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

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

10312

Often the same singular term does not ensure reliable inference

10316

We should decide whether singular terms are genuine by their usage

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

10519

The abstract/concrete distinction is in the relations in the identity-criteria of object-names

10520

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

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

10514

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

10513

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

10518

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

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