One last refuge for an outside to the conditions lies not among the things that are but among the things that *cannot* be: if anything escapes structure, surely it is the impossible, which answers to no way things could go. Yet even there the conditions hold. Even the things that *cannot* be wear the Triconditions: a genuine substantial impossibility decomposes into a being, a structure, and an interval.

> [!info]
> **Core concept.** If anything could escape structure, surely it's the impossible—what can't be at all. This section closes even that exit. Take the standard impossibilities: a stone too heavy for its maker to lift, an immovable object meeting an irresistible force, two bodies in the same place. Each one, to be the impossibility it is, still decomposes into a being, a structure, and an interval—persistence, space, and time. The impossible case presupposes the very space of possibilities in which it's ruled out. So the three conditions have no outside, not even among the things that cannot be. (The step from operative here to necessary is borrowed from the chapter's other arguments, not made here.)

> [!argument]
> **Closing the Impossibility Escape** · *from the substantial impossibilities to Triconditional Necessity*
>
> 1. Some substantial impossibilities are paradigm cases: the stone too heavy to be lifted, the immovable meeting the irresistible, two bodies co-located.
>
> 1. Each decomposes into a being (Φ), a relational structure (S), and an interval (T).
>
> 1. The impossibility presupposes the very possibility-space in which it is foreclosed.
>
> 1. So the case presupposes T ∧ S ∧ Φ already operative.
>
> 1. The lift from "operative in this case" to "necessary" is not made here: it is borrowed from [§3.3.4](<3. Convergence.md>) (conceivability), the modal triconditional result ([§3.2](<3.2 Triconditional Necessity Positive Account.md>)), or the ∅-result ([§3.2.6](<3. Convergence.md>)).
>
> 1. So, *given* the chapter's established □(T ∧ S ∧ Φ), even the substantial impossibilities fall under it: the Triconditions have no outside, not even among the things that cannot be.

*Dependency.* [§1.3](<1.3 Change.md>), [§1.4](<1.4 Three Conditions.md>); paradigm cases only: borderline "impossibilities" like the round square are type-clashes and are excluded. *Status:* an independent stage on a shared foundation. This Move carries the Triconditions into the impossibility domain, a reach no other Move supplies; like every Move in [§3.3](<3.3 Triconditional Necessity Negative Account.md>), it borrows the lift to necessity rather than making it here (step 5), and the □-conclusion it shares is carried by the other Moves in [§3.3](<3.3 Triconditional Necessity Negative Account.md>) (the unevenness [§3.3.6](<3. Convergence.md>) audits).[^3-3-50-1]

[^3-3-50-1]: A dialectical companion to the argument that even substantial impossibilities presuppose the Triconditions, *ad hominem* and so kept out of the derivation: a classical theist who concedes that not even omnipotence can actualize a substantial impossibility has, in that very concession, granted the operative Triconditions. Each conceded impossibility decomposes into a being (Φ), a structure (S), and an interval (T). It binds an opponent who holds the concession rather than proving the conclusion, so it is unsound as a freestanding argument and does no load-bearing work here; the □-conclusion is carried by the main argument above and, for the lift to necessity, by [§3.3.4](<3. Convergence.md>).


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← [3.3.4 The Conceivability Trap](<3.3.4 The Conceivability Trap.md>) | [3.3.6 Uneven Overdetermination](<3.3.6 Uneven Overdetermination.md>) →
