Hume's challenge is a generous and disciplined attempt to thin Time. He grants that states follow states. He just does not see anything holding them together: one state, then the next, and the "then" does no work. No necessary connection, no causal arrow. Just sequence.

The replies here grant his narrowest claim (constant conjunction does not by itself entail necessity) and contest the broader one by testing whether each form can state succession without handing over directional succession through Substance. The structural-level engagement (defending the producing-relation against eliminativist pressure) is carried by [§2.6.8](<2.6.8 Ontological Identity.md>); this section takes up the modal-contingency arm.

(Hume, David, (1748) 1999) [§VII] argues that our impression of causal necessity is a psychological habit projected onto the world, not a feature discovered within it. His contemporary inheritors ((Lewis, David, 1986) [pp. ix–xvi], (Loewer, B., 1996), (Beebee, Helen, 2006)) sharpen the point into the Best System Account: laws of nature are the axioms of the simplest, strongest systematization of the pattern of events, not constraints that govern it. Succession without enforcement — order that simply obtains.

Time, as [§1.4.1](<1.4.1 Time.md>) defines it, is different. Not bare sequence: directional, asymmetric, productive, with the earlier state grounding the later, an arrow running through. Hume grants the sequence and denies the arrow. The three forms we are about to take up each miss the same thing: directional succession through Substance cannot be granted while the arrow is denied. The concession and the denial are the same sentence.

*First.* The bare-succession form holds that states can follow one another without any carrying medium. States follow states, the ordering is all Time needs, and nothing about Substance makes the next state follow the previous. Indexed order, not enforcement.

That concession is already enough, but note where it is enough. Try thinning succession further. Read "indexed order" as a block universe (B-theory; Mellor -(Mellor, D. H., 1998), *Real Time II*): time-slices arranged by index, all moments equally real, ordered by a tenseless before/after, no privileged now. On this reading, "persistence" just means qualitative similarity across slices; nothing is carried through. Can the thinner reading hold?

Consider what the thinning requires. An ordering of slices by index is one of two things. Either it is a function from integers to qualitative profiles applied to the manifold, in which case the manifold itself has to have enough structure to be indexable at all, an intrinsic distinction of positions that the arithmetic is tracking, not supplying. Or the ordering is free-floating abstract, a function unattached to any manifold, in which case it is not a time-series anymore, just a set of profiles paired with numerals, two disjoint structures sitting next to each other.

The first reading borrows the structural fact it is trying to replace. The second yields an abstract set of profiles paired with indices rather than a concrete temporal manifold. It does not collapse into ∅: the set still has members and formal structure. Its limitation is instead that the abstract pairing does not by itself realize temporal succession or causal persistence. Grant succession at any strength sufficient to state the position, and the Mutual Containment Result ([§2.6.5](<2.6.5 Mutual Containment.md>)) takes over: succession requires something that persists (Substance) across a structured interval (Space). Whether it is called "produced" or "enforced" is not the hinge; that something is sequenced at all is.

The bare-succession form is the wager that replacement is never more than mere sequence. Put exactly: replacement is not bare succession. It requires something that can be replaced, something that replaces it, and structure in which the replacement counts as replacement rather than mere juxtaposition. Strip the being, the interval, and the relation, and the Humean has not described thinner succession. They have removed the conditions under which succession is describable at all.

*Second.* The asymmetric-before form grants more ground than the first and tries to hold a thinner line. Sequence is real. Co-instantiation is real. But before-and-after is treated as a brute relational fact between states: the ordering is there, causation is not. Tim Maudlin (*The Metaphysics Within Physics* -(Maudlin, Tim, 2007)) goes further, making time's arrow a fundamental primitive of the manifold: asymmetry that needs no further grounding.

