1. Puzzles of Material Constitution
Paradoxes 2017

2. Persistence through Time: Basic Worries

3. Identity over Time

4. G. W. Leibniz
17th century philosopher, mathematician, physicist, inventor…
Developed calculus.
Argued that we lived in the best of all possible worlds.

5. Leibniz’s Law
For any two objects X and Y: If X = Y, then X and Y share all the same properties. As we’ve noted, this is logically equivalent to the following principle: For any two objects X and Y: If X and Y do not share all the same properties, then X ≠ Y.

6. Identity over Time B1 B2

7. Simple Worry
B1 has shape S B2 does not have shape S So B1 and B2 do not share the same properties. Therefore, (LL) B1 ≠ B2.

8. Relationalism B1 B2

9. Relationalism
B1 has S and B1 does not have S  Contradiction B1 has S at t1 and B1 does not have S at t2  No Contradiction

10. Simple Worry
B1 has shape S at t1 B2 does not have shape S at t2 So B1 and B2 do not share the same properties. Therefore, (LL) B1 ≠ B2.

11. David K. Lewis American philosopher Student of Quine
Did important work in probability theory, linguistics (semantics), metaphysics, philosophy of mind…

12. The Problem of Temporary Intrinsics
According to Lewis, the relational analysis does not work. Having a shape is not a relation to a time. Your shape depends on how you are, not how you are related to something else.

13. The Ship of Theseus

14. Video Time!

15. 5 Solutions Deny: An object goes where its parts go.
Deny: An ordinary object can survive gradual change (SOMETIMES).
Deny: An ordinary object can survive gradual change (EVER).
Deny: Transitivity of identity.
Deny: Ships exist wholly at a time (4-Dimensionalism).

16. 1. Deny: An object goes where its parts go.
In the video, Professor Wang doesn’t say why we should be worried about this solution. But think about the simple case of a jar with a lid.

17. 2. Deny: An ordinary object can survive gradual change (SOMETIMES).
Whenever you have a long sequence of gradual change, this can add up to a big change. Saying things don’t survive the gradual change is problematic (next slide) but saying they do is also: sorites paradox – Next class!

18. 3. Deny: An ordinary object can survive gradual change (EVER).
This view denies a lot about our common notions of possession, creation, destruction, etc.

19. Unconsidered Solution
An object require change to exist. Enigmatic Greek philosopher Heraclitus believed “all is flux” and “upon those who step into the same rivers, different and again different waters flow.” Does this solve the problem?

20. 4. Deny: Transitivity of identity
Transitivity: If A = B and B = C, then A = C.

21. 4. Deny: Transitivity of identity
Conceptual question: can a relation really be identity if it is not transitive?

22. 5. Four-Dimensionalism (“Worm Theory”)
On the four-dimensionalist view, you are never wholly located at one time, only part of you is. You are a 4D “worm” and at any time only one small part of you exists.

23. 5. Four-Dimensionalism (“Worm Theory”)
Compare: your spatial parts: no contradiction that your left side has a different shape from your right side. Application to SoT: A and B have overlapping parts at one time, but it makes no sense to ask of a ship-at-a-time whether it is A or B.

24. Material Constitution

25. L.A. Paul Wrote her dissertation at Princeton under David Lewis.
Professor at the University of North Carolina– Chapel Hill
Awarded a prestigious Guggenheim Fellowship

26. The Statue and the Clay
Suppose we have a statue (named ‘Statue’) and it is made out of a piece of clay (named ‘Clay’).
Since we’re philosophers, we say that Clay materially constitutes Statue.
Q: Is material constitution the same thing as identity? Statue = Clay?

27. Reasons to Say “Statue = Clay”
How many things are in this picture? If you said “one,” then you think that Statue = Clay. Some philosophers think it is hard to imagine how two distinct things can be located in the same place, sharing all the same parts.

28. The Statue and the Clay
t1:
Statue exists.
Clay exists. t2 t1

29. The Statue and the Clay t1: Statue exists. Clay exists. t2:
No Statue. t2 t1

30. Leibniz’s Law
For any two objects X and Y: If X = Y, then X and Y share all the same properties. As we’ve noted, this is logically equivalent to the following principle: For any two objects X and Y: If X and Y do not share all the same properties, then X ≠ Y.

31. Paradox?
Principle: For any X and Y: if X and Y are located in exactly the same place and have all the same parts, then X = Y. Conclusion #1: Statue = Clay. Leibniz’s Law: For any two objects X and Y: If X and Y do not share all the same properties, then X ≠ Y. Observation: Clay has the property: it can survive a smashing. Statue does not have this property. Conclusion # 2: Statue ≠ Clay.

32. Most Common Solution: Pluralism
The first Principle was wrong. Two things can occupy the same space and have all the same parts. Statue ≠ Clay. Material constitution is not identity.

33. Pluralism

34. 5. Four-Dimensionalism (“Worm Theory”)
On the four-dimensionalist view, you are never wholly located at one time, only part of you is. You are a 4D “worm” and at any time only one small part of you exists.

35. 4D Views vs. Statue & Clay
The 4D view doesn’t seem to help us with the statue and clay. “We can simply stipulate that Statue and Clay exist at exactly the same spatiotemporal locations: when Clay comes into existence, so does Statue, and when it is destroyed, so is Statue”

36. Overdeterminism Statue causes scale to read 120.
Clay causes scale to read 120.
There are two reasons why scale reads 120.

37. Nihilism

38. The Statue and the Clay
Nihilism is the view that NO composite objects exist. There are particles, and they can be arranged in a state-shape, but there are no statues. This *annihilates* the worry about what statues/ clay lumps are.