John D. Norton


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In the material theory of induction, inductive inferences are warranted by domain specific facts. Those facts are in turn supported by further inductive inferences. This volume examines the largescale structure of the resulting tangle of inductive inferences and relations of inductive support. 
The LargeScale Structure of Inductive Inference. BSPSopen/University
of Calgary Press, 2024. Download 

Mousa Mohammadian, William Peden and Elay Shech have each written commentaries on The Material Theory of Induction in a symposium organized by the journal, Metascience. Here is my responses and my thanks to them.  "Author’s response to Mousa Mohammadian, William Peden and Elay Shech," Symposium on The Material Theory of Induction, in Metascience.31 (2022), pp. 317–323. Download.  
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.  "Author's Responses," Studies in History and Philosophy of Science, 85 (2021), pp. 114–126. 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. The Material Theory of Induction. Contents: Preface Prolog 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 Epilog 
The Material Theory of
Induction. BSPSOpen/University of Calgary
Press, 2021. Open access. FREE download under a CCBYNCND 4.0 Creative Commons license. 

The measure problem in eternal inflationary cosmology arises because we try to force a probability distribution where it is not warranted. The problem is solved by asking which inductive logic is picked out by the background conditions. That logic is the same highly nonadditive inductive logic as applies to an infinite lottery.  "Eternal Inflation: When Probabilities Fail," Prepared for special edition "Reasoning in Physics," Synthese, eds. Ben Eva and Stephan Hartmann. Draft.  
The replicability of experiment, the gold standard of evidence, is not supported by a universal principle of replicability in inductive logic. A failure of replication may not impugn a credible experimental result; and a successful replication can fail to vindicate an incredible experimental result.The evidential import of successful replication of an experiment is determined by the prevailing background facts. Their success has fostered the illusion of a deeper, exceptionless principle.  "Replicability of Experiment," Theoria, 30(No. 2) (2015), pp. 229248. Download.  
1, 3, 5, 7, ... ?  Standard accounts of inductive inference are unstable, meriting skeptical attack. They have misidentified its fundamental nature. Accounts of inductive inference should not be modeled on those of deductive inference that are formal and noncontextual. Accounts of inductive inference should be contextual and material. I summarize the case for a material theory of induction.  "A Material Defense of Inductive Inference," in Stephen Hetherington and David Macarthur, eds., Living Skepticism: Essays in Epistemology and Beyond. Leiden: Brill, 2022. pp. 5472.Download. 
The inductive problem of extending the sequence 1, 3, 5, 7, is solved when these numbers are the ratios of the incremental distances fallen in successive unit times. The controlling fact is Galileo's assumption that these ratios are invariant under a change of the unit of time. It admits few laws and only one is compatible with the twonumbered initial sequence 1, 3.  "Invariance of Galileo's Law of Fall under a Change of the Unit of Time." Download.  
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," in P. Achinstein, ed., Scientific Evidence: Philosophical Theories and Applications. Johns Hopkins University Press, 1905. pp. 934. Download.  
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. 64770. Download.


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, nonprobabilistic 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," Philosophy of Science, Philosophy of Science, 77 (2010) pp. 76577. Download  