Consider what this does. An asymmetric relation between states is either a label applied from outside (a convention we impose, with nothing in Nature answering to it) or a structural fact about Nature itself. If it is a label, it is a label for one of two things. Either it removes the ordering along with the arrow (leaving co-present states with nothing to index, the ∅ distribution [§2.7](<2.7 Nothing to Consider.md>) forecloses) or it keeps the ordering and imposes only the direction: the direction-conventionalist's line, on which the series is real but no fact of Nature settles which way it runs. The second reading does not thin Time; it relocates the arrow to a mind-independent gradient, the thermodynamic move [§4.2.3](<4.2.3 Emergent Time.md>) takes up. Neither branch yields an asymmetry that is real, in Nature, and not already Exchange under another name. If it is structural (whether read as a consequence of deeper machinery or as a Maudlin-style primitive) then "asymmetric relation" and "Exchange" are doing exactly the same work. Two names, one structure.

Maudlin's primitivism (the view that time's directionality is a fundamental feature of the world, not reducible to anything more basic) refuses reduction in any direction. Time's passage is not to be analyzed via entropy gradients, nor reduced to tenseless B-theory relations, nor deflated to psychological flow; it is a fundamental directional structure of the world that fundamental physics already presupposes whenever its laws are stated as differential equations evolving an initial state forward (*The Metaphysics Within Physics* -(Maudlin, Tim, 2007), ch. 4). Take the position on its own terms. The directionality is real, primitive, ontologically irreducible. It still attaches to states standing in directional relation across a manifold that bears the primitive. The primitive is the directionality of something: three structural conditions the primitivism cannot dissolve. Maudlin's primitive is what T, S, and Φ jointly amount to once a defender insists on irreducibility. The role structure does not refute the primitivism. It states what the primitivism is the structure of.

*Third.* The Best System Account (BSA) is a sophisticated deflationary form of the challenge, and it is genuinely beautiful as a systematization. On BSA, laws of nature are the axioms of the simplest, strongest way to describe the total pattern, not constraints that govern it. Regularities get described, not enforced. The picture is the Humean mosaic: a distribution of local matters of fact, no necessary connections between them (Lewis, David, 1986); (Loewer, B., 1996).

The standard non-Humean replies in the contemporary literature treat laws as relations among universals (Armstrong, D. M., 1983), *What Is a Law of Nature?* or as primitive necessitating relations between properties (Dretske, F. I., 1977); (Tooley, M., 1977). The reply here is structurally different. It is not that something enforces the regularity above and beyond the distribution; it is that any vocabulary capable of stating the regularity already runs on the structural conditions the Humean meant to deflate.

Lewis's doctrine of Humean supervenience says everything supervenes on the distribution of local qualities together with the spatiotemporal relations among their instances. Those relations belong to the supervenience base rather than being derived from the qualities alone. The mosaic is therefore distributed across an already structured manifold, not used to construct that manifold (Lewis, David, 1986), pp. ix–xvi. This is the load-bearing concession, and it runs under the whole account.

Consider what a regularity actually is. For events of type A to be reliably followed by events of type B, the Humean has already granted a distribution across a spatiotemporal manifold and a pattern stated over that distribution. That concession is enough. If the regularity is brute, the Humean offers systematization rather than a governing explanation; that is a deliberate feature of the view, not an internal contradiction. If the regularity is grounded in an invariant feature of the manifold, the account moves toward a non-Humean structure. The present argument can therefore claim that BSA presupposes spatiotemporal structure, but it cannot infer a productive causal arrow from regularity alone. A mosaic without a manifold is not a mosaic: it is a set with no ordering.

The BSA does not escape structure. It describes structure in Humean vocabulary, having already conceded the primitive spatiotemporal manifold that is the structure in question. The Humean wants regularity without necessity. Strip Nature and regularity has nothing to regulate.

A kindred deflationary move drops causal vocabulary entirely in favor of symmetric functional relations between variables: (Russell, B., 1913) ["On the Notion of Cause"] argues causation has no place in mature physics; (Norton, J. D., 2003) carries the case forward. The reply is the same, shaped differently: functional relations between variables presuppose the variables' distinctness (Space) and persistence (Substance), and any functional relation with a privileged direction of dependency presupposes Time's asymmetry. Thermodynamic variants (that temporal asymmetry emerges from entropy gradients rather than obtaining structurally) come up in [§4.2.3](<4.2.3 Emergent Time.md>).

