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
The nominalist is tied by standard semantics to first-order, denying higher-order abstracta
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
Anything which refers tends to be called a 'name', even if it isn't a noun
Nominalists see proper names as a main vehicle of reference
5. Theory of Logic / G. Quantification / 1. Quantification
Nominalists should quantify existentially at first-order, and substitutionally when higher
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Quantifiers are needed to refer to infinitely many objects
Substitutional semantics has no domain of objects, but place-markers for substitutions
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Substitutional language has no ontology, and is just a way of speaking
Maybe a substitutional semantics for quantification lends itself to nominalism
A true universal sentence might be substitutionally refuted, by an unnamed denumerable object
7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
Is being just referent of the verb 'to be'?
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
Nominalists say predication is relations between individuals, or deny that it refers
9. Objects / A. Existence of Objects / 3. Objects in Thought
If objects are thoughts, aren't we back to psychologism?
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
Aristotelian essentialism is about shared properties, individuating essentialism about distinctive properties
Aristotelian essentialism involves a 'natural' or 'causal' interpretation of modal operators
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
Essentialist sentences are not theorems of modal logic, and can even be false
'Essentially' won't replace 'necessarily' for vacuous properties like snub-nosed or self-identical
'Is essentially' has a different meaning from 'is necessarily', as they often cannot be substituted
9. Objects / D. Essence of Objects / 14. Knowledge of Essences
If essences are objects with only essential properties, they are elusive in possible worlds
9. Objects / F. Identity among Objects / 2. Defining Identity
Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
The use of possible worlds is to sort properties (not to individuate objects)
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
In possible worlds, names are just neutral unvarying pegs for truths and predicates
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Dispositional essences are special, as if an object loses them they cease to exist