Matthew Leifer Hi Matthew - thanks for taking the time to read my essay and for the thought-provoking comments! My responses:
Your first concern is that my idea of a falsification tree assumes Karl Popper's falsificationism. But on the contrary my idea is built upon one of the major historical objections to falsificationism, and so it can actually help illuminate what's wrong with falsificationism. Popper thought falsificationism solved Hume's problem of induction by showing that scientists don't reason inductively at all, they only reason deductively: "If theory T is true then we won't see counter-evidence E, we do see counter-evidence E, therefore T is false". The influential objection emphasized by Quine, Duhem, Kuhn, and others, is precisely the existence of the set of assumptions A, needed to properly deduce not-E from T, that may be completely open-ended, making falsification inevitably inconclusive, thereby allowing induction in through the backdoor. The first two levels of a falsification tree encapsulate this objection to falsificationism.
I also don't think my idea assumes a global scientific method, it only assumes that in every science there is disagreement over whether or not some theory should be abandoned or not given our evidence. My essay illustrates this by suggesting falsification trees for everyday reasoning, astronomy, quantum foundations, and neuroscience, and one could go on. There is no demand on sociologists (for e.g.) to adopt the 5-sigma standard of discovery.
Your second concern is that falsification trees will be impossible to build when adversarial collaborators disagree on whether a theory really does make a certain assumption, if it is to entail the absence of counter-evidence E. That's a great point and one I did not deal with in my essay! But I'm not convinced that it's a real issue. Here's why. In my figure on page 6, level three of the tree has the critic arguing that the assumptions (introduced by the advocate at level 2) are actually true. Your concern is that we may not make it to level three if the critic instead wants to deny that assumption A is even needed to get to not-E from T. The transition from one level of the tree to the next is not meant to be easy: to get a third level, the critic must indeed agree on the need for the assumptions at level 2. But here the advocate only needs to present a logically consistent scenario in which both T and E are true (due to A being false). For example, All leaves are green (T) yet I experience some blue leaves (E) but only because "no spay-painting of leaves" (A) is false. You are effectively imagining a disagreement over whether such a scenario can be consistently spelled out. Your suggestion is I think not plausible for this trivial example, and I'd need to see some examples to be convinced that this would be at all prevalent in an adversarial collaboration aimed at evaluating a real scientific theory. But even if it happens, a branch of the tree gets stunted until there is further progress, but at least we know where the disagreement ultimately lies, which is part of the point of employing this structure.
Part of my motivation here arises from the endless stalements we see between the Tim's and Lev's of this world. Do you think you know exactly what their disagreement over many worlds ultimately boils down to? I haven't a clue (despite having read literally everything that both have published on the topic). Would you like to know? I think you would (I know I would) and I believe an adversarial collaboration where they construct such a tree for the rest of us would get us there.