One narrower point, stated exactly. The self-refutation charge (that a denial of the structural conditions presupposes them in the act of denying) establishes the conditions' actuality wherever the denial is performed, not their necessity across worlds where no such performance occurs. The move from actuality to necessity is the work of §§3–7 and does not rest here. The result is narrower: the deflationary vocabularies are parasitic on the structure they are meant to replace, wherever they are stated.

One rejoinder remains. A Humean might grant the parasitism and insist it is just how description works: any vocabulary capable of saying anything borrows structure from what it says it about, and that is no refutation of deflationism, just a feature of having a language at all. Look at the words the deflation reaches for. Holds. Runs. Deeper. Reach. Underneath. Ground. Foundation. Each one names the structure the deflation was meant to do without.

The reply runs at a deeper level than vocabulary. Hume published the *Enquiry* in 1748, and the argument has reached every reader since through a directed causal chain: ink pressed into paper, the marks holding their positions from Edinburgh to here, each transmission running forward and not back, copied and carried across 278 years with the content intact. The content of Hume's position denies the productive bond; the vehicle by which that content has reached readers is the very causal structure the content denies.

The same reply reaches a closer case. Hume's account of necessity runs from observation through habit to projected expectation: repeated conjunctions, formed habit, projected necessity. There is a class of cases where that order is reversed: cases where the regularity is *established*, in a single act, by an agent who specifies it. The Anscombean and interventionist traditions (Anscombe, G. E. M., 1971), "Causality and Determination"; (Woodward, James, 2003), *Making Things Happen* have pressed a kindred line against the spectator's epistemology for half a century: an agent who establishes a regularity by an intervention has first-person access to causal efficacy that no abstraction-from-conjunctions can supply. A programmer who specifies a function settles in advance what the function will return on inputs it has never been called on: no series of conjunctions, no time for habit to form, just a stipulation that holds because the system bears it. The constant conjunction is *constituted* by the stipulation, not abstracted from a history of it. The deflationary epistemology has no machinery for the reversed order, and the cases where the order runs that way are not exotic: they are the cases where regularities are most cleanly established. What the stipulation requires to take effect is the same triple the descriptive case required to be statable: a structural setting, a domain across which the stipulation ranges, and something the regularity holds across. The structure is met from the agent's side as it was met from the describer's side.

*What converges.* Time is the Condition [§1.4.1](<1.4.1 Time.md>) defines, bearing the succession role [§1.1](<1.1 Reality.md>) extracts, and each deflationary form fails to remove it: bare succession cannot be indexed without borrowing the manifold it meant to replace (or thinning into an abstract pairing that realizes no succession at all); asymmetric before-and-after is either a label applied from outside, which removes the ordering or relocates the arrow ([§4.2.3](<4.2.3 Emergent Time.md>)), or a structural fact about Nature, which is Exchange under another name; and the Best System Account admits the spatiotemporal manifold into its own supervenience base rather than deriving it, describing the structure in Humean vocabulary rather than replacing it.

Three forms, each conceding the structure they mean to deflate, and one rejoinder undone twice over: by the medium of its own transmission and by the cases its spectator's epistemology cannot reach. The deflationary move reinstates the structure it meant to remove. The narrower Humean point (that constant conjunction does not entail necessity) is not what the argument contests; it is a constraint the argument accepts and obeys, refusing to read necessity off bare regularity and routing the necessity claim instead through structural analysis and the Cartesian datum that change occurs. That discipline is Hume's bequest, inherited rather than overturned. The causal-transmission point is narrow and literal: the argument has reached us only through the structure its content tries to deflate. The next section takes up the information-theoretic challenge ([§4.1.5](<4.1.5 Information-Theoretic Foundationalism.md>)): whether reality reduces to bits from which T, S, and Φ emerge rather than hold as structural conditions.


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← [4.1.3 Principle of Sufficient Reason](<4.1.3 Principle of Sufficient Reason.md>) | [4.1.5 Information-Theoretic Foundationalism](<4.1.5 Information-Theoretic Foundationalism.md>) →
