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|Counterpart Theory||IV 26f
Counterpart theory/Lewis: alternative to modal logic with modal operators - then we have no non-eliminable singular term.
Four basic predicates: Wx (x is a possible world) - ((s)> Quantity) - Ixy (x is inside the poossible world y) - ((s)> containment, element relation) - Ax (x is actual) - ((s)> existence) - Cxy (x is a counterpart of y) - ((s)> correspondence, bearer of possibl.>cross world identity)- Eight postulates/logical form: P1: (x)(y)(Ixy>Wy) - everyday language translation: (Nothing is in something other than a world) - P2: (x)(y)(z)(Ixy & Ixz. > y = z) - (Nothing is in two worlds) - P3: (x)(y)(Cxy > E zIxz) - (whatever is a counterpart, is always in a world) - P4: (x)(y)(Cxy> E zlyz)- (Whatever has a counterpart, is in a world) P5: (x)(y)(z)(Ixy&Izy&Cxz. > x = z) - (Nothing is a counterpart of something in the same world) P6: (x)(y)(Ixy>Cxx) - (Every thing in a world is a counterpart of itself) - P7: (Ex)(Wx&(y)(Iyx ↔ (Ay)) - (A World contains all and only actual things) - P8: ExAx - (Something s actual) - The world mentioned in P7 is unique because of P2 and P8 - World/logical form/Actual world/Lewis: - @ = def ix(y)(Iyx ↔ Ay) (the actual world).
Counterpart relation: is generally not an equivalence relation - i.e. It does not apply between the pairs with the same first term (as Carnap would say. Lewis: no thing is in several worlds) - no matter how you tried to identify them - it is not transitive either, because similarity is not transitive - it is not symmetrical either: E.g. assuming x3 in w3 is a mixture of you and your brother and resembles you more than anything else in w3, so x3 is your counterpart.
But assuming the similarity of x3 with your brother is much greater, then you are not the counterpart of x3 - a thing does not need to have a CP in every world.
Counterpart theory/CPT/Lewis: we need counterpart relations in order to be able to determine the essence of something - Problem CPR are not very secured - problem:> similarity.
Counterpart theory/Lewis: Problem: e.g. two pairs of twins in different possible worlds - they are more similar to the two than any other thing - Question: (double de-re) could the first twins not have lived on two different planets as relatives? - simply de re: Originally the two could simply not have be related (in the same world)? - If that is counterintuitive depends on how the question is asked - Lewis: Double de-re questions should be avoided - they result in duplicate counterpart relations - pairs of counterparts should not be construed as counterparts of pairs. ((s)> Bizet/Verdi).
Referentially transparent/De re/Modal/Normal CPT/Lewis: in my CPT all modal de re predications are referentially transparent - i.e. something has the same counterparts, no matter how we refer to them.
Counterpart theory/Lewis: from it follows that the real imperator is not free to cross the Rubicon or not - only his counterpart could refrain - counterpart relations (CPR) and proximity to possible worlds are equally a matter of similarity, but they are independent of one another.
Die Identität von Körper und Geist Frankfurt 1989
Konventionen Berlin 1975
Philosophical Papers Bd I New York Oxford 1983
Philosophical Papers Bd II New York Oxford 1986
Cl. I. Lewis
Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991