by [embedded content] Besides illustrating that it is simply not a good description of how we make inferences in science to assume that non-black armchairs confirm the hypothesis that all ravens are black, Hempel’s paradox — at least in my reading of it — makes a good argument for a causal account of confirmation of empirical generalizations. Contrary to positivist theories of confirmation, the paradox shows that to have a good explanation in sciences, we have to make references to causes. Observed uniformity does not per se confirm generalizations. We also have to be able to show that uniformity does not appear by chance, but is the result of causal forces at work (such as e.g. genes in the case of ravens. Assume you’re a Bayesian turkey (chicken) and hold a nonzero
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Besides illustrating that it is simply not a good description of how we make inferences in science to assume that non-black armchairs confirm the hypothesis that all ravens are black, Hempel’s paradox — at least in my reading of it — makes a good argument for a causal account of confirmation of empirical generalizations. Contrary to positivist theories of confirmation, the paradox shows that to have a good explanation in sciences, we have to make references to causes. Observed uniformity does not per se confirm generalizations. We also have to be able to show that uniformity does not appear by chance, but is the result of causal forces at work (such as e.g. genes in the case of ravens.
Assume you’re a Bayesian turkey (chicken) and hold a nonzero probability belief in the hypothesis H that “people are nice vegetarians that do not eat turkeys and that every day I see the sun rise confirms my belief.” For every day you survive, you update your belief according to Bayes’ Rule
P(H|e) = [P(e|H)P(H)]/P(e),
where evidence e stands for “not being eaten” and P(e|H) = 1. Given that there do exist other hypotheses than H, P(e) is less than 1 and a fortiori P(H|e) is greater than P(H). Every day you survive increases your probability belief that you will not be eaten. This is totally rational according to the Bayesian definition of rationality. Unfortunately — as Bertrand Russell famously noticed — for every day that goes by, the traditional Christmas dinner also gets closer and closer …
Studying only surface relations won’t do. Not knowing the nature of the causal structures and relations that give rise to what we observe, explanations serve us as badly as the one used by the turkey. Not knowing why things are the way they are, we run the same risk as the Russellian turkey.
No causality, no confirmation/explanation.