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Chapter 26: Collapse Quantifiers and Observation Scope

26.1 The Scope of Observation​

Classical quantifiers (∀, ∃) range over fixed domains. In collapse logic, quantifiers become observation protocols—universal quantification requires observing all instances simultaneously, existential needs only witness single collapse.

Principle 26.1: Quantifiers define observation scope and collapse protocol in logical space.

26.2 Universal Collapse​

Definition 26.1 (Universal Quantification): ∀x:P(x)≡⋀x∈D∣P(x)⟩=∣T⟩\forall x : P(x) \equiv \bigwedge_{x \in D} |P(x)\rangle = |T\rangle

Requires:

  • Simultaneous observation of all domain elements
  • Coherent collapse to true
  • Maintains entanglement across domain
  • Single false collapses entire statement

26.3 Existential Witness​

Definition 26.2 (Existential Quantification): ∃x:P(x)≡⋁x∈D∣P(x)⟩≠∣F⟩all\exists x : P(x) \equiv \bigvee_{x \in D} |P(x)\rangle \neq |F\rangle_{all}

Requires:

  • Search through domain
  • Single true witness suffices
  • Collapse upon finding
  • Maintains possibility cloud until witness

The Quantifier Collapse: When thinking "all swans are white," consciousness attempts universal observation across swan-space. Finding one black swan collapses the universal. "Some swan is black" maintains possibility cloud until witness appears. Quantifiers organize the scope and protocol of logical observation.