Sydney Shoemaker, writing at Cornell in 1969, constructs a universe built on local freezes: a region in which nothing moves, decays, or interacts for a stretch of time, then resumes exactly where it left off, displaced from the ongoing world by the length of the freeze. He multiplies the case into three rooms subject to periodic freezes on staggered intervals, a universe built to let observers in one region infer the freezes of another by clock comparison. Run the arithmetic long enough and the periodicities coincide: once every sixty years, all three regions freeze at once. During that year, by Shoemaker's construction, nothing changes anywhere in the universe. And yet, the argument runs, time still passes.

The inference is staged with such care that the paper became the canonical modern defense of time-without-change in the analytic literature, the standing objection to every Aristotelian who thinks time requires motion. The objection is serious. Pressed to the global limit, however, it collapses under its own construction.

Shoemaker ("Time Without Change," *The Journal of Philosophy* -(Shoemaker, Sydney, 1969)) offers the most carefully constructed defense of time without change in the analytic literature. Local cessation of change is coherent: a region of a universe can freeze while the rest continues, and the frozen region can be re-integrated into the ongoing temporal order when it resumes. That is true, and the present account grants it without cost. What is contested is whether the scenario extends to a universe-wide cessation of change while time continues to pass: whether Shoemaker's construction, pressed to the global case, describes a coherent modal possibility or collapses into incoherence when the apparatus that supports the inference is removed.

The literature on time-without-change runs back to Aristotle's *Physics* (Aristotle, (4th c. BCE) 1984), IV.10–14, where time is defined as the number of motion with respect to the before-and-after, and an unchanging universe therefore fails the conditions for time's obtaining. Newton's *Principia* -(Newton, Isaac, 1687) develops the opposing substantivalist position: absolute time flows uniformly without regard to anything external, and its passage is independent of whatever change happens to take place within it. McTaggart ("The Unreality of Time," -(McTaggart, J. M. E., 1908)) poses the foundational question of what change itself consists in, the A-series/B-series distinction that structures the modern debate. Prior ("Changes in Events and Changes in Things," -(Prior, A. N., 1968)) sharpens the change-theoretic tradition. Shoemaker's 1969 paper is the modern inheritor of Newtonian substantivalism (time as an independent substance whose passage does not depend on any change within it) and the argument's most rigorously worked-out form. Newton-Smith (*The Structure of Time* -(Newton-Smith, W. H., 1980)) defends the Shoemaker conclusion at length.

Against the substantivalist line: Le Poidevin (*Change, Cause, and Contradiction* -(Le Poidevin, Robin, 1991)) presses the verificationist worry about the global-freeze extension; Lombard (*Events: A Metaphysical Study* -(Lombard, Lawrence Brian, 1986)) develops an events-based metaphysics on which change is constitutive of time; (Forbes, Graeme, 1993) challenges the inferential structure of Shoemaker's thought experiment; Mellor (*Real Time II* -(Mellor, D. H., 1998)) and Craig (*The Tensed Theory of Time* -(Craig, William Lane, 2000)) defend change-theoretic views from B-theoretic and tensed angles respectively; Horwich (*Asymmetries in Time* -(Horwich, Paul, 1987)) works the change-primitive side of the debate; Sider (*Four-Dimensionalism* -(Sider, Theodore, 2001)) develops the perdurantist alternative on which change is cashed out through temporal parts; Dainton (*Time and Space*, 2nd ed. -(Dainton, Barry, 2010)) gives the standard survey; Bardon (*A Brief History of the Philosophy of Time* -(Bardon, Adrian, 2013)) places Shoemaker's contribution in its long historical arc. The present reply sits within the change-theoretic tradition, closest to the Mellor–Le Poidevin wing, and adds what neither specifies on its own: Shoemaker's inference runs on the very persistence the scenario was trying to eliminate, and that persistence is named explicitly by the structural-role apparatus of [§2.6](<2.6 Triconditionality of Nature.md>).

The challenge bears directly on [§2.6](<2.6 Triconditionality of Nature.md>). The Modal Identity established there is bidirectional: necessarily, change-possibility obtains if and only if T ∧ S ∧ Φ obtains, and the two are one structural fact under two descriptions. Shoemaker's argument exhibits, if successful, time during an interval in which no change is occurring. That does not by itself break the book's Modal Identity, whose left side is the *possibility* of change rather than its continuous actuality. A globally frozen interval bracketed by change may still belong to a world in which change is possible. The relevant question is therefore whether the case preserves change-capacity and structural continuity, not whether a transition occurs during every interval. What follows is narrow by design. The reply locates the substantivalist move as a relocation rather than an elimination.

