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 is the paradox?
- 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 is the paradox?
- 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 is the paradox?
- 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 is the paradox?
- 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.
- c and are not identical:
- 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 is the paradox?
- 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.
- The restored ship appears to qualify equally to be the original, but not the same ship.
- 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.
- Counter example of (2) :
- Modified ship of Theseus problem: