**[[161_P0_Origin-Stage|P0]] (Origin):** There is **Something rather than Nothing**. Existence is not a default state; it is an active assertion against the void. The fact of existence is the first bit of information ($1 \neq 0$).
[[161_P0_Origin-Stage|P0]] does not claim to explain existence; it claims existence is undeniable. Leibniz's question is indeed profound, but the question itself presupposes an asker who exists. The move from "Why something?" to "Therefore nothing" is a non-sequitur. [[161_P0_Origin-Stage|P0]] asserts that existence is axiomatic—it cannot be derived from something more fundamental because any derivation would itself exist. This is not a weakness but a recognition of explanatory bedrock. The full answer to Leibniz's question requires the complete P-sequence, culminating in [[009_A2.2_Self-Grounding|self-grounding]] necessity (Lambda).
Sunyata is not absolute nothingness but the absence of inherent, independent existence. Buddhist metaphysics asserts dependent origination (pratityasamutpada)—things exist interdependently, not independently. The teaching of emptiness presupposes a teacher, a teaching, and a student who exist. Nagarjuna's Madhyamaka explicitly denies nihilism (ucchedavada) as a misunderstanding of sunyata. Emptiness is the nature of what exists, not the denial of existence.
Virtual existence is still existence. A simulation exists as a pattern of information in whatever substrate runs it. The simulation hypothesis relocates the ground of existence (from naive physical objects to computational substrate) but does not eliminate existence. If we are simulated, the simulator exists. The regress must terminate somewhere in actual existence. [[161_P0_Origin-Stage|P0]] is preserved.
[[161_P0_Origin-Stage|P0]] asserts existence, not Parmenidean monism. The distinction between Something and Nothing ([[161_P0_Origin-Stage|P0]]) does not entail that all distinctions are illusory. Change and multiplicity exist within Being—they are modes of existence, not transitions between Being and Non-Being. Subsequent axioms ([[162_P1_Consciousness-Stage|P1]]-[[166_P5_Incompleteness-Stage|P5]]) articulate how existence differentiates through consciousness, information, coherence, and agency.
The quantum vacuum is not nothing. It is the lowest energy state of quantum fields—a highly structured mathematical object with energy density, virtual particle pairs, and Casimir effects. Vacuum fluctuations are fluctuations of something (field values around ground state), not creation ex nihilo in the metaphysical sense. Physics describes transformations of existing structures, not the emergence of existence from absolute non-existence.
Quantum mechanics cannot operate in a null ontology. The formalism presupposes existence:
Hilbert Space Necessity:
The state space must contain at least one non-zero vector. Quantum states |\psi\rangle \in \mathcal{H} describe something that exists in superposition; they cannot describe absolute nothing.
Vacuum State is Not Nothing:
The vacuum |0\rangle is the ground state of a field—the state of minimum energy, not absence of existence. It has:
\rho_{vac} \approx 10^{-9} J/m³ (observed dark energy)\langle 0|\phi^2|0\rangle \neq 0Operators Require Operands:
Observable \hat{A} acting on |\psi\rangle yields eigenvalue a:
This presupposes |\psi\rangle exists. Measurement is extraction of information from something that exists.
Axiom of Existence:
In all possible worlds, something exists. The empty world is not in the accessibility relation.
Kripke Frame Analysis:
Let \mathcal{F} = (W, R) be a Kripke frame.
W = set of possible worldsR \subseteq W \times W = accessibility relationFor any w \in W: D_w \neq \emptyset (domain of w is non-empty).
Proof that Empty World is Impossible:
1. Suppose w_\emptyset is an empty world: D_{w_\emptyset} = \emptyset
2. Consider proposition P = "Something exists"
3. w_\emptyset \models \neg P requires evaluating P in w_\emptyset
4. But evaluation is a relation between world and proposition
5. Relations require relata (world, proposition) to exist
6. If w_\emptyset exists (as world in W), then W \neq \emptyset
7. Therefore w_\emptyset cannot be truly empty: its existence as a world contradicts its emptiness
8. \therefore No empty world exists \square