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Single Idea 8704

[filed under theme 9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta ]

Full Idea

What the mathematician labels an 'object' in her discipline, is called 'a place in a structure' by the structuralist.

Gist of Idea

Structuralists call a mathematical 'object' simply a 'place in a structure'

Source

Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.5)

Book Ref

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.97

A Reaction

This is a strategy for dispersing the idea of an object in the world of thought, parallel to attempts to eliminate them from physical ontology (e.g. Idea 614).

Related Idea

Idea 614 Heraclitus said sometimes everything becomes fire [Heraclitus, by Aristotle]

The 16 ideas with the same theme [what we should take abstract object to be]:

9607 The greatest discovery in human thought is Plato's discovery of abstract objects [Brown,JR on Plato]
16086 Objects lacking matter are intrinsic unities [Aristotle]
12990 Real (non-logical) abstract terms are either essences or accidents [Leibniz]
8647 Not all objects are spatial; 4 can still be an object, despite lacking spatial co-ordinates [Frege]
10545 Abstract objects may not cause changes, but they can be the subject of change [Dummett]
9885 The existence of abstract objects is a pseudo-problem [Dummett]
10487 I am a fan of abstract objects, and confident of their existence [Boolos]
10414 Abstract objects are constituted by encoded collections of properties [Zalta, by Swoyer]
10558 Abstract objects are actually constituted by the properties by which we conceive them [Zalta]
17785 Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry]
10403 If properties are abstract objects, then their being abstract exemplifies being abstract [Swoyer]
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]
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]
8704 Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend]