Combining Texts
Ideas for
'works', 'Identity and Existence in Logic' and 'Nominalism and Substitutional Quantifiers'
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12 ideas
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 [Marcus (Barcan)]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
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21777
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Negation of negation doubles back into a self-relationship [Hegel, by Houlgate]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
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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 [Marcus (Barcan)]
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10788
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Nominalists see proper names as a main vehicle of reference [Marcus (Barcan)]
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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 [Marcus (Barcan)]
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5. Theory of Logic / G. Quantification / 2. Domain of Quantification
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10791
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Substitutional semantics has no domain of objects, but place-markers for substitutions [Marcus (Barcan)]
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10790
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Quantifiers are needed to refer to infinitely many objects [Marcus (Barcan)]
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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 [Marcus (Barcan)]
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10795
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Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)]
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10798
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A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)]
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5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
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18763
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Basic variables in second-order logic are taken to range over subsets of the individuals [Anderson,CA]
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5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
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18771
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Stop calling ∃ the 'existential' quantifier, read it as 'there is...', and range over all entities [Anderson,CA]
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