P4's dilemma assumes that v'(f(Q)) ≠ v(f(Q)) is implausible, but under functional dependence, functional consistency requires only that f applied to the new base value v'(Q) yields the correct eigenvalue, which is a constraint satisfied, not violated, by context-change.

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Context-change(as used in semantics and philosophy of language): A shift in the circumstances, conditions, or settings that affect how something is evaluated or understood.
Eigenvalue(as used in mathematics and formal logic): A special number associated with a mathematical function or transformation that remains unchanged in a particular way—think of it as a function's 'characteristic value.'
Functional consistency(as used in formal logic): The requirement that a function (a rule that transforms inputs into outputs) always works the same way and produces reliable, predictable results.
Functional dependence(as used in logic and mathematics): A relationship where one thing's properties or values are completely determined by another thing's properties—like how the output of a math function depends entirely on its input.
P4's dilemma(as referenced in formal logic discussions): A specific logical problem or puzzle (likely from a philosophical paper or argument) that presents two seemingly impossible choices or contradictory conclusions.
v(f(Q)) and v'(f(Q))(as used in formal logic notation): Symbolic notation where v means 'the value of' and f(Q) is a function applied to something called Q; the prime mark (') indicates this is a new or different version after some change.

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