You observe a green apple. According to Bayesian confirmation theory, what is the relationship between this observation and the hypothesis 'All ravens are black'?
AIt does not confirm the hypothesis at all — only observations of ravens can confirm claims about ravens
BIt disconfirms the hypothesis, because the apple is irrelevant evidence
CIt confirms the hypothesis, but only infinitesimally, because almost all objects are non-black non-ravens
DIt confirms the hypothesis as strongly as observing a black raven, because they are logically equivalent
On the Bayesian account, E confirms H if P(H|E) > P(H). The green apple is a non-black non-raven, which satisfies the logically equivalent form of the hypothesis. So formally it does raise our credence in H — but only infinitesimally. The key Bayesian insight is that the degree of confirmation depends on how informative the evidence is: there are vastly more non-black things than ravens, so seeing one more non-black non-raven barely moves the needle. Observing a black raven, by contrast, is much more confirmatory because ravens are rare and the observation was therefore much more probable given H than given ¬H.
Question 2 Multiple Choice
A scientist is testing whether a new drug reduces inflammation. Which observation provides stronger Bayesian confirmation for the hypothesis 'This drug reduces inflammation'?
AA patient who did not take the drug and showed no change — this is consistent with the hypothesis
BA patient who took the drug and showed reduced inflammation — this was more likely to occur if the hypothesis is true
CBoth observations confirm the hypothesis equally, since both are consistent with it
DNeither observation confirms anything because consistency with a hypothesis is not evidence for it
Bayesian confirmation is not about consistency but about the likelihood ratio P(E|H)/P(E|¬H). A patient who took the drug and improved is highly likely given H and less likely given ¬H (where improvement is just random), so the likelihood ratio is large — strong confirmation. A patient who did not take the drug and showed no change is equally probable whether or not the drug works, so the likelihood ratio is near 1 — negligible confirmation. The Bayesian framework explains why 'consistent with the hypothesis' is not the same as 'confirms the hypothesis.'
Question 3 True / False
According to Bayesian confirmation theory, confirmation is a matter of degree rather than an all-or-nothing relation between an observation and a hypothesis.
TTrue
FFalse
Answer: True
This is one of the most important conceptual contributions of Bayesian confirmation theory. Rather than asking 'does E confirm H?' (binary), Bayesian theory asks 'by how much does E raise the probability of H?' The answer depends on the prior probability of H and the likelihood ratio P(E|H)/P(E|¬H). The same observation can strongly confirm one hypothesis and weakly confirm another. This graduated picture resolves many apparent paradoxes — like why the green apple 'confirms' all ravens are black but in such a negligible way that it feels like no confirmation at all.
Question 4 True / False
Hempel resolved the ravens paradox by arguing that the green apple definitely does not confirm 'Most ravens are black,' because primarily objects in the relevant reference class (ravens) can confirm claims about that class.
TTrue
FFalse
Answer: False
Hempel's actual response was the opposite: he accepted that the green apple does (weakly) confirm 'All ravens are black,' because it satisfies the logically equivalent formulation 'All non-black things are non-ravens.' Hempel argued that our intuition that the apple is irrelevant reflects a pragmatic point about where we expect evidence to come from, not a logical error. It was Hempel's acceptance of the paradoxical conclusion — not its rejection — that motivated philosophers to search for better accounts. The Bayesian approach, which came later, explains why the apple confirmation feels trivial without denying it.
Question 5 Short Answer
Explain why the Bayesian account of confirmation handles the ravens paradox more satisfyingly than simply accepting that the green apple fully confirms 'All ravens are black.'
Think about your answer, then reveal below.
Model answer: The Bayesian account distinguishes between whether something confirms a hypothesis and how much it does so. The green apple does technically confirm 'All ravens are black' — P(H|green apple) > P(H) — but only infinitesimally. This is because confirmation depends on the likelihood ratio P(E|H)/P(E|¬H), and since there are vastly more non-black non-raven objects than there are ravens, seeing one more green apple barely changes our credence in the hypothesis. Observing a black raven, by contrast, is far more informative because ravens are rare. The Bayesian framework explains why the apple confirmation is negligible without denying that it exists, which is more satisfying than simply saying 'it doesn't confirm at all.'
The key move is making confirmation gradational. Hempel was stuck with a binary notion (confirms or doesn't confirm), which forced him to either accept the absurd-seeming conclusion that the apple fully confirms or reject it and lose logical consistency. Bayesian theory dissolves the dilemma: both the raven and the apple confirm, but to vastly different degrees, and the difference in degree corresponds exactly to our intuition that the raven observation is the relevant evidence.