Paradoxes of Confirmation

The paradoxes of confirmation are puzzles showing that intuitively plausible principles of evidential support lead to absurd or arbitrary results.

Definition

The paradoxes of confirmation are cases in which widely accepted conditions on the confirmation relation entail counterintuitive conclusions, such as that a green apple confirms that all ravens are black, or that the same evidence supports incompatible predicates.

Scope

This topic covers Hempel's raven paradox, which arises from the equivalence and Nicod conditions, and Goodman's new riddle of induction ('grue'), which shows that confirmation cannot be a purely syntactic relation. It addresses proposed resolutions, including Bayesian relevance treatments and Goodman's appeal to entrenchment.

Core questions

• Why does observing a non-black non-raven seem to confirm that all ravens are black?
• What is wrong with treating confirmation as a syntactic relation between sentences?
• How does 'grue' show that not all regularities are projectible?
• Can probabilistic or pragmatic accounts dissolve these paradoxes?

Key concepts

• Nicod's criterion
• equivalence condition
• projectibility
• grue
• entrenchment

Key theories

Raven paradox

Hempel shows that the equivalence and instance conditions imply that observing a non-black non-raven confirms 'all ravens are black', which seems absurd.

New riddle of induction

Goodman defines 'grue' (green before some time t, blue after) and shows that the same evidence equally confirms 'all emeralds are green' and 'all emeralds are grue', so projectibility must depend on more than syntax.

History

Hempel posed the raven paradox in his 1945 study of confirmation logic; Goodman introduced the grue predicate in 1955, reframing the problem of induction as the problem of identifying which predicates are projectible. Both remain touchstones for any theory of confirmation.

Debates

Bayesian versus syntactic resolutions

Bayesians argue that a non-black non-raven confirms the hypothesis only negligibly, dissolving the raven paradox quantitatively, while Goodman's riddle resists purely formal treatment and motivates appeals to entrenchment.

Key figures

• Carl Hempel
• Nelson Goodman
• Jean Nicod

Seminal works

• hempel1945
• goodman1955

Frequently asked questions

What is 'grue'?

Goodman defines 'grue' as applying to things examined before a future time t and found green, or not so examined and blue. Past observations of green emeralds confirm both 'all emeralds are green' and 'all emeralds are grue', yet these make opposite predictions after t, showing confirmation depends on which predicates are projectible.