Discussion
What does the universal quantifier assert?
Answer: A
Universal quantification says that the body holds whatever object the variable is taken to denote, and it is naturally combined with implication. Existential quantification claims one such object, and validity concerns models rather than objects. Distinguishing quantification over objects within a model from quantification over models is essential, since both appear in the semantics and confusing them makes the definitions incoherent. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.
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