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  • https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Gentle_Introduction_to_the_Art_of_Mathematics_(Fields)/02%3A_Logic_and_Quantifiers/2.05%3A_Quantified_Statements
    All of the statements discussed in the previous sections were of the “completely unambiguous” sort; that is, they didn’t have any unknowns in them. Admittedly, we’ve used variables to refer to sentenc...All of the statements discussed in the previous sections were of the “completely unambiguous” sort; that is, they didn’t have any unknowns in them. Admittedly, we’ve used variables to refer to sentences (or sentence fragments) themselves, but we’ve said that sentences that had variables in them were ambiguous and didn’t even deserve to be called logical statements. The notion of quantification allows us to use the power of variables within a sentence without introducing ambiguity.

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