Infinity classification
If the Divine does not ontologically encompass all existent reality (i.e., if creation, human consciousness, matter, or evil exist exterior to God), God is mathematically bounded. Even if God's magnitude is unbounded within His own domain, the existence of an exterior set ¬G of measure ε > 0 reduces God to an Assumed (Relative/Bounded) Infinite, whereas Absolute (Unrestricted) Infinity requires God = Universal Set (U), leaving no exterior reality.
Nothing exists outside of God. All matter, consciousness, space-time, humans, and animals are modes, expressions, or appearances within the Divine continuum. God has no exterior boundary.
Theological equivalents: Advaita Vedanta (Brahman), Acintya-Bhedabheda, Spinoza's Monism, Radical Panentheism
G ≡ U
Exterior: G' = ∅ (Empty Set)
Measure: μ(U \ G) = 0
Exterior Domain (¬G) = ∅ (Impossible / Zero Volume)
God is declared infinite in magnitude/power, yet human free will, matter, or creatures possess distinct ontological existence outside God's being. Because an exterior domain (¬G) occupies existential volume ε > 0, God is strictly bounded by that which God is not.
Theological equivalents: Classical Dualistic Theism (Creatio ex Nihilo), Deism, Zoroastrian Dualism, Pluralism
G ⊂ U and G ∪ ¬G = U
Exterior: ¬G ≠ ∅ (Creation, Free Will, Matter, or Evil exist distinct from God)
Measure: μ(¬G) = ε > 0
| Metric | Absolute infinite | Assumed infinite |
|---|---|---|
| Total Reality Coverage | 100% (G = U) | < 100% (G = U - ¬G) |
| Human / Creature Status | Internal modal expression / wave in the ocean of God | Exterior ontological entity with distinct boundary |
| Set-Theoretic Paradox | Resolves boundary paradox; challenges absolute transcendence of evil | Preserves creature autonomy, but mathematically invalidates absolute infinity |
| Venn Representation | Nested concentric subsets within one boundless canvas | Disjoint or partially intersecting circles with distinct boundary margins |