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Cause/Bigelow/Pargetter: Thesis: a cause is neither sufficient nor necessary for an effect.
Reason: there is a backup system that could have produced the same effect.
If the updated system failed. E.g. you could have also eaten another slice of bread. Different food intake can have exactly the same effect.
Blur/Imperfection/Bigelow/Pargetter: it is a characteristic feature of living systems. Nevertheless, this is not an intrinsic feature.
Cause/Lewis/Bigelow/Pargetter: Lewis allows that a cause is not a necessary condition for the effect. Nevertheless, he explains causation by necessity. Namely, through chains of necessary conditions. (1973b, 1986d, 1979).
Cause/Mackie/Bigelow/Pargetter: he arrives at similar results like Lewis, but with strict conditionals. (> Cause/Mackie)
Cause/INUS/Mackie: (Mackie 1965) Thesis: not a sufficient but necessary part of an unnecessary but sufficient condition.
Cause/Lewis/Mackie/Bigelow/Pargetter: both come from a chain of necessary conditions. They differ in how the links of the chain are to be connected.
Lewis: through contrafactual conditioning
Mackie: through strict conditionals. Their antecedents can be so complex that we cannot specify them in practice.
Backup system/Bigelow/Pargetter: (see above) would cause a contrafactual conditional to fail. Nevertheless, Lewis records the cause as a cause because it contributes to the chain.
Mackie: dito, because the deviant cause is part of a sufficient condition.
BigelowVsLewis/BigelowVsMackie: both theories have disadvantages.
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990