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Ideas for 'fragments/reports', 'fragments/reports' and 'Plural Quantification Exposed'

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2 ideas

5. Theory of Logic / G. Quantification / 6. Plural Quantification
Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo]
     Full Idea: If my arguments are correct, the theory of plural quantification has no right to the title 'logic'. ...The impredicative plural comprehension axioms depend too heavily on combinatorial and set-theoretic considerations.
     From: Øystein Linnebo (Plural Quantification Exposed [2003], §4)
Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo]
     Full Idea: According to its supporters, second-order logic allow us to pay the ontological price of a mere first-order theory and get the corresponding monadic second-order theory for free.
     From: Øystein Linnebo (Plural Quantification Exposed [2003], §0)