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Microscope Here is a systematic survey of the many accounts of induction and confirmation in the literature with a special concern for the basic principles that ground inductive inference. I believe it is possible to see that all extant accounts depend on one or more of three basic principles. "A Little Survey of Induction," Prepared for Conference on Scientific Evidence, Center for History and Philosophy of Science, Johns Hopkins University, April 11-13, 2003; to appear in P. Achinstein, ed., Scientific Evidence: Philosophical and Historical Perspectives (provisional title).Preprint on philsci-archive.pitt.edu

I do not believe, however, that any of these principles works universally and can ever be applied without some sort of adjustment to the case at hand. This has led to a proposal about the nature of inductive inference. I urge that we have been misled by the model of deductive inference into seeking a general theory in which inductive inferences are ultimately licensed by their conformity to universal schemas. Instead, in a "material theory of induction," I urge that inductive inference is licensed by facts that prevail in particular domains only, so that "all induction is local." "A Material Theory of Induction" Philosophy of Science 70(October 2003), pp. 647-70. Download.

In other studies I defend the power of induction. I believe that the popular underdetermination thesis is essential groundless speculation based on a superficial treatment of inductive inference; and that the much feared threat of "grue" to induction is greatly overrated. "Must Evidence Underdetermine Theory?" in The Challenge of the Social and the Pressure of Practice: Science and Values Revisited, M. Carrier, D. Howard and J. Kourany, eds., Pittsburgh: University of Pittsburgh Press, 2008, pp. 17-44. Download.

"The Formal Equivalence of Grue and Green and How It Undoes the New Riddle of Induction." Synthese, (2006) 150: 185-207. Download.

The probability calculus is not the universal logic of induction; there is no such thing. An axiom system disassembles the probability calculus into distinct notions about induction, which it is urged, may be invoked independently to tailor a logic of induction to the problem at hand. The probability calculus fails as the inductive logic of certain indeterministic systems. "Probability Disassembled," British Journal for the Philosophy of Science, 58 (2007), pp. 141-171. Download.
A simple indeterministic system is displayed and it is urged that we cannot responsibly infer inductively over it if we presume that the probability calculus is the appropriate logic of induction. The example illustrates the general thesis of a material theory of induction, that the logic appropriate to a particular domain is determined by the facts that prevail there. "Induction without Probabilities." Download.
See also "Induction without Probabilities" in Goodies.
The epistemic state of complete ignorance cannot be a probability distribution. The instruments that characterize it are innocuous platitudes of evidence: the principle of indifference and certain invariance conditions. However the literature has misdiagnosed these instruments as defective since these instruments rule out the representation of complete ignorance by probability distributions. "Ignorance and Indifference." Download.
Mercury's perihelion motion This paper illustrates how the material theory of induction can be used to assess evidence claims made historically in science. Two cases are considered: Einstein's 1905 thermodynamic argument for light quanta and his 1915 recovery of the anomalous perihelion motion of Mercury. "History of Science and the Material Theory of Induction: Einstein's Quanta, Mercury's Perihelion." Download.
Dual Venn diagram Forming the dual is a familiar operation in logic and mathematics. Truth is the dual of falsity; and (A or B) is the dual of (A and B). Here I develop the corresponding notion for additive measures, such as probability measures. The resulting dual additive measures are degrees of disbelief and turn out to obey their own peculiar calculus. An ignorance state is conveniently characterized as one that is self-dual. "Disbelief as the Dual of Belief" Download.
mud thumb While Bayesian analysis has enjoyed notable success with many particular problems of inductive inference, it is not the one true and universal logic of induction. I review why the Bayesian approach fails to provide this universal logic of induction. Some of the reasons arise at the global level through the existence of competing systems of inductive logic. Others emerge through an examination of the individual assumptions that, when combined, form the Bayesian system: that there is a real valued magnitude that expresses evidential support, that it is additive and that its treatment of logical conjunction is such that Bayes' theorem ensues. “Challenges to Bayesian Confirmation Theory,” Prepared for Prasanta S. Bandyopadhyay and Malcolm Forster (eds.), Philosophy of Statistics: Vol. 7 Handbook of the Philosophy of Science. Elsevier. Download draft.
graph What if, like me, you don't think that the probability calculus is the One, True Logic of Induction? Then you want to know what other logics are possible. Here I map out a large class of inductive logics that originate in the idea that the inductive support B affords A, that is "[A|B]," is defined in terms of the deductive relations among propositions. I demonstrate some very general properties for these logics. In large algebras of propositions, for example, inductive independence is generic in all of them. A no-go result forces all the logics to supplement the deductive relations among propositions with intrinsically inductive structures. "Deductively Definable Logics of Induction" Download.

For a less formal development, see "What Logics of Induction are There?" in Goodies.
No rules In a material theory of induction, inductive inferences are warranted by facts that prevail locally. This approach, it is urged, is preferable to formal theories of induction in which the good inductive inferences are delineated as those conforming to some universal schema. An inductive inference problem concerning indeterministic, non-probabilistic systems in physics is posed and it is argued that Bayesians cannot responsibly analyze it, thereby demonstrating that the probability calculus is not the universal logic of induction. "There are No Universal Rules for Induction" Download
De Sitter Spacetimes What should we infer from the possibility of observationally indistinguishable spacetimes? I urge they are not a manifestation of the dubious thesis of the evidential underdetermination of theory, but a form of indeterminism within a theory. Moreover inductively discriminating among the spacetime requires inductive inferences that are "opaque" in the sense the we cannot see through them to their warrant. "The Inductive Significance of Observationally Indistinguishable Spacetimes." Download
Which are the good inductive inferences or the proper relations of inductive support? We have sought for millennia to answer by means of universally applicable formal rules or schema. These efforts have failed. Background facts, not rules, ultimately determine which are the good inductive inferences. No formal rule applies universally. Each is confined to a restricted domain whose background facts there authorize them.

My book, The Material Theory of Induction is now available as a full manuscript. Contents:

1. The Material Theory of Induction Stated and Illustrated
2. What Powers Inductive Inference?
3. Replicability of Experiment
4. Analogy
5. Epistemic Virtues and Epistemic Values: A Skeptical Critique
6. Simplicity as a Surrogate
7. Simplicity in Model Selection
8. Inference to the Best Explanation: The General Account.
9. Inference to the Best Explanation: Examples
10. Why Not Bayes
11. Circularity in the Scoring Rule Vindication of Probabilities
12. No Place to Stand: the Incompleteness of All Calculi of inductive Inference
13. Infinite Lottery Machines
14. Uncountable Problems
15. Indeterministic Physical Systems
16. A Quantum Inductive Logic
Download complete manuscript of April 24, 2020.
Material Theory book
A special issue of Studies in History and Philosophy of Science is on the material theory of induction and has 14 papers. Here are my responses to those papers. Download draft.