Persistence and Change

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persistence endurantism perdurantism temporal parts change

Core Idea

How does an object remain the same thing while undergoing change — how can the leaf be green in summer and red in autumn, yet be one and the same leaf? Endurantism holds that objects are wholly present at each moment of their existence; they persist by enduring, and change is a matter of having different properties at different times. Perdurantism holds that objects are extended through time and have temporal parts — the summer-leaf and the autumn-leaf are distinct temporal stages of a single four-dimensional entity. A third view, stage theory (exdurantism), says that ordinary objects are instantaneous stages, and 'persistence' is really a relation of counterpart-hood between stages. Each theory handles the puzzle of change differently and faces characteristic objections: endurantism struggles with temporary intrinsics, while perdurantism must explain why temporal parts compose unified objects.

How It's Best Learned

Read Lewis's 'On the Plurality of Worlds' section 4.2 on temporary intrinsics for the perdurantist case, then Haslanger's 'Endurance and Temporary Intrinsics' for the endurantist response. Try to formulate the problem of change precisely before evaluating the solutions.

Common Misconceptions

Explainer

You know from philosophy of time that the present moment has a special status — questions about whether the past and future exist, and how time flows, are among the deepest in metaphysics. Persistence and change bring those questions down to the level of ordinary objects. A leaf is green in summer and red in autumn. A ship has all its planks replaced one by one. You were a child and are now an adult. In each case, we unreflectively say it is the *same* object across the change. But what makes that true? This is the persistence problem, and it has two serious answers.

Endurantism says that objects persist by being wholly present at each moment of their existence. The leaf in summer and the leaf in autumn are the very same object, fully present at both times, just with different properties at different times. Change is simply a matter of having property P at time t1 and property Q at time t2. This matches ordinary intuition — we don't think the summer leaf and autumn leaf are different objects. But endurantism faces the problem of temporary intrinsics, articulated by David Lewis: if the same object is wholly present at both times, and has greenness at one time and redness at the other, how can it have both properties? Properties seem to be intrinsic to their bearers — if an object is green, it is green full stop, not green-relative-to-a-time. Endurantists respond by relativizing property instantiation to times: the leaf instantiates greenness-at-t1 and redness-at-t2.

Perdurantism avoids the problem by saying objects have temporal parts — distinct stages or slices that compose the whole object across time. The summer leaf and the autumn leaf are different temporal parts of a single extended four-dimensional entity. Change is not the same object having different properties; it is different temporal parts having different properties. This is analogous to spatial parts: the top of a tree is green and the roots are brown, and we don't find this contradictory because they are different spatial parts. Perdurantism extends this logic into the time dimension. Lewis endorsed this view precisely because it dissolves the temporary intrinsics problem — each temporal part simply has its intrinsic properties, full stop.

A third position, stage theory (associated with Ted Sider and Katharine Hawley), holds that ordinary objects just are instantaneous temporal stages — there is no four-dimensional worm, only a series of stages connected by counterpart relations. "The leaf" refers to a stage; when we say the leaf persisted, we mean this stage and a later stage stand in the appropriate counterpart relation. Each theory predicts different answers to edge cases: the Ship of Theseus, personal identity over time, and the metaphysics of growth and decay. The persistence debate is thus not merely abstract — it structures how we think about identity, survival, and what matters in change.

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Prerequisite Chain

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsThe Distributive PropertyVariables and Expressions ReviewIntroduction to PolynomialsAdding and Subtracting PolynomialsMultiplying PolynomialsFactorialPermutationsCombinationsCounting Principles: Addition and Multiplication RulesIntroduction to Graph TheoryPropositional Logic FoundationsLogical Inference and Proof RulesProof Strategies in Discrete MathematicsSoundness and Completeness of Propositional LogicSoundness and Completeness of First-Order LogicCompactness Theorem for First-Order LogicBasic Model TheoryLöwenheim-Skolem TheoremsGödel's Incompleteness TheoremsIntroduction to Intuitionistic LogicIntroduction to Modal LogicTemporal LogicPhilosophy of TimePersistence and Change

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