Outline:

  • The Paradox of Change
  • Chrysippus’ Paradox
  • The Paradox of 101 Dalmatians
  • The Paradox of Constitution
  • The Ship of Theseus Paradox

Summary:

  • Some Definitions
    • Paradoxes: arguments from apparently undeniable premises to obviously unacceptable conclusions.
    • LL: x=y=>[f(x)->f(y)].
    • NI: if a=b is true, then it is necessarily true.
    • ND: if a!=b is true, then it is necessarily true.
  • The Paradox of Change
    • What is the paradox?
      • Photo A: old dog with a gray muzzle
      • Photo B: young dog without a gray muzzle.
      • A and B are photographs of the same dog Oscar.
      • Dog in B has a property that the dog in A lacks => A and B are not photos of the same dog. Contradiction.
  • What are the solutions?
    • (1) Properties are relations to times: t, and t’.
    • (2) Extend the object in time as well as space: photos capture distinct temporal parts.
  • What are the objections?
    • To (1): Properties are complicated relations, not only relations to times.
    • To (2): Objects are not “wholly present” at any given time.
  • Chrysippus’ Paradox
    • What is the paradox?
      • In time t’, Oscar loses tail.
      • In time t<t’, Oscar-minus (the whole dog minus his tail) and Oscar are distinct.
      • In time t’, by ND, Oscar and Oscar-minus are distinct, since Oscar has a property at t’ that Oscar-minus lacks. Contradiction.
  • What are the 4 responses?
    • Deny there are such things as Oscar-minus.
    • The parts of an object are essential.
    • Objects of different kinds can occupy the same space at the same time, but objects of the same kind cannot.
    • Temporal parts of distinct objects can occupy the same space at the same time.
  • The Paradox of 101 Dalmatians
    • What is the paradox?
      • If Oscar-minus is a dog, then Oscar minus a hair is also a dog.
      • There are at least 101 dogs (actually many more).
  • What are the responses/solutions?
    • Maximality principle: no proper part of a dog is a dog.
    • Lewis: deny that the “many” are Dalmatians or deny that Dalmatians are many.
  • The Paradox of Constitution
    • What is the paradox?
      • Day 1: statue s1 is made from clay c, so c is identical to s1.
      • Day 2: statue s2 is made from clay c, so c is identical to s2.
      • Day 3: a part of s2 is replaced by a new piece of clay, c’.
      • s1 is identical to c on day 1, s2 is identical to c on day 2 => s1 is identical to s2 =>  s2 exists on day 2. Contradiction.
      • s2 is identical to c on day 3 => c is c’, contradicting NI.
  • What are the solutions?
    • c and  are not identical:
      • c exists prior to the existence of .
      • s1 possesses the property of being destroyed while c does not.
      •  possesses the property of being squeezed into a ball in the future while does not.
      • Frame the issue in terms of c and s that (partially) coincide throughout their entire existence.
      • c is a temporally extended object whose day 1 stage is identical to  and whose day 2 stage is identical to s2 => since day 1 and day 2 are different, s1 and s2 are not NI.
      • Counterpart theory: different concepts are associated with different counterpart relations and hence with different criteria of trans-world identity.
  • The Ship of Theseus Paradox
    • What is the paradox?
      • A wooden ship restored by replacing all its planks and beams.
      • Does the ship remain same?
  • What are the views?
    • The restored ship appears to qualify equally to be the original, but not the same ship.
      • Hobbes.
      • Wiggins (1967) and Parfit (1984): brain duplication scenarios.
      • The restored ship is identical to the original one, since it exhibits a greater degree of spatio-temporal continuity with the original (Wiggins 1967).
        • Problem of intuition: identity is preserved by spatio-temporal continuity v.s. identity is preserved in the process of dismantlement and reassembly.
      • The restored ship is not identical to the original one.
        • Kripke (1980): Table T is made out of wood H; In world w, T is made out of H’; In world w’, T is made out of H, and T’ is made out of H’. Since T and T’ are not identical in w’, table made out of H’ in w is not T.
        • Analogy: In actual world: original ship O, and remodeled ship S; In world w, S’ is built out of the same parts of S. Since S’ and O are different in w, S is not identical to O. (Assumption: S and S’ are the same ship.)
        • Additional paradox from Kripkean argument: S eventuates from O by replacing one part of O one day at a time. By transitivity of identity, O and S are the same.
          • Kripke reply: whether O could change in S is irrelevant.
  • Connections between two issues: the ship of Theseus problem & the question of the necessity of origin.
    • Modified ship of Theseus problem:
      • Two ships: O and O’, and O’ never sets sail; Planks are removed from O’ and used to replace corresponding planks of O, resulting in S. Do O and O’ have equal claim to be S?
      • Criticisms:
        • Conflict with the common sense principle (1) that the material of an object can be totally replenished or replaced without affecting its identity (Salmon 1979).
        • Conflict with the additional common sense principle (2) that replacement by a single part or small portion preserves identity.
          • Counter example of (2) :
            • Two exactly similar sandals A and B;
            • A is brand new and B is worn out;
            • Parts of A and B are exchanged => A’ and B’;
            • By ND, A and A’ are distinct, and B and B’ are distinct;
            • Contradicting with intuition.