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Single Idea 8918

[from 'Abstract Objects' by Gideon Rosen, in 18. Thought / E. Abstraction / 7. Abstracta by Equivalence ]

Full Idea

On Frege's suggestion, functional terms that pick out abstract expressions (such as 'direction' or 'equinumeral') have a typical form of f(a) = f(b) iff aRb, where R is an equivalence relation, a relation which is reflexive, symmetric and transitive.

Gist of Idea

Functional terms can pick out abstractions by asserting an equivalence relation

Source

Gideon Rosen (Abstract Objects [2001], 'Way of Abs')

Book Reference

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.7


A Reaction

[Wright and Hale are credited with the details] This has become the modern orthodoxy among the logically-minded. Examples of R are 'parallel' or 'just as many as'. It picks out an 'aspect', which isn't far from the old view.