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For the clearest and most precise view of Deutsch's philosophy of science in the context of quantum theory, read his paper The logic of experimental tests, particularly of Everettian quantum theory: https://www.sciencedirect.com/science/article/pii/S135521981... There's a breakdown of the paper here: https://www.youtube.com/watch?v=DHLTBOJ5hoQ&t=42s A quote mentioning Bayesian Epistemology: Prevailing discussions (e.g. Dawid & Thébault, 2014; Greaves & Myrvold, 2010) of the testability of various versions of quantum theory have approached the matter indirectly, in terms of support or confirmation – asking how our credence (degree of belief) for a theory should be changed by experiencing results of experiments. However, experimental confirmation is a philosophically contentious concept. Notably, it is rejected root and branch by Popper (1959). I shall present an account of the nature and methodology of scientific testing that closely follows Popper׳s. It differs from his, if at all,3 by regarding fundamental science as exclusively explanatory. That is to say, I take a scientific theory to be a conjectured explanation4 (explanatory theory) of some aspects of the physical world – the explicanda of the theory – that is testable (I shall elaborate what that means below) by observation and experiment. A scientific explanation is a statement of what is there in reality, and how it behaves and how that accounts for the explicanda. Neither confirmation nor credence nor ‘inductive reasoning’ (from observations to theories or to justifications of theories as true or probable) appear in this account. So in this view the problem described in Section 1 is about testing theories. This contradicts the ‘Bayesian’ philosophy that rational credences obey the probability calculus and that science is a process of finding theories with high rational credences, given the observations. It also contradicts, for instance, instrumentalism and positivism, which identify a scientific theory with its predictions of the results of experiments, not with its explanations. My argument here, that Everettian quantum theory is testable, depends on regarding it as an explanatory theory, and on adopting an improved notion of experimental testing that takes account of that. Scientific methodology, in this conception, is not about anyone׳s beliefs or disbeliefs. Rather, it assumes that someone has conjectured explanatory theories (though it says nothing about how to do that), and it requires those who know (i.e. are aware of) those theories and want to improve them, to attempt to locate specific flaws and deficiencies and to attempt to correct those by conjecturing new theories or modifications to existing theories. Explicanda in the sciences usually involve appearances of some sort (e.g. the perceived blueness of the sky). Theoretical matters can also be explicanda (e.g. that classical gravity and electrostatics both have an inverse-square force law), but those will not concern us here. Explanations of appearances typically account for them in terms of an unperceived, underlying reality (e.g. differential scattering of photons of different energies) that brings about those appearances (though not only them). |
this would be basically
for all i in S1 p(evidence | theory i) = 0
for all i in S2 p(evidence | theory i) = k * p(evidence)
I would say that most scientific evidence is of this sort, except that the probabilities for the "falsified" theories can also be a little bit above 0 to account for measurement error.
Edit: Actually it may be fruitful to introduce a distinction similar to the one probability theory has... In probability theory there is a difference between sample and event. An event is a set of samples. In our case, I believe we want a distinction between a theory... and a lets call it micro-theory. To pick a funny and memorable example a theory could be something like "there is a Loch Ness monster". Now a micro-theory could be something like "there is a Loch Ness monster, that is invisble, and makes no sounds, but it can be detected by radar... and... and...". So it would include all these additional constraints. So the theory it's composed of a lot of these micro theories right. Now if we take photos of every inch of Loch Ness, and we don't find any Loch Ness monster, we make it less likely that there is a monster right. We may say "oh we were careless, and just missed it" but if we keep looking eventually that becomes an impossibility. So we disprove a bunch of micro theories, but some will remain. Our previous micro theory that among other thing says that the monster is invisible remains. And whats worse the relative likelyhood of them is unchanged compared to the no monster.
p(cant get monster on photo | no monster) = k p (cant get monster on photo) and
p(cant get monster on photo | invisible monster) = k p (cant get monster on photo)
Now if we want to further increase our belief in "no monster" we would have to go after these wacky micro-theories and disprove them, using e.g. radar. But given that a sensible person assigns those micro-theories low prior likelyhood we may be satisfied with the situation and not bother.
So basically these was just Popperianism in Bayesianism clothing right? Almost... Notice the very last point. We allowed ourselves not to bother with theories of invisible monsters. Because of our prior likelyhood.