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The Whewell-Mill Debate.   Updated 3/29/99

The original paper.   Updated  2/3/99. (163 KB)

Abstract: The debate between William Whewell and John Stuart Mill is not only hard in the sense that both sides are difficult to understand, but the issue itself is unresolved.  Whewell’s idea of predictive tests is similar to the method of cross validation in statistics and machine learning, except that Whewell applies it in a hierarchical way at multiple levels.  Or at least, that is how Whewell argues that hypothesis testing works in science.  In contrast, the received view of theory testing is that the confirmation of rival hypotheses is measured by their degree of fit with the total evidence, provided that the rival hypotheses are equally simple.  However, there is a growing realization that predictive tests are stronger in many ways.  What this suggests is that the history of science could be used as a source of examples against which theories of learning may be tested.  The purpose of this paper is to explain and highlight some of the features of Whewell’s theory of hypothesis testing that are relevant to the continuing controversies about confirmation. 

1. The Central Points
2. The Role of Concepts in Science
3. Examples of Scientific Inference
4. Empiricism about Concepts and Recent Hypothetico-Deductivism
5. Newton’s Apple and the Relational Nature of Evidence
6. The Consilience of Inductions and other Tests of Hypotheses
7. The Fundamental Antithesis between Subject and Object
8. The Evidential Nature of Necessity
9. Logical versus Historical Theories of Confirmation
10. Auxiliary Assumptions and the Correction of Errors
11. Summary and Conclusions