed are also given, albeit concisely.

Induction proceeds from the certain to the uncertain, or so it is commonplace to say. On the contrary, induction is inference from uncertain evidence to uncertain conclusions. This conception of induction is articulated in this chapter. Philosophers have argued that the acceptance of statements in science and other epistemically virtuous enterprises should not be explicated as inductive inference from evidence to hypothesis. It would be misleading to construe the acceptance of theories based on inductive inference from observational evidence to theoretical conclusions. These and other contentions suggest the most fundamental reason philosophers have for rejecting the model of scientific acceptance based on inductive inference: that rejection and acceptance is influenced by conceptual change, by radical shifts in the way people conceive of the world rather than being based simply upon inference from evidence to hypothesis.

This chapter presents a theory of inductive inference and rational acceptance in scientific enquiry. A concept of relevant deduction is defined as a concept in which the truth of each and every premise of a deductive argument is essential to establishing the truth of the conclusion by deduction from the premises. This definition is based on the completely abstact notion of a minimally inconsistent sets of statements. In terms of this same abstract logical concept and the relation of probability, this chapter designs a concept of inductive inference that is a principle of rationality. This concept of inductive reference is shown to form the basis of a principle of acceptance in which two important epistemic utilities are maximised.

Considers the popular doctrine of reliabilism, the thesis that distinguishing between internal and external guarantees of reliability dissolves Hume's problem, since there may well be an external guarantee, in the way the world actually is, of the reliability of standard inductive practice. Indeed, we have good evidence that the world is so constituted to favour these practices. Furthermore, regarding the past predictive success of inductive inferences as good evidence of the reliability of the procedure of inductive inference itself is no less circular than using deductive arguments to justify deductive inference. These claims are examined and rejected.

Hume's argument for inductive scepticism is presented, and some ‘quick’ rejoinders to it are considered. Two of the most popular are (1) that it begs the question that only deductive arguments are valid, and omits consideration of probabilistic arguments, and (2) that inductive reasoning is partly constitutive of what we mean by valid inference, and so needs no independent justification. Both these rejoinders are rejected (1) because an examination of Hume's text clearly shows that he was talking about any sort of putatively sound argumentation, including probabilistic arguments; and (2) because it misses the point, which is to show why we can reliably expect the course of nature to continue in the way predicted on the basis of past evidence.

This chapter criticizes a familiar group of ideas about “inductive” inference, and uses that criticism to promote a different group. Many hold on to the position that induction is rational because, if not, factual knowledge will collapse. For the purposes of this chapter, induction is regarded as a pattern of arguments used to answer questions of proportion or frequency, e.g. “how many Fs are G?” “what is the rate of G in the Fs?” “Are all Fs G?” Nelson Goodman suggests, however, that the F and the G in a good inductive argument cannot simply be anything. Some kind of “naturalness” constraint is required on the involved predicates. Most philosophers would agree with Goodman even if they do not agree regarding what the constraint is or from where it comes.

This chapter suggests that language may facilitate children's acquisition of mentalistic concepts by serving as an aid to analogical reasoning and inductive inference. That is, language invites children to compare different behaviors that otherwise they would not attempt to align, thus promoting inferences about non-obvious commonalities across distinct expressions of mental states, such as belief, desire, attention, and intention. A large body of research suggests that, in the realm of physical objects, infants use information provided in language to draw inferences about non-obvious commonalities. In the realm of mental states, language may function similarly to facilitate children's abstraction of mentalistic concepts. The chapter considers two different aspects of this process. First, it argues that language in general, used in conversation, is intricately linked to mentalistic concerns as it embodies communicative intent and intentional focus, taking into account and attempting to influence the beliefs and desires of the conversational participant. Second, mental terms may act as labels that invite recognition across different behaviors and situations, leading to the development of mentalistic concepts by the abstraction of commonalities across behaviors.