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Branched Time/Possible Worlds/Bigelow/Pargetter: we allow the time to be branched, i.e. to every past there are several futures. We should also allow such development to be possible within one. That is, two parts could have the same origin. Likewise, fusion and temporary joining together of parts.
Problem: it is surprising that such parts would then have at least a temporal part in common.
Suppose we meet Jane from another part of the same possible world. Let us look at this:
Counterfactual conditional: if we had not met Jane, she would not have existed.
BigelowVsLewis: according to him, that must be true.
Bigelow/Pargetter: according to us, it is clearly wrong. There must therefore be at least one possible world in which Jane exists and we do not meet her. And this possible world must contain us all and Jane, although there is no connection between us.
LewisVsVs: he would then have to assume any other connection and a corresponding counterfactual conditional: "... an ancestor or descendant of us could have met an ancestor or descendant of her," etc.
BigelowVsLewis: that is still wrong in the questionable world and less plausible than the above counterfactual conditional. This shows the fallacy of the temporal theory.
BigelowVsLewis: he is in a dilemma: either he takes the world-companions-relation as a primitive basic concept or he allows modal basic concepts.
Counterpart Relation/Lewis/Bigelow/Pargetter: However, Lewis still relies on a more important relation, the counter-relation: it is also not a good candidate for an unanalyzed basic concept, but nevertheless it also needs modal basic concepts.
BigelowVsLewis/BigelowVsCounterpart Theory/Bigelow/Pargetter: it also leads to circularity because it presupposes modal concepts. That is, it cannot justify modal logic.
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990