Teaching & Learning Guide for: The Paradox of Confirmation
Authors: Fitelson Branden 
Published: July 2008

Author's Introduction

The early twentieth century witnessed a shift in the way philosophers of science thought about traditional ‘problems of induction’. Keynes championed the idea that Hume's Problem was not a problem about causation (which had been the traditional reading of Hume) but rather a problem about induction. Moreover, Keynes (and later Nicod) viewed such problems as having both logical and epistemological components. Hempel picked up where Keynes and Nicod left off, by formulating a rigorous formal theory of inductive logic. This spawned a new branch of philosophy of science called confirmation theory. Hempel's theory of confirmation was based on a few very simple (and seemingly plausible) assumptions about (instantial) ‘inductive‐logical support’. However, as Hempel himself was keenly aware, even such simple and seemingly plausible assumptions give rise to various puzzles and paradoxes. The two most famous paradoxes of confirmation were discovered by Hempel and Goodman. This article discusses Hempel's paradox (which is known as ‘the’ paradox of confirmation, since it was discovered first). However, many of the historical developments surrounding Hempel's paradox (also known as the ‘raven paradox’) are also crucial for understanding Goodman's later (‘grue’) paradox.

Author Recommends:

Branden Fitelson, ‘The Paradox of Confirmation’, Philosophy Compass 1/1 (2006): 95–113, doi: 10.1111/j.1747-9991.2006.00011.x.

In this article, I explain how the inconsistency between Hempel's intuitive resolution and his official theory of confirmation affects the historical dialectic about the paradox and how it illuminates the nature of confirmation. After the survey, I argue that Hempel's intuitions about the paradox of confirmation were basically correct, and that it is his theory that should be rejected, in favor of a (broadly) Bayesian account of confirmation.

C. G. Hempel, ‘Studies in the Logic of Confirmation’ (I and II), Mind 54 (1945): 1–26, 97–121, dois: DOI: 10.1093/mind/LIV.213.1; DOI: 10.1093/mind/LIV.214.97.

This is the locus classicus of traditional (instantial) confirmation theory. It is here that original motivations for, traditional approaches to, and paradoxes of confirmation are discussed in depth for the first time, under the rubric ‘confirmation theory’. Hempel's discussion (which picks up where Keynes and Nicod left off) is chock full of crucial historical, logical, and epistemological insights.

J. M. Keynes, A Treatise on Probability (London: Macmillan, 1921).

Keynes does not get enough credit in this context. But, basically, chapters 18 to 23 of this classic book planted the seeds for almost all of modern confirmation theory. Nicod and Hempel (as well as Hosiasson‐Lindenbaum, Carnap, and others) were, basically, just picking‐up where Keynes left off.

J. Nicod, The Logical Problem of Induction (1923), reprinted in Foundations of Geometry and Induction (London: Routledge, 2000).

Nicod's essay expands upon Keynes's work. Nicod is the first to use the term ‘confirmation’, in connection with a relation of ‘inductive‐logical support’. Nicod endorses several key confirmation‐theoretic principles (which were already advanced by Keynes). In the hands of Hempel, Nicod's work later becomes an important historical foil.

J. Hosiasson–Lindenbaum, ‘On Confirmation’, Journal of Symbolic Logic 5 (1940): 133–48.

This essay contains most (if not all) of the basic ingredients of the ‘Bayesian’ approaches to the paradox of confirmation that appeared later. It also sheds much light on an important dispute between Keynes and Nicod concerning one of the claims Keynes makes (in his Treatise) about ‘long‐run convergence’ in certain (instantial) confirmation‐theoretic problems. This paper also contains one of the earliest rigorous axiomatizations of conditional (subjective or logical) probability.

R. Carnap, Logical Foundations of Probability (Chicago, IL: University of Chicago, 1950).

This is Carnap's encyclopaedic work on inductive logic and probability. There is a tremendous amount of wisdom in here. For present purposes, the sections on Hempel's theory of confirmation (in contrast to probabilistic approaches to confirmation, such as Hosiasson–Lindenbaum's and Carnap's) are probably most important and salient (see §§87–8).

I. J. Good, ‘The Paradox of Confirmation’, British Journal for the Philosophy of Science 11 (1960): 145–9.

C. Chihara, ‘Quine and the Confirmational Paradoxes’, in Midwest Studies in Philosophy. Vol. 6: The Foundations of Analytic Philosophy, eds. Peter A. French, Theodore E. Uehling, Jr., and Howard K. Wettstein (Minneapolis, MN: University of Minnesota Press, 1981), 425–52.

J. Earman, Bayes or Bust: A Critical Examination of Bayesian Confirmation Theory (Cambridge, MA: MIT Press, 1992), specifically: pp. 63–73.

R. M. Royall, Statistical Evidence: A Likelihood Paradigm (New York, NY: Chapman & Hall, 1997), specifically: the Appendix on ‘The Paradox of the Ravens’.

C. McKenzie and L. Mikkelsen, ‘The Psychological Side of Hempel's Paradox of Confirmation’, Psychonomic Bulletin & Review 7 (2000): 360–6.

P. Maher, ‘Probability Captures the Logic of Scientific Confirmation’, in Contemporary Debates in the Philosophy of Science, ed. Christopher Hitchcock (Oxford: Blackwell, 2004), 69–93.

P. Vranas, ‘Hempel's Raven Paradox: A Lacuna in the Standard Bayesian Solution’, British Journal for the Philosophy of Science 55 (2004): 545–60.

This is a list of seven of my favourite papers on the paradox of confirmation, since 1950 (listed in chronological order). Most of these are coming from a broadly ‘Bayesian’ perspective. In particular, I recommend Vranas as a good starting point here.

Online Materials:

http://fitelson.org/probability/

Probability & Induction (PHIL 148, UC‐Berkeley, Spring 2008)

This is the Web site for an undergraduate course on probability and induction that I taught at UC‐Berkeley in Spring 2008. Much of the course focuses on confirmation theory (including the paradoxes of confirmation). There are many links there to lecture notes, papers, books and other salient online resources.

http://fitelson.org/confirmation/

Confirmation (graduate seminar, UC‐Berkeley, Fall 2007)

This is the Web site for a graduate seminar on confirmation that I taught at UC‐Berkeley in Fall 2007. This seminar is a historical trace of induction/confirmation, from Aristotle to Goodman (mostly, focusing on the 20th century and the paradoxes of confirmation).

Sample Syllabus:

See the online syllabi for Confirmation and/or Probability & Induction (above).

Note: those online syllabi contain electronic copies of many of the salient readings.