Ideas from 'Abstract Objects' by Bob Hale [1987], by Theme Structure

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1. Philosophy / F. Analytic Philosophy / 4. Ordinary Language
Questions about objects are questions about certain non-vacuous singular terms
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
We should decide whether singular terms are genuine by their usage
If singular terms can't be language-neutral, then we face a relativity about their objects
Often the same singular term does not ensure reliable inference
Plenty of clear examples have singular terms with no ontological commitment
An expression is a genuine singular term if it resists elimination by paraphrase
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
The abstract/concrete distinction is based on what is perceivable, causal and located
Colours and points seem to be both concrete and abstract
Token-letters and token-words are concrete objects, type-letters and type-words abstract
The abstract/concrete distinction is in the relations in the identity-criteria of object-names
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
There is a hierarchy of abstraction, based on steps taken by equivalence relations
8. Modes of Existence / D. Universals / 1. Universals
Realists take universals to be the referrents of both adjectives and of nouns
It is doubtful if one entity, a universal, can be picked out by both predicates and abstract nouns
If F can't have location, there is no problem of things having F in different locations
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
Objections to Frege: abstracta are unknowable, non-independent, unstatable, unindividuated
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
Shapes and directions are of something, but games and musical compositions are not
Many abstract objects, such as chess, seem non-spatial, but are not atemporal
If the mental is non-spatial but temporal, then it must be classified as abstract
Being abstract is based on a relation between things which are spatially separated
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
The modern Fregean use of the term 'object' is much broader than the ordinary usage
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
We can't believe in a 'whereabouts' because we ask 'what kind of object is it?'
9. Objects / F. Identity among Objects / 1. Concept of Identity
The relations featured in criteria of identity are always equivalence relations
9. Objects / F. Identity among Objects / 3. Relative Identity
We sometimes apply identity without having a real criterion