A clarification before the moves. The dispute is not with Shoemaker's local scenario: rooms that freeze while others continue are coherent, and the argument of [§2.6](<2.6 Triconditionality of Nature.md>) does not contest them. Nor is the dispute with Shoemaker's inferential apparatus considered in isolation: given three regions freezing on staggered intervals, one can indeed calculate when they coincide, and the calculation is sound. What is contested is the step from the local scenario, where change continues in the unfrozen regions, to the global scenario, where the universe as a whole freezes. Three forms of the move take up the objection at three depths: the inferential-structure form, the level-invariance form, and the extension-to-the-limit form. The space they canvass is the space Shoemaker's argument can occupy. The reply argues that each confirms the Modal Identity rather than breaking it.

*First.* The inference is always from observed change, not to time-without-change. Shoemaker's observers reconstruct A's frozen interval by reference to B's and C's ongoing change: by counting B's cycles while A is frozen, by watching the clock. When all three regions freeze simultaneously, no such reconstruction is available from inside the freeze. The claim that time still passes during the global freeze is not a direct measurement but an extrapolation from the periodicities on either side of the gap, underwritten by the assumption that the pattern continues across it. That assumption is Substance (the persistence condition [§2.6](<2.6 Triconditionality of Nature.md>) names) carrying the identity of the periodicity across the interval. Without Φ operating across the freeze, the post-freeze regions are not the pre-freeze regions resumed; they are new regions with coincidentally similar patterns, and the inference collapses into correlation. Shoemaker's reasoning works because the universe stays the same universe across the pause. A universe that does not stay the same across the pause cannot underwrite the reasoning. The scenario describes a gap inside a universe whose Substance remains intact across it. That persistence is precisely what the structural conditions name.

*Second.* Level-invariance ([§2.1.7](<2.1.7 Two Readings.md>)) applies to the containing universe, not just to each region. The regions are genuinely distinct (S). The freezes occur in a determinate order relative to one another (T). The containing frame persists across the freezes to underwrite each region's re-emergence with preserved identity (Φ). The simultaneous freeze is a local phenomenon within a structured universe, a phenomenon the universe's structural conditions make describable in the first place. Shoemaker has described a universe with change in which certain regions undergo periodic cessation, not a universe without change. The time-without-change the argument purports to exhibit is always the frozen region rather than the universe, and the scale of the freeze is not the scale of the claim.

*Third.* Pushed to the global limit, the scenario contains no internal clock or observer during the freeze. That creates an epistemic and verification problem, not an immediate metaphysical contradiction: a thought experiment may specify unobserved structure, and observers before and after may infer a duration from the wider history. The structural reply should therefore not depend on the absence of a thinker. Its narrower point is that the construction preserves cross-freeze identity, periodic dispositions, and the possibility of resumed change; it is a frozen interval within a change-permitting world, not a world lacking the conditions of change. The fully extended Shoemaker scenario is therefore not a universe with time but no change; it is a universe with change containing a region where nothing happens, which is exactly the case the first two replies already handle. The bidirectional identity survives because the scenario, followed through, never actually breaks it. The Aristotelian position is recovered by the structural apparatus: time is not the number of motion merely, but motion's structural conditions are internal to what time consists in. Strip them and what remains is not empty duration but ∅.

A kindred move drops the Shoemaker apparatus for classical Newtonian absolutism: time is an independent substance whose passage does not depend on any change within it. Newton's *Principia* -(Newton, Isaac, 1687) articulates the position most clearly, and (Newton-Smith, W. H., 1980) carries it forward. The reply is the same in older vocabulary, with one dependency made explicit. An absolute time independent of change must still be individuated (this moment of absolute time distinct from that moment), and, on the change-theoretic conception of Temporality defended at [§1.4.1](<1.4.1 Time.md>) (Directionality as structural, not imposed) and abductively at [§7.2](<7.2 Time.md>), that individuation is the structural fact [§2.6](<2.6 Triconditionality of Nature.md>) identifies. Absolute-time substantivalism relocates the structural roles into the substance of time itself rather than eliminating them; the substance of time contains distinctness of moments (S), directed ordering (T), and persistence across the ordering (Φ) as the conditions of its being a time at all.[^4-2-2-absolute-time-substantivalism]

Another kindred: a deflationary verificationist move (Le Poidevin, Robin, 1991); earlier (Ayer, A. J., 1936) that the global-freeze scenario is meaningless because no possible observation could confirm or disconfirm it. The structural reply accepts the verificationist point for the specific purpose for which it was introduced while declining the broader verificationism: the scenario is not meaningless; it is underspecified in a way that dissolves under analysis, which is a stronger claim than verificationism alone supports.

