Hempel's Ravens
The paradox of confirmation
First published: C. G. Hempel, "Studies in the Logic of Confirmation", *Mind* 54 (1945): 1–26, 97–121.
"All ravens are black" is logically equivalent to "all non-black things are non-ravens." Observing a white shoe confirms the latter — and therefore the former?
Hempel's paradox: by standard confirmation logic, observing a black raven confirms "all ravens are black." But that hypothesis is logically equivalent to its contrapositive ("all non-black things are non-ravens"), and observing a white shoe (non-black, non-raven) confirms the contrapositive — and hence the original. So white shoes confirm the blackness of ravens. The absurdity reveals subtleties in formal confirmation theory; standard resolutions (Bayesian) accept the inference but show that the confirmation from a white shoe is vanishingly tiny compared to that from a black raven, given relative class sizes.
Formulation
(1) "All ravens black" ≡ "All non-black things non-ravens." (2) Observing P-and-Q instance confirms "All Ps are Qs." (3) Therefore white shoe (non-black, non-raven) confirms "all ravens black." Most readers find (3) absurd.
Dimensions Engaged
Observer
Observer · Knowledge Extent: what is the structure of empirical confirmation?
Information
Bears on how informational content of evidence depends on the hypothesis space.
Responses — How Schools Engage
Affirms / takes the bait 2
The paradox is a serious problem for the logical-positivist account of confirmation; resolving it required moving from purely syntactic to probability-theoretic accounts.
Confirmation is a structural relation between hypothesis and evidence; the symmetry the paradox exploits is genuine and forces refinement of formal confirmation theory.
Reframes the question 2
Bayesian naturalism: yes, white shoes do confirm, but by a negligible amount given that the class of non-black things is astronomically larger than the class of ravens. The paradox dissolves quantitatively.
The intuition that white shoes do not confirm reflects the lack of *practical* relevance; in actual scientific contexts the relevant evidence is targeted, not symmetric.
Holds it inconclusive 1
Various resolutions (Goodman's grue exacerbates the puzzle; Bayesian, eliminative, and tacking-paradox responses persist). A live foundation for confirmation theory.
Related Experiments
Experiments engaged by an overlapping set of schools — likely to surface the same fault lines.
Further reading
- Hempel (1945), op. cit.
- Earman, *Bayes or Bust?* (1992)
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