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#4285·Dirk MeulenbeltOP, about 17 hours agoCriticism 1: The Decomposition is Arbitrary
The objection: The entire theorem rests on splitting a hypothesis h into (h ∨ e) and (h ∨ ¬e) and then showing the second part gets negative support. But why split it that way?
Critics argue this is a choice, not a necessity. Define "the part that goes beyond the evidence" differently and you get different results.
This is the most common objection in the literature. Ellery Eells argued the key assumption has been "almost uniformly rejected," because the propositions generated by Popper and Miller's decomposition contain content from both the evidence and the hypothesis tangled together, so they don't cleanly capture "the part that goes beyond the evidence." (Eells, 1988, British Journal for the Philosophy of Science 39, 111–116 — PDF)
Chihara and Gillies proposed "a new condition on what constitutes 'the part of a hypothesis that goes beyond the evidence' that is incompatible with Popper and Miller's condition, "arguing this refutes the impossibility of inductive support. (Chihara & Gillies, Philosophical Studies 58, 1990 — PDF)
Placeholder Criticism: The Decomposition is NOT Arbitrary
Deutsch argues the decomposition is not arbitrary: it follows necessarily from the probability calculus itself. He and Leonardis have been working on a paper to make this clearer, noting that "Popper and Miller's two papers on this are very condensed and mathematical and use special terminology they created," which has made the result difficult for others to evaluate fairly. The difficulty of presentation has been mistaken for a flaw in the argument. (Joseph Walker Podcast, Ep. 139)
Deutsch never actually explains why the decomposition is necessary. Therefore this criticism is a placeholder and to be updated once someone finds out his reasoning.