The Material Theory
of Induction
JOHN D. NORTON
2016, 2017, 2018, 2020
Draft at April 23, 2020
Contents
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 39 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 1016 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 1316 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 finetuning 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 1315 were
simplified, this chapter proposes that there is a
nonprobabilistic inductive logic native to a real science,
quantum mechanics. 

Epilog  draft 