XVI. Identity through time (II): identity through individuation
XVI. a. Introduction
- Object persisting through change in relational properties since changes
potentially wholly due to changes in objects around object
- Object persisting through change in intrinsic properties
XVI. b. The problem of intrinsic change
- Relation of identity ≠ other equivalence relations further property of
substitutivity
- Leibniz’s law of indiscernibles: if object x identical to object y object x &
object y having exact same properties
- X having P1 at t1 & x having P2 at t2 where P1 & P2 = contrary properties
Prescribing contradictory properties to single object at different times
- Question appeal to time making properties less (in)compatible requiring
solution to object surviving change in own properties
XVI. c. Possible solutions to the problem of identity
1) Presentism
- Thesis: only things existing in present moment existing
- Only properties of object = properties object having in present moment
o “Object O1 having property P1 at t1” false if T ≠ t1
- Intrinsic properties of object = properties of object in present moment with
≠ past/future intrinsic properties object ≠ possibly possessing contrary
intrinsic properties
2) Building time into properties
- Building time reference into property “object O1 having property P1 at
moment t1” = “object O1 having property-P1-at-moment-t1” object able
instantiating contrary properties at different times
o Example: “redness-at-t1” compatible with “blueness-at-t2” ; “redness-
at-t1” incompatible with “blueness-at-t1”
3) Lewis’s theory of temporal parts
- Building time reference into object “object O1 having property P1 at
moment t1” = “object-O1-at-moment-t1 having property P1”
- Understanding of objects as composed of temporal parts – object
maintaining identity through qualitative change in properties due to object
being composed of linked temporal parts differing in intrinsic properties
over time
o Possibility of object having conflicting temporal parts at different times
(i.e., ‘chipped’ & ‘≠ chipped’)
- “O-at-moment-t1” = temporal part of object O
“O-at-moment-t2” = different temporal part of object O
XVI. a. Introduction
- Object persisting through change in relational properties since changes
potentially wholly due to changes in objects around object
- Object persisting through change in intrinsic properties
XVI. b. The problem of intrinsic change
- Relation of identity ≠ other equivalence relations further property of
substitutivity
- Leibniz’s law of indiscernibles: if object x identical to object y object x &
object y having exact same properties
- X having P1 at t1 & x having P2 at t2 where P1 & P2 = contrary properties
Prescribing contradictory properties to single object at different times
- Question appeal to time making properties less (in)compatible requiring
solution to object surviving change in own properties
XVI. c. Possible solutions to the problem of identity
1) Presentism
- Thesis: only things existing in present moment existing
- Only properties of object = properties object having in present moment
o “Object O1 having property P1 at t1” false if T ≠ t1
- Intrinsic properties of object = properties of object in present moment with
≠ past/future intrinsic properties object ≠ possibly possessing contrary
intrinsic properties
2) Building time into properties
- Building time reference into property “object O1 having property P1 at
moment t1” = “object O1 having property-P1-at-moment-t1” object able
instantiating contrary properties at different times
o Example: “redness-at-t1” compatible with “blueness-at-t2” ; “redness-
at-t1” incompatible with “blueness-at-t1”
3) Lewis’s theory of temporal parts
- Building time reference into object “object O1 having property P1 at
moment t1” = “object-O1-at-moment-t1 having property P1”
- Understanding of objects as composed of temporal parts – object
maintaining identity through qualitative change in properties due to object
being composed of linked temporal parts differing in intrinsic properties
over time
o Possibility of object having conflicting temporal parts at different times
(i.e., ‘chipped’ & ‘≠ chipped’)
- “O-at-moment-t1” = temporal part of object O
“O-at-moment-t2” = different temporal part of object O