*What closes.* Three depths and none lets the global extension stand. The inference from local freeze to global freeze runs on Substance (the very persistence condition Φ specifies) carrying the identity of the periodicity across the interval; without that persistence the post-freeze regions are new regions with coincidentally similar patterns, and the inference collapses into correlation. Level-invariance: the scenario describes a structured universe containing regions of freeze, not an unstructured universe frozen entire. The fully extended scenario preserves cross-freeze identity, periodic dispositions, and the possibility of resumed change; it is a frozen interval within a change-permitting world, which is exactly the case the first two replies already handle.

The emergent-time objection, that time is derivative rather than fundamental, is [§4.2.3](<4.2.3 Emergent Time.md>). The momentariness objection, that persistence is illusory, is [§4.2.8](<4.2.8 Stage Theory.md>). The changeless-ground objection, that a timeless being grounds the structure from outside, is [§4.2.1](<4.2.1 The Changeless Ground.md>). The Shoemaker objection occupies a distinct position relative to these three: it grants that time is real and that persistence obtains, and contests only the bidirectional linkage of change and time. The reply is therefore correspondingly narrow: the target is the global extension of the local scenario, not the coherence of time or of persistence in general.

What Shoemaker's argument supports is stronger than merely local cessation: it gives a serious model of an interval, potentially global, during which no change occurs while temporal structure is retained. The structural account can grant this because its modal claim concerns permission for change, not uninterrupted occurrence. The claim of [§2.6](<2.6 Triconditionality of Nature.md>) is that the fundamental ontological structure cannot instantiate Time without instantiating change, not that every subregion must undergo change at every moment. Shoemaker has produced a counterexample to a claim the argument does not make.

One clarification for the Shoemakerian reader. The argument addressed here is the 1969 time-without-change paper, not Shoemaker's signature causal theory of properties (*Causality and Properties*, 1980; *Identity, Cause, and Mind*, 1984/2003), on which properties are individuated by their causal powers. That broader thesis is not a further counterexample to [§2.6](<2.6 Triconditionality of Nature.md>) but an instance of it: causal individuation presupposes the very structural roles the account names, since a causal power is exercised across an ordering (T), among distinct relata (S), and is borne by what persists long enough to exercise it (Φ). The omission of the causal theory from the reply above reflects the scope of the time-without-change objection, not a narrowing of the account.

What the paper actually gives its readers, followed through, is not the universe-without-change it seems to promise but something better: the sharpest available demonstration that inferring time-without-change requires a standpoint where change is occurring.

[^4-2-2-absolute-time-substantivalism]: The reply that absolute-time substantivalism relocates the structural roles rather than eliminating them is not neutral between conceptions of time, and the dependency is worth marking. A purist who takes time to be bare duration (mere ordering, with influence occurring within time rather than constituting it) can decline the identification of a moment's individuation with T ∧ S ∧ Φ. Two costs attend the exit, and the relational account pays neither. First, individuating the moments of an empty, changeless absolute time without relational extension requires primitive thisness: the haecceity Leibniz's identity of indiscernibles and the hole-argument literature press, which sophisticated substantivalism can absorb only by surrendering haecceitism; the relational individuation [§2.6](<2.6 Triconditionality of Nature.md>) supplies (S) needs no such posit. Second, by the lights of the change-theoretic conception defended here (a cost the purist will not grant is one) a duration stripped of all influence is ordering without succession, the [§2.6.7](<2.6.7 Triconditional Cross-Entailment.md>) ordered-set structure rather than Time. The line can be held, but at the price of primitive identity and the divorce of time from succession: a trade the relocation reply exposes rather than the neutral refutation it can be mistaken for.


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← [4.2.1 The Changeless Ground](<4.2.1 The Changeless Ground.md>) | [4.2.3 Emergent Time](<4.2.3 Emergent Time.md>) →
