Condition-Individuation supports three axis-specific formal disciplines in two stages. First, its determinacy-plus-LEM clause and irreducibility clause distinguish T, S, and Φ as three admitted domains of inquiry. Second, the native structure of each axis motivates a specialized formal apparatus. The result is temporal, spatial, and substantial logic — three disciplines with different target vocabularies and formal resources, sharing whatever classical floor the framework separately defends.

Stage one individuates axes, not consequence relations. Irreducibility means that the content of T-claims does not reduce without remainder to S- or Φ-content. It does not follow that one background logic cannot govern claims from all three domains, or that non-reducible predicates require non-intertranslatable logics. The legitimate conclusion at this stage is weaker: each axis calls for its own theory-specific vocabulary and axiomatization if its native structure is to be represented.

Stage two supplies that differentiation. T carries temporal modalities (succession, precedence, simultaneity); S carries spatial relations (region, inclusion, connection, proximity); Φ carries identity, persistence, and part/whole. The native structure is supplied by the upstream derivations at §[§1.4](<1.4 Three Conditions.md>) and 2.4–2.6, not by LEM. Formal systems regimenting those structures can therefore differ in syntax, axioms, and semantics. Temporal logic and spatial logic are established disciplines; *substantial logic* is the framework's synthetic umbrella over several traditions. The claim earned is discipline-level formal differentiation, not a deduction that Reality contains exactly three mutually exclusive logics merely because it contains three irreducible axes.

The distinctness shows in a single ordinary claim. Take *the cup was on the table before you drank from it*. Three inferences run through it at once, along three axes. *Before you drank* is temporal: it places the resting earlier than the drinking, licensing inferences of precedence and tense (T). *On the table* is spatial: it locates the cup in contact with and supported by the surface, licensing inferences of region, contact, and inclusion (S). *The cup* — the same one throughout — is substantial: one persisting bearer across both the resting and the drinking, not two cups sharing a name, licensing inferences of identity and persistence (Φ). None of the three cashes out in another's vocabulary: *before* is not a region, *on* is not a moment, and *the same cup* is neither a time nor a place. Restate the precedence in the spatial apparatus and you have changed the subject, not translated it — the axis-level irreducibility Condition-Individuation establishes, met in a single sentence. Three logics, no common coin.

The literature delivers exactly this. Temporal logic is a mature formal discipline (Prior, A. N., 1957); (Prior, A. N., 1967); (Pnueli, Amir, 1977); (Goldblatt, Robert, 1992) with operators F, P, G, H tracking *will sometime*, *was sometime*, *will always*, and *has always been*; branching-time versus linear-time families axiomatize different commitments about T-structure. Spatial logic is similarly mature (Tarski, Alfred, 1959) on topology in formal language; (Randell, D. A., Z. Cui, and A. G. Cohn, 1992) on region-connection calculus; (Aiello, M., I. Pratt-Hartmann, and J. van Benthem (eds.), 2007) *Handbook of Spatial Logics* with operators for region, inclusion, connection, proximity. Substantial logic, the present argument's umbrella term for the formal-ontology, mereology, classical-identity, and substance-metaphysics literatures that together cover the Φ-axis (the *logic of being qua being* in Aristotle's sense, *Metaphysics* Γ 1003a21), is the author's coinage rather than a label any of those literatures use of themselves. The term is licensed by the role the literatures jointly play (regimenting bivalent inference over the existence-axis of persistence-and-identity) rather than by any prior unification under the label. Under that umbrella the literatures are developed under several rubrics: formal ontology (Husserl, Edmund, 1900–01) *Logical Investigations*; (Smith, Barry, 2003), mereology (Leśniewski, Stanisław, 1916); (Simons, Peter, 1987) *Parts*, classical first-order logic with identity (Quine, W. V. O., 1960) *Word and Object*, and substance metaphysics (Wiggins, David, 2001) *Sameness and Substance Renewed*; (Lowe, E. J., 2006) *The Four-Category Ontology*. Each was developed by working logicians and ontologists without the framework's metaphysics in hand.

That working logicians and ontologists who were not consulting the present framework converged on formal work settling along exactly the three existence-axes Condition-Individuation individuates is itself a striking fact. The clustering is read at [§2.9](<2.9 Precedent Convergence.md>) as another case of the precedent-convergence pattern; the forward derivation explains why they settled where they did. The three logics are taken as the root layer of the stratified scientific architecture at [§2.10.2](<2.10.2 The Stratified Architecture.md>). The metalogical position the foregoing derivation owns (logic as metaphysically grounded, structurally individuated, realist, and foundational to the sciences) is made explicit at [§2.10.3](<2.10.3 The Metalogical Position.md>).[^2-10-1-three-logics-ch4]

[^2-10-1-three-logics-ch4]: The three-logics derivation (temporal, spatial, and substantial logic as axis-individuated formal disciplines) is engaged in Chapter 4. Quine is the principal substantial-logic ancestor and the divergence point on whether identity is one discipline among many or part of classical first-order logic *simpliciter* ([§4.1.6](<4.1.6 Quinean Modal Skepticism.md>)). Conventionalism asks whether axis-individuation is structural rather than chosen ([§4.1.7](<4.1.7 Modal Conventionalism.md>)); structural realism (Ladyman & Ross) is the closest ally on Reality's carvable joints, diverging on whether the joints are these three ([§4.3.9](<4.3.9 Structural Realism.md>)); mereological nihilism asks whether substantial logic has anything composite to regiment ([§4.3.11](<4.3.11 Mereological Nihilism.md>)); and Tegmark asks whether the three logics are mathematical structures rather than features of Reality ([§4.3.7](<4.3.7 Mathematical Universe Hypothesis.md>)).


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← [2.10 Three Logical Strata](<2.10 Three Logical Strata.md>) | [2.10.2 The Stratified Architecture](<2.10.2 The Stratified Architecture.md>) →
