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Single Idea 10522

[filed under theme 9. Objects / F. Identity among Objects / 1. Concept of Identity ]

Full Idea

The relations which are featured in criteria of identity are always equivalence relations.

Clarification

An equivalence relation is transitive, symmetric and reflexive

Gist of Idea

The relations featured in criteria of identity are always equivalence relations

Source

Bob Hale (Abstract Objects [1987], Ch.3.III)

Book Ref

Hale,Bob: 'Abstract Objects' [Blackwell 1987], p.57

A Reaction

This will only apply to strict identity. If I say 'a is almost identical to b', this will obviously not be endlessly transitive (as when we get to k we may have lost the near-identity to a). Are 'two threes' identical to 'three twos'?

The 23 ideas from 'Abstract Objects'

10308 Questions about objects are questions about certain non-vacuous singular terms [Hale]
10310 Objections to Frege: abstracta are unknowable, non-independent, unstatable, unindividuated [Hale]
10307 The modern Fregean use of the term 'object' is much broader than the ordinary usage [Hale]
10312 Often the same singular term does not ensure reliable inference [Hale]
10313 Plenty of clear examples have singular terms with no ontological commitment [Hale]
10314 An expression is a genuine singular term if it resists elimination by paraphrase [Hale]
10316 We should decide whether singular terms are genuine by their usage [Hale]
10318 Realists take universals to be the referrents of both adjectives and of nouns [Hale]
10315 We can't believe in a 'whereabouts' because we ask 'what kind of object is it?' [Hale]
10321 We sometimes apply identity without having a real criterion [Hale]
10322 If singular terms can't be language-neutral, then we face a relativity about their objects [Hale]
10511 It is doubtful if one entity, a universal, can be picked out by both predicates and abstract nouns [Hale]
10513 Many abstract objects, such as chess, seem non-spatial, but are not atemporal [Hale]
10514 If the mental is non-spatial but temporal, then it must be classified as abstract [Hale]
10512 The abstract/concrete distinction is based on what is perceivable, causal and located [Hale]
10517 Colours and points seem to be both concrete and abstract [Hale]
10518 Shapes and directions are of something, but games and musical compositions are not [Hale]
10523 Being abstract is based on a relation between things which are spatially separated [Hale]
10522 The relations featured in criteria of identity are always equivalence relations [Hale]
10519 The abstract/concrete distinction is in the relations in the identity-criteria of object-names [Hale]
10520 Token-letters and token-words are concrete objects, type-letters and type-words abstract [Hale]
10524 There is a hierarchy of abstraction, based on steps taken by equivalence relations [Hale]
10521 If F can't have location, there is no problem of things having F in different locations [Hale]