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Single Idea 10630

[filed under theme 18. Thought / E. Abstraction / 7. Abstracta by Equivalence ]

Full Idea

The new kind of abstract objects are not creations of the human mind. ...The existence of such objects depends upon whether or not the relevant equivalence relation holds among the entities of the presupposed kind.

Gist of Idea

Abstracted objects are not mental creations, but depend on equivalence between given entities

Source

B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2)

Book Ref

Hale,B/Wright,C: 'The Reason's Proper Study' [OUP 2003], p.17

A Reaction

It seems odd that we no longer have any choice about what abstract objects we use, and that we can't evade them if the objects exist, and can't have them if the objects don't exist - and presumably destruction of the objects kills the concept?

The 23 ideas from B Hale / C Wright

10622 The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
10624 The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright]
10626 Objects just are what singular terms refer to [Hale/Wright]
10630 Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright]
10631 If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright]
10627 Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright]
10629 If structures are relative, this undermines truth-value and objectivity [Hale/Wright]
10628 The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright]
8784 Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright]
8786 One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright]
8783 Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright]
8787 The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright]
8788 Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright]
12223 It is a fallacy to explain the obscure with the even more obscure [Hale/Wright]
12224 Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright]
12225 Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright]
12226 The identity of Pegasus with Pegasus may be true, despite the non-existence [Hale/Wright]
12227 Abstractionism needs existential commitment and uniform truth-conditions [Hale/Wright]
12228 Equivalence abstraction refers to objects otherwise beyond our grasp [Hale/Wright]
12231 Reference needs truth as well as sense [Hale/Wright]
12229 Maybe we have abundant properties for semantics, and sparse properties for ontology [Hale/Wright]
18443 A successful predicate guarantees the existence of a property - the way of being it expresses [Hale/Wright]
12230 Singular terms refer if they make certain atomic statements true [Hale/Wright]