I found this a particularly interesting paper. I’m in firm agreement with the main gist of Williams’ view- that the notion of typicality is in principle better adapted to deal with chancy similarity than the notion of ‘non-remarkableness’. That said, we found plenty of potential pressure points.
– Firstly, I’m not sure that quantum mechanics really has as wide-reaching consequences as is assumed in the paper. Depending on your response to the measurement problem, it could be that outcomes such as plates flying off sideways are not genuine quantum possibilities after all, because the low-amplitude branches are in some way ‘lost in the noise’. Although I think this issue is worth further investigation, I don’t think it’s critical to the debate between Williams, Hawthorne, and Lewis. Their worries can be raised about considerably less unlikely events – in fact, we can restrict consideration just to sequences of coin tosses without significant cost.
– One thought I had about the original ‘Similarity’ proposal – if we read ‘laws’ not always as fundamental microphysical laws, but (depending on context) various kinds of more emergent laws, we could save the proposal without having to introduce quasi-miracles or typicality. A plate flying off sideways may or may not be a violation of quantum-mechanical laws, but it is certainly a violation of the Newtonian laws which hold to a good degree of approximation at the macroscopic level. And maybe these Newtonian laws are the salient laws for consideration of the counterfactual. Similarly with counterfactuals like ‘if I drop this icecube into that mug of hot tea, the icecube will melt’. We don’t even need to go to QM to get counterexamples to this; statistical mechanics describes certain highly-unlikely scenarios where the molecular impacts conspire to prevent melting. But if the salient laws are thermodynamic laws, then the cube must melt. This suggestion is in the spirit of the proposal about deterministic chance I discuss here.
– One serious option that Williams doesn’t seem to exclude is a contextualism about ‘remarkableness’. This would involve events being classified as remarkable or not taking into account the centred world in which they occur. So a string of 100 heads in a row when flipping a fair coin is remarkable taken by itself, but not when we take into account that it is embedded within a string of a trillion coin flips. If we flip a trillion times, we could reasonably expect a string of 100 heads to occur somewhere.
This suggestion seems to ameliorate all of the problems Williams raises for ‘Similarity*’. The monkey producing the dissertation will not be remarkable in the context of worlds where the chances were arranged such that it had a 20% chance of producing one. The problem of the abundance of quasi-miracles is defused by noting that in the context of a long and varied future which is likely to contain various individually unlikely coincidences, particular individual coincidences will no longer count as remarkable. The remarkable subpattern problem can similarly be treated as not remarkable when taken in context of a very long pattern which overall is not particularly remarkable.
How different from the typicality account is this ‘contextualized remarkableness’ account? I’m inclined to say ‘not much’. However, it remains to be seen how the context-shifting would work out in detail – perhaps this kind of account might lead to failures of Agglomeration. It seems to be a big merit of the typicality account that Agglomeration is validated.
– We’d all have liked more detail in the typicality proposal, with particular reference to how the class of relevant natural properties is to be characterized, and which mathematical definition of randomness is to be used. Another concern was what a ‘small, localised atypicality’ might be (as appealed to in point 3 of Chancy Similarity*) – wasn’t typicality explicitly a global notion?
– Despite all this, we thought the typicality account a promising one and liked the way it could be applied both to chancy counterfactuals and to the Elga’s problem of fit.