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

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1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis

10308

Questions about objects are questions about certain non-vacuous singular terms

2. Reason / D. Definition / 12. Paraphrase

10314

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

10316

We should decide whether singular terms are genuine by their usage

10312

Often the same singular term does not ensure reliable inference

10313

Plenty of clear examples have singular terms with no ontological commitment

10322

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

10512

The abstract/concrete distinction is based on what is perceivable, causal and located

10517

Colours and points seem to be both concrete and abstract

10520

Token-letters and token-words are concrete objects, type-letters and type-words abstract

10519

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

10524

There is a hierarchy of abstraction, based on steps taken by equivalence relations

8. Modes of Existence / D. Universals / 1. Universals

10318

Realists take universals to be the referrents of both adjectives and of nouns

10521

If F can't have location, there is no problem of things having F in different locations

10511

It is doubtful if one entity, a universal, can be picked out by both predicates and abstract nouns

8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta

10310

Objections to Frege: abstracta are unknowable, non-independent, unstatable, unindividuated

9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta

10518

Shapes and directions are of something, but games and musical compositions are not

10513

Many abstract objects, such as chess, seem non-spatial, but are not atemporal

10514

If the mental is non-spatial but temporal, then it must be classified as abstract

10523

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

10307

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

10315

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

10522

The relations featured in criteria of identity are always equivalence relations

9. Objects / F. Identity among Objects / 3. Relative Identity

10321

We sometimes apply identity without having a real criterion