Ideas from 'Nominalism and Substitutional Quantifiers' by Ruth Barcan Marcus [1978], by Theme Structure
[found in 'Philosophy of Logic: an anthology' (ed/tr Jacquette,Dale) [Blackwell 2002,0-631-21868-8]].
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
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10794
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The nominalist is tied by standard semantics to first-order, denying higher-order abstracta
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5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
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10788
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Nominalists see proper names as a main vehicle of reference
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10786
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Anything which refers tends to be called a 'name', even if it isn't a noun
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5. Theory of Logic / G. Quantification / 1. Quantification
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10799
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Nominalists should quantify existentially at first-order, and substitutionally when higher
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5. Theory of Logic / G. Quantification / 2. Domain of Quantification
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10790
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Quantifiers are needed to refer to infinitely many objects
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10791
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Substitutional semantics has no domain of objects, but place-markers for substitutions
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5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
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10785
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Maybe a substitutional semantics for quantification lends itself to nominalism
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10798
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A true universal sentence might be substitutionally refuted, by an unnamed denumerable object
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10795
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Substitutional language has no ontology, and is just a way of speaking
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7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
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10787
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Is being just referent of the verb 'to be'?
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8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
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10789
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Nominalists say predication is relations between individuals, or deny that it refers
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9. Objects / A. Existence of Objects / 3. Objects in Thought
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10796
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If objects are thoughts, aren't we back to psychologism?
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9. Objects / F. Identity among Objects / 2. Defining Identity
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10797
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Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all
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