The Material Theory
of Induction


2016, 2017, 2018, 2020

Draft at April 23, 2020

Copyright 2016, 2017, 2018 John D. Norton

John D. Norton
Department of History and Philosophy of Science
University of Pittsburgh
Pittsburgh PA USA 15260

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Download the entire volume in a single pdf. Version of June 26, 2018.

Or individual chapters:

    Preface draft
    Prolog draft
1. The Material Theory of Induction Stated and Illustrated draft
Inductive inferences are not warranted by conformity with some universally applicable formal schema. They are warranted by background facts. The theory is illustrated with Marie Curie's inductive inference over the crystallographic properties of Radium Chloride.

2. What Powers Inductive Inference? draft
The principal arguments for the material theory are given. Any particular inductive inference can fail reliably if we try it in a universe hostile to it. That the universe is hospitable to the inference is a contingent, factual matter and is the fact that warrants it.

The material theory asserts that there are no universal rules of inductive inference. All induction is local.Chapters 3-9 will show how popular and apparently universal rules of inductive inference are defeasible and that their warrants in individual domains are best understood as deriving from particular background facts.
3. Replicability of Experiment draft
There is no universal inductive principle in science formulated in terms of replicability of experiment. Replication is not guaranteed to have inductive force. When it does, the force derives from background facts peculiar to the case at hand.  
4. Analogy draft
Efforts to characterize good analogical inferences by their form have collapsed under the massive weight of the endless complexity needed to formulate a viable, general rule. For scientists, analogies are facts not argument forms, which fits nicely with the material view.
5. Epistemic Virtues and Epistemic Values: A Skeptical Critique draft
Talk of epistemic values in inductive inference misleads by suggesting that our preference for simpler theories is akin to a free choice, such as being a vegetarian. The better word is criterion, since they are not freely chose, but must prove their mettle in guiding us to the truth.
6. Simplicity as a Surrogate draft
There is no viable principle that attaches simpler hypotheses to the truth. Appeals to simplicity are shortcuts that disguise more complicated appeals to background facts.
7. Simplicity in Model Selection draft
Statistical techniques, such as the Akaike Information Criterion, do not vindicate appeals to simplicity as a general principle. AIC depends on certain strong, background assumptions independent of simplicity. We impose a simplicity interpretation on the formula it produces.  
8. Inference to the Best Explanation: The General Account draft
9. Inference to the Best Explanation: Examples draft
There is no clearly defined relation of explanation that confers special inductive support on some hypotheses or theories. The important, canonical examples of IBE can be accommodated better by simpler schemes involving background facts. The successful hypotheses or theories accommodate the evidence. The major burden in real cases in science is to show that competing accounts fail, either by contradicting the evidence or taking on evidential debt.

Chapters 10-16 address Bayesian confirmation theory, which has become the default account of inductive inference in philosophy of science, in spite of its weaknesses. Chapters 10, 11 and 12 address general issues. Chapters 13-16 display systems in which probabilistic representation of inductive strengths of support fails.
10. Why Not Bayes? draft
While probabilistic analysis of inductive inference can be very successful in certain domains, it must fail as the universal logic of inductive inference. For an inductive logic must constrain systems beyond mere logical consistency. The resulting contingent restrictions will only obtain in some domains. Proofs of the necessity of probabilistic accounts fail since they require assumptions as strong as the result they seek to establish.
11. Circularity in the Scoring Rule Vindication of Probabilities draft
The scoring rule approach employs only the notion of accuracy and claims that probabilistic credences dominate. This chapter shows that accuracy provides little. The result really comes from an unjustified fine-tuning of the scoring rule to a predetermined result.
12. No Place to Stand: The Incompleteness of All Calculi of Inductive Inference draft
An inductively complete calculus of inductive inference can take the totality of evidential facts of science and, from them alone, determine the appropriate strengths of evidential support for the hypotheses and theories of science. This chapter reviews informally a proof given elsewhere that no calculus of inductive inference, probabilistic or not, can be complete.
13. Infinite Lottery Machines draft
Such machines choose among a countable infinity of outcomes without favor. While the example is used to impugn countable additivity, it actually also precludes even finite additivity.
14. Uncountable Problems draft
If we enlarge the outcome spaces to continuum size, we find further inductive problems that cannot be accommodated by a probabilistic logic. They include those derived from the existence of metrically nonmeasuable sets.

15. Indeterministic Physical Systems draft
The indeterminism of a collection of indeterministic systems poses problems in inductive inference. They cannot be solved by representing strengths of inductive support as probabilities, unless one alters the problem posed.  
16. A Quantum Inductive Logic draft
While the examples of Chapters 13-15 were simplified, this chapter proposes that there is a non-probabilistic inductive logic native to a real science, quantum mechanics.
      Epilog draft