**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*,*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.

- Day 1: statue s1 is made from clay

- 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.

**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.

- Kripke reply: whether

- Kripke (1980): Table

- 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.

- Two exactly similar sandals

- Counter example of (2) :

- Two ships:

- Modified ship of Theseus problem: