A thorough investigation of the large-scale structure of relations of inductive support within the material theory of induction, according to which inductive inferences are warranted not by universal rules but by facts particular to each other.
The Large-Scale Structure of Inductive Inference investigates the relations of inductive support on the large scale, among the totality of facts comprising a science or science in general. These relations form a massively entangled, non-hierarchical structure which is discovered by making hypotheses provisionally that are later supported by facts drawn from the entirety of the science. What results is a benignly circular, self-supporting inductive structure in which universal rules are not employed, the classical Humean problem cannot be formulated and analogous regress arguments fail.
The earlier volume, The Material Theory of Induction proposed that individual inductive inferences are warranted not by universal rules but by facts particular to each context. This book now investigates how the totality of these inductive inferences interact in a mature science. Each fact that warrants an individual inductive inference is in turn supported inductively by other facts. Numerous case studies in the history of science support, and illustrate further, those claims. This is a novel, thoroughly researched, and sustained remedy to the enduring failures of formal approaches to inductive inference.
With The Large-Scale Structure of Inductive Inference, author John D. Norton presents a novel, thoroughly researched, and sustained remedy to the enduring failures of formal approaches of inductive inference.
About the Author
John D. Norton is a distinguished professor of history and philosophy of science at the University of Pittsburgh. He works in history and philosophy of physics and general philosophy of science. He is co-founder of philsci-archive, a preprint server in the philosophy of science, and of &HPS, a conference series in the integrated history and philosophy of science.
List of Figures
List of Tables
Preface
Introduction
1 The Material Theory of Induction, Briefly
The material theory of induction is introduced, and its application to a range of types of inductive inference is illustrated. The theory asserts that there are no universal rules or schema for inductive inference. Instead, inductive inferences or relations of inductive support are warranted by facts specific to the domain of application.
Part I — General Claims and Arguments
2 Large-Scale Structure: Four Claims
The main claims concerning the large-scale structure of inductive inference are introduced and defended.
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1. Relations of inductive support have a nonhierarchical structure.
2. Hypotheses, initially without known support, are used to erect nonhierarchical structures.
3. Locally deductive relations of support can be combined to produce an inductive totality.
4. There are self-supporting inductive structures.
The remaining chapters provide further defenses of the claims and illustrations of them.
3 Circularity
The nonhierarchical relations of inductive support in science admit circularities of large and small extent. These circularities are benign. They do not force contradictions or assured underdetermination of the facts in the structure. They are akin to the benign circularities common elsewhere in the sciences, where there is no presumption that the mere presence of a circularity dooms the structure.
4 The Uniqueness of Domain-Specific Inductive Logics
Might a single body of evidence support factually competing theories equally well? The result would be inductive anarchy since the competing theories would warrant competing inductive logics. This anarchy is precluded by an instability in the inductive competition between such theories. A small evidential advantage by one secures more favorable facts that amplify its advantage at the expense of competing theories.
5 Coherentism and the Material Theory of Induction
The circularities among relations of support in the material theory of induction are similar to the circularities of justification in a coherentist theory of justification in epistemology. This similarity is superficial. The coherentist theory concerns beliefs and the mental operations that connect them. Inductive inference concerns logical relations among propositions independent of our thoughts and beliefs. Contrary to my initial expectations, the resources of coherentist epistemology prove to be of little help or relevance to the material theory of induction.
6 The Problem of Induction
The problem of induction lies in the failure of universal rules of induction to be justified. They must either justify themselves or enter into an infinite regress of justification by distinct rules. The material theory of induction dissolves the problem since it has no universal rules of induction. Attempts to resurrect the problem in the regresses and vicious circularities within the nonhierarchical relations of support fail.
Part II — Historical Case Studies
7 The Recession of the Nebulae
Hubble’s finding in 1929 that nebulae recede with a velocity proportional to their distance might appear to be a simple generalization from measurements of specific nebulae to a generalization about all nebulae. However, his analysis did not respect any hierarchy of generalizations. Since Hubble lacked distance measurements for nearly half of the nebulae in his data set, he needed a complicated set of intersecting inductive inferences to
recover his result.
