Jon, De Morgan introduced the term 'universe of discourse', and Peirce adopted it for his three universes. Every logician since then, both Platonists and non-Platonists, have related logic to whatever they call a universe of discourse in the same way as Peirce. They all use an existential quantifier in exactly the same way that Peirce used the line of identity in EGs and the existential quantifier in his algebra of 1885. Whenever logicians talk about anything x that exists in any universe of discourse, they write ∃x in their logic. Those are very clear, precise statements. I don't want to speculate about any other meaning of the word 'existence'. John
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