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

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1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
Questions about objects are questions about certain non-vacuous singular terms
2. Reason / D. Definition / 12. Paraphrase
An expression is a genuine singular term if it resists elimination by paraphrase
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
We should decide whether singular terms are genuine by their usage
Often the same singular term does not ensure reliable inference
Plenty of clear examples have singular terms with no ontological commitment
If singular terms can't be language-neutral, then we face a relativity about their objects
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