Symbols

The notation used throughout the argument, collected for reference. Each symbol is defined in full where it is introduced; the italic tag at the end of an entry points to the section where it first appears.

The Conditions

T · Temporality · The Condition of Reality such that succession is necessarily possible. First use: §1.4.

S · Spatiality · The Condition of Reality such that distinction is necessarily possible. First use: §1.4.

Φ · Physicality · The Condition of Reality such that exchange is necessarily possible. First use: §1.4.

T(x), S(x), Φ(x) · Predicate form · Applied to an individual x, each says that x instantiates the corresponding Condition.

Exists(x) · Existence predicate · Exists(x) =df T(x) ∧ S(x) ∧ Φ(x). To exist is to instantiate all three Conditions. First use: §1.5.

Structural terms

C · Change · Schematic letter for the change-event. First use: §1.3.

N · Nature · N =df T ∧ S ∧ Φ. The definition is box-free; the necessity □(T ∧ S ∧ Φ) is the earned result Triconditional Necessity (§2.5). First use: §1.4.4.

R · Reality · The totality of what is real, identified with Nature in □(R = N). First use: §1.1.

∅ · Null State · Absolute nothingness. First use: §2.7.1.

G · Classical God · The Maximally Great Being, defined by negation of the structural roles: ¬T, ¬S, ¬Φ. Subject of the modal-ontological arguments ◇□G and ◇□¬G. First use: §6.1.

Logical notation

□ · Necessity operator · □P is true just when P holds across every configuration of Reality. First use: §1.2.

◇ · Possibility operator · ◇P is true just when P holds in at least one configuration of Reality. First use: §1.2.

∧ ∨ ¬ → ↔︎ · Logical connectives · Conjunction, disjunction, negation, material conditional, biconditional.

∀ ∃ · Quantifiers · ∀ is the universal quantifier, read for all; ∃ is the existential quantifier, read there exists.

∴ · Therefore · Reserved for the conclusion lines of formal syllogisms.

=df · Defined as · Introduces a stipulative definition.

Variables

P, Q · Propositional variables · Schematic propositional variables, ranging over contentful claims. First use: §1.2.

w, w′, w₀, w₁, w₂, w∗ · Possible-world variables · w is the generic world; w′ the counterworld of the §2.1.5 negation reductio; w₀ the candidate world posited to lack the structural Conditions at §2.7.4; w₁, w₂, … enumerated worlds; w∗ the dual world introduced under bilateral symmetry at §6.1 and Appendix B item 16. First use: §2.1.5.