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Was there a specific reason that prevented researchers in Boolean algebra to invent such quantifiers in the flexible format that are known today earlier?

Since the compact symbols for multiplication and sum were all there, it's surprising that they weren't used immediately after Boole's invention in logic.

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    $\begingroup$ Because predicate calculus is not operative in natural language the way propositional logic is, it is an artificial paraphrase, see Why did the mid-19th century and earlier thinkers fixate on one-place predicates? And extensions of Aristotelian term logic that were used to handle relational inferences since middle ages did not need detachable quantifiers. Sommers's modern formalization of "natural logic" does not use them, for example, see expose on Siris. $\endgroup$
    – Conifold
    Commented Nov 30, 2020 at 1:46
  • $\begingroup$ @Conifold do you know what motivated Frege to invent universal quantifiers? $\endgroup$
    – GEP
    Commented Nov 30, 2020 at 12:18
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    $\begingroup$ Trying to construct "ideal language" that "leaves nothing implicit", and his graphic script was structurally different from the modern predicate calculus. Peirce invented quantifiers independently at about the same time to develop a theory of relations. His notation for them, sum and product signs, comes from the obvious algebraic analogy, and his general calculus outline, filtered through Schröder, Peano and Russell, is what we use today, see Who superseded Peano's dot notation?. $\endgroup$
    – Conifold
    Commented Nov 30, 2020 at 14:19

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This is likely to be for the same reason as to why arithmetic wasn't formalised until long after arithmetic was discovered: there was no point to it. Peano Arithmetic was formalised when the question of formalising the foundations of mathematics became a successful research direction, likewise with the propositional and predicate logical calculi once Boolean algebra showed how to formalise logic.

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