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Contradiction/LewisVsimpossible world/Lewis: There is no object, no matter how fantastic, about which one could say the truth by contradicting oneself.
Impossible world/Stalnaker: problem: if it is defined by a contradiction P and ~P. - Then this contradiction is transmitted to the real world - through the modal operator in w, P. - Because it is then true in the real world that it is true in the other possible world.
Another problem: if there is a impossible world., the possible world with P and those with ~P are no longer complements. - Problem: even the most bizarre possible world will not be at the same time in a set of possible worlds and its complement.
Solution: New Def impossible world: about which a contradiction is true - This does not makes the real world impossible.
Impossible world/Actualism/Stalnaker: the actualist has no problems with impossible world, because he can simply understand them as conflicting sets of propositions. - LewisVs/LewisVsreplacement world: conversely, propositions are sets of possible worlds.
Ways a World may be Oxford New York 2003