Version 1 of #4285

Criticism 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)