8 Newton on Universal Gravitation
Newton’s celebrated argument for universal gravitation contains two cases of pairs of propositions such that each deductively entails the other member of the pair. Although the individual inferences of this arch-like structure are deductive, its overall import is inductive, and it is the more secure for being constructed from deductive component inferences rather than inductive component inferences.
9 Mutually Supporting Evidence in Atomic Spectra
Atomic emission spectra were observed in the nineteenth century and early twentieth century to be grouped into distinct series. By means of the Ritz combination principle, evidence of the structure of some series supports the structure of others, and vice versa, forming many relations of mutual support. The Ritz combination principle itself initially supplied evidential support for the nascent quantum theory. Soon the more developed quantum theory provided support for a corrected version of the Ritz combination principle.
10 Mutually Supporting Evidence in Radiocarbon Dating
Historical artifacts can be dated by traditional methods of history and archaeology or by the method of radiocarbon dating. The results of each method are used to check and calibrate the results of the other method. When the two sets of results are well adjusted, they mutually support each other, illustrating the arch-like structure of relations of support.
11 The Determination of Atomic Weights
It took over half a century after Dalton proposed his atomic theory of the elements for chemists to break a circularity in molecular formulae and atomic weights and establish that water is H2O and not HO, or HO2, or H4O, and so on. Their analysis employed relations of inductive support of bewildering complexity at many levels, from that of specific substances to that of general theory. Their efforts illustrate the complex, nonhierarchical character of relations of inductive support.
12 The Use of Hypotheses in Determining Distances in Our Planetary System
As late as the eighteenth and nineteenth centuries, astronomers still struggled to provide exact values for distances within our planetary system. Triangulation, also called parallax in astronomy, was the only direct method available. It was too weak. Since antiquity, astronomers were only able to arrive at definite results by supplementing their analyses with hypotheses that in turn would require subsequent support. Early hypotheses failed to find this support. The heliocentric hypothesis of Copernicus succeeded.
13 Dowsing: The Instabilities of Evidential Competition
The instability of competition among competing theories is illustrated by the rivalry between proponents and critics of dowsing. Over four centuries, they competed at the level of theory, advancing different conceptions of the processes at issue, and at the level of phenomena, disputing whether the dowsing successes were pervasive or illusory. Mutually reinforcing evidential successes by critics eventually led to securing their position at the expense of that of the dowsers, whose views were reduced to a pseudoscience.
14 Stock Market Prediction: When Inductive Logics Compete
Four systems are routinely used now to predict future prices on the stock market, each comprising a small inductive logic. Each is based on a factual hypothesis concerning stock price dynamics. Since the hypotheses disagree in factually ascertainable matters, their competition is unstable. Only one would survive if investors and pundits fully pursued and took proper notice of the evidence.
Afterword
Index
Norton’s important new book will be an essential touchstone for all future work on the logic of scientific reasoning. According to Norton, relations of inductive support in science form an intricate web. Norton’s account of this web is enriched by deep dives into illuminating episodes from the history of science. The book is also enlivened by Norton’s clear and accessible writing and characteristic good humor.
—Marc Lange, Theda Perdue Distinguished Professor of Philosophy, University of North Carolina at Chapel Hill
Norton’s book is a must read for anyone who wonders about what makes science rational. In the face of centuries of skepticism about, and backlash against science, Norton provides the strongest case ever that all is good (or can be good) with science. The perspective is fresh, the arguments are probing, and the assembled historical data is awe inspiring.
—Hans Halvorson, Stuart Professor of Philosophy, Princeton University
There is much to admire about this book. It presents the most elaborate exposition and defence of Norton’s material theory of induction, it discusses Norton’s original view of the problem of induction, it combines philosophical theorizing in an exemplary way with beautifully chosen case studies, and it is, like all of Norton’s work, superbly written. Last but not least, it gives those (like us Bayesians) who disagree with Norton much to think about. A must-read for anyone interested in the philosophy of science.
—Stephan Hartmann, MCMP, LMU Munich