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Summary

  • The hyp.-ded. model is weak in the following ways: — i) it neglects the context of discovery — ii) it is too strict regarding what data should be considered relevant (logical implication) — iii) it is also overpermissive regarding relevant data (disjunctive inclusion)
  • Thus, the theory requires that some auxiliary measure be brought in to reduce the strictness of the model but this must in some way also limit overpermissiveness - a difficult ask.
  • Generalised ravens: — i) All Fs are G — ii) => All non-Gs are non-F
    • Therefore, an observation of a non-G that is a non-F supports i)
  • Past responses: — Hempel: result is true under idealised conditions. — Quine: a projective predicate is necessary for inductive support and the complement above is not projective. — Goodman: support must confirm All Fs are G and disconfirm No Fs are G.
  • Looking at contrastive explanation may help: — Some, but not all, support for contrapositives does provide more general support. — Linked to suitability of foil to fact. — i.e. to the closeness in their causal history (in this case we are looking at the closeness of the contrapositive instance and the direct instance)
  • Hence our background knowledge plays a large role in determining when it is suitable to infer direct support from contrapositive support.
  • Mill's method of agreement seems to be of relevance here: — When looking at 2 effects, one holds the effects fixed and manipulates the causal histories of both events in order to determine their cause. — However, there is a problem here regarding the possible plurality of causes. — But, as indicated above, the way around this is to use our background knowledge to select instances that are likely to have similar causal histories.

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What do I think?
- Can one just deal with the ravens e.g. by arguing that the observation in question is indeed a case of support but that support is so small as to not play any role when one is considering the validity of statement i) in the relevant section above?
— Would the correct Bayesian way of phrasing this be to say that P(E|H) = P(E) (hence P(H|E) = P(H))?

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Lipton I B E

Chris Wilcox