Intermittent objects

David W. Agler

The Pennsylvania State University

A scenario

  1. At \(t_1\), Tek hands his watch to a watchmaker.
  2. The watchmaker then disassembles the watch.
  3. At \(t_2\), there are the watch parts lying on the table.
  4. The watchmaker then reassembles the watch.
  5. Let \(t_3\) refer to the time that the parts from \(t_2\) have been reassembled into a watch where the parts are in the same relative places as the parts of the watch at \(t_1\).

graph LR
A("watch")
M("disassembled watch parts P")
B("watch made of P")
A --> M
M --> B

The question of intermittent objects

  1. Does the watch stop existing at \(t_2\) when it is disassembled?
  2. Is the watch at \(t_3\) one and the same watch as the watch at \(t_1\)?

Exercise

Answer both questions

Intermittent objects

Intermittent objects (IO)

An IO is an object \(A\) that exists at \(t_1\), does not exist at \(t_2\), and then exists again at \(t_3\) as \(B\) and \(A=B\).

You can think of an IO as a gappy object.

Three theories

Do IOs exist?

  • T1: No. The watch exists, ceases to exist in its disassembled state, and then, once reassembled, is not the original watch.
  • T2: No. The watch exists, continues to exist as a watch in its disassembled state, and then, once reassembled, is one and the same watch.
  • T3: Yes. The watch exists, ceases to exist, and then exists again as one and the same watch.

Theory 1

Theory 1 says IOs do not exist. Two claims:

  • C1: Ceases to exist in its disassembled state
  • C2: Once reassembled, is not the original watch.

graph LR
A("watch")
M("no watch")
B("new watch")
A --> M
M --> B

T1 says once an O is disassembled, it is destroyed forever.

Theory 1: Reasons

  • P1: No object can have two beginnings (Locke)
  • P2: If there were IOs, then the watch would have two beginnings.
  • C: Therefore, when the watch parts are reassembled, there is a new watch.

Problems: Intuitions 1

Intuition 1: Watches survive disassembly and reassembly.

  • I give the watchmaker my Grandfather’s watch.
  • It is disassembled and returned.
  • The watchmaker and I both act as though it is the original watch.

If the watchmaker presented me a qualitatively similar watch, I would demand my Grandfather’s watch.

Problems: Intuitions 2

Intuition 2: The watch survives as a watch in its disassembled state.

  • Your watch is in a disassembled state.
  • Theory 1 says the watch does not exist.
  • I smash the parts to bits.

You would feel as though I’ve destroyed your watch.

Theory 1 - Summary

Both claims of Theory 1 seem wrong.

  • C1: Ceases to exist in its disassembled state
  • C2: Once reassembled, is not the original watch.

Theory 2

Theory 2 says IOs do not exist. Single claim:

  • C1: The watch continues to exist as a watch in its disassembled state.

It is responsive to the insight that if the parts were destroyed, you would have destroyed the watch.

graph LR
A("watch")
M("watch in a disassembled state")
B("same watch")
A --> M
M --> B

T2 - Alternatively put

T2 says

  • objects have “lapses” in their intactness, e.g., cars, bicycles
  • some objects are disassembled most of the time, e.g., tents, guns, saxophone

T2 - Diachronic sortal identity

T2 seems to view objects as maintaining their kindness in their disassemble state

  • A watch stays a watch (the object’s kind) while it is disassembled
  • A bicycle stays a bicycle (the object’s kind) while it is disassembled

diachronic sortal identity

An object \(A\) at \(t_1\) is one and the same object as object \(B\) at \(t_2\) only if (1) \(A\) and \(B\) are spatiotemporally continuous with each other and (2) \(A\) and \(B\) belong to the same dominant kind \(K\).

Theory 2: Reason 1 (repairs)

  • If an object went out of existence when it was disassembled, then it would be impossible to repair any object.
  • Therefore, a watch needs to exist as a watch in a disassembled (scattered) state in order to be repaired.

Theory 2: Reason 2 (language)

  • My gaming PC is dusty.
  • I disassemble it and lay out the parts on a table.
  • My daughter walks in and says “what are you doing with your computer.”

