The Triconditional Identity ([§2.6.10](<2.6.10 Triconditional Identity.md>), Theorem 5) names Nature as jointly characterized by exactly three Conditions: Temporality, Spatiality, and Physicality. Why three, and why these three? ∅ is dissolved on the side of being at [§2.7](<2.7 Nothing to Consider.md>), showing that no Reality coherently lacks any of T, S, or Φ; the three are derived from what change's possibility requires at [§2.4](<2.4 Structural Requirement.md>); the cross-entailments that show the three are one Nature are worked at §[§2.6.1](<2.6.1 Three Conditions, One Nature.md>)–2.6.10. Each of these results works from within the framework's own derivational machinery. A *Condition-Individuation Criterion* supplies an external, methodological check: it screens what counts as a candidate Condition in the first place, before the derivational work runs.

> [!lemma]
> **Condition-Individuation** · **L4** · *Lemma toward Triconditional Identity*
>
> X is a Condition of Reality only if X comes with a natural quantifier-pair ⟨*X-positive, X-negative*⟩ such that the Law of Excluded Middle applies exhaustively to empirical existence-claims along the X-axis (every empirical existence-claim at X-instantiation is determinately either X-positive or X-negative, with no third option) and X is irreducible to any other LEM-applicable axis.

A Condition is a real existence-axis along which any question of being has a determinate yes-or-no answer, and the axis is not merely another existence-axis under a different description.

The three Conditions satisfy the Criterion via three quantifier-pairs that ordinary language has independently carved out. Physicality (Φ) takes the pair *something / no thing*: some thing has being, or no thing does, and the binary is exhaustive. Spatiality (S) takes the pair *somewhere / nowhere*: some thing is at some location, or no thing is anywhere, and the binary is exhaustive. Temporality (T) takes the pair *sometime / never*: some thing happens at some time, or nothing ever happens, and the binary is exhaustive. That ordinary language has *exactly* these three quantifier-pairs for existence-instantiation, and no fourth of equal grammatical naturalness, is weak structural evidence: confirmation rather than derivation. The Criterion's load-bearing work runs through the LEM-clause and the irreducibility-clause; the grammar observation is an independent indicator that Nature's three existence-axes are tracked by ordinary language as well as by structural derivation. The load-bearing claim does not rest on the grammar observation.

*The two-part screen.* The Criterion has two clauses, both necessary. The LEM-clause screens for axes along which existence-instantiation is bivalent; the irreducibility-clause screens for axes not already reducible to other axes screened-in. A candidate that passes the LEM-clause may still fail the irreducibility-clause if Theorem 5's biconditional N ↔ □(T∧S∧Φ) ↔ □◇C shows the candidate to be co-equivalent with one already among the Triconditions. Together the two clauses give a tight individuation procedure: produce the quantifier-pair, demonstrate LEM-at-existence, demonstrate irreducibility. Earn all three and the candidate has Condition-status. Fail any one and it does not.

*Candidate fourth Conditions, screened.* The Criterion rules out otherwise tempting additions. *Cause* as a fourth Condition fails on metaphysical grounds: causation is a relation among Φ-instances across T-succession and S-extension, not an axis along which existence is itself instantiated. To be caused is to be a Φ-being whose persistence is conditioned by other Φ-beings' prior persistence (T-direction) across some interval (S-relation); causation is a derived structure within the three existing axes, not a fourth. Grammar confirms this: no natural quantifier-pair *somehow / nohow* of equal standing has emerged, and *every event has a cause or no event does* is not LEM-at-existence but a contingency-relation claim, handled in [§2.8.4](<2.8.4 Necessity Precedes Contingency.md>) *Necessity Precedes Contingency*. Hume's worry about necessary causal connection -(Hume, David, (1739–1740) 2000); -(Hume, David, (1748) 1999) is the canonical opponent in this territory. *Information* as a fourth Condition fails by similar lights: information-instantiation reduces to Φ-instantiation under a particular description and does not carve a new existence-axis. *Consciousness* as a fourth Condition fails because experiences are had by Φ-beings at S-positions in T-succession; experiences are a particular kind of Φ-instantiation rather than a fourth existence-axis (Chapter 7). *Change* passes the LEM-clause via the modal-axis pairing *possible / impossible* (◇C / ¬◇C), but fails the irreducibility-clause: Theorem 5's N ↔ □◇C identifies □◇C with □(T∧S∧Φ), so the modal-axis is co-equivalent with the three existence-axes rather than a fourth independent axis. ◇C is the modal-side of the same Nature, not a fourth Condition.

