Ideas of Ruth Barcan Marcus, by Theme
[American, 1921 - 2012, Professor at Yale University. Famous for the 'Barcan Formula'.]
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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 / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
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11181
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Aristotelian essentialism involves a 'natural' or 'causal' interpretation of modal operators
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11184
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Aristotelian essentialism is about shared properties, individuating essentialism about distinctive properties
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9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
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11180
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Essentialist sentences are not theorems of modal logic, and can even be false
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11186
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'Essentially' won't replace 'necessarily' for vacuous properties like snub-nosed or self-identical
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11185
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'Is essentially' has a different meaning from 'is necessarily', as they often cannot be substituted
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9. Objects / D. Essence of Objects / 14. Knowledge of Essences
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11182
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If essences are objects with only essential properties, they are elusive in possible worlds
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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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10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
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11183
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The use of possible worlds is to sort properties (not to individuate objects)
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10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
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11187
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In possible worlds, names are just neutral unvarying pegs for truths and predicates
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26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
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11189
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Dispositional essences are special, as if an object loses them they cease to exist
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