Two pieces of linguistic evidence:

  1. She calls the disassembled parts “your computer”
  2. The predicate “is disassembled” rightly applies to “my computer”

T2: Problem 1

One problem with T2 are its implications.

  1. We will show that T2 violates the one-object-to-a-place principle
  2. Showing this involves a few steps.

one-object-to-a-place principle

For any given spatial region \(R\) at an instant of time \(t\), there can be at most one material object wholly occupying \(R\).

There cannot be two distinct objects \(A\) and \(B\) (\(A\neq B\)) that wholly occupy the same space at the same time.

One-object principle (examples)

  • In the space occupying my desk, there is a single desk (not two desks, not a desk and a chair)
  • If I am holding a single sheet of paper, there is just that single sheet. There are not two sheets or the piece of paper and some other object.

Exercise

one-object-to-a-place principle

For any given spatial region \(R\) at an instant of time \(t\), there can be at most one material object wholly occupying \(R\).

Exercise

Do you believe in the one-object-to-a-place principle?

  • If yes, think of at least one more supporting example.
  • If no, think of a possible counterexample.

Burke’s disassembly

  1. At \(t_1\), there is a table made from thirty pieces of wood
  2. The table is then disassembled and made into a chair.
  3. At \(t_2\), there is a chair.
  4. The chair is then dismantled and parts are made into a stool and the remaining parts are made into a birdhouse.
  5. At \(t_3\), there is a stool and a birdhouse.
  6. The stool and birdhouse are dismantled, and all thirty pieces are made into a table of the same size, shape, style, etc. as the table at \(t_1\).
  7. At \(t_4\), there is a table.

Burke’s questions

graph LR
T1("table at t1")
C("chair at t2")
S("stool at t3")
B("birdhouse at t3")
T4("table at t4")
T1 --> C
C --> S
C --> B
S --> T4
B --> T4

  1. If the table survives as a disassembled object, where is it in space at \(t_2\)?
    • T2 supporter: It is where the chair is.
  2. If the table is where the chair is, then is that object a chair?
    • Common sense: Yes.

Result: The table and the chair wholly occupy the same spatial region, violating the one-object-to-a-place principle.

T2 - Summary

  • Theory 2 says that watches survive as watches in their disassembled state.
  • Burke shows that this violates the one-object-to-a-place principle

Both theories rejecting IOs are problematic.

Summary of T1 and T2

  • T1 says Os are destroyed when they are disassembled.
  • T2 says Os continue to exist as the kind of thing it is while it is disassembled (accepts scattered objects).

It is time to accept IOs!

Theory 3

Theory 3 says IOs exist! Two main claims

  • C1: Objects go out of existence when disassembled
  • C2: Objects can survive back into existence (gappy objects). Rebirth!

graph LR
A("watch")
M("no watch")
B("same watch")
A --> M
M --> B

Theory 3: Reason 1 (intuitions)

  • Consistent with Grandfather’s watch scenario.
  • If you hand me the reassembled watch, I take it to be my Grandfather’s watch.

Theory 3: Reason 2 (Burke’s disassembly)

  • No problem with Burke’s disassembly scenario
  • Does not violate the one-O-to-one place because Os don’t survive when disassembled.

Problem 1 (intuitions)

One problem we raised was that if you destroyed the parts of the watch when it is disassembled, you would be held at fault for destroying the watch. This seemingly would apply to T3.

Exercise

Assume you hold there are IOs. Come up with a response to this problem.

Problem 2 (poppy objects)

  • Suppose a watch \(W_1\) is on your desk at \(t_1\)
  • It pops out of existence at \(t_2\)
  • A qualitatively identical watch \(W_2\) (or two watches \(W_3\)) pop into existence at \(t_3\)

What criteria could you use to say whether the \(W_1 = W_2\)?

Response

  • You could just add some type of spatiotemporal condition on the parts.
  • In cases of disassembly and reassembly, there is sameness of the parts (spatiotemporal continuity of the parts).
  • Os can survive disassembly and reassembly but not popping out of existence entirely.

Implications of IOs

Let’s consider some quasi-practical questions surrounding the existence of IOs.

Ownership

Suppose there are three people:

  1. Tek - ship owner (sailor)
  2. Liz - ship owner (sailor)
  3. Sam - ship builder and repairer

Sam

Sam has two warehouses

graph TD
subgraph B["Warehouse B"]
  Y[" "]
end
subgraph A["Warehouse A"]
  X[" "]
end
classDef plain fill:none,stroke:none
class A,B plain

  • Sam is terrible with his finances.
  • Shady with his business.

Liz

Liz is wealthy, a seasoned sailor, and owns a ship.

  • She wants to repair her existing ship
  • Asks Sam to replace old boards with new boards

Tek

Tek is poor, a seasoned sailor, and does not own a ship

  • He wants to a new ship
  • To cut costs, he wants it made from old boards (parts)

Payment rendered

  1. Sam takes payment from Liz and puts her ship \(X\) in Warehouse \(A\)
  2. Sam takes payment from Tek.

graph TD
subgraph B["Warehouse B"]
  Y["Empty"]
end
subgraph A["Warehouse A"]
  X["X"]
end
classDef plain fill:none,stroke:none
class A,B plain

Business genius

  1. Sam and his team disassemble \(X\) and replace parts from \(X\) with new parts.
  2. The parts from \(X\) are moved to Warehouse \(B\) and used to create ship \(Z\).
  3. At the end of a week, there are two ships \(Y\) in \(A\) and \(Z\) in \(B\).

graph TD
subgraph B["Warehouse B"]
  Y["Z"]
end
subgraph A["Warehouse A"]
  X["Y"]
end
classDef plain fill:none,stroke:none
class A,B plain

Sam saves money by not having to buy old ship parts.

Fire

  • There is a fire in Warehouse A.
  • Ship \(Y\) is destroyed.
  • This leaves ship \(Z\) in Warehouse \(B\)

graph TD
subgraph B["Warehouse B"]
  Y[" Z "]
end
subgraph A["Warehouse A - Destroyed"]
  X[" Y is destroyed "]
end
classDef plain fill:none,stroke:none
class A,B plain

Sam leaves town with the money (burns down his house)

Who owns ship Z?

  • It is your job to decide who owns Ship Z.
  • Listen to both arguments carefully

Tek’s argument

Ship Z belongs to me!

  1. I paid Sam for a ship made of used boards and ship \(Z\) in warehouse \(B\) fits that description.
  2. Liz asked for a ship composed of new boards and ship \(Z\) is not composed of new boards
  3. Liz’s ship was disassembled. Once disassembled, her ship no longer existed.
  4. The parts from Liz’s ship were moved to Warehouse B where they were used to create a new ship.

Liz’s argument

No! Ship Z belongs to me!

  1. I accept that you paid Sam for a ship that fits the description of ship \(Z\).
  2. I accept that ship \(Z\) is not the ship I paid for.
  3. I accept that my ship was disassembled.
  4. I also accept that the parts were moved and used to create a ship in Warehouse \(B\).

But …

Liz’s argument (continued)

  1. I reject the claim that my ship \(X\) stopped existing when it is was disassembled. Instead, ship \(Z\) is my ship just in a reassembled state. \(X=Z\).

Look at this board right here: it has my initials on it.

Exercise

Exercise

Who owns Ship Z in Warehouse B?

  1. Make the strongest case you can.
  2. Draw a diagram

Resurrection of the body

Resurrection of the body

  • Suppose you will be resurrected at some time after you die.
  • Some religions believe in resurrection of the body

Resurrection of the Body

God will grab the parts \(P\) of your body at some time \(t_i\) while you were alive and reconstruct you at \(t_{i+j}\) with \(P\)

Resurrection and IOs

  • resurrection of the body sounds like disassembly and reassembly.
  • Death, decay, and decomposition is a natural disassembly and God’s resurrection of us is a reassembly

Resurrection by reassembly

God is able to resurrect our bodies after they have died by reassembling us: taking our parts (atoms) and putting them in a spatial-chemical configuration that we had when we were alive.

Four problems

There are four problems:

  1. Double resurrection problem
  2. Cannibal problem
  3. Annihilation problem
  4. Gap Problem

O1: Double resurrection problem

Paul dies at 60 years-old. Call him \(A\).

  1. God uses the particles of 10 year-old Paul. Call them \(B\)
  2. God uses the particles of 45 year-old Paul. Call them \(C\)

But we have a duplication problem!

  • If Paul can be resurrected, then \(B=A\) and \(C=A\). Therefore, \(B=C\)
  • But, intuitively, \(B\neq C\).

Response

  • God reconstructs you using the body you had before you died.
  • Avoids the duplication problem

O2: Cannibal problem

  • Tek is evil, he wants to avoid going to hell and wants to prevent reconstruction
  • Tek knows (from the duplication problem) that God will try to reconstruct him using the parts he has before he dies.

So …

O2: Cannibal problem (continued)

  • Tek captures many good people
  • He eats them, but keeps them alive as long as possible
  • His body absorbs their particles

Now Tek is made up of good people \(A, B, \ldots Z\).

  • Tek and his victims die
  • God cannot reconstruct Tek without failing to reconstruct his victims

O2: Cannibal problem

Exercise

Play God. How can you resurrect the bodies of both Tek and his victims (so you can punish Tek and reward his victims) while still using the bodies of both Tek and the victims before they died?

Response (Staggered resurrection)

The standard reply is that God will engage in staggered resurrection.

  • God will reassemble Tek
  • Gradually replace the cannibalized parts with new parts
  • Use the removed parts to reconstruct Tek’s victims

O3: Annihilation problem

  • Tek took Metaphysics and knows that the way out of hell is not through cannibalism
  • Tek also took a Health class and read that you can get Kuru (fatal brain (prion) disease from eating human brains)
  • Tek just took a Physics class and learned about a new method: annihilation!

O3: Annihilation problem

  • Collide a particle with its antiparticle (particle with same mass but opposite electric charge and quantum numbers) and the particles destroy each other.
  • Particles turn into pure energy (photons)
  • Particles are destroyed and so God cannot take pure energy and reconstruct me!

Response

Apparently, you can create particles from energy. Breit and Wheeler (1934) took two photons, smashed them together, and created matter. IDK

O4: Gap Problem

The gap problem involves IOs.

  • T1: If O is reassembled, a new O is created in its place
  • T2: O never stops existing when it is disassembled.
  • T3: There are IOs.

O4: IOs (Scope)

Suppose you believe that there are IOs. This does not necessarily mean:

  1. Every object can survive disassembly and reassembly
  2. In particular, human beings can survive this.

O4: Augustine’s Manuscript

  1. Suppose there is a manuscript written by St. Augustine.
  2. It is burned (turned to ash) in 457
  3. It is an all-time favorite of God so he reconstructs from the ash in 459.

O4: The true author?

It is argued that the manuscript of 459 is not the original manuscript of Augustine.

  • The 457 manuscript was written by Augustine (he wrote the words)
  • The 459 manuscript was written by God (God rewrote Augustine’s words)

The manuscript is a forgery!

O4: The true builder?

A child builds a tower of blocks.

  1. The child’s older brother knocks it down.
  2. I feel bad and so rebuild the tower exactly how it was.

The new tower is not the child’s tower. It is my tower that I reconstructed in the image of the child’s.

O4: Resurrection

  • Analogously, human beings (and living things in general) are not IOs.
  • We are different from artefacts in that we cannot survive disassembly and reassembly.

Why?

Origin and identity

  1. Our origin is part of who / what we are: we are natural beings with a natural origin (our parents).
  2. We are also beings with an evolutionary history. That history defines what we are (evolved from apes).
  3. The stages of our life our the result of the operation of natural processes.
  4. The reconstructed being is a being with a divine origin and it lacks an evolutionary history.
  5. The reconstructed being is an entirely different species.

Origin and identity

Response

Are we IOs?

  1. If we are intermittent objects, then we can be resurrected via body reassembly.
  2. If we are not, then why not? Is our origin, evolution, and the fact that the stages of our life are due to natural operations essential to who we are?