*From screen to closure.* Taken by itself, the Criterion's force is asymmetric: it places the burden of proof on any proposed fourth (produce the quantifier-pair, demonstrate LEM-at-existence on it, demonstrate irreducibility to the Triconditions). Without all three, the proposal has not earned Condition-status. Set beside the Sufficiency of Structure result ([§2.4.10](<2.4.10 Sufficiency of Structure.md>)), the screen adds a further constraint. If a candidate fourth X is necessary for the possibility of change, then ◇C → X; the converse at [§2.4.10](<2.4.10 Sufficiency of Structure.md>) gives T∧S∧Φ → ◇C; chaining them yields T∧S∧Φ → X. Thus any candidate fourth must obtain wherever the Triconditions are instantiated. That entailment does not by itself prove reducibility: an entailed property may still be irreducible. The remaining work is therefore exactly the Criterion's second clause. A genuine fourth must show that it is not merely a consequence, determinable, relation, or redescription of the three despite being entailed by them. The argument closes the easy routes to a fourth and leaves a precise irreducibility burden rather than pretending that entailment alone settles identity.[^2-6-11-condition-individuation-ch4]

What the foreclosure does not settle lies one level back, and the limit is worth marking exactly. The result runs *through* the analysis of change as causally structured succession among distinct, persisting states ([§1.3](<1.3 Change.md>); the framework-invariant form at [§2.4.5](<2.4.5 Forward Conditional.md>)): succession, distinction, and exchange. That a fourth is foreclosed *given* that analysis is delivered as a burden-shift — the easy routes are closed and a precise irreducibility burden remains with the proposer — while the claim that the three-role analysis is itself the privileged carving of Reality is not established from outside it. The analysis is defended by the necessity of each role and by the self-application that any rival analysis is itself a change exhibiting the three: both showing the Triconditions cannot be thought past, not that a carving beyond all analysis has been inspected. The residual question is therefore not whether a fourth Condition might be articulated within the framework (it cannot be) but whether one is bound to the starting analysis of change at all, the form deflationism presses at [§4.1.8](<4.1.8 Metaontological Deflationism.md>).

*Literature.* The Criterion redirects three lines of work. Aristotle on LEM (*De Interpretatione* 9; *Metaphysics* Γ 3–4) is the historical ancestor for treating LEM as ontologically rather than merely logically binding. Quine -(Quine, W. V. O., 1948) and the broader Quinean tradition treat existence as univocal (the value of a bound variable). The Criterion does not need to reject that thesis: one univocal existential quantifier can range over beings that necessarily satisfy several irreducible structural conditions. Its disagreement with Quine is instead about whether T, S, and Φ mark objective joints that every existent must instantiate, not about whether *exists* changes meaning from one axis to another. Sider -(Sider, Theodore, 2011) and the structural-realism literature treat Reality as jointly carved at specific structural joints; the Criterion is a specific structural-realist commitment about which joints Reality has. Intuitionist reservations about LEM (Brouwer, Heyting) apply to unbounded mathematical claims; dialetheist reservations (Priest) apply to paradoxical propositions; neither bears on the Criterion's restriction to empirical existence-claims along the three Conditions.

[^2-6-11-condition-individuation-ch4]: Condition-Individuation (the two-clause LEM-plus-irreducibility screen on candidate Conditions) is engaged in Chapter 4. The canonical opponent of the LEM-applicable axis carving is Quine's existence-univocity ([§4.1.6](<4.1.6 Quinean Modal Skepticism.md>)); structural realism and Sider are the closest ally that nonetheless diverges on which joints ([§4.3.9](<4.3.9 Structural Realism.md>)), Tegmark's mathematical universe presses for fourth-Condition mathematical axes ([§4.3.7](<4.3.7 Mathematical Universe Hypothesis.md>)), and conventionalism/anti-realism about laws presses on the irreducibility-clause ([§4.1.7](<4.1.7 Modal Conventionalism.md>)).


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← [2.6.10 Triconditional Identity](<2.6.10 Triconditional Identity.md>) | [2.6.12 Necessity's Nature](<2.6.12 Necessity's Nature.md>) →
