Ideas from 'To be is to be the value of a variable..' by George Boolos [1984], by Theme Structure
[found in 'Logic, Logic and Logic' by Boolos,George [Harvard 1999,0-674-53767-x]].
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expand these ideas
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
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7785
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The use of plurals doesn't commit us to sets; there do not exist individuals and collections
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4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
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10699
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Does a bowl of Cheerios contain all its sets and subsets?
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
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10225
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Monadic second-order logic might be understood in terms of plural quantifiers [Shapiro]
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10736
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Boolos showed how plural quantifiers can interpret monadic second-order logic [Linnebo]
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10780
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Any sentence of monadic second-order logic can be translated into plural first-order logic [Linnebo]
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5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
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10697
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Identity is clearly a logical concept, and greatly enhances predicate calculus
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5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
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13671
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Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Shapiro]
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5. Theory of Logic / G. Quantification / 6. Plural Quantification
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10267
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We should understand second-order existential quantifiers as plural quantifiers [Shapiro]
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10698
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Plural forms have no more ontological commitment than to first-order objects
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5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
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7806
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Boolos invented plural quantification [Benardete,JA]
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7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
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10700
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First- and second-order quantifiers are two ways of referring to the same things
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