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The Ship of Theseus 89
[I]f, for example, that ship of Theseus, concerning the difference whereof
made by continual reparation in taking out the old planks and putting in new,
the sophisters of Athens were wont to dispute, were, after all the planks were
changed, the same numerical ship it was at the beginning; and if some man
had kept the old planks as they were taken out, and by putting them afterwards
together in the same order, had again made a ship of them, this, without
doubt, had also been the same numerical ship with that which was at the
beginning; and so there would have been two ships numerically the same,
which is absurd. (Hobbes Chapter 11, 136)
P1. T1 is identical with T2.
P2. It is not the case that T2 is identical with T3.
P3. T3 is identical with T1 (assumption for reductio ).
C1. T3 is identical with T2 (transitivity of identity, P1, P3).
C2. T2 is identical with T3 (symmetry of identity, C1).
C3. It is not the case that T2 is identical with T3 and T2 is identical with
T3 (conjunction, P2, C2).
C4. It is not the case that T3 is identical with T1 (r eductio , P3 – C3).
23
The Problem of
Temporary Intrinsics
Montserrat Bordes
Lewis , David . On the Plurality of Worlds . Oxford : Blackwell , 1986 .
Lowe , E. J. “ The Problems of Intrinsic Change: Rejoinder to Lewis . ” Analysis
48 ( 1988 ): 72 – 7 .
Moore , G. E. Philosophical Studies . London : Oxford University Press , 1922 .
Our pre - theoretic beliefs tell us that ordinary things such as trees, people,
or chairs change their properties during their existence. We can say that
ordinary things persist – they exist at different times – and change; that is,
they persist and have complementary properties (P, not - P) at distinct times.
What remains controversial, however, is the way in which ordinary things
persist. We commonly distinguish between ordinary things and events.
Some think that unlike football games, weddings, and smiles, ordinary
things persist by having only spatial, not temporal parts; they appear to
endure rather than perdure. Something endures if and only if it persists by
being wholly present at different times; something perdures if and only if
it persists by having distinct temporal parts at different times (Lewis).
Opponents of endurantism think that ordinary things endure, whereas their
histories, which are types of events, perdure (Lowe). Perdurantists hold that
both events and ordinary things have not only three spatial dimensions but
also a temporal one: they have (the worm view) or are (the stage view)
temporal parts.
Just the Arguments: 100 of the Most Important Arguments in Western Philosophy,
First Edition. Edited by Michael Bruce and Steven Barbone.
© 2011 Blackwell Publishing Ltd. Published 2011 by Blackwell Publishing Ltd.
The Problem of Temporary Intrinsics 91
Is there a rationale for preferring one theory of persistence to another?
Lewis thought that the argument from temporary intrinsics (ATI) shows
compellingly that endurantism is untenable. His reasoning can be presented
as follows. Ordinary things undergo change of their temporary intrinsic
properties; that is, they gain or lose (monadic) properties, that they have in
virtue of the way they themselves are, not in virtue of their relations to
other things. Put differently, A ’ s intrinsic properties are properties shared
by every duplicate of A (Moore and Lewis).
Endurantist and perdurantist explanations of change are incompatible.
To illustrate this, let us suppose that A is P at time t and that A also
existed at a past time t ’ when A was not - P. For a perdurantist, this amounts
to A ’ s having a temporal part that is P at t and A ’ s having another part
that is not - P at t ’ . For an endurantist, A itself (not a proper part of it) is
P at t and not - P at t ’ . Supporters of endurantism, then, face a contradiction,
that A itself is both P and not - P, that is also at odds with Leibniz ’
Law of the Indiscernibility of Identicals: given that A endures from t ’ to
t , A must therefore be the same from t ’ to t (A at t ’ is diachronically
identical to A at t ), and A should have the same properties at both
times (A at t ’ should be indiscernible from A at t ). Lewis states that endurantism
cannot account for the existence of temporary intrinsic properties
demanded by ATI, since the efforts to solve the contradiction deny either
the nonrelational nature of properties, their instrinsicality, or their
temporality.
P1. Ordinary things change their intrinsic properties (properties that ordinary
things have in virtue of the way they themselves are, not in virtue
of their relations to other things).
P2. Properties can be either of two mutually exclusive types: extrinsic or
intrinsic.
P3. If ordinary things change their intrinsic properties, then ordinary things
persist; that is, they exist at different times.
C1. Ordinary things persist ( modus ponens , P1, P3).
P4. If ordinary things persist, then they either endure (persist by being
wholly present and numerically identical at more than one time) or
perdure (persist by having temporal parts or being partially present at
more than one time).
C2. Ordinary things either endure or perdure ( modus ponens , P4, C1).
P5. Indiscernibility (having the same intrinsic properties) is a necessary
condition of numerical identity (the Law of Indiscernibility of Identicals
implied by Leibniz ’ Law).
P6. If ordinary things endure, then ordinary things cannot remain numerically
identical if they have incompatible (like P and not - P) intrinsic
properties (general instantiation, P5).
92 Montserrat Bordes
P7. If ordinary things cannot remain numerically identical if they have
incompatible properties, then either intrinsic properties are either disguised
relations to times or the only intrinsic properties of ordinary
things are those they have in the present.
C3. If ordinary things endure, then either intrinsic properties are either
disguised relations to times or the only intrinsic properties of ordinary
things are those they have in the present (hypothetical syllogism, P6,
P7).
P8. If ordinary things perdure, then their incompatible properties belong to
different things (i.e., their different temporal parts).
P9. If intrinsic properties are disguised relations to times, then all properties

The Ship of Theseus 89

[I]f, for example, that ship of Theseus, concerning the difference whereof

made by continual reparation in taking out the old planks and putting in new,

the sophisters of Athens were wont to dispute, were, after all the planks were

changed, the same numerical ship it was at the beginning; and if some man

had kept the old planks as they were taken out, and by putting them afterwards

together in the same order, had again made a ship of them, this, without

doubt, had also been the same numerical ship with that which was at the

beginning; and so there would have been two ships numerically the same,

which is absurd. (Hobbes Chapter 11, 136)

P1. T1 is identical with T2.

P2. It is not the case that T2 is identical with T3.

P3. T3 is identical with T1 (assumption for reductio ).

C1. T3 is identical with T2 (transitivity of identity, P1, P3).

C2. T2 is identical with T3 (symmetry of identity, C1).

C3. It is not the case that T2 is identical with T3 and T2 is identical with

T3 (conjunction, P2, C2).

C4. It is not the case that T3 is identical with T1 (r eductio , P3 – C3).

23

The Problem of

Temporary Intrinsics

Montserrat Bordes

Lewis , David . On the Plurality of Worlds . Oxford : Blackwell , 1986 .

Lowe , E. J. “ The Problems of Intrinsic Change: Rejoinder to Lewis . ” Analysis

48 ( 1988 ): 72 – 7 .

Moore , G. E. Philosophical Studies . London : Oxford University Press , 1922 .

Our pre - theoretic beliefs tell us that ordinary things such as trees, people,

or chairs change their properties during their existence. We can say that

ordinary things persist – they exist at different times – and change; that is,

they persist and have complementary properties (P, not - P) at distinct times.

What remains controversial, however, is the way in which ordinary things

persist. We commonly distinguish between ordinary things and events.

Some think that unlike football games, weddings, and smiles, ordinary

things persist by having only spatial, not temporal parts; they appear to

endure rather than perdure. Something endures if and only if it persists by

being wholly present at different times; something perdures if and only if

it persists by having distinct temporal parts at different times (Lewis).

Opponents of endurantism think that ordinary things endure, whereas their

histories, which are types of events, perdure (Lowe). Perdurantists hold that

both events and ordinary things have not only three spatial dimensions but

also a temporal one: they have (the worm view) or are (the stage view)

temporal parts.

Just the Arguments: 100 of the Most Important Arguments in Western Philosophy,

First Edition. Edited by Michael Bruce and Steven Barbone.

The Problem of Temporary Intrinsics 91

Is there a rationale for preferring one theory of persistence to another?

Lewis thought that the argument from temporary intrinsics (ATI) shows

compellingly that endurantism is untenable. His reasoning can be presented

as follows. Ordinary things undergo change of their temporary intrinsic

properties; that is, they gain or lose (monadic) properties, that they have in

virtue of the way they themselves are, not in virtue of their relations to

other things. Put differently, A ’ s intrinsic properties are properties shared

by every duplicate of A (Moore and Lewis).

Endurantist and perdurantist explanations of change are incompatible.

To illustrate this, let us suppose that A is P at time t and that A also

existed at a past time t ’ when A was not - P. For a perdurantist, this amounts

to A ’ s having a temporal part that is P at t and A ’ s having another part

that is not - P at t ’ . For an endurantist, A itself (not a proper part of it) is

P at t and not - P at t ’ . Supporters of endurantism, then, face a contradiction,

that A itself is both P and not - P, that is also at odds with Leibniz ’

Law of the Indiscernibility of Identicals: given that A endures from t ’ to

t , A must therefore be the same from t ’ to t (A at t ’ is diachronically

identical to A at t ), and A should have the same properties at both

times (A at t ’ should be indiscernible from A at t ). Lewis states that endurantism

cannot account for the existence of temporary intrinsic properties

demanded by ATI, since the efforts to solve the contradiction deny either

the nonrelational nature of properties, their instrinsicality, or their

temporality.

P1. Ordinary things change their intrinsic properties (properties that ordinary

things have in virtue of the way they themselves are, not in virtue

of their relations to other things).

P2. Properties can be either of two mutually exclusive types: extrinsic or

intrinsic.

P3. If ordinary things change their intrinsic properties, then ordinary things

persist; that is, they exist at different times.

C1. Ordinary things persist ( modus ponens , P1, P3).

P4. If ordinary things persist, then they either endure (persist by being

wholly present and numerically identical at more than one time) or

perdure (persist by having temporal parts or being partially present at

more than one time).

C2. Ordinary things either endure or perdure ( modus ponens , P4, C1).

P5. Indiscernibility (having the same intrinsic properties) is a necessary

condition of numerical identity (the Law of Indiscernibility of Identicals

implied by Leibniz ’ Law).

P6. If ordinary things endure, then ordinary things cannot remain numerically

identical if they have incompatible (like P and not - P) intrinsic

properties (general instantiation, P5).

92 Montserrat Bordes

P7. If ordinary things cannot remain numerically identical if they have

incompatible properties, then either intrinsic properties are either disguised

relations to times or the only intrinsic properties of ordinary

things are those they have in the present.

C3. If ordinary things endure, then either intrinsic properties are either

disguised relations to times or the only intrinsic properties of ordinary

things are those they have in the present (hypothetical syllogism, P6,

P7).

P8. If ordinary things perdure, then their incompatible properties belong to

different things (i.e., their different temporal parts).

P9. If intrinsic properties are disguised relations to